Evaluating the Impact of Climate Change on Rainfall Intensity-Duration-Frequency
(IDF) Curves in Alabama Using Dynamically-Downscaled Precipitation Data
by
Golbahar Mirhosseini
A dissertation submitted to the Graduate Faculty of
Auburn University
in partial fulfillment of the
requirements for the Degree of
Doctor of Philosophy
Auburn, Alabama
August 3, 2013
Keywords: Climate change, Global Climate Models (GCMs),
Intensity-Duration-Frequency (IDF) curve, Temporal downscaling
Copyright 2013 by Golbahar Mirhosseini
Approved by
Approved by
Puneet Srivastava, Co-chair, Associate Professor of Biosystems Engineering
Xing Fang, Co-chair, Associate Professor of Civil Engineering
Latif Kalin, Associate Professor, School of Forestry and Wildlife Sciences
Keith Ingram, Associate Research Scientist of Agricultural and Biological Engineering,
University of Florida
ii
Abstract
Rainfall intensity-duration-frequency (IDF) curves are extensively used for
hydrologic designs. A design based on inaccurate rainfall characteristics can lead to
malfunction of infrastructure, excessive design cost, and loss of life. It is expected that
the frequency and magnitude of future extreme rainfalls will change due to increases in
greenhouse gas (GHG) concentrations. Quantifying potential effects of climate change by
reviewing and updating IDF curves for future climate scenarios and adapting to them is
one way to reduce vulnerability. This study was undertaken to evaluate expected changes
in IDF curves from the current climate to the projected future climate. Six combinations
of global and regional climate models were used to develop the IDF curves under future
climate scenarios. Three-hourly precipitation data were temporally downscaled using two
different disaggregation methods: stochastic and artificial neural network (ANN). In the
second chapter, stochastic method was used to downscale three-hourly precipitation into
15-min precipitation amount and IDF curves were developed. The results of all six
climate models suggest that the future rainfall intensities are expected to decrease for
short duration events (i.e., less than 2 hours). However, for longer duration events, the
results are not consistent across the models. In the third chapter, a feed-forward, back-
propagation ANN model was developed to estimate maximum 15-, 30-, 45-, 60-, and
120-min precipitations. The results were also compared with the disaggregated rainfalls
derived using the stochastic method.
iii
Results indicate that future rainfall intensities for short duration (< 2 hours) events are
expected to decrease by 33% to 74%. However, a large uncertainty exists in the projected
rainfall intensities of longer duration events. In chapter 4, uncertainty associated with the
studied models was quantified using kernel density estimator and probability-based IDF
curves were created. The resultant IDF curves incorporating all models were also
developed. Although the results derived from different climate projections show large
uncertainty associated with climate models, all of them indicate decrease in future rainfall
intensity for short duration rainfall events, especially for durations less than 2 hours. The
methodology developed can be used for developing IDF curves for other parts of the
United States and the world.
iv
Acknowledgments
I read somewhere that ?The only way to find out how to do a Ph.D. is to do one?.
Well, I did one, but not alone. Many have helped and supported me along this difficult,
long journey and I will be forever thankful to them. I would like to express my sincere
gratitude to my major advisor, Dr. Puneet Srivastava for his help, support and
encouragement along the way. I would like to express my heartfelt gratitude to my co-
advisor, Dr. Xing Fang for his valuable suggestions, help and guidance. I am so grateful
to my advisory committee, Dr. Latif Kalin and Dr. Keith Ingram for helpful suggestions,
guidance and support. I owe them my heartfelt appreciation. Special thanks to Dr. Lydia
Stefanova for her valuable suggestions and assistance during this journey. I will be
forever grateful to her. I would also like to thank Dr. Sumit Sen, Dr. Vaishali sharda, Dr.
Ajay Sharda and Dr. Suresh Sharma for their friendship and encouragement during the
course of this study.
I am indebted to my parents for their unconditional love, continues
encouragement, support and for telling me that I could do anything and actually believing
it. I am thankful to my sister and brother-in-law for encouraging me to dream big and
sending their constant support and love across the world for the past four years. I would
not be where I am today if it wasn?t for them.
v
I would not be able to finish this journey if not for my husband. I cannot even
begin to thank him enough for all he has done for me. His love and support means the
world to me. He believed in me when I didn?t and never stopped encouraging me. My
deepest gratitude and love to him for believing in me so I could believe in myself. I could
not have asked for a better partner to share my life with.
Making this dream come true was not able without the love, support and
encouragement of all my family and friends. With sincere thanks.
Golbahar Mirhosseini
July 2013
vi
Table of Contents
Abstract .......................................................................................................................... ii
Acknowledgments ......................................................................................................... iv
List of Tables................................................................................................................. ix
List of Figures .................................................................................................................x
1. Introduction .............................................................................................................1
1.1. Climate Change .................................................................................................1
1.2. General Circulation Models (GCMs) .................................................................2
1.3. Regional Circulation Models (RCMs) ................................................................3
1.4. Climate Model Scenarios ...................................................................................5
1.5. Bias Correction ..................................................................................................8
1.6. Downscaling Techniques ...................................................................................8
1.6.1. Spatial Downscaling .......................................................................................8
1.6.2. Temporal Disaggregation ............................................................................. 12
1.7. Intensity-Duration-Frequency (IDF) Curves .................................................... 14
1.8. Problem Statement .......................................................................................... 19
1.9. Dissertation Objectives .................................................................................... 20
1.10. Dissertation Structure ................................................................................... 20
2. The Impact of Climate Change on Rainfall Intensity-Duration-Frequency (IDF)
Curves in Alabama ........................................................................................................ 22
2.1. Abstract ........................................................................................................... 22
2.2. Introduction ......................................................................................................... 23
2.3. Materials and Methods ........................................................................................ 26
2.3.1. Data and Model Used ................................................................................... 26
2.3.2. Bias correction ............................................................................................. 34
2.3.3. Temporal Downscaling ................................................................................ 35
vii
2.3.4. Performance ................................................................................................. 37
2.3.5. Creating IDF curves ..................................................................................... 38
2.4. Results and Discussion ........................................................................................ 40
2.4.1. Bias correction ............................................................................................. 40
2.4.2. Performance ................................................................................................. 40
2.4.3. IDF curves ................................................................................................... 45
2.5. Summary and Conclusions .................................................................................. 54
3. Developing Rainfall Intensity-Duration-Frequency (IDF) Curves For Alabama
Under Future Climate Scenarios Using Artificial Neural Network (ANN) ..................... 56
3.1. Abstract ........................................................................................................... 56
3.2. Introduction ..................................................................................................... 57
3.3. Methodology ................................................................................................... 59
3.3.1. Data and Model Used ............................................................................... 59
3.3.2. Bias Correction and Temporal Downscaling ............................................. 60
3.3.3. Artificial Neural Network ......................................................................... 61
3.3.4. ANN Model Input Data ............................................................................ 62
3.3.5. ANN Model Training and Performance Measures .................................... 65
3.3.6. Intensity-Duration-Frequency (IDF) Curves ............................................. 66
3.4. Results and Discussion .................................................................................... 66
3.4.1. Performance ............................................................................................. 66
3.4.2. IDF Curves ............................................................................................... 71
3.5. Summary and Conclusions .............................................................................. 80
4. Developing Probability-based IDF Curves Using Kernel Density Estimator ........... 82
4.1. Abstract ........................................................................................................... 82
4.2. Introduction ..................................................................................................... 83
4.3. Methodology ................................................................................................... 86
4.3.1. Data.......................................................................................................... 86
4.3.2. Probability Density Function (PDF).......................................................... 87
4.3.3. Kernel Density Estimation ........................................................................ 88
4.3.4. Probability-based IDF Curves ................................................................... 96
4.4. Results and Discussion .................................................................................... 96
viii
4.4.1. Optimal bandwidth selection .................................................................... 96
4.4.2. Probability-based IDF Curves ................................................................... 97
4.5. Summary and Conclusions ............................................................................ 113
5. Conclusions ......................................................................................................... 115
5.1. Summary and Conclusions ............................................................................ 115
5.1.1. Objective 1 ............................................................................................. 116
5.1.2. Objective 2 ............................................................................................. 117
5.1.3. Objective 3 ............................................................................................. 118
6. Future research .................................................................................................... 120
References ................................................................................................................... 121
Appendix A ................................................................................................................. 134
Monthly Cumulative Distribution Functions (CDF) To Perform Bias Correction ......... 134
Appendix B ................................................................................................................. 144
Rainfall Intensity-Duration-Frequency Maps ............................................................... 144
Appendix C ................................................................................................................. 186
Scatter Plots of Observed and Modeled Rainfall Depths Using the ANN Model and the
Stochastic Method ....................................................................................................... 186
Appendix D ................................................................................................................. 206
IDF Maps, using ANN model for rainfall disaggregation ............................................. 206
Appendix E ................................................................................................................. 226
Probability-based IDF curves for Alabama .................................................................. 226
Appendix F .................................................................................................................. 325
IDF curves for Alabama .............................................................................................. 325
ix
List of Tables
Table 2-1 Performance measures between the disaggregated time series and measured
statistics of 15-min rainfall ............................................................................................ 43
Table 2-2 Performance measures between the maximum rainfall of disaggregated time
series and measured statistics ......................................................................................... 44
Table 2-3 Performance measures between the sample and theoretical cumulative
distributions using Kolmogorov-Smirnov (K-S) test ...................................................... 44
Table 2-4 Comparisons of IDF curves under the current and future climate scenario for
Auburn, AL ................................................................................................................... 50
Table 3-1 The Akaike Information Criterion (AIC) and Normalized Mean Square Error
(NMSE) calculated for the nine combinations of input variables in order to determine
optimal input variables of the ANN model. .................................................................... 64
Table 3-2 Performance of the ANN model for training, validation, and testing datasets for
every month and every rainfall duration. ........................................................................ 67
Table 3-3 Comparisons of IDF curves under the current and future climate scenarios for
Auburn, AL using two temporal downscaling methods, the ANN model and the
stochastic method. ......................................................................................................... 78
Table 4-1 Examples of kernel functions ......................................................................... 90
Table 4-2 Optimal bandwidth selection for Auburn, 15-min rainfall duration ................. 97
Table 4-3 Uncertainty quantification for 15-min rainfall duration, Auburn, AL............ 101
Table 4-4 Uncertainty quantification of rainfall depths (mm) projected from different
climate models for Auburn, AL and London, ON ........................................................ 106
x
List of Figures
Figure 1.1 Representation of a climate model setup .........................................................4
Figure 1.2 Predicted changes in winter precipitation over Central/ Southern Europe
between the present day and 2080 predicted by the RCM (right) and GCM (left). ............5
Figure 1.3 Total global annual CO2 emissions [in gigatons of carbon (GtC/year)] for six
scenario groups. ...............................................................................................................7
Figure 1.4 Downscaling techniques allow the use of GCMs outputs as inputs into regional
climate and weather models. From
http://www.southwestclimatechange.org/climate/modeling/downscaling retrieved on
03/12/2013 .................................................................................................................... 10
Figure 1.5 Rainfall Intensity-Duration-Frequency (IDF) curve ....................................... 15
Figure 2.1 Location of rain gauge stations (red squares) and NARCCAP 50-km resolution
grid centers (green dots, HRM3-HadCM3) used to develop IDF curves for Alabama. .... 27
Figure 2.2 Monthly Cumulative Distribution Functions (CDFs) to perform bias
correction- Model data is from HRM3-HadCM3 model ................................................. 42
Figure 2.3 Rainfall intensity map; 50-year rainfall of 6-hr, 12-hr, 24-hr and 48-hr
durations (mm) under future climate using HRM3-HadCM3 projected data ................... 46
Figure 2.4 IDF curves under current and future climate using HRM3-HadCM3, CRCM-
CGCM3 and HRM3-GFDL models for Auburn, AL ...................................................... 48
Figure 2.5 IDF curves under current and future climate using CRCM-CCSM, RCM3-
GFDL and ECP2-GFDL models for Auburn, AL ........................................................... 49
Figure 2.6 Rainfall intensity vs. return period under current and future climate for a 12-hr
rainfall using a) HRM3-HadCM3, b) HRM3-GFDL, c) RCM3-GFDL, d) CRCM-
CGCM3, e) CRCM-CCSM and f) ECP2-GFDL model .................................................. 53
xi
Figure 3.1 Scatter plots of observed and modeled maximum a) 15-min, b) 30-min, c) 45-
min, d) 60-min, and e) 120-min rainfall depths using the ANN model (left panels) and the
stochastic method (right panels) for July. ....................................................................... 71
Figure 3.2 Rainfall intensity map; 100-year rainfall of 15-, 30-, 45- and 60-min durations
(mm) under future climate using HRM3-HadCM3 projected data .................................. 72
Figure 3.3  IDF curves for 10-yr and 100-yr return periods under current and future
climate (using HRM3-HadCM3, CRCM- CGCM3, and HRM3-GFDL CRCM-CCSM
and RCM3-GFDL models) for Auburn, AL. .................................................................. 76
Figure 4.1 Comparison of kernel density estimate (right) and histogram (left). The
individual kernels are the red dashed curves and the kernel density estimate the blue
curves. ........................................................................................................................... 90
Figure 4.2 Probability-based IDFs when stochastic method used for disaggregation for
15-, 30-, 45-min,1- ,2-, 3-, 6-, 12-, 24- and 48-hr rainfall duration-graphs are presented
for Auburn, AL. ............................................................................................................. 99
Figure 4.3 Resultant IDF curves for Auburn, AL using the stochastic method .............. 100
Figure 4.4 Projected rainfall depth range from six climate models (bars show minimum
and maximum) and the red dot represents the rainfall depth derived from the probability-
based IDF. ................................................................................................................... 102
Figure 4.5 Projected rainfall depth range (bars show minimum and maximum and the red
dot represents the rainfall depth derived from the probability-based IDF) for Auburn, AL
(left side) and London, Ontario, Canada (right side). .................................................... 104
Figure 4.6 Resultant IDF curves under future and current climate for Auburn, AL when
the stochastic method was used for rainfall disaggregation........................................... 108
Figure 4.7 Probability-based IDFs when ANN model used for disaggregation for 15-, 30-,
45-min,1- and 2-hr rainfall duration-graphs are presented for Auburn, AL. .................. 110
Figure 4.8 Resultant IDF curves for Auburn, AL using ANN model ............................ 111
Figure 4.9 Resultant IDF curves under future and current climate for Auburn, AL ....... 112
1
Chapter 1
1. Introduction
1.1. Climate Change
Climate is a complex system consisting of the oceans, land, atmosphere, snow, and
ice. Changes in climate can happen due to natural events such as volcanic eruptions, solar
radiation variations, earth internal dynamics, orbital irregularities or human activities, etc.
?Climate change? is a term usually used to describe changes caused by human activities
(Solaiman 2011). During the last century, the concentration of carbon dioxide (CO2) and
other greenhouse gases (GHGs) in the earth?s atmosphere has risen due to increased
industrial activities (Prodanovic et al. 2007). This increase in GHG concentrations is
causing large-scale variations in atmospheric processes, which can then lead to changes
in precipitation and temperature characteristics.
The global average temperature has increased 0.74?C during the 20th century, and
projections indicate that it will continue to increase over the next hundred years (IPCC
2007). Changes in temperature can be associated with changes in precipitation, causing
more drought, floods, heat waves, melting ice caps, sea level rise, or more frequent
extreme rainfalls (IPCC 2007). Based on the Fourth Assessment Report of the
Intergovernmental Panel on Climate Change (IPCC 2007), between 75 and 250 million
people may experience increased water stress in the next 10 years because of climate
change (Muller 2007).
2
All these changes will increase challenges with respect to water resources as they
become more pronounced. Degradation of water quality, property damage, and potential
loss of life due to flooding are caused by extreme rainfall events. Damage from erosion
can impact areas from farm fields to stream banks adjacent to important infrastructure
(Wright et al. 2010). To prepare for future climate changes, it is imperative that we
review and update current standards for water management infrastructure design. This
would prevent water management infrastructures from performing below the designated
guidelines in the future (Prodanovic et al. 2007).
1.2.General Circulation Models (GCMs)
The first climate model was developed by Norman Phillips (1956). This mathematical
model could successfully show monthly and seasonal patterns in the troposphere (Cox
2002). Other scientists started working to develop General Circulation Models (GCMs) in
the late 1960s, when the first oceanic and atmospheric model was developed at the
National Oceanic and Atmospheric Administration (NOAA) Geophysical Fluid
Dynamics Laboratory (Lynch 2006, NOAA 2007). The National Center for Atmospheric
Research (NCAR) developed the Community Atmosphere Model in the early 1980s
(Collin 2004), and many more climate models have been created since then. These
General Circulation Models (GCMs) are currently the best tools to study the effects of
climate change. They are the current state-of-the-art in climate science. The main goal of
these models is to identify the climate system?s functioning, employing various sciences
such as physics and chemistry (Prodanovic et al. 2007). GCMs use complicated equations
representing the physical processes of the atmosphere. Significant computing resources
are required to produce meaningful forecasts in this complex system, which includes
3
interactions between the different components of ocean layers, temperature gradients,
trade winds, solar radiation, clouds, land masses and ocean currents (Prodanovic et al.
2007). To capture large-scale circulation flows, GCMs operate at medium coarse
resolutions (between 250 and 600 km). GCMs picture the climate in three dimensions
throughout the globe, with 10 to 20 vertical layers in the atmosphere and as many as 30
layers in the ocean (IPCC 2007). GCMs are the best tools available to obtain projections
of different variables, such as precipitation, temperature, humidity, solar radiation, wind
speed, etc. Figure 1.1 displays how a climate model is built. The world is broken up into
many smaller areas or grid cells depending of the resolution of the model. The location of
each grid cell is determined based on its position on earth. There are vertical layers above
each grid cell that can be defined at different pressure levels.
The lower left picture shows all the physical processes happening in each grid cell of
the model. Different kinds of surfaces (e.g. ocean, land, ice) are defined in the model, and
various variables such as temperature, wind, and many others will be calculated in the
model (http://www.cmmap.org).
1.3. Regional Circulation Models (RCMs)
Regional Climate Models (RCMs) perform the same as GCMs but over a restricted
domain, which allows higher resolution and leads to more detailed outputs (Barron and
Sorooshian 1997). They are downscaling tools that add high-resolution information to
large-scale projections of GCMs. By resolving features down to 50 km or less, RCMs
provide more accurate depictions of surfaces, such as coastlines, mountain topographies,
small islands, etc. RCMs also make a more realistic representation of small islands as
4
compared to global models, where their climate would be considered the same as the
surrounding ocean (Barron and Sorooshian 1997, Jones et al. 2004).
Like GCMs, they are full, physically-based models that represent all the interactions
and processes between climate system components (Jones et al. 2004). Dynamical,
statistical, and hybrid (statistical-dynamical) methods are three techniques used to obtain
regional climate projections; RCMs are categorized in a dynamical technique group
(Jones et al. 2004). They can be thought of as being composed of three layers. One layer
is largely driven by the GCM, another layer builds on some locally specific data, and the
third layer uses its own physics-based equations to resolve the model based on data from
Figure 1.1 Representation of a climate model setup
(from http://www.cmmap.org/learn/modeling/whatIs2.html retrieved on 03/12/2013)
5
model based on data from the other two. The results are comparatively local projections
that are informed by both local specifics and global models. This process requires
significant computational resources because it depends on the use of complex
models. Figure 1.2 demonstrates an example of precipitation prediction by RCM and
GCM over the Alps and Pyrenees between the present and 2080. It is obvious that more
detailed results can be obtained by incorporating RCM that can represent the effects of
these mountains on the weather much better than GCM.
1.4.Climate Model Scenarios
To predict or estimate the changes that might be expected to happen in future climate,
some assumptions about the status of future (e.g. CO2 concentration, population growth,
and economic development) need to be made (IPCC 2007). IPCC has developed a set of
future emission scenarios called Special Report on Emissions Scenarios (SRES). Four
qualitative storylines yield four sets of scenarios called ?families?: A1, A2, B1, and B2.
Figure 1.2 Predicted changes in winter precipitation over Central/ Southern Europe between the present
day and 2080 predicted by the RCM (right) and GCM (left).
(from http://climateprediction.net/content/regional-climate-models retrieved on 03/12/2013)
6
The A1 scenario family assumes a future of global population that reaches the highest
point at mid-century and drops from that time forward, very rapid economic growth, and
rapid introduction of new and more efficient technologies (IPCC 2007). The A1 scenario
family includes three groups identified by their technological emphasis: fossil-intensive
(A1FI), non-fossil energy sources (A1T), or a balance across all sources (A1B). The
A1FI and A1T scenarios specifically analyze the alternative energy technology
developments and hold other driving forces constant.
The A2 scenario (Nakicenovic et al. 2000) family assumes a population of 15 billion
by 2100. Self-reliant nations, slower changes in technology, and increased incomes are
some of the factors that define the scenario. Economic development is regionally
oriented, and economic growth and technological changes are more fragmented and
slower than in other storylines. A continuous increase in CO2 emissions related to land
use as a result of the increasing population without a proportional increase in agricultural
productivity is also demonstrated in this scenario (Nakicenovic et al. 2000).
The B1 scenario family considers a world with the same global population as A1,
rapid changes in the economy, and the introduction of clean and resource-efficient
technologies. This scenario?s emphasis is on global solutions to economic, social, and
environmental sustainability without additional climate initiatives.
The B2 scenario family highlights local solutions to economic, social, and
environmental sustainability. The world?s population is increasing at a lower rate
compared to the A2 scenario. There are intermediate levels of economic development and
less rapid and more diverse technological change than in the B1 and A1 scenarios.
7
In most scenarios, the global forest area will decrease for some decades due to the
population increase and income growth. They will increase by the end of the 21st century,
with the greatest increase in the B1 and B2 scenario families. Agricultural land use
changes are associated with changing food demands. Many other social, technological,
and economic factors affect agricultural, forest, and other types of land change. All of the
driving forces mentioned above will affect CO2 and other GHG emissions. Figure 1.3
shows the range of total CO2 emissions in gigatons of carbon (GtC/year) from all sources
(energy, industry, and land-use change) for different scenario groups from 1990 to 2100.
Figure 1.3 Total global annual CO2 emissions [in gigatons of carbon (GtC/year)] for six scenario
groups.
8
1.5. Bias Correction
General Circulation Models (GCMs) are important tools in evaluating climate change
impacts and decision-making (Wood et al. 2004, Li et al. 2010). However, since models
are not perfect, a 20th century climate projected from a model is not the same as the
climate of the 20th century based on observations. Hence, GCM precipitation outputs
cannot be used in hydrological models or in decision-making without performing some
form of bias correction (Sharma et al. 2007, Hansen et al. 2006, Feddersen and Andersen
2005). A realistic presentation of future precipitation from global climate models is
extremely important for vulnerability and impact assessment (Wood et al. 2004,
Schneider et al. 2007). Therefore, modelers use bias correction techniques to represent
more realistic GCM outputs by establishing a relationship between climate model outputs
and observations and then using that relationship to transform the simulated 21st century
climate to a "best guess" 21st century climate. These techniques are given a variety of
names in the literature, such as statistical downscaling, histogram equalizing, and
quantile-based mapping (Piani et al. 2010).
1.6. Downscaling Techniques
1.6.1. Spatial Downscaling
GCMs are developed to simulate the current climate and predict the future climate
change under different climate scenarios. However, the projected climate at a global scale
9
does not provide a satisfactory output to use in a hydrological model at a watershed or
regional scale (Solaiman 2011). The spatial resolution of GCMs usually ranges from 250
km to 600 km, which is a coarse resolution for studies at a watershed scale. The accuracy
of GCMs decreases at smaller temporal and spatial scales. Therefore, the projected results
from the GCMs are downscaled to a higher resolution level (Solaiman 2011).
?Downscaling? is based on the view that the regional climate is conditioned by the
climate on a larger scale (Von Storch 1995, 1999a). Information is cascaded "down" from
larger to smaller scales. The regional climate is the result of the interplay of the overall
atmospheric or oceanic circulation and of regional specifics, such as topography, land-sea
distribution, and land use (Von Storch 1995, 1999a). The confidence that may be placed
in downscaled climate change information is dependent on the validity of the large-scale
fields from the GCM. Since different variables have different characteristic spatial scales,
some variables are considered more realistically simulated by GCMs than others.
However, there is no consensus in the community about what level of spatial aggregation
is required for the GCM to be considered skillful.
Two common downscaling techniques are dynamical downscaling and statistical
downscaling. Running a set of regional climate models, dynamical downscaling process
uses the relatively coarse resolution output from the GCMs as a continuously updated
boundary condition for the high-resolution regional models. The most common technique
to perform dynamical downscaling is using RCMs (Brissette et al. 2007, Solaiman 2011).
Utilizing dynamical downscaling requires computational efforts that make it impractical
when several GCMs and emission scenarios are used (Maurer et al. 2007). Figure 1.3
10
shows how the downscaling techniques can provide a better representation of GCMs with
higher resolution output to use in regional climate change studies.
Statistical downscaling is more popular due to its relative computational ease.
Generally, they are categorized as weather generators, transfer functions and weather
typing schemes. Weather generators are statistical models that generate random but
realistic daily sequences of variables, such as precipitation and temperature. These data
Figure 1.4 Downscaling techniques allow the use of GCMs outputs as inputs into regional
climate and weather models. From
http://www.southwestclimatechange.org/climate/modeling/downscaling retrieved on 03/12/2013
11
are sometimes called synthetic data. Usually, they generate precipitation first, and other
data are later derived using the statistical relationships between precipitation and these
data (Von Storch 1999b, Katz and Parlange 1996). Transfer functions use a quantitative
relationship, such as regression models or linear or non-linear interpolations (Von Storch
1999b). Sailor and Li (1999) modeled local temperature at different stations in the U.S.
using multiple regression models, and Dehn and Buma (1999) specified precipitation at a
French Alpine site. An alternative to linear regression is piecewise linear or nonlinear
interpolation, such as kriging tools (Wackernagel 2003). Biau et al. (1999) used this
approach to relate local precipitation to large-scale pressure distributions. Other studies
have used cubic splines to specify precipitation (Buishand and Klein Tank 1996,
Buishand and Brandsma 1997, 1999). Another non-linear technique is based on Artificial
Neural Networks (ANNs), which is more powerful than other methods, but the
interpretation of the dynamical character of the relationships is less easy (Von Storch
1999b).
Weather typing schemes are based on a more traditional synoptic climatology
concept, including analogs and phase space partitioning. They define weather classes
related to local and regional climate variations (Von Storch 1999b). These weather
classes are defined synoptically or fitted specifically for downscaling purposes by
constructing indices of airflow (Conway et al. 1996). Weighting the local climate states
with the relative frequencies of the weather classes and then the frequency, distribution,
or mean of the regional climate are derived, and climate change is estimated by
determining the frequency of weather classes (Von Storch 1999b). The regional and local
climates are usually obtained from observations. Zorita et al (1995) introduced the analog
12
method for downscaling and its applicability for the specification of precipitation was
tested by Cubasch et al. (1996), Martin et al. (1996), and Biau et al. (1999). Techniques
that partition the large-scale state phase space such as Classification Tree Analysis are
other methods which are mathematically more demanding techniques (Zorita et al. 1995,
Lettenmaier 1999).
1.6.2. Temporal Disaggregation
Many hydrologic models or studies related to hydrology and continuous watershed
simulations require long-term meteorological data, such as precipitation (Burian et al.
2000). However, most of the available precipitation data are in hourly or daily intervals,
which are still not small enough time intervals to estimate the accurate hydrologic
response for small watersheds or developing IDF curves. Time intervals on the order of
minutes (e.g. 15-min or 30-min) are suggested for accurate characterization in urban
settings or many other hydrologic studies (Burian et al. 2000). To obtain such high
temporal resolution data, the hourly or daily data need to be disaggregated. Several
techniques have been developed and proposed to disaggregate precipitation data. Most of
these methods discuss disaggregation of the daily or longer time interval precipitation
(e.g. Hershenhorn and Woolhiser 1987, Glasby et al. 1995). Liou (1970) developed a
method using four explicit distributions to disaggregate the hourly rainfall to 15-min.
rainfall. The selection of distribution to use in a specific storm hour was based on a
comparison of precipitation depths in that hour with those of the preceding and
successive hours. Ormsbee (1989) developed two disaggregation models to disaggregate
hourly precipitation data. One model, called a discrete model, disaggregates the hourly
13
precipitation to three 20-min intervals precipitation. The other model a continuous
model  disaggregates the hourly rainfall into 1- to 30-min time intervals.  The
probability distribution of the accumulated rainfalls at different time steps was used by
Pandey (1994) to investigate the scaling nature of probability distribution. They used the
multi-fractal multiplicative cascades theory to explain the rainfall probability
distributions at different time scales and tested the method on an example in Quebec.
Results showed that the method can successfully estimate the distribution of short
duration rainfall.
Socolofsky et al. (2001) introduced a method to downscale daily precipitation data to
hourly data. The method breaks daily precipitation into possible storm intensity patterns
by selecting samples of measured event statistics from hourly observed precipitation data.
Rodriguez-Iturbe et al. (1987, 1988) investigated two point-process based models. In
the Rectangular Pulses Model, storms arrive according to a Poisson process. In this
model, each event has a random duration and constant intensity. The second model
simulates a storm arising from a Poisson process when each storm is associated with a
cluster of cells and each of the cells has a random depth and duration. Examples of
clustered Poisson models are the Bartlett-Lewis and Neyman-Scott models (Rodriguez-
Iturbe et al. 1987, 1988, Islam et al. 1990, Onof and Wheater 1993). Other models have
been used to capture the variability between and within storms but they usually rely on
extrapolating scaling at course resolution to finer scales (Schertzer and Lovejoy 1987,
Gupta and Waymire 1993, Olsson 1996, Veneziano et al. 1996). Hershenhorn and
Woolhiser (1987) and Econonpouly et al. (1990) developed a model to disaggregate daily
rainfall by simulating the number of storms in a day and the amount, duration, and
14
starting time of each event. The number of rainfall events, duration, and start time are
obtained from an estimated probability distribution fit to observed hourly data within the
same climatological regime.
Several other studies investigated the possibility of using Artificial Neural Networks
(ANNs) for rainfall temporal downscaling. Burian et al. (2000) compared the results of
rainfall disaggregation using an ANN model with two other methods; linear model and a
continuous deterministic rainfall disaggregation model (Ormsbee 1989). Results of their
study indicated that the latter two models underpredicted maximum rainfall intensities
and were outperformed by the ANN model. Dibikie and Coulibaly (2006) evaluated the
ANN model in disaggregating precipitation and compared it with the linear regression
model and concluded that ANN outperforms the statistical models. Other studies have
also reported better performance in predicting heavy rainfall events using the ANN model
compared to linear regression downscaling methods (Weichert and Burger 1998).
1.7.Intensity-Duration-Frequency (IDF) Curves
An IDF curve presents the probability of a given rainfall intensity and duration
expected to occur at a particular location. Figure 1.5 shows an IDF graph. Lines on the
graph represent probability. For example, the five-year line would represent rainfall
events with a probability of occurring once every five years. Another way to explain it is
that the probability of a five-year magnitude storm happening in any given year is 1/5 or
20%. The information presented on the IDF graph is based on a statistical analysis of an
actual storm prediction (Bedient and Huber 1988).
15
Each line in the IDF graph shows rainfall events with the same occurring probability
for different durations. A 50-year storm, for example, can be a 50-year, 15-min storm, a
50-year, 1-hr storm or a 50-year 12-hr storm. Rainfall intensity is higher for short storms
and lower for longer storms (Bedient and Huber 1988).
An IDF curve is one of the most common hydrologic tools for designing various
structures, such as, stormwater management facilities, erosion and sediment control
structures, flood protection structures, and drainage structures in urban areas (McCuen
1989, Prodanovic et al. 2007). Typically, standards are set for designs that require the
minimum capacity in terms of rainfall return periods. For example, storm sewers are
typically designed to carry a minimum of a five-year storm meaning that all the runoff
Figure 1.5 Rainfall Intensity-Duration-Frequency (IDF) curve
16
from a five-year storm from the upstream of the sewer system must fit in the sewer
without overflowing. The first step toward designing different water management
structures (e.g. dams, channels, detention ponds) is to identify the characteristics of
design storm in terms of duration, return period and intensity. Time of concentration of
the watershed draining to the hydraulic structure usually dictates the design storm
duration. Storm return period is assigned based on economic assessments and risk
analysis (probability of damage, loss of life in case of failure). For example, a 5- to 10-yr
return period is used for designing roadside channels (Brown et al. 2001), where the cost
of failure is negligible. Whereas, a much larger return period is used for designing small
dams (100-yr and longer), where there is a great risk of loss of life in case of failure.
With knowledge of the storm return period, the design rainfall intensity is then acquired
from the developed IDF curves of the region. The rainfall intensity and duration of
design storm dictate the cost of the hydraulic structure, and any uncertainty in estimation
of these parameters can impose great design uncertainties.
IDF curves are created by analyzing historic rainfall event statistics. More complete
and longer data provide a better statistical analysis. Cumulative frequency analysis is
used to analyze the rainfall records by determining the event intervals with a specific
magnitude for a range of metrics within the rainfall data (e.g. a 30-min storm with the
maximum rainfall value that occurs at a 25-yr interval). A Cumulative Distribution
Function (CDF) is usually used for fitting the precipitation data. For a given return
period (Tr), the cumulative frequency (F) is:
=1 1                                                         (1)
17
With knowledge of the cumulative frequency, the maximum rainfall intensity can be
found using an appropriate theoretical distribution function. The most common
distribution functions used for developing IDF curve are Gumbel, Log-Pearson Type III,
Weibull, and Generalized Extreme Value (GEV) distributions.
In the U.S., IDFs are presented in the form of isohyetal maps in three reports:
Technical Paper No. 40 (TP-40) (Hershfield 1961) presents the IDF curves for durations
from 30 minutes to 24 hours and return periods from one to 100 years; Technical Paper
No. 49 (Miller 1964) shows the IDFs for durations from two to 10 days for return periods
of two to 100 years; and Hydro-35 (Frederick et al. 1977) showed the IDFs for durations
from five to 60 minutes for just two return periods; two and 100 years. NOAA Atlas 14
presents updated precipitation-frequency atlas of the United States for durations from five
minutes to 60 days (Bonnin et al. 2004). Updating precipitation-frequency is still an
ongoing process and is expected to be completed by June 2013.
 Many different studies have been undertaken to develop the rainfall IDF curves.
Huard et al. (2010) estimated the IDF curves using Bayesian analysis instead of the
classical approach. Svensson et al. (2007) compared different methods of IDF curve
estimation from fragmented records for Scotland. Even though studies have investigated
various methods for developing IDF curves, studies associated with changes to IDF
curves due to climate change are limited. Simonovic and Peck (2009) updated the rainfall
IDF curves for the period from 1961 to 2002 under two climate scenarios for the city of
London, Ontario, Canada. In a continuous study, Solaiman and Simonovic (2011)
developed future IDF curves using 27 climate change scenarios for the city of London,
Ontario, Canada. IDF curves were created for durations from one to 24 hours and return
18
periods from two to 100 years. The results of their study showed 20-40% changes in
different durations for all return periods. The climate change impact on rainfall IDF
curves was evaluated by Wang et al. (2013) in the Apalachicola River basin (Florida
Panhandle coast) using two climate models: HRM3?HadCM3 and RCM3?GFDL. Their
study suggested that, based on HRM3?HadCM3 projections, there will be no significant
changes in rainfall intensity at the upstream and middle stream stations, but higher
rainfall intensity is expected at the downstream station. Analysis of the RCM3?GFDL
projections, on the other hand, showed that rainfall intensity is expected to increase from
upstream to downstream. The future IDF curves developed by Nguyen et al. (2006, 2007)
were developed using two climate model projections; HadCM3 and CGCM2 showed a
large difference in the IDF curves of these two models.
 Using the projections from CGCM2 B2 to develop the IDF curves for the Grand
River and Kenora Rainy River regions in Ontario indicated an increase from 24% to 35%
in the 24-hour rainfall intensity for the 2050s and 2080s (Coulibaly and Shi 2005).
Another study investigated the climate change impact on rainfall IDF curves using the
outputs from the CRCM climate model for Southern Quebec (Mailhot et al. 2009). An
analysis of the results showed a 50% decrease by 2050 for rainfall durations of two and
six hours and a 32% decrease for 12- and 24-hour rainfall durations. The IDF curves
developed from the projections of RCM A2 for the next 80 years for Denmark showed
that an increase of 2 to 15% in extreme rainfalls is expected (Onof and Arnbjeg-Nielsen
2009).
19
1.8. Problem Statement
Changes in extreme rainfall events can lead to a revision of standards for designing
civil engineering infrastructures. It can also lead to the reconstruction and/or upgrade of
existing civil engineering infrastructures. Current design standards are based on historic
climate information. For example, a dam that is designed to control a 100-year flood
event will provide a significantly lower level of protection if the intensity and duration of
the 100-year flood event increases. To prepare for future climate changes, it is imperative
that we review and update the current standards for water management infrastructure
design. This would prevent water management infrastructures from performing below the
designated guidelines in the future (Prodanovic et al. 2007).
 Most of the studies related to the impact of climate change on future rainfall
intensity do not consider short rainfall durations for developing the IDF curves (e.g. 10-
or 15-min). The reason is that the future projections derived from GCMs are usually
provided at coarse temporal resolutions; as a result, downscaling is required to obtain a
high temporal resolution data. However, in most studies (Wang et al. 2013, Svensson et
al. 2007), temporal disaggregation has been skipped and IDF curves developed with the
available precipitation data from the GCMs.
 Another issue with some of the studies is using only one or two GCM projections to
develop the future rainfall IDFs (Wang et al. 2013, Nguyen et al. 2006, 2007, Coulibaly
and Shi 2005, Mailhot et al. 2009). There are significant uncertainties in the results of
different GCMs. The difference in physical parameterizations, especially of radiative and
20
precipitation-forming processes, amongst different GCMs and RCMs, the simplification
of complex processes in the atmosphere, and the difference in initial and boundary
conditions for each climate projection are some of the reasons that explain the existing
uncertainty. Therefore, using only one climate model may represent one of many possible
results and cannot be considered representative of the future. Therefore, it is important to
use more than one GCM for a complete and thorough assessment of possible changes in
the future.
1.9. Dissertation Objectives
The objectives of this dissertation are as follows:
1. To develop rainfall IDF curves for Alabama under future climate change scenarios;
using a stochastic method to disaggregate three-hourly precipitations into 15-
minute precipitations.
2. Use Artificial Neural Network (ANN) to estimate the maximum 15-, 30-, 45-, 60-,
and 120-min rainfall depths from three-hourly precipitations for the creation of
future IDF curves for Alabama.
3. To develop probability-based IDF curves incorporating climate projections from
six different climate models.
1.10. Dissertation Structure
This dissertation includes six chapters. Chapter 1 provides an introductory overview,
a review of literature, and the objectives of the study. A brief review of different climate
change models, climate model scenarios, bias correction and downscaling techniques,
21
and a review of studies related to the assessment of climate change on IDF curves is
presented. Chapters 2 through 4 present a discussion of the methodology and results of
the three objectives outlined above. Chapter 2 discusses the development of rainfall IDF
curves for Alabama under future climate change scenario. The details of performing
temporal disaggregation using stochastic method are also presented. The results of this
chapter have already been published in the Regional Environmental Change (Mirhosseini
et al. 2012). Chapter 3 describes the methodology used to develop an ANN model to
estimate the maximum rainfall depths (15-, 30-, 45-, 60-, and 120-min) from three-hourly
precipitations. It also presents the future IDF curves developed using the ANN
disaggregation model and compares the outcomes with the previous chapter?s results.
This chapter has been submitted for publication to the Hydrological Processes Journal
(Mirhosseini et al. 2013). Chapter 4 documents the development of a probability-based
IDF curve using a kernel density estimator using all climate models investigated in this
research. This chapter will be submitted to Journal of Hydrologic Sciences for
publication. Chapter 5 presents the conclusions of this research. Finally, suggestions for
future work are presented in Chapter 6.
22
Chapter 2
2. The Impact of Climate Change on Rainfall Intensity-Duration-Frequency (IDF)
Curves in Alabama
2.1. Abstract
Changes in the hydrologic cycle due to increase in greenhouse gases (GHG) are
projected to cause variations in intensity, duration, and frequency of precipitation events.
Quantifying the potential effects of climate change and adapting to them is one way to
reduce vulnerability. Since rainfall characteristics are often used to design water
management infrastructures, reviewing and updating rainfall characteristics (i.e.,
Intensity-Duration-Frequency (IDF) curves) for future climate scenarios is necessary.
This study was undertaken to assess expected changes in IDF curves from the current
climate to the projected future climate. To provide future IDF curves, 3-hourly
precipitation data simulated by six combinations of global and regional climate models
were temporally downscaled using a stochastic method. Performance of the downscaling
method was evaluated and IDF curves were developed for the State of Alabama. The
results of all six climate models suggest that the future precipitation patterns for Alabama
are expected to veer towards less intense rainfalls for short duration events. However, for
long duration events (i.e. > 4 hours), the results are not consistent across the models.
Given that a large uncertainty existed for projected rainfall intensity of these six climate
models, developing an ensemble model as a result of incorporating all six climate
23
models, performing an uncertainty analysis and creating a probability based IDF curves
could be proper solutions to diminish this uncertainty.
2.2. Introduction
There is a misunderstanding on the subject of climate change that causes great
confusion about its potential effects on natural resources and human lives (Miller and
Yates 2006). Much of the public is left with two extreme and opposing views about
climate change: either climate change is happening at the greatest rate and soon nothing
will be left on earth, or climate change is a fiction that can be safely ignored. However,
neither of these impressions are useful in making management decisions about natural
resources.
An analysis of temperature records shows a significant warming trend around the
world during the 20th century (Miller and Yates 2006). The global average temperature
increased by 0.74 C over the 20th century. The changing temperature has caused changes
in the seasonal timing of runoff in mountainous areas (Stewart et al. 2004). Despite the
total increase in winter precipitation in the western U.S. and some parts of Canada; spring
snowpacks have been melting earlier (Stewart et al. 2004). Along with the change in
temperature, there will be changes in the hydrologic cycle, leading to changes in
precipitation and runoff. Sea level rise and new stresses on ecological systems (e.g.
forests and freshwater aquatic systems) may be additional climate change impacts on
biological and physical systems.
There is scientific evidence that human activities play a significant role in the
temperature increase. During the last century, the concentration of carbon dioxide (CO2)
and other greenhouse gases (GHGs) in the earth?s atmosphere have risen due to increased
24
industrial activities (e.g. burning fossil fuels can release carbon dioxide into the
atmosphere) (Prodanovic et al. 2007). This increase in GHG concentrations is causing
large-scale variations in atmospheric processes, which can lead to changes in
precipitation and temperature characteristics. There is scientific agreement on some
important features of the possible hydrologic changes: there will be an increase in the
average precipitation around the world (Miller and Yates 2006). However, this does not
imply that more precipitation will occur everywhere. Climate change impacts on
precipitation are less certain on the regional scale, and climate models are not consistent
in predicting the expected precipitation. The water supply will depend on the quantity and
timing of local and regional precipitation, which may change with global climate change.
While it is not possible to make very accurate predictions regarding the overall quantity
of precipitation for a specific region, scientific theory suggests that there will be more
intense but less frequent periods of precipitation. In other words, there may be longer
periods of drought alternating with heavy rainfalls.
Changes in extreme rainfall events often present challenges for water
management utilities. Heavy runoff can degrade the water quality, forcing additional
costs for treatment and increasing the risk of water supply contamination by pathogens
(Miller and Yates 2006). Property damage and potential loss of life due to flooding are
also caused by extreme rainfall events (Wright et al. 2010). Heavy precipitation caused
by a hurricane in 1999 left a water treatment plant in Greenville, NC, surrounded by
floodwaters and damaged the utilities? infrastructure, costing about 11 million dollars
(Miller and Yates 2006).
25
Drought can also decrease the capability of water utilities to meet water demands and
enforce emergency restrictions. A severe drought in 2002 left many Colorado reservoirs
dangerously low (Miller and Yates 2006). Forest fires are becoming common as the
temperature increases. Fire can cause serious effects on downstream water quality and
reservoir sedimentation. Erosion can damage areas from farm fields to stream banks
adjacent to important infrastructure (Wright et al. 2010). For example, in 1996, a flood
occurred after a Buffalo Creek fire, which caused severe sediment and debris flow into
Denver?s Strontia Springs Reservoir. It required cleanup and resulted in long-term water
quality effects, imposing heavy costs on the utility (Miller and Yates 2006).
Such extreme events may become common and more difficult to anticipate in the
future because of global climate change. They can lead to a revision of standards for
designing civil engineering infrastructures. It can also lead to the reconstruction and/or
upgrade of existing civil engineering infrastructures. Current design standards are based
on historic climate information. For example, a dam that is designed to control a 100-year
flood event will provide significantly less protection if the intensity and duration of the
100-year flood event increases. Many industries have already started long-term planning
in the context of uncertainty. Accounting for potential changes in water consumption
patterns because of socio-economic or demographic changes is an example of water
utilities? long-term planning. Climate change, as an extra source of uncertainty, is
becoming significantly relevant to water resource managers (Miller and Yates 2006).
Like any other source of uncertainty, the best practice is to attempt to understand the
possible changes that can happen in the future and the consequences that these changes
can have on the management of infrastructure. Therefore, to prepare for future climate
26
changes, it is imperative that we review and update the current standards for water
management infrastructure design. This will prevent water management infrastructure
from performing below the designated guidelines in the future (Prodanovic et al. 2007).
This study was funded by the National Oceanic and Atmospheric Agency (NOAA)
Regional Integrated Sciences and Assessments (RISA) program. Its main objective was
to create IDF curves for Alabama using high-resolution projections (for 2038-2070)
derived from dynamical downscaling of General Circulation Models (GCMs) by
Regional Climate Models (RCMs) and to evaluate the impact of climate change on IDF
curves.
2.3. Materials and Methods
2.3.1. Data and Model Used
The stations providing long-term historical precipitation data for Alabama are shown
in Figure 2.1. The observed (historical) precipitation data at 15-minute intervals were
obtained from the NOAA National Climatic Data Center (NCDC Online Climate Data
Directory 2005). Historical simulations of precipitation for 1968 to 2000 and future
projections for 2038 to 2070 were obtained from the North American Regional Climate
Change Assessment Program (NARCCAP) at three-hour intervals with a spatial
resolution of 50 km (Sebastien et al. 2007, Richard et al. 2007). NARCCAP was designed
to investigate the uncertainties in future climates at a regional scale (Mearns et al. 2007).
To this end, it uses several GCM historical simulations and projections from the
Intergovernmental Panel on Climate Change (IPCC) Coupled Model Intercomparison
Project and dynamically downscales them using a set of RCMs. The regional
27
downscaling process uses the relatively coarse resolution output from the GCMs as a
continuously updated boundary condition for the high-resolution RCMs.
Figure 2.1 Location of rain gauge stations (red squares) and NARCCAP 50-km
resolution grid centers (green dots, HRM3-HadCM3) used to develop IDF
curves for Alabama.
28
The regional downscaling domain of NARCCAP covers the U.S. and most of Canada
(Mearns et al. 2007, 2009, Sebastien et al. 2007, Richard et al. 2007).
As mentioned above, future projections of precipitation data for this study were
obtained from the NARCCAP website. Six different dynamically downscaled datasets
were used. In the entries below, the datasets are named with the RCM identifier, followed
by the identifier of the GCM providing boundary conditions.
1. HRM3-HadCM3:
The Hadley Centre Coupled Model, version 3 (HadCM3) was developed at the
Hadley Centre in the United Kingdom. It is a coupled atmosphere-ocean general
circulation model (AOGCM) and was one of the major models used in the IPCC Third
Assessment Report in 2001 (Gordon et al. 2000, Pope et al. 2000, Collins et al. 2001).
Two components of HadCM3 are the atmospheric model (HadAM3) and the ocean model
(HadOM3), which includes a sea ice model. The model?s resolution is about 300 km
(Jana and Majumder 2010). Unlike the earlier models developed at the Hadley Centre and
elsewhere, HadCM3 does not need a flux adjustment to produce a good simulation. It has
higher ocean resolution than HadCM2, which is one of the major features of this model.
It also provides a good match between the oceanic and atmospheric components. The
ocean mixing scheme has been improved in this model, as well. The HadOM3 resolution
is 1.25 degrees longitude x 1.25 degrees latitude. It has 20 levels and a time step of one
hour. The HadAM3 horizontal resolution is 3.75 longitude x 2.5 degrees latitude. There
are 19 levels in the vertical.
29
The Hadley Centre Regional Model, version 3 (HRM3) is a configuration of the
HadCM3 model that provides high resolution projections of regional climates for impact
studies; the resolution is about 50 km (Gordon et al. 2000; Pope et al. 2000; Johns et al.
2003). The Hadley Centre for the UK climate impact programme, first used the model in
2002, and it has been used for many high-resolution simulation studies since then. HRM3
includes the same atmospheric component as HadCM3, but some modifications were
made to the model physics. It provides a higher spatial resolution of a local area by taking
the boundary conditions of coarse resolution global model simulations (Gordon et al.
2000, Pope et al. 2000, Johns et al. 2003).
2. CRCM-CGCM3:
The Coupled Global Climate Model, version 3 (CGCM 3.1) was developed at the
Canadian Centre for Climate Modelling and Analysis (CCCma). CCCma is a division of
the Climate Research Branch of the Meteorological Service of Canada of Environment
Canada, based at the University of Victoria in Victoria, British Columbia. Three
atmosphere and three coupled atmosphere-ocean GCMs have been produced since 2000
at this center.
CGCM3 uses the same component that was used in developing CGCM2, and it
also uses the updated atmospheric component of the Third Generation Atmospheric
General Circulation Model, AGCM3 (Flato and Boer 2001, Kim et al. 2002, 2003). Like
AGCM2, the horizontal structure of the main prognostic variables is presented by the
spectral transform method, and the vertical representation is in terms of a rectangular
finite element defined for a hybrid vertical coordinate (Laprise and Girard 1990).
30
AGCM3 has a higher horizontal resolution than AGCM2. The vertical domain is deeper,
and the vertical resolution is higher. CGCM3 extends from surface to the stratopause
region, and this region spans 32 layers.
CRCM 4.2 is a Canadian Regional Climate Model developed at the Universit? du
Qu?bec ? Montr?al based on the fully elastic, non-hydrostatic Euler equations (Laprise et
al. 1998, Caya and Laprise 1999). The physical parameterization is mostly based on
CCCma GCM3. Solar radiative transfers were improved with three bands in the near-
infrared region and one band in the visible region (Puckrin et al. 2004). The radiative
effects of GHGs are considered separately for CO2, CH4, N2O, CFC11, and CFC12. The
land surface scheme is the Canadian LAnd Surface Scheme (CLASS) 2.7 (Verseghy
1991, Verseghy et al. 1993). CLASS uses three soil layers (0.1 m, 0.25 m and 3.75 m
thickness). It includes prognostic equations for energy and water conservation for the
three soil layers and a thermally and hydrologically distinct snowpack where applicable.
3. HRM3-GFDL:
GFDL CM 2.1 is a coupled atmosphere-ocean general circulation model (AOGCM)
developed by the Geophysical Fluid Dynamics Laboratory (GFDL) at Princeton
University (Anderson et al. 2004). It is one of the major models used in the Fourth
Assessment Report, along with HadCM3. The atmospheric component (AM 2.1) covers
180? to 45?W longitude, 10?N to 75?N latitude and has a 24-level atmosphere run at a
resolution of two degrees in the east-west and 2.5 degrees in the north-south direction.
This resolution is sufficient to resolve the large mid-latitude cyclones responsible for
weather variability.
31
The atmosphere model includes a representation of radiative fluxes, mixing in the
atmospheric boundary layer, representations of the effects of stratus and cumulus clouds,
a scheme for representing drag on upper-level winds caused by gravity waves, changes in
the spatial distribution of ozone, and the ability to represent the impact of multiple
greenhouse gasses.
The ocean component has 50 levels running at one degree in the east-west direction,
and it varies from one degree to 1/3 degree along the equator in the north-south direction.
This resolution is good enough to resolve the equatorial current system. The other
parameterization includes a free surface height that changes in response to evaporation,
the precipitation and convergence of ocean currents, the absorption of sunlight tied to
observed chlorophyll concentrations, and a representation of the oceanic mixed layer.
4. CRCM-CCSM:
The Community Climate System Model (CCSM) is a coupled climate model
developed at the National Center for Atmospheric Research (NCAR) in Boulder,
Colorado. It simulates past, present, and future climates (Collins et al. 2006a). The model
includes ocean, atmosphere, sea ice and land surface. CGCM3 is the third generation of
coupled models designed to produce realistic simulations and includes an atmosphere
model (CAM3) (Collins et al. 2004, 2006b), the land surface (CLM3) (Oleson et al. 2004;
Dickinson et al. 2006), the sea ice (CSIM5) (Briegleb et al. 2004), and an ocean model
based on Parallel Ocean Program (POP) version 1.4.3 (Smith and Gent 2002). Each
component is designed to conserve total water, energy, mass, and fresh water. The CAM3
is based on the Eulerian spectral dynamical core with triangular spectral truncation
32
(Collins et al. 2006b). The zonal resolution at the equator ranges from 3.75 degrees to
1.41 degrees. It includes 16 vertical layers (Collins et al. 2006b).
The ocean model has a horizontal resolution of three degrees or one degree. There are
25 levels extending to 4.75 km in the three-degree version and 40 levels extending to
5.37 km in the one-degree version. The sea-ice model is integrated on the same horizontal
grid as the ocean model (Collins et al. 2006b).
The CLM3 model is built based on the nested sub-grid hierarchy of scales
representing land units, soil or snow columns, and plant functional types (Oleson et al.
2004). CCSM3 considers the effect of competition for water among plant functional
types. One of the major goals in developing the land model was to reduce the positive
continental temperature biases during boreal winter. The relationship between fractional
snow coverage and snow height was modified. The biogeophysics formulation was
modified to increase the sensible and latent heat fluxes over sparsely vegetated surfaces.
In previous versions of CCSM, a constant value for dense vegetation was considered for
the turbulent transfer coefficient between soil and the overlying canopy air. The new
formulation considers this coefficient to be dependent on the density of the canopy,
characterized by leaf and stem area indices (Oleson et al. 2004, Collins et al. 2006a).
RCM3-GFDL:
Regional Climate Model (RCM3 or RegCM) version 3, is a three-dimensional,
hydrostatic, compressible, primitive equation, -coordinate regional climate model
originally developed at the National Center for Atmospheric Research (NCAR). It uses
the NCAR CCM3 radiation scheme. The solar component which accounts for the effect
of H2O, O3, CO2, and O2, uses the -Eddington approximation (Keihl et al. 1996). It
33
includes 18 spectral intervals from 0.2 to 5 m. The surface physics are performed using
Biosphere-Atmosphere Transfer Scheme version 1e (BATS1e) (Dickinson et al. 1993).
BATS is a surface package designed to describe the role of vegetation and interactive soil
moisture in modifying the surface-atmosphere exchanges of momentum, energy, and
water vapor. The model has a vegetation layer; a snow layer; a surface soil layer, 10 cm
thick, or a root zone layer, 1-2 m thick; and a third deep soil layer, 3 m thick. The model
also includes a planetary boundary layer scheme, convective precipitation schemes, a
large-scale precipitation scheme, a pressure gradient scheme, a lake model, and an
aerosols and dust model.
5. ECP2-GFDL:
The updated data from the Regional Spectral Model were developed at the
Experimental Climate Prediction Center (ECPC) at the Scripps Institute of
Oceanography. It was originally called ECPC. The main difference between ECPC and
ECP2 is the employment of spectral nudging. Spectral nudging forces the regional model
solution to closely follow its driven global model for scales that are usually close to and
above the synoptic scale. ECPC combines a spectral damping of horizontal wind
tendency and areal average correction of temperature, moisture, and surface pressure,
while ECP2 does not use the moisture correction component of the spectral nudging,
which results in better simulation of precipitation. Also, a larger domain of ECP2 can
more closely match the region modeled by the other RCMs.
34
2.3.2. Bias correction
Models are not perfect; a 20th century simulated climate, projected from a model is
not the same as the climate of the 20th century coming from observations. Hence, GCM
precipitation outputs cannot be used in hydrological models or in decision making
without performing some form of bias correction (Sharma et al. 2007; Hansen et al. 2006;
Feddersen and Andersen 2005). A realistic presentation of future precipitation from
global climate models is extremely important for vulnerability and impact assessment
(Wood et al. 2004; Schneider et al. 2007). Therefore, modelers use bias correction
techniques to represent more realistic GCM outputs by establishing a relationship
between climate model outputs and observations, then using that relationship to transform
the simulated 21st century climate to a "best guess" 21st century climate. These techniques
are given a variety of names in the literature, such as statistical downscaling, histogram
equalizing and quantile-based mapping (Piani et al. 2010).
For this study, a quantile-based mapping method proposed by Li et al. (2010) was
used. In this method, monthly rainfall values were used to define the CDF error of
historical model runs relative to observations. This error was used to correct the model
CDF for the future period by calculating a scaling factor from the monthly totals. The
scaling factor is defined as bias-corrected rainfall total for a given month, divided by the
non-bias-corrected total. Prior to disaggregation of 3-hourly rainfall events, the 3-hourly
totals were multiplied by this scaling factor (Li et al. 2010).
35
2.3.3. Temporal Downscaling
High temporal resolution (e.g., 15-min, 30-min, and 1-hr) data are needed to create
the IDF curves. Since NARCCAP provides future climate data at 3-hour intervals, it is
necessary to temporally downscale the precipitation data. Different types of downscaling
techniques have been developed over the years; they can be categorized as weather
generators, transfer functions (e.g. linear regression, stochastic method and artificial
neural networks) and weather typing schemes (Von Storch 1999b).
The temporal downscaling method employed in this study is a modified version of a
stochastic method introduced by Socolofsky et al. (2001). They used the method to
downscale daily precipitation data to hourly data. The method developed for this project
breaks 3-hourly precipitation into possible storm intensity patterns by selecting samples
of measured event statistics from a 15-min observed precipitation data (Socolofsky et al.
2001). Most stochastic methods are based on two popular models, Neyman-Scott and
Bartlett-Lewis (Rodriguez-Iturbe et al. 1987, Islam et al. 1990). One of the main reasons
for selecting the Socolofsky method was the reduction of computational effort needed to
perform the method compared with the above-mentioned approaches.
2.3.3.1 Stochastic method
For the purpose of disaggregation, a month-specific database of observed
36
precipitation data was created. This database includes several observed rainfall events
with high temporal resolution (15 minute interval). An ?event? was defined as a
continuous sequence of precipitation, separated by 30 minutes of dry weather. In case an
event was longer than 3 hours, it was further divided into 3-hr subintervals starting from
the beginning of the rainfall. As such, the database was composed of multiple years of
observed events, separated by month, where each event was no longer than 3 hours.
For each month in the database, the events were sorted based on their total
accumulated rainfall depth and created a CDF using the rainfall depths, such that each
point on the CDF corresponds to actual, measured storm event in the database. In other
words, each observed event is corresponded with a probability.
To disaggregate a 3-hr GCM forecast for August 1st, 2038 between 9:00 to 12:00
a.m., with a magnitude of 300 mm (call it DT), the downscaling algorithm stochastically
selects several (and not one) observed events from the database and distributes them
randomly over the 3-hr period. This means, the algorithm follows these steps:
1- Given a 3-hourly rainfall with magnitude of DT, the algorithm first searches
the historic CDF for the ordinate ?a? corresponding to DT.
2- A random number is generated from uniform distribution between 0 and ?a?,
call it ?u1?.
3- ?ui? is the probability of the randomly selected historic event. The magnitude of
the observed event with probability of ?ui? is read from the historic CDF (name
Di) and its distribution is retrieved from the database.
4- New DT is calculated by subtracting Di from DT.
37
5- This process then repeats for the new DT
6-Stop when n is the number of observed events selected.
2.3.4. Performance
 This method?s performance was tested to ensure its ability to disaggregate the 3-
hourly precipitation data to 15-min data. 3-hourly precipitation time series at each 15-min
gauge were created by adding the measured 15-min precipitation, and the disaggregation
method was tested in its ability to disaggregate the 3-hourly data into a 15-min synthetic
time series. To evaluate the performance of the disaggregation method, the statistics of
measured and synthetic time series were compared as suggested by Socolofsky et al.
(2001) and Choi et al. (2008). The statistical parameters of the maximum rainfall values
were also calculated to ensure the model captured the peaks. Because the disaggregation
method is stochastic, 30 model runs were performed at each station and the mean value of
statistics over all 30 runs was used in the error quantification.
One of the statistics used to evaluate the performance of the disaggregation
method was ?zero rainfall probability?. According to the explained method, the stochastic
algorithm selects a number of observed events randomly from a database and distributes
them stochastically over a 3-hr period (12 time slots of 15 minutes). Some of the slots
might remain empty (no rainfall). The final product is a newly generated distribution
which has no similarity to any of the individual historic events. For validation, the
algorithm was run 30 times on some selected events with known distribution and reported
the average metric. Becasue the method is stochastic, for each run, different historic
events are selected from the database and randomly distributed over 12 time slots. So the
?zero rainfall probability? from each run is different from the other. The other statistic
38
used for validation of the method was performance measures between the maximum
rainfall of disaggregated time series compared to reference rainfall. As explained earlier,
several reference rainfall events with known distributions were selected and
disaggregated using the explained scheme. The resultant distributions were compared to
the reference distribution and the statistical analysis was performed to acquire the
goodness of fit measures (e.g. R2 of zero rainfall probability and maximum rainfall).
When a single 3-hr event was disaggregated, the maximum partial rainfall depth for a
given period within that event was calculated. These maxima are not compared by taking
the maximum of the monthly or annual disaggregated rainfalls but by taking the
maximum of disaggregated selected events for each month and rainfall duration. For any
of these events, the model was run 30 times and the mean statistics was presented.
2.3.5. Creating IDF curves
 Generalized Extreme Value (GEV) distribution was selected as the best probability
distribution for Alabama based on different tests (e.g. probability plots, goodness of fit
and L-moment ratio) in a study by Durrans and Brown (2001). The GEV distribution is a
continuous probability distribution that combines Gumbel, Frechet and
Weibull distributions and it is based on extreme value theory (Coles, 2001). This
distribution was used in this study for creating IDF curves. The GEV distribution has
cumulative distribution function:
39
( ; ) = exp [ ( )]
( ) = (1+ ) 0
e ( ) =0
Where
 ,
> 0 ,
 GEV parameters have been estimated using the method of moments (MOM)
(Hosking et al. 1985, Bhunya et al. 2007). Kolmogorov-Smirnov (K-S) test was used to
evaluate the performance of the fit.
The steps below describe the process of creating IDF curves:
1. Obtain annual maximum series of precipitation depth for a given duration (15,
30 and 45 min, 1, 2 , 3, 6, 12, 24 and 48 hr)
2. Use GEV distribution to find precipitation depths for different return periods
(2, 5, 10, 25, 50 and 100 years)
3. Repeat the first two steps for different durations
4. Plot depth versus duration for different frequencies
40
2.4. Results and Discussion
2.4.1. Bias correction
As mentioned earlier, the quantile-based mapping method proposed by Li et al.
(2010) was used in this study. Bias correction was done on a monthly basis for each of
the six climate models. CDFs of observed data from all stations and CDFs of climate
model data for the same period were compared to each other. The 21st century projections
were then corrected based on the differences between theses CDFs. In this method,
monthly rainfall values were used to define the CDF error of historical model runs
relative to observations and this error was used to correct the model CDF for the future
period by calculating a scaling factor from the monthly totals (Li et al. 2010). The
resulting bias-corrected model projections were used for the remainder of this study.
Figure 2.2 shows the observed and modeled CFDs for each month when bias correction
was performed for HRM3-HadCM3 model. The CDFs for the remaining models are
presented in Appendix A.
2.4.2. Performance
The statistical measures used in the error quantification for typical months in
winter (February) and summer (August) are presented in Table 2-1. In addition, statistical
parameters of maximum rainfall values were calculated to make sure that the
disaggregation model was capturing the peaks (Table 2-2).
41
January
Rainfall (mm)
0 100 200 300 400 500
F(x
)
0.0
0.2
0.4
0.6
0.8
1.0
Observed
Model
February
Rainfall (mm)
0 100 200 300 400 500
F(x
)
0.0
0.2
0.4
0.6
0.8
1.0
Observed
Model
March
Rainfall (mm)
0 200 400 600 800
F(x
)
0.0
0.2
0.4
0.6
0.8
1.0
Observed
Model
April
Rainfall (mm)
0 100 200 300 400 500
F(x
)
0.0
0.2
0.4
0.6
0.8
1.0
Observed
Model
May
Rainfall (mm)
0 100 200 300 400 500 600 700
F(x
)
0.0
0.2
0.4
0.6
0.8
1.0
Observed
Model
June
Rainfall (mm)
0 100 200 300 400 500 600
F(x
)
0.0
0.2
0.4
0.6
0.8
1.0
Observed
Model
42
Figure 2.2 Monthly Cumulative Distribution Functions (CDFs) to perform bias correction- Model
data is from HRM3-HadCM3 model
July
Rainfall (mm)
0 100 200 300 400 500 600 700
F(x
)
0.0
0.2
0.4
0.6
0.8
1.0
Observed
Model
August
Rainfall (mm)
0 100 200 300 400 500 600 700
F(x
)
0.0
0.2
0.4
0.6
0.8
1.0
Observed
Model
September
Rainfall (mm)
0 100 200 300 400 500 600
F(x
)
0.0
0.2
0.4
0.6
0.8
1.0
Observed
Model
October
Rainfall (mm)
0 100 200 300 400 500
F(x
)
0.0
0.2
0.4
0.6
0.8
1.0
Observed
Model
November
Rainfall (mm)
0 100 200 300 400 500
F(x
)
0.0
0.2
0.4
0.6
0.8
1.0
Observed
Model
November
Rainfall (mm)
0 100 200 300 400 500
F(x
)
0.0
0.2
0.4
0.6
0.8
1.0
Observed
Model
43
These results show that the method was performing well in disaggregating the 3-
hour interval precipitation to 15-min data. Performance of GEV parameter estimation was
also evaluated using Kolmogorov-Smirnov (K-S) test (Massey 1951). The critical value
between sample and theoretical cumulative distributions at 95% level of confidence
=0.05) was 0.234. The maximum distance between the sample and theoretical
cumulative distributions needs to be less than the critical value.
Table 2-1 Performance measures between the disaggregated time series and measured statistics
of 15-min rainfall
Month Station Statistics R2 MAE RRSE
February Auburn, AL P02 0.910.82 0.010.0003 0.310.62
August Auburn, AL P02 0.820.78 0.050.002 0.690.81
P0: probability of zero rainfall, 2: the variance of 15-min rainfall, R2 : linear regression, MAE:
mean absolute error and RRSE: root relative squared error
Table 2-3 shows statistical measures used for this evaluation. Based on the K-S test
results, on all attempts GEV distribution fit to the sample CDFs with minimal error. The
test results were always smaller than the critical value at 95% confidence and had a small
standard error.
44
Table 2-2 Performance measures between the maximum rainfall of disaggregated time series and
measured statistics
R2 MBE*
min 15 30 45 60 120 15 30 45 60 120
Jan 0.67 0.69 0.75 0.80 0.81 -14.6 -9.08 -10.9 -9.5 -8.9
Feb 0.75 0.75 0.78 0.73 0.75 -8.57 -10.8 -10.4 -11.5 -7.4
Mar 0.77 0.78 0.81 0.82 0.85 17.6 -3.9 -10.6 -10.03 -10.3
Apr 0.65 0.68 0.80 0.85 0.85 7.42 -9.7 -8.6 -8.4 -8.21
May 0.68 0.70 0.73 0.75 0.77 -5.9 -7.5 -8.3 -9.2 -10.4
Jun 0.72 0.75 0.78 0.78 0.82 -6.7 -11.1 -9.3 -9.8 -12.9
Jul 0.67 0.69 0.72 0.73 0.81 -5.01 -9.8 -10.7 -9.2 -8.97
Aug 0.69 0.73 0.75 0.77 0.79 -8.40 -8.18 -9.2 -10.4 -9.6
Sep 0.75 0.78 0.79 0.80 0.81 -3.2 -9.2 -8.6 -8.1 -8.9
Oct 0.78 0.80 0.80 0.81 0.82 -9.02 -9.8 -9.5 -11.5 -8.4
Nov 0.65 0.70 0.76 0.78 0.83 -24.6 -6.4 -9.4 -8.9 -4.9
Dec 0.73 0.75 0.77 0.81 0.84 -12.9 -6.8 -8.3 -10.8 -9.7
Ave. 0.71 0.73 0.77 0.78 0.81 -6.15 -8.52 -9.48 -9.78 -9.04
* MBE: Mass Balance Error (%)
Table 2-3 Performance measures between the sample and theoretical cumulative distributions
using Kolmogorov-Smirnov (K-S) test
Models
Kolmogorov-Smirnov R2 **
Average Max Min Std.*  Average Max Min Std.*
HRM3-HadCM3 0.092 0.201 0.043 0.026 0.980 0.996 0.926 0.011
CRCM-CGCM3 0.086 0.195 0.039 0.024 0.982 0.996 0.937 0.010
HRM3-GFDL 0.089 0.175 0.038 0.024 0.981 0.996 0.922 0.011
CRCM-CCSM 0.087 0.178 0.035 0.023 0.982 0.997 0.933 0.01
RCM3-GFDL 0.104 0.218 0.042 0.034 0.971 0.997 0.910 0.01
ECP2-GFDL 0.088 0.178 0.031 0.024 0.982 0.997 0.933 0.01
The critical value at =0.05 is 0.234
* Standard deviation
** Coefficient of determination
45
2.4.3. IDF curves
IDF curves for Alabama were created as a series of 60 maps for each of the 6
NARCCAP regional climate projections (360 maps total) for 10 different rainfall
durations and 6 different return periods.
An example of the type of maps that can be generated is illustrated in Figure 2.3
using HRM3-HadCM3 projections. Maps for the remaining models are presented in
Appendix B. Comparing these maps with NOAA Technical Paper 40 (TP-40) (Hershfield
1961) shows that changes in future IDF curves are expected with the future climate (TP-
40 is not shown in the figure).
For example, for a 50-yr return period with 6-hr duration, 191 mm of precipitation
on average is expected to fall in the southwestern part of the state. Based on TP-40, this
amount is 152 mm? about 25 % less than what is predicted for the future. The largest
projected 12-hr rainfall value (about 329 mm) is expected to happen in southwest
Alabama. For the same region and duration, TP-40 (Hershfield 1961) shows about 203
mm of rainfall, 62% less than what is expected in future. Changes in future rainfall
intensity are expected to continue for other rainfall durations and return periods, but it is
not possible to discuss the results of all 360 maps in details. Therefore, City of Auburn in
Alabama was selected as an example from which to discuss the results in more detail.
Figure 2.4 and figure 2.5 show the future and current IDF curves using all six NARCCAP
regional climate projections for Auburn, AL for the two different return periods of 10 and
100 years.
46
Figure 2.3 Rainfall map; 50-year rainfall of 6-hr, 12-hr, 24-hr and 48-hr durations (mm) under future
climate using HRM3-HadCM3 projected data
47
Figure 2.4 (a-b) shows IDF curves under both the future and current climates for
Auburn when HRM3-HadCM3 projections were used to develop future IDF curves.
Figure 2.4a demonstrates that the projected rainfall intensity for a 10-yr return period
tends to decrease by 20% when the rainfall duration is less than 4 hours, and is expected
to increase by 42% for rainfall durations of more than 4 hours. Also, rainfall intensity
tends to increase by 38% if the rainfall duration exceeds 6 hours and is expected to
decrease by 20% for durations less than 6 hours when the return period is 100 years
(Figure 2.4b).
Figure 2.4 (c-d) depicts the changes in IDF curves when CRCM-CGCM data were
used. For a 10-yr return period, rainfall intensity tends to be reduced by 5l%. Results also
show a 49% decrease for a 100-yr return period. Using HRM3-GFDL projections
presents a 26% decline in rainfall intensity for durations less than 4 hours and a 65%
increase for durations more than 4 hours (Figure 2.4e). Likewise, a 22% decrease and a
129% increase are expected to be observed for durations of less than and more than 4
hours, respectively (Figure 2.4f).
Figure 2.5 (a-b) displays future and current IDF curves developed using the CRCM-
CCSM model. Forty three percent and 49% declines are expected to be noticed for all
durations when the return period is 10-yr and 100-yr, respectively. Results of utilizing the
RCM3-GFDL model for developing IDF curves are presented in Figure 2 .5 (c-d). A 34%
rainfall intensity reduction was observed for durations less than 5 hours, while there was
a 27% increase for longer durations (Figure 2.5c). A 14% decline for durations of less
than 3 hours and a 55 % increase in rainfall intensities for longer durations was also
observed (Figure 2.5d). Figure 2.5 (e-f) demonstrates changes in rainfall intensity
48
employing the ECP2-GFDL model. Both the 10 and 100-yr return periods saw 33% and
37% reductions, respectively for all rainfall durations.
a) Auburn, 10-yr
Duration (hr)
0.1 1 10 100
Ra
inf
all
int
en
sit
y(
mm
/h
r)
1
10
100
1000
HRM3-HadCM3
Current
-20%
42%
b) Auburn, 100-yr
Duration (hr)
0.1 1 10 100
Ra
inf
all
int
en
sit
y(
mm
/h
r)
1
10
100
1000
HRM3-HadCM3
Current
-20%
38%
c) Auburn, 10-yr
Duration (hr)
0.1 1 10 100
Ra
inf
all
int
en
sit
y(
mm
/h
r)
1
10
100
1000
CRCM-CGCM3
Current
-51%
d) Auburn, 100-yr
Duration (hr)
0.1 1 10 100
Ra
inf
all
int
en
sit
y(
mm
/h
r)
1
10
100
1000
CRCM-CGCM3
Current
-49%
e) Auburn, 10-yr
Duration (hr)
0.1 1 10 100
Ra
inf
all
int
en
sit
y(
mm
/h
r)
1
10
100
1000
HRM3-GFDL
Current
-26%
65%
f) Auburn, 100-yr
Duration (hr)
0.1 1 10 100
Ra
inf
all
int
en
sit
y(
mm
/h
r)
1
10
100
1000
HRM3-GFDL
Current
-22%
129%
Figure 2.4 IDF curves under current and future climate using HRM3-HadCM3, CRCM- CGCM3 and
HRM3-GFDL models for Auburn, AL
49
a) Auburn, 10-yr
Duration (hr)
0.1 1 10 100
Ra
inf
all
int
en
sit
y(
mm
/h
r)
1
10
100
1000
CRCM-CCSM
Current
-43%
b) Auburn, 100-yr
Duration (hr)
0.1 1 10 100
Ra
inf
all
int
en
sit
y(
mm
/h
r)
1
10
100
1000
CRCM-CCSM
Current
-49%
c) Auburn, 10-yr
Duration (hr)
0.1 1 10 100
Ra
inf
all
int
en
sit
y(
mm
/h
r)
1
10
100
1000
RCM3-GFDL
Current
-34%
27%
d) Auburn, 100-yr
Duration (hr)
0.1 1 10 100
Ra
inf
all
int
en
sit
y(
mm
/h
r)
1
10
100
1000
RCM3-GFDL
Current
-14%
55%
e) Auburn, 10-yr
Duration (hr)
0.1 1 10 100
Ra
inf
all
int
en
sit
y(
mm
/h
r)
1
10
100
1000
ECP2-GFDL
Current
-33%
f) Auburn, 100-yr
Duration (hr)
0.1 1 10 100
Ra
inf
all
int
en
sit
y(
mm
/h
r)
1
10
100
1000
ECP2-GFDL
Current
-37%
Figure 2.5 IDF curves under current and future climate using CRCM-CCSM, RCM3-GFDL and ECP2-GFDL
models for Auburn, AL
50
Table 2-4 summarizes the discussed results for different return periods using six
climate models for Auburn, AL.
Table 2-4 Comparisons of IDF curves under the current and future climate scenario for Auburn,
AL
Model Return period Average Percentage difference in rainfall intensity
 HRM3-HadCM3
2-yr and 5-yr  duration(t) >3 hrs: 49% increaset <3 hrs: 22 % decrease
10-yr t >4 hrs: 42% increaset <4 hrs: 20 % decrease
50-yr t >5 hrs: 33% increaset <5 hrs: 20 % decrease
100-yr t >6 hrs: 38% increaset <6 hrs: 20 % decrease
CRCM-CGCM3 all return periods 50% decrease for all durations
HRM3-GFDL
2-5 and 10 years  t >4 hrs: 50% increaset <4hrs: 29 % decrease
50- and 100-yr t >4 hrs: 100% increaset <4hrs: 22 % decrease
CRCM-CCSM all return periods 44% decrease for all durations
RCM3-GFDL
2-yr t >12 hrs: 13% increaset <12 hrs: 38 % decrease
5 years t >6 hrs: 23% increaset <6 hrs: 34 % decrease
10 years t >5 hrs: 27% increaset <5 hrs: 34 % decrease
50 years t >4 hrs: 44% increaset <4 hrs: 20 % decrease
100 years t >3 hrs: 55% increaset <3 hrs: 14 % decrease
ECP2-GFDL
2-yr t >12 hrs: 15% increaset <12 hrs: 46 % decrease
5-yr t >17 hrs: 3% increaset <17 hrs:41 % decrease
10, 50 and 100-yr 36% decrease for all durations
51
As the results above clearly demonstrate, the six different NARCCAP-based
projections are not identical. Analyzing all maps for the state of Alabama shows the same
disparity as Auburn. Two of the models (CRCM-CGCM3 and CRCM-CCSM) show a
decrease in future rainfall intensity for all return periods and all rainfall durations for
Alabama. The other four suggest that, depending on the return period, future rainfall
intensities could decrease below and increase above a specific rainfall duration. The
disparity in results could be due to many factors. Dai (2006) performed a study in which
precipitation characteristics in eighteen climate models were analyzed and compared with
historical data. The study pointed out that some of the climate models? deficiencies in
measuring tropical rainfall were correlated with biases in the Sea Surface Temperature
(SST) (Dai, 2006). The SST biases in the CGCM3 model are in accordance with dry
biases in the Caribbean Sea and the Gulf of Mexico, so it may underestimate variables
such as precipitation (Dai, 2006). It was also noted that the HadCM3 model simulates a
realistic precipitation pattern, but that the results of climate models vary for different
regions in the world (Dai, 2006). Therefore, it should be noted that these models are
different in nature, and many variables could be involved in creating discrepancies.
Differing results could be attributed to different types of GCMs and RCMs or to initial
conditions and boundary conditions for each climate projection? but they all agree that
for short durations of rainfall (usually less than 4 hours), rainfall intensity is expected to
decrease or remain close to the current values. Results suggests that the current standard
and guidelines, which use short rainfall durations for designing water management
infrastructures (e.g. a roadside channel, a detention pond for a small drainage area), can
serve their purpose in the future well.
52
As mentioned earlier the results of six different NARCCAP-based projections are
not consistent with respect to larger events. To further explore the results of larger events,
graphs presented in Figure 2.6 were prepared. In this figure rainfall intensity for a 12-hr
rainfall under future and current climate was plotted for different return periods. Figure
2.6a presents the results when HRM3-HadCM3 projections were used to develop future
IDF curves. It shows that if a given rainfall intensity under current climate occurs once
every 20 years (the probability of that given rainfall happening in any year; p=5%), the
same rainfall intensity is expected to happen once every 2 years (p=50%), under future
climate. Figure 2.6 (b-c) also show increase in rainfall intensity under future climate
using HRM3-GFDL and RCM3-GFDL projections. On the other hand, Figure 2.6d that
presents the results of using CRCM-CGCM3 projections, suggests that if a given rainfall
intensity under current climate occurs once every 2 years (p=50%), the same rainfall
intensity is expected to happen once every 10 years (p=10%) under future climate.
Likewise, Figure 2.6e and 2.6f show reduction in future rainfall intensity. How these
results will affect designing different structures will be discussed below.
The first step towards designing different water management structures (e.g.
dams, channels, detention ponds) is to identify the characteristics of design storm in
terms of duration, return period and intensity. Time of concentration of the watershed
draining to the hydraulic structure usually dictates the design storm duration. Storm
return period is assigned based on economic assessments and risk analysis (probability of
damage, loss of life, etc. in case of failure). For example, a 5- to 10-yr return period is
used for designing roadside channels (Brown et al. 2001) where the cost of failure is
negligible whereas a much larger return period is used for designing small dams where
53
a) Auburn, 12-hr
Return Period (yr)
0 20 40 60 80 100
Ra
inf
all
int
en
sit
y(
mm
/h
r)
0
2
4
6
8
10
12
14
16
18
HRM3-HadCM3
Current
b) Auburn, 12-hr
Return Period (yr)
0 20 40 60 80 100
Ra
inf
all
int
en
sit
y(
mm
/h
r)
0
5
10
15
20
25
30
HRM3-GFDL
Current
c) Auburn, 12-hr
Return Period (yr)
0 20 40 60 80 100
Ra
inf
all
int
en
sit
y(
mm
/h
r)
0
5
10
15
20
25
RCM3-GFDL
Current
d) Auburn, 12-hr
Return Period (yr)
0 20 40 60 80 100
Ra
inf
all
int
en
sit
y(
mm
/h
r)
0
2
4
6
8
10
12
14
CRCM-CGCM3
Current
e) Auburn, 12-hr
Return Period (yr)
0 20 40 60 80 100
Ra
inf
all
int
en
sit
y(
mm
/h
r)
0
2
4
6
8
10
12
14
CRCM-CCSM
Current
f) Auburn, 12-hr
Return Period (yr)
0 20 40 60 80 100
Ra
inf
all
int
en
sit
y(
mm
/h
r)
0
2
4
6
8
10
12
14
ECP2-GFDL
Current
Figure 2.6 Rainfall intensity vs. return period under current and future climate for a 12-hr rainfall using a)
HRM3-HadCM3, b) HRM3-GFDL, c) RCM3-GFDL, d) CRCM-CGCM3, e) CRCM-CCSM and f) ECP2-GFDL
model
54
there is a great risk of life in case of failure. Knowing the storm return period, the design
rainfall intensity is then acquired from developed IDF curves of the region. Rainfall
intensity and duration of design storm dictate the cost of the hydraulic structure, and any
uncertainty bound to estimation of these parameters can greatly impose design
uncertainties. For example, figure 2.6 a, b and c suggest design rainfall intensities of 16,
28 and 23 mm/hr, respectively for a 100-yr return period and 12-hr duration while figure
2.6d and 2.6f recommend 9 mm/hr and figure 2.6e proposes 8 mm/hr as a design rainfall
intensity (design rainfall intensity based on current IDF curves for this specific example
is 12 mm/hr). As can be clearly seen, there is a large uncertainty existed on projected
rainfall intensity of these six climate models for long durations. Developing probability-
based IDF curves as a result of incorporating all six climate models could be a better way
to present the results.
2.5. Summary and Conclusions
This study developed IDF curves under future climate scenarios for Alabama,
which were then compared to the IDF curves under the current climate. Six high-
resolution projections (for 2038-2070) derived from dynamical downscaling of GCMs by
RCMs were used in this study. Results of the four climate model projections  HRM3-
HadCM3, HRM3-GFDL, RCM3-GFDL and ECP2-GFDL  suggest that future rainfall
intensity could decreases or increases depending on the return period. Results of the
remaining two model projections  CRCM-CGCM3 and CRCM-CCSM  indicate a
reduction in future rainfall intensity for all return periods and all rainfall durations for
Alabama. A large uncertainty of projected rainfall intensity of these six climate models
55
for long durations makes it difficult to obtain strong conclusions about the expected
changes on future rainfall intensity in Alabama. A variety of factors cause the differing
results; a likely reason is the difference in physical parameterizations, especially of
radiative and precipitation-forming processes, amongst different GCMs and RCMs, as
well as the difference in initial and boundary conditions for each climate projection?but
the result they all have in common is that the precipitation pattern for Alabama veers
toward less intense rainfalls for short rainfall durations. From results discussed above, we
can conclude that the current standards and guidelines for designing municipal
management infrastructures based on short rainfall durations can continue to serve well in
the future. This conclusion is solely based on the results of the six climate model
projections used in this study and not all existing climate models and scenarios. Using
additional climate model projections in the future will help to make a stronger conclusion
in this regard. Also, given the large uncertainty in the output from GCMs and disparity in
the results of these models, creating a probability based IDF curves could be a better way
to presents the IDF curves.
56
Chapter 3
3. Developing Rainfall Intensity-Duration-Frequency (IDF) Curves For Alabama
Under Future Climate Scenarios Using Artificial Neural Network (ANN)
3.1. Abstract
Hydrologic design of water management infrastructures is based on specific design
storms derived from historic rainfall events available in the form of intensity-duration-
frequency (IDF) curves. However, it is expected that the frequency and magnitude of
future extreme rainfalls will change due to increase in greenhouse gas concentrations in
earth?s atmosphere. This study evaluated potential changes in current IDF curves for
Alabama under projected future climate scenarios. Three-hourly precipitation data
simulated by five combinations of global and regional climate models were temporally
downscaled using Artificial Neural Networks (ANNs). A feed-forward, back-propagation
model was developed to estimate maximum 15-, 30-, 45-, 60-, and 120-min
precipitations. The results were also compared to disaggregated rainfalls derived using
the stochastic method. Comparison of these two methods indicated that the ANN model
provided superior performance in estimating maximum rainfall depths, while the
stochastic method tended to under-predict maximum rainfall depths. Developed IDF
curves indicate that future rainfall intensities for the rainfall events less than 2 hours are
expected to decrease by 33% to 74% from current ones when ANN model is used, while
large uncertainty exists in the projected rainfall intensities of longer duration events. This
finding was independent of the temporal downscaling method used.
57
3.2. Introduction
Hydrologic design of storm water management facilities, culverts, flood protection
structures, erosion and sediment control structures, and many other hydraulic structures
are based on specific design storms derived from historic rainfall events as available in
the form of intensity-duration-frequency (IDF) curves (McCuen 1998, Prodanovic et al.
2007). An IDF curve is a tabular or graphical illustration of the probability that a given
rainfall intensity will happen (Wolcott et al. 2009). A design based on an inaccurate
design storm can result in malfunction of infrastructure, loss of life in the case of failure,
or excessive cost if the design storm is overestimated.
An increase in greenhouse gas concentrations, such as carbon dioxide (CO2), in the
earth?s atmosphere during the last century can cause large-scale variations in atmospheric
processes and, as a result, changes in precipitation and temperature characteristics
(Prodanovic et al. 2007). One of the expected impacts of the changes in precipitation
characteristics is a change in the frequency and magnitude of extreme rainfalls, which can
lead to revision of existing standards for designing civil engineering infrastructures. It
can also require the rebuilding and/or upgrading of existing infrastructures.
One way to be prepared for possible changes, and to decrease vulnerability of
hydraulic infrastructures to climate change, is to predict potential effects (as manifested
by IDF curves) and adapt to them (Prodanovic et al. 2007).
58
A recent study by Mirhosseini et al. (2012) (Chapter 2) developed future IDF
curves for Alabama using high-resolution projections (for 2038?2070) derived from
dynamical downscaling of General Circulation Models (GCMs) by Regional Climate
Models (RCMs). A stochastic method was used in order to disaggregate 3-hourly
precipitation to 15-min precipitation. Following the previous study, the main objective of
the present study was to create IDF curves for Alabama using an Artificial Neural
Network (ANN) to estimate the maximum 15-, 30-, 45-, 60-, and 120-min precipitation
depths. An additional objective was to compare the performance of ANN model
downscaling with the performance of the stochastic model used by Mirhosseini et al.
(2012).
The artificial neuron concept was first introduced by McCulloch and Pitts (1943)
and ANNs have existed since then (Dwason and Wilby 2001). ANN models have been
used for both spatial and temporal downscaling of temperature and precipitation. They
also have been used for rainfall?runoff modelling and flood forecasting (Dwason and
Wilby 2001). There are studies investigating performance of ANN models to temporally
disaggregate rainfall. They compared results of ANN disaggregation with other methods
as well. Burian et al. (2000) developed an ANN model and evaluated its performance by
comparing it with two other methods; a linear model and a continuous deterministic
rainfall disaggregation model (Ormsbee 1989). Viability of an ANN model for rainfall
disaggregation was evaluated in a study by Dibikie and Coulibaly (2006). Evaluation of
ANN model was done by comparing the results with linear regression model.
59
In this chapter developing an ANN model to estimate the maximum 15-, 30-, 45-, 60-,
and 120-min rainfall depths from 3-hourly precipitations will be discussed. Results were
used to create future IDF curves and then were compared to the results of previous
chapter, the impact of climate change on the IDF curves was evaluated afterwards.
3.3. Methodology
3.3.1. Data and Model Used
Historical (observed) rainfall data at 15-minute intervals were obtained from the
NOAA National Climatic Data Center Online Climate Data Directory. Locations of 34
rain gauge stations in Alabama are presented in Figure 1. Simulated historical
precipitations for the period 1968?2000 and projected precipitations for the period 2038?
2070 at a temporal resolution of 3 hours and a spatial resolution of 50 km were obtained
from the North American Regional Climate Change Assessment Program (NARCCAP)
(Sebastien et al., 2007, Richard et al., 2007). Maximum and minimum temperatures for
the same periods were obtained at daily intervals.
Five different dynamically downscaled datasets were used for the study and derived
from five NARCCAP projections: HRM3-HadCM3 (Hadley Centre Regional Model and
Hadley Centre Coupled Model, version 3), CRCM-CGCM3 (Canadian Regional Climate
Model and Coupled Global Climate Model), HRM3-GFDL (Hadley Centre Regional
Model and Geophysical Fluid Dynamics Laboratory model), CRCM-CCSM (Canadian
Regional Climate Model and The Community Climate System Model), and RCM3-
GFDL (Regional Climate Model and Geophysical Fluid Dynamics Laboratory model). A
60
complete description of these models can be found in chapter 2, section 2.3.1. It should
be noted that ECP2-GFDL model used in the previous study was not used in the current
study because of the lack of availability of the future temperature variables needed to
develop an ANN model.
3.3.2. Bias Correction and Temporal Downscaling
As mentioned in chapter 2, a quantile-based mapping method proposed by Li et al.
(2010) was used to perform bias correction. For this method, monthly rainfall values
were used to define the cumulative distribution function (CDF) of errors of historical
model runs relative to the observations. This error was used to correct the model CDF for
the future period by calculating a scaling factor from the monthly totals for each month
(January?December). This error was used to correct the model CDF for the future period
by calculating a scaling factor from the monthly totals. The scaling factor is defined as
the bias-corrected rainfall total for a given month divided by the non-bias-corrected total.
Prior to the disaggregation of 3-hourly rainfall events, 3-hourly totals were multiplied by
their corresponding monthly scaling factors (Li et al., 2010). The same method was used
for bias correction of temperature data.
Creating IDF curves requires high temporal resolution rainfall data. NARCCAP
future climate data are provided at 3-hour intervals, which make temporal downscaling a
necessary task. Different types of downscaling techniques have been discussed in many
studies (Von Storch 1999b, Rodriguez-Iturbe et al. 1987, Islam et al. 1990, Socolofsky et
al. 2001). The temporal downscaling method employed in a recent study by Mirhosseini
et al. (2012) was a modified version of the stochastic method introduced by Socolofsky et
al. (2001). Results of that study showed that stochastic method tends to underpredict
61
precipitation. A study by Burain et al. (2000) compared the results of rainfall
disaggregation using a feed-forward ANN model and two other methods; linear model
and a continuous deterministic rainfall disaggregation model introduced by Ormsbee
(1989). Based on their study both of these models underpredicted maximum rainfall
intensities as compared to ANN model. Several other studies also showed the same
results (Dibikie and Coulibaly 2006, Weichert and Burger 1998). Therefore, in the
current study, ANN model was used to find the maximum 15-, 30-, 45-, 60-, and 120-min
rainfall depths from 3-hourly precipitations.
3.3.3. Artificial Neural Network
ANN models are not deterministic models. They learn from examples, train
themselves using the input and target outputs presented to them, and adjust parameters
until they are able to provide meaningful outputs (Burian et al., 2001). Artificial Neural
Networks have been used to solve different hydrological and water resources problems
(Halff et al. 1993, Smith and Eli 1995, Minns and Hall, 1996), and have proven to be
powerful tools for solving difficult problems. ANN models have also been successfully
used for temporal downscaling of precipitation. For example, Burian et al. (2000, 2001)
used an ANN model to disaggregate hourly rainfall into sub-hourly and found it to be a
viable method.
The ANN disaggregation model developed for this study was a feed-forward, back-
propagation model. The model includes three layers: input, hidden, and output layers.
The connections between neurons in feed-forward networks are in the forward direction.
Output is calculated from each neuron (processing unit) of the ANN model, starting from
62
the input layer and moving forward through the hidden layers to the outputs (Burian et
al., 2001). The function that determines the behavior between the input and output layers
is called transfer function. The hyperbolic tangent sigmoid transfer function was used in
this study.
Training and learning functions are used to adjust the weights and biases of the
network. The Levenberg-Marquardt back propagation training function and the gradient
descent with momentum weight/bias learning function were used to develop the ANN
model. Back-propagation explains the direction of propagation for calculating the errors.
Making adjustments to the network weight (learning process) is a separate step which
depends on the results of the training step (Burian et al., 2001). Determination of the
learning rate has a significant impact on the performance of the model. Having too large
values, the ANN model would remember only the training data due to the weight
oscillation. On the other hand, too small values will significantly increase training time
(Burian et al. 2000, 2001, Isik et al. 2012). Learning rate used to develop the ANN model
in this study was determined to be 0.16, as compared with a range of 0.01 to 0.95 in other
studies (Maier and Dandy 2000).
3.3.4. ANN Model Input Data
Finding appropriate input variables is an important step when developing an ANN
model (Maier and Dandy 2000, Dawson and Wilby 2001, Bowden et al. 2005). Many
methods of selecting significant input variables have been developed, such as, using prior
knowledge of the system, linear cross-correlation methods, and using partial mutual
information algorithms (Bowden et al. 2005, May et al. 2008). The Akaike Information
Criterion (AIC) and Normalized Mean Square Error (NMSE) were two criteria or
63
performance parameters used in this study to find the best input datasets. The AIC has
been widely used as a model input selection method (Qi and Zhang 2001, Ren and Zhao
2002, Zhao et al. 2008, Kalin et al. 2010, Isik et al. 2012), and can be calculated using the
equations below (Qi and Zhang 2001):
= log( ) +
where  is the number of model parameters (input variables),  is the number of
observations and is the maximum likelihood estimate of variance of the residual
term or the mean square error (MSE) between the observed and simulated data.
= )
where  is the observed data and  is the output of the ANN model.
More precisely, yobs used to train, validate, and test ANN models are the maximum
15-, 30-, 45-, 60-, and 120-min precipitations derived from observed rainfall data at
stations in Alabama. The model with the minimum AIC value was selected as the best
one.
The NMSE estimates the overall deviations between the observed and simulated
values, and it ranges from 0 to + . A model with a zero NMSE is a perfect model. If
NMSE is 1, the model is as good as the observed mean values, and greater than 1 shows a
poor model (Weigend and Gershenfeld, 1993; Singh et al., 2007).
= ))
where  is the mean of the observed data.
There are 60 (12 months by 5 rainfall durations) ANN models developed in this
study. For each model, nine different combinations of possible input variables were
64
selected for each month and rainfall duration (15-, 30-, 45-, 60-, and 120-min). The above
two criteria were then calculated for each combination in order to identify the optimum
input variables. As an example, Table 3-1 presents the results of selecting input variables
for January. The results in Table 3-1 shows that 3-hourly precipitation (P3), daily
precipitation (Pdaily), monthly precipitation (Pmonthly), and maximum and minimum
temperatures (Tmax and Tmin) were selected as optimum input data or variables for the
ANN model. The results for the remaining months also suggest that the above inputs are
the optimum data for developing the ANN model.
Table 3-1 The Akaike Information Criterion (AIC) and Normalized Mean Square Error (NMSE)
calculated for the nine combinations of input variables in order to determine optimal input
variables of the ANN model.
No. Input Variables
AIC NMSE
15-
min
30-
min
45-
min
60-
min
120-
min
15-
min
30-
min
45-
min
60-
min
120-
min
1 P t-3, P3, P t+3 1.80 1.95 1.95 1.94 1.53  0.48 0.32 0.24 0.19 0.05
2 P t-3, P3, P t+3, Pdaily,P
monthly
1.76 1.91 1.92 1.89 1.49  0.44 0.30 0.22 0.17 0.05
3 P t-3, P3, P t+3, P daily,P
monthly, Tmax, Tmin
1.74 1.88 1.89 1.87 1.50  0.42 0.28 0.20 0.16 0.05
4 P3, Pdaily, Pmonthly 1.76 1.92 1.92 1.89 1.52  0.44 0.30 0.22 0.17 0.05
5 P3, Pdaily, Pmonthly, Pannual 1.76 1.91 1.91 1.90 1.49  0.44 0.30 0.22 0.18 0.05
6 P3, P daily, Pmonthly, Tmax, Tmin 1.71 1.88 1.88 1.87 1.48  0.32 0.22 0.18 0.14 0.04
7 P3, Pdaily, Pmonthly, Pannual ,T
max, Tmin
1.74 1.89 1.91 1.87 1.53  0.42 0.28 0.21 0.17 0.05
8 P3, Pdaily, Pmonthly, Pannual,T
max, Tmin, elev.
1.74 1.89 1.89 1.87 1.48  0.42 0.28 0.20 0.16 0.04
9 P t-3, P3, P t+3, Tmax, Tmin 1.77 1.92 1.93 1.89 1.54  0.45 0.30 0.22 0.17 0.05
P3 is 3-hourly precipitation; P t-3, P t+3 are precipitations 3 hr before and 3 hr after P3;  Pdaily, Pmonthly, and
Pannual are 24-hr, monthly, and annual sums of precipitation, respectively; Tmax, Tmin are maximum and
minimum temperatures; and elev. is the elevation of the station.
65
In this study, target data of the ANN model are the maximum 15-, 30-, 45-, 60-, and
120-min precipitation. The main advantage of this study is that the output of the ANN
model are the maximum precipitation of different durations that are needed later to create
the IDF curves. This method is computationally more efficient as compared to finding the
disaggregated rainfall for each interval and then finding the maximum rainfalls for five
different durations.
3.3.5. ANN Model Training and Performance Measures
The ANN model was trained with input and target datasets using the training function
discussed in section 3.3.3. Model accuracy usually increases with an increase in training,
but there is a point at which more training does not improve model performance, and
sometimes even gets worse (Burian et al., 2000; 2001). Identifying this point can be done
with trial and error. For the ANN model evaluated in this study, 60% of observed data
were used for training, 20% for validation, and the last 20% for testing. Burian et al.
(2001) investigated a number of training iterations to develop an ANN model for hourly
rainfall disaggregation and found that the performance of the model improves when the
iteration numbers increase from 100 to 1000?1500, and that it worsens for higher values.
For this study, the iteration number of 1000 was selected. The determination of the
number of hidden neurons in an ANN model is a matter of experimentation (Burian et al.
2000, 2001, Isik et al. 2012). In our investigation, performance of the ANN model for 1-
30 hidden neurons was evaluated, and eventually 6 hidden neurons were selected for
developing the model.
The performance measures for evaluation of the ANN model were Nash-Sutcliffe
Efficiency coefficient (NSE) and correlation coefficient (R). Again, Normalized Mean
66
Square Error (NMSE) and Akaike Information Criterion (AIC) were used to find the
optimum input data. The results of the ANN model were also compared to the results of
the rainfall disaggregation using stochastic method from the previous chapter.
3.3.6. Intensity-Duration-Frequency (IDF) Curves
Future IDF curves were created for Alabama using Generalized Extreme Value
(GEV) distribution. As mentioned in Chapter 2, this method was selected as the best
probability distribution for Alabama in a study by Durrans and Brown (2001). Method of
moments (MOM) was used to estimate the GEV parameters (Hosking et al., 1985;
Bhunya et al., 2007) and performance of the fit was evaluated by Kolmogorov-Smirnov
(K-S) test (Massey 1951). Based on the K-S test results, GEV distribution fitted to the
sample CDFs with minimal error. Statistical measures used for this evaluation are
presented in Table 2-3 (Chapter 2). IDF curves where created by obtaining the annual
maximum precipitation depth for different rainfall durations (e.g. 15-, 30- and 45- min, 1-
and 2-hr.). GEV distribution was then used to find the precipitation depths for different
return periods (e.g. 2, 5, 10 years) and it was repeated for different durations. Finally
depth versus duration was plotted for different frequencies to develop the IDF curves.
3.4.Results and Discussion
3.4.1. Performance
Temporal disaggregation was performed for each month and rainfall duration
separately. The statistical measures used in the error quantification are presented in Table
3-2. Both R and NSE for all months are greater than or equal to 0.6, and higher R and
67
NSE values were obtained for longer durations. These results show that the developed
ANN model performed very well in disaggregating the 3-hour interval precipitations and
finding the maximum of 15-, 30-, 45-, 60-, and 120-min rainfall depths.
Table 3-2 Performance of the ANN model for training, validation, and testing datasets for every
month and every rainfall duration.
Performance Month Training  Validation Test AllR NSE  R NSE R NSE  R NSE
15-min
Jan 0.73 0.60 0.80 0.63 0.80 0.63 0.60 0.80
Feb 0.80 0.61 0.83 0.70 0.81 0.70 0.80 0.65
Mar 0.75 0.60 0.82 0.70 0.82 0.70 0.80 0.65
Apr 0.80 0.62 0.80 0.63 0.82 0.70 0.80 0.64
May 0.83 0.70 0.84 0.70 0.86 0.73 0.84 0.70
Jun 0.90 0.74 0.87 0.75 0.90 0.80 0.90 0.75
Jul 0.90 0.74 0.86 0.74 0.90 0.80 0.90 0.75
Aug 0.86 0.73 0.90 0.80 0.88 0.80 0.86 0.75
Sep 0.80 0.65 0.94 0.84 0.92 0.82 0.90 0.77
Oct 0.81 0.65 0.86 0.74 0.88 0.77 0.84 0.71
Nov 0.80 0.61 0.81 0.66 0.84 0.70 0.81 0.65
Dec 0.71 0.60 0.80 0.60 0.84 0.70 0.80 0.61
30-min
Jan 0.82 0.70 0.86 0.75 0.90 0.80 0.85 0.72
Feb 0.85 0.72 0.90 0.80 0.87 0.75 0.86 0.75
Mar 0.84 0.70 0.88 0.80 0.88 0.77 0.90 0.74
Apr 0.85 0.73 0.86 0.73 0.90 0.80 0.86 0.75
May 0.90 0.80 0.90 0.78 0.91 0.82 0.90 0.80
Jun 0.91 0.84 0.92 0.85 0.93 0.87 0.92 0.85
Jul 0.92 0.84 0.94 0.86 0.93 0.86 0.92 0.85
Aug 0.92 0.84 0.93 0.86 0.94 0.88 0.92 0.85
68
Sep 0.88 0.75 0.97 0.92 0.97 0.91 0.94 0.90
Oct 0.86 0.74 0.90 0.80 0.91 0.81 0.90 0.80
Nov 0.86 0.74 0.87 0.76 0.90 0.80 0.87 0.80
Dec 0.81 0.70 0.85 0.72 0.90 0.80 0.85 0.73
45-min
Jan 0.90 0.80 0.90 0.81 0.92 0.83 0.90 0.80
Feb 0.88 0.78 0.91 0.82 0.91 0.81 0.90 0.80
Mar 0.90 0.80 0.92 0.84 0.92 0.85 0.91 0.82
Apr 0.90 0.80 0.90 0.81 0.92 0.84 0.90 0.82
May 0.93 0.86 0.93 0.87 0.94 0.90 0.93 0.90
Jun 0.95 0.90 0.95 0.91 0.96 0.92 0.95 0.91
Jul 0.95 0.90 0.96 0.92 0.96 0.92 0.95 0.91
Aug 0.95 0.84 0.95 0.86 0.96 0.88 0.95 0.86
Sep 0.91 0.84 0.98 0.94 0.97 0.93 0.96 0.91
Oct 0.90 0.81 0.93 0.86 0.94 0.85 0.92 0.84
Nov 0.90 0.81 0.91 0.82 0.93 0.84 0.91 0.82
Dec 0.86 0.74 0.90 0.80 0.93 0.84 0.90 0.80
60-min
Jan 0.90 0.81 0.92 0.85 0.93 0.90 0.92 0.84
Feb 0.91 0.83 0.93 0.86 0.93 0.85 0.92 0.84
Mar 0.92 0.84 0.94 0.89 0.94 0.89 0.93 0.87
Apr 0.92 0.86 0.93 0.86 0.94 0.88 0.93 0.87
May 0.95 0.89 0.95 0.90 0.96 0.92 0.95 0.90
Jun 0.96 0.93 0.97 0.94 0.97 0.94 0.97 0.94
Jul 0.97 0.93 0.97 0.94 0.97 0.94 0.97 0.94
Aug 0.96 0.93 0.97 0.94 0.98 0.95 0.97 0.94
Sep 0.94 0.88 0.99 0.97 0.98 0.96 0.98 0.94
Oct 0.93 0.86 0.95 0.90 0.96 0.90 0.94 0.90
Nov 0.93 0.86 0.93 0.87 0.95 0.90 0.94 0.87
69
Dec 0.90 0.80 0.92 0.83 0.94 0.86 0.92 0.83
120-min
Jan 0.97 0.95 0.98 0.96 0.98 0.96 0.98 0.96
Feb 0.98 0.95 0.98 0.96 0.98 0.96 0.98 0.96
Mar 0.98 0.96 0.99 0.97 0.99 0.97 0.98 0.97
Apr 0.99 0.97 0.98 0.97 0.99 0.98 0.99 0.97
May 0.99 0.98 0.99 0.98 0.99 0.98 0.99 0.98
Jun 0.99 0.98 0.99 0.99 0.99 0.98 0.99 0.98
Jul 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99
Aug 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99
Sep 0.99 0.95 0.99 0.97 0.99 0.97 0.99 0.97
Oct 0.98 0.97 0.99 0.98 0.99 0.97 0.99 0.97
Nov 0.98 0.96 0.98 0.96 0.99 0.97 0.98 0.96
Dec 0.97 0.95 0.98 0.96 0.99 0.97 0.98 0.96
R: Correlation coefficient
ENS: Nash?Sutcliffe model efficiency coefficient
ANN model results were also compared with the results of the stochastic method
used by Mirhosseini et al. (2012). Figures 3.1(a-e) show scatter plots of observed and
predicted maximum 15-, 30-, 45-, 60-, and 120-min rainfalls in a typical summer month
(July) from the ANN model and the stochastic method. Scatter plots for the remaining
months are presented in Appendix C. Comparison of the results from these two methods
indicates that the ANN model performed better in estimating maximum rainfall. The
perfect prediction line (1:1 line) shown on each plot divides the under-predictions from
over-predictions. These plots suggest that ANN model predictions closely distribute
along the perfect prediction line, and that the stochastic method tends to under-predict
maximum rainfall intensities.
70
a) ANN model
Predicted max 15-min rainfall depth (in)
0.0 0.5 1.0 1.5 2.0 2.5
Ob
se
rv
ed
m
ax
15
-m
in
ra
inf
all
de
pt
h
(in
)
0.0
0.5
1.0
1.5
2.0
2.5
Overprediction
Underprediction
Perfect prediction
a) Stochastic model
Predicted max 15-min rainfall depth (in)
0.0 0.5 1.0 1.5 2.0 2.5
Ob
se
rv
ed
ma
x1
5-m
in
ra
inf
all
de
pt
h(
in)
0.0
0.5
1.0
1.5
2.0
2.5
Overprediction
Underprediction
Perfect prediction
b) ANN model
Predicted max 30-min rainfall depth (in)
0 1 2 3 4
Ob
se
rv
ed
ma
x3
0-m
in
ra
inf
all
de
pt
h(
in)
0
1
2
3
4
Overprediction
Underprediction
Perfect prediction
b) Stochastic model
Predicted max 30-min rainfall depth (in)
0 1 2 3 4
Ob
se
rv
ed
ma
x3
0-m
in
ra
inf
all
de
pt
h(
in)
0
1
2
3
4
Overprediction
Underprediction
Perfect prediction
c) ANN model
Predicted max 45-min rainfall depth (in)
0 1 2 3 4 5
Ob
se
rv
ed
m
ax
45
-m
in
ra
inf
all
de
pt
h(
in
)
0
1
2
3
4
5
Overprediction
Underprediction
Perfect prediction
c) Stochastic model
Predicted max 45-min rainfall depth (in)
0 1 2 3 4 5
Ob
se
rv
ed
ma
x4
5-m
in
ra
in
fal
l
de
pt
h(
in)
0
1
2
3
4
5
Overprediction
Underprediction
Perfect prediction
71
3.4.2. IDF Curves
The future IDF curves for Alabama were developed for five GCM models and for six
return periods (2-, 5-, 10-, 25-, 50-, and 100-yr).  The results of future IDF curves were
also presented as a series of maps (total 150 maps = 5 durations ? 6 return periods ? 5
GCM models) for the five NARCCAP regional climate projections. An example of the
generated maps is illustrated in figure 3.2. Figure 3.2 shows the maps created for a 100-yr
return period and durations of 15-, 30-, 45-, and 60-min.
d) ANN model
Predicted max 60-min rainfall depth (in)
0 1 2 3 4 5
Ob
se
rv
ed
ma
x6
0-m
in
ra
inf
all
de
pt
h
(in
)
0
1
2
3
4
5
Overprediction
Underprediction
Perfect prediction
d) Stochastic model
Predicted max 60-min rainfall depth (in)
0 1 2 3 4 5
Ob
se
rv
ed
ma
x6
0-m
in
ra
in
fal
l
de
pt
h
(in
)
0
1
2
3
4
5
Overprediction
Underprediction
Perfect prediction
e) ANN model
Predicted max 120-min rainfall depth (in)
0 1 2 3 4 5
Ob
se
rv
ed
ma
x1
20
-m
in
ra
inf
all
de
pt
h
(in
)
0
1
2
3
4
5
Overprediction
Underprediction
Perfect prediction
e) Stochastic model
Predicted max 120-min rainfall depth (in)
0 1 2 3 4 5
Ob
se
rv
ed
ma
x1
20
-m
in
ra
in
fal
l
de
pt
h(
in)
0
1
2
3
4
5
Overprediction
Underprediction
Perfect prediction
Figure 3.1 Scatter plots of observed and modeled maximum a) 15-min, b) 30-min, c) 45-min, d) 60-min, and e)
120-min rainfall depths using the ANN model (left panels) and the stochastic method (right panels) for July.
72
Figure 3.2 Rainfall; 100-year rainfall of 15-, 30-, 45- and 60-min durations (mm) under future climate
using HRM3-HadCM3 projected data
73
The remaining maps for other durations and other models are shown in Appendix D.
Comparing these maps with NOAA Technical Paper 40 (TP-40) (Hershfield 1961) and
NWS HYDRO-35 (Frederick et al. 1977) shows that changes in future IDF curves are
expected with the future climate. The largest projected rainfall for all the durations shown
in figure 3.2 is expected to happen in the southwest Alabama. For example, for a 100-yr
return period with 30-min duration, between 51 and 72 mm of rainfall is expected to fall
in the southwestern part of the state. Tp-40 reports amounts from 76 and 89 mm
(Hershfield 1961).This amount is expected to be between 66 and 86 mm for 1-hr rainfall
duration. Based on TP-40 (Hershfield 1961), this amount is reported between 102 and
114 mm? about 35% and 25% more than what is predicted for the future. The smallest
projected rainfall amounts are expected to occur in the north and northwest Alabama. For
a 100-yr return period and a 15-min rainfall duration, between 20 and 23 mm of rainfall
is predicted. HYDRO-35 (Frederick et al. 1977) reported this amount to be in a range of
44 and 46 mm which is about 52% on average more than the predicted rainfall for future.
Since it is not possible to discuss the results of all 150 maps in detail, City of Auburn in
Alabama was selected as an example to discuss the results. Figure 3.3 presents the future
IDF curves at Auburn using five NARCCAP regional climate projections for the two
different return periods of 10 and 100 years and rainfall durations of 15-, 30-, 45-, 60-
and 120-min (Results for durations longer than 2-hr are presented in Mirhosseini et al.
(2012) so they will not be discussed here). Future results include the IDFs created with
disaggregated rainfalls from both the ANN models and the stochastic method.
Figures 3.3a and b depict the IDF curves under the future and current climates using
HRM3-HadCM3 projections for developing the future IDFs. Figure 3.3a shows that if the
74
ANN model is used for rainfall disaggregation, projected rainfall intensity for a 10-yr
return period tends to be reduced by 34%. However, the stochastic method suggested a
decrease of 20%. Figure 3.3b presents the changes in rainfall intensity for a 100-yr return
period. It shows that the rainfall intensity tends to decrease by 20% when using stochastic
method and 41% when ANN model was used for rainfall disaggregation.
The CRCM-CGCM3 projections show that the rainfall intensity for a 10-yr return
period was reduced by 71% when the ANN model was used for rainfall disaggregation,
compared to a 68% decrease using the stochastic method (Figure 3.3c). Figure 3.3d
shows the results for a 100-yr return period. Figures 3.3e and f display the IDF curves
developed using the HRM3-GFDL model. Future rainfall intensity is expected to decline
by 40% when the ANN model is used for disaggregation, while the stochastic method
suggests a 26% decline (Figure 3.3e). For a 100-yr return period, future rainfall intensity
tends to decrease by 22% and 41% when the stochastic method and ANN model are used
for rainfall disaggregation, respectively (Figure 3.3f).
Figures 3.3g-j show IDF curves developed using CRCM-CCSM and RCM3-GFDL
projections. Graphs show the future IDF curves developed using two different rainfall
disaggregation methods (the ANN model and the stochastic method) and compare them
to the current IDF curves. Sixty percent (stochastic method) and 63% (ANN model)
declines in rainfall intensities are expected for a 10-yr return period (Figure 3.3g). For the
100-yr return period, 59% (stochastic method) and 66% (ANN model) decreases in future
rainfall intensities are expected.
75
a) Auburn, 10-yr, HRM3-HadCM3
Duration (hr)
0.1 1
Ra
inf
all
int
en
sit
y(
mm
/h
r)
10
100
Stochastic
Current
ANN model
-20%
-34%
b) Auburn, 100-yr, HRM3-HadCM3
Duration (hr)
0.1 1
Ra
inf
all
int
en
sit
y(
mm
/h
r)
10
100
Stochastic
Current
ANN model-20%
-41%
c) Auburn, 10-yr, CRCM-CGCM3
Duration (hr)
0.1 1
Ra
inf
all
int
en
sit
y(
mm
/h
r)
10
100
1000
Stochastic
Current
ANN model
-68%
-71%
d) Auburn, 100-yr, CRCM-CGCM3
Duration (hr)
0.1 1
Ra
inf
all
int
en
sit
y(
mm
/h
r)
10
100
1000
Stochastic
Current
ANN model
-65%
-74%
e) Auburn, 10-yr, HRM3-GFDL
Duration (hr)
0.1 1
Ra
inf
all
int
en
sit
y(
mm
/h
r)
10
100
Stochastic
Current
ANN model
-26%
-40%
f) Auburn, 100-yr, HRM3-GFDL
Duration (hr)
0.1 1
Ra
inf
all
int
en
sit
y(
mm
/h
r)
10
100
Stochastic
Current
ANN model
-22%
-41%
76
Figure 3.3i displays the results when RCM3-GFDL data were used for developing the
IDF curves. Utilizing the ANN model for disaggregation indicates that rainfall intensities
are expected to decline by 44% for a 10-yr return period, while the stochastic method
suggests a 34% decrease. A 41% decline in rainfall intensities was also observed for a
100-yr return period while utilizing the ANN model for temporal downscaling. This
g) Auburn, 10-yr, CRCM-CCSM
Duration (hr)
0.1 1
Ra
inf
all
int
en
sit
y(
mm
/h
r)
10
100
1000
Stochastic
Current
ANN model
-60%
-63%
h) Auburn, 100-yr, CRCM-CCSM
Duration (hr)
0.1 1
Ra
inf
all
int
en
sit
y(
mm
/h
r)
10
100
1000
Stochastic
Current
ANN model
-59%
-66%
i) Auburn, 10-yr, RCM3-GFDL
Duration (hr)
0.1 1
Ra
inf
all
int
en
sit
y(
mm
/h
r)
10
100
Stochastic
Current
ANN model
-34%
-44%
j) Auburn, 100-yr, RCM3-GFDL
Duration (hr)
0.1 1
Ra
inf
all
int
en
sit
y(
mm
/h
r)
10
100
Stochastic
Current
ANN model
-14%
-41%
Figure 3.3 IDF curves for 10-yr and 100-yr return periods under current and future climate (using HRM3-
HadCM3, CRCM- CGCM3, and HRM3-GFDL CRCM-CCSM and RCM3-GFDL models) for Auburn, AL.
77
value showed an approximate 14% decrease when the stochastic method was used
(Figure 3.3j).
Table 3-3 summarizes the results for different return periods using five climate
models for Auburn, AL. The ANN model and stochastic method agree that future rainfall
intensities for durations less than 2 hours are expected to decrease. However, they don?t
provide identical results. When HRM3-HadCM3 projections were used to develop the
IDF curves, the ANN model suggested a decrease by 37% on average for Auburn, while
the stochastic method indicated a 21% decline on average. The ANN model and
stochastic method indicate almost the same results when CRCM-CGCM3 and CRCM-
CCSM models were used to create IDF curves under the future climate. Utilizing HRM3-
GFDL data shows a 41% decrease on average when the ANN model was used as a
disaggregation method, while the stochastic method indicates a 26% decrease on average.
Using RCM3-GFDL data for developing future IDF curves, ANN model suggests that
future rainfall intensity is expected to decrease by 44% on average while the stochastic
method shows a 31% decline. Several studies have investigated performance of ANN
models for rainfall disaggregation and have compared their result with other methods.
Burian et al. (2000) compared the results of rainfall disaggregation using an ANN model
with two other methods; linear model and a continuous deterministic rainfall
disaggregation model (Ormsbee 1989). Their study indicated that the latter two models
underpredicted maximum rainfall intensities and were outperformed by the ANN model
ANN model.
78
Table 3-3 Comparisons of IDF curves under the current and future climate scenarios for Auburn,
AL using two temporal downscaling methods, the ANN model and the stochastic method.
Model Return period Average Percentage difference in rainfall intensityANN model Stochastic method
 HRM3-HadCM3
2-yr 33% decrease 24% decrease
5-yr 36% decrease 21% decrease
10-yr 34% decrease 20% decrease
50-yr 40% decrease 20% decrease
100-yr 41% decrease 20% decrease
Average 37% decrease 21% decrease
CRCM-CGCM3
2-yr 66% decrease 68% decrease
5-yr 70% decrease 68% decrease
10-yr 71% decrease 68% decrease
50-yr 73% decrease 66% decrease
100-yr 74% decrease 65% decrease
Average 71% decrease 68% decrease
HRM3-GFDL
2-yr 38% decrease 32% decrease
5-yr 40% decrease 28% decrease
10-yr 41% decrease 26% decrease
50-yr 41% decrease 23% decrease
100-yr 41% decrease 22% decrease
Average 41% decrease 26% decrease
CRCM-CCSM
2-yr 58% decrease 60% decrease
5-yr 62% decrease 60% decrease
10-yr 63% decrease 60% decrease
50-yr 66% decrease 60% decrease
100-yr 66% decrease 59% decrease
Average 63% decrease 60% decrease
RCM3-GFDL
2-yr 45% decrease 48% decrease
5 years 47% decrease 40% decrease
10 years 44% decrease 34% decrease
50 years 42% decrease 20% decrease
100 years 42% decrease 14% decrease
Average 44% decrease 31% decrease
79
Dibikie and Coulibaly (2006) evaluated the viability of an ANN model to
disaggregate precipitation and compared it with a liner regression model and concluded
that an ANN outperforms the statistical models. Other studies also reported better
performance in predicting heavy rainfall events when using an ANN model as compared
to linear regression downscaling methods (Weichert & Burger 1998). One reason for
better performance of ANNs could be that a neural network can approximate complex,
highly non-linear relationships without a priori assumptions (Dibikie and Coulibaly
2006). Also, ANNs allow the data to define the functional form while regression models
assume a functional form. Therefore, it is believed that neural networks are more
powerful tools than other downscaling methods (Von Storch et al. 2000, Dibikie &
Coulibaly 2006).
Results show that no matter which temporal downscaling method was used, the
five different climate model projections were not identical. Analyzing all the developed
IDF curves for the state of Alabama (data not presented) also shows a similar disparity as
observed for Auburn. The CRCM-CGCM3 and CRCM-CCSM models demonstrate a
decrease in future rainfall intensity for Alabama, while the other three models suggest
that a decrease below and increase above a specific rainfall duration can occur, depending
on the return period. As was mentioned by Mirhosseini et al. (2012), the difference in the
climate model results could occur due to different initial and boundary conditions for
each of the climate projections, or the differences in physical parameterizations (such as
precipitation-forming processes) amongst different GCMs and RCMs. Despite the
disparity in future projections from the investigated models, they all suggest that future
rainfall intensities for short durations are expected to decrease. The results of larger
80
events and their effects on designing different water management structures were
explored in further detail in Mirhosseini et al. (2012).
3.5. Summary and Conclusions
This study investigated the viability of using ANNs to estimate maximum 15, 30,
45, 60, and 120-min precipitations in order to develop IDF curves under the future
climate scenarios. The results were also compared to disaggregated rainfall using the
stochastic method. Comparison of these two methods indicates that the ANN model
provides superior performance in estimating the maximum 15-, 30-, 45-, 60-, and 120-
min precipitations.
Scatter plots created to evaluate the performance of the ANN model suggest that
the predictions of the ANN model more closely approximated the perfect prediction line,
and that the stochastic method under-predicts the maximum rainfall amounts. Using the
ANN model for rainfall disaggregation, IDF curves for Alabama under the future climate
scenario were developed from dynamically downscaled NARCCAP projections. Results
were further compared to the current IDF curves. Comparison of the developed ANN
model with the stochastic method shows that both methods agree that future rainfall
intensities (for duration less than 2 hours) are expected to decrease. Both methods
estimate almost similar decreases in rainfall intensities when CRCM-CGCM3 and
CRCM-CCSM models were used to create IDF curves under the future climate.
However, the ANN model suggests greater declines in rainfall intensities compared to the
stochastic method when HRM3-HadCM3, HRM3-GFDL, and RCM3-GFDL projections
were used.
81
Analyzing the results for longer durations presented in details in Mirhosseini et al.
(2012), revealed that there is a large uncertainty in the projected rainfall intensity of the
investigated climate models for long durations (> 4 hours). This uncertainty prevents us
from giving strong conclusions about the expected changes in future rainfall intensity for
long duration rainfall events in Alabama. However, projections from all of the climate
models (disaggregated with both temporal downscaling methods) show a decrease for
shorter rainfall durations (i.e., less than 2 hours). Therefore, it can be concluded that the
existing IDF curves for designing water management infrastructures based on short
rainfall durations will continue to be useful in the future. This conclusion is based solely
on the results of the selected climate model projections used in this and the previous
study by Mirhosseini et al. (2012), and not on all existing climate models and scenarios.
Perhaps using additional model projections will help researchers to better understand the
possible changes in future rainfall intensities. Also, given the large uncertainty in the
output from the GCMs, performing an uncertainty analysis and creating probability based
IDF curves, which can better present the results, especially for longer durations, is being
undertaken in order to complete the current and previous studies.
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Chapter 4
4.      Developing Probability-based IDF Curves Using Kernel Density Estimator
4.1. Abstract
Many hydrologic structures are designed based on Intensity-Duration-Frequency
(IDF) curves. A design based on an inaccurate design storm can cause problems, such as,
malfunction of the infrastructure, excessive cost, or loss of life. In Chapter 2, IDF curves
under future climate scenarios were created for Alabama using six different NARCCAP-
based projections. The results demonstrated that these models do not project identical
results, and there is uncertainty regarding future rainfall intensities projected by these six
climate models. Understanding the uncertainties associated with climate model outputs
can help decision-makers to explain the impacts of climate change with more confidence.
Therefore, the main objective of this chapter is to develop probability-based IDF curves
incorporating climate projections from six different climate models using a kernel density
estimator. The resulting IDF curves help understand uncertainties associated with
projected rainfall intensities. IDF curves were previously created using two different
temporal disaggregation methods: a stochastic method and an ANN model. A kernel
density estimator was applied to the resulting estimated rainfall intensities from both
methods and probability-based IDFs were developed. In addition to the probability-based
IDFs, typical IDF curves that incorporated all models were also developed. Using the
median of the distribution as the ?most likely? outcome the results are
83
presented in the form of IDF graphs. A comparison of the results with the current IDF
curves for Auburn indicated that, when the stochastic method was used for rainfall
disaggregation, future rainfall intensity could decreases or increases depending on the
return period. The resultant IDF curves for Auburn indicate that future rainfall intensities
are expected to decrease by 29% to 39% for durations less than six to eight hours and to
increase by 14% to 19% for longer durations. Results of the ANN model for durations
less than two hours indicates that the precipitation pattern for Alabama veers toward less
intense rainfalls for the investigated durations and for all the return periods. This decrease
is expected to be between 48% and 52% for Auburn.
4.2.Introduction
As mentioned in previous chapters, many hydrologic structures are designed based on
IDF curves (McCuen 1998, Prodanovic et al. 2007), and a design based on an inaccurate
design storm can result in malfunction of infrastructure, loss of life in the case of failure,
or excessive cost if the design storm is overestimated. In the previous chapters, the
development of future IDF curves was discussed, and the results were compared with
current IDF curves. The results demonstrated that the six different NARCCAP-based
projections are not identical and that there is uncertainty regarding the projected rainfall
intensities of these six climate models. Decision-makers can benefit from understanding
the uncertainties associated with climate model outputs to explain the impacts of climate
change with more confidence (Colglazier 1991, Solaiman 2011). Uncertainties in the
outputs of climate models arise from imperfect knowledge of physical processes,
inadequate information, or analytical resources. For example, complex atmospheric and
84
oceanographic processes are being simplified, and imprecise assumptions about different
climatic processes have been made.
Uncertainties also exist in estimating the future GHG concentrations, and, as a result,
changes in the carbon cycle can be another source of uncertainty of rainfall projections.
Despite the fact that the fundamentals of the GHG physics effect are well-founded and an
increase in CO2 concentrations has been recorded since the industrial revolution, there is
still discussion and debate about this issue (Solaiman 2011).
In addition, the data are available at a coarse spatial and temporal resolution, which
can cause disparities between GCMs when at a regional scale. The earth system?s inborn
complexity and the inability to predict exact and accurate human behavior are other
sources of climate model uncertainty (Wilby and Harris 2006, Stainforth et al. 2007,
Buytaert et al. 2009, Solaiman 2011).
The spatial resolution of GCMs usually ranges from 200 to 600 km, but there is an
increased need for high-resolution data for climate change assessment and impact studies,
and it is accepted that the accuracy of GCMs decrease at finer scales. Variables such as
temperature and precipitation from GCMs can be misrepresented because of the coarse
resolution. Details of land surfaces, water surfaces and topography are not represented
well in some climate models, so the models are unable to predict the high variability in
clouds and precipitation and to provide accurate projections (Widmann et al., 2003,
Brissette et al. 2007).
Different initial boundary conditions are another source of uncertainty (Stainforth et
al. 2007). Another source of uncertainty could be forcing uncertainty. For example, using
model simulations based on different scenarios of GHG concentrations in the future
85
completely depends on the activities undertaken to control these emissions (Cubasch et
al. 2001).
Quantifying uncertainties from climate models has been the subject of many studies
related to impact assessment (Solaiman 2011). Selecting the most suitable models is one
of the key factors in performing reliable climate change assessment research (Tebaldi and
Smith 2009). Many studies have used just one climate model to evaluate the impact of
climate change in the future. The problem with using one GCM is that, with the presence
of significant uncertainties, one model is only one of many possible realizations and may
not be representative of the future. Therefore, it is very important to use as many models
as possible to present the results in a probabilistic way. Unfortunately, few studies have
used a collection of climate models. New and Hulme (2000) used Bayesian Monte Carlo
simulations to introduce a probabilistic framework to quantify the climate model?s
uncertainty. Another study used a CMIP2 multi-model ensemble with equally probable
realizations to estimate the probabilities of climate change (Raisanen and Palmer 2001).
Recently, Solaiman (2011) used a kernel density estimator to quantify the uncertainty
associated with 11 GCMs for the city of London, Canada. Another study by Giorgi and
Mearns (2003) introduced the Reliability Ensemble Averaging (REA) method to estimate
the probability of regional precipitation and temperature change. Nine GCMs with two
emission scenarios the A2 and B2 emission scenarios were used in this study.
Bayesian statistics was applied to compute a future climate distribution by using observed
data and corresponding simulations from GCMs (Tebaldi et al. 2004, 2005). It was
assumed that GCM ensembles illustrate an example of a full potential climate model
space consistent with the observed climate using Probability Distribution Functions
86
(PDFs) at a regional scale. Their study was extended by Smith et al. (2009). They
introduced a univariate approach to take into account one region at a time.
A probabilistic framework was developed by Wilby and Harris (2006) to combine the
results of four GCMs and two emission scenarios. A Monte Carlo approach was used to
find the elements of uncertainty. Cumulative Distribution Functions seemed to be the
most sensitive in selecting the climate change scenarios and downscaling different
models. Another study by Ghosh and Mujumdar (2007) developed a method to evaluate
the uncertainty of climate models to investigate future drought scenarios in a non-
parametric manner. More promising results were obtained compared to other parametric
methods.
Since all of the investigated climate models in this study provided different results,
developing probability-based IDF curves seemed to be an appropriate solution to quantify
uncertainties in projected rainfall intensities. Therefore, this chapter presents a
methodology to develop probability-based IDF curves using non-parametric kernel
density estimation.
4.3.Methodology
4.3.1. Data
As mentioned in the previous two chapters, simulated precipitations for 2038 to 2070
at a temporal resolution of three hours and a spatial resolution of 50 km were obtained
from the North American Regional Climate Change Assessment Program (NARCCAP)
(Sebastien et al., 2007, Richard et al., 2007). Simulated temperature projections at daily
intervals were also obtained from NARCCAP. Using these datasets, future rainfall
87
intensities (for each duration and frequency) were estimated for each NARCCAP
regional climate projections. The estimated rainfall intensities were then used to develop
the probability-based IDFs.
Probability-based IDF curves were developed from the results of rainfall intensities
estimated by the stochastic method (for 15-, 30-, 45-min, 1-, 2-, 3-, 6-,12-, 24- and 48-hr
as well as the ANN model (for 15-, 30-, 45-min, 1-hr and 2-hr).
4.3.2. Probability Density Function (PDF)
To deal with the uncertainty associated with climate models, a practical method that
is robust and flexible enough to handle data variety should be used. It should also be
statistically consistent in application across regional, local, and global scales. It needs to
provide consistent results to be able to get as much information as possible from the data
(Solaiman 2011). Most parametric approaches are unable to meet all mentioned
requirements (Solaiman 2011, Zucchini 2003).
The probability distribution of a continuous random variable (x) is described in terms
of a Probability Distribution Function (PDF). A PDF is usually used to explain the nature
of data (Zucchini 2003). Probabilities associated with (x) can be estimated using the
following relationship:
( ) = ( )                      (4.1)
The goal is usually to estimate ( ) from a sample of data ,? . It can be
estimated using a parametric approach that assumes f(x) is a member of some parametric
family of distributions and then estimates the assumed distribution?s parameters from the
88
data. This approach is easy to apply but is not useful if the distribution assumption is
incorrect (Miller et al. 1965, Zucchini 2003). Lack of flexibility is one of the major
drawbacks of parametric approaches (Lall et al. 1996). Therefore, using non-parametric
approaches prevents us from making assumptions about the f(x) and estimates the PDF
directly from the data (Zucchini 2003). A histogram is widely known as a non-parametric
estimator of the PDF. It is very simple to use, but its disadvantage is discontinuity.
Moreover, there are other non-parametric methods that are better than histograms
(Adamowski 1985, Solaiman 2011).
A non-parametric approach to estimate the PDF can be used for uncertainty
quantification of climate models. Methods such as K-nearest neighbor methods, kernel
methods, Bayesian-spline methods, maximum likelihood methods, and orthogonal series
methods are examples of non-parametric approaches that have been used (Adamowski
1985, Solaiman 2011).
4.3.3. Kernel Density Estimation
Among the methods mentioned above is a method called the kernel density estimation
method. This method has been used widely in hydrology, flood frequency analysis, and
rainfall resampling as a more reliable and flexible approach than parametric approaches
(Sharma et al. 1997, Lall 1995, Adamowski 1985).
Weight functions or kernels convolution centered on the empirical frequency
distribution of the data, form a kernel density estimator. The kernel density function can
be estimated using the following equation:
89
( ) = 1                          (4.2)
where ) is the kernel function. Thus, a PDF can be a kernel function.
The kernel density estimator is sometimes called Parzen-Rosenbalt after Emanuel
Parzen and Murray Rosenbalt, who are assumed to have created the kernel density
estimator in its current form (Rosenbalt 1956, Parzen 1962).
The kernel density estimator of a sample ,?  from a distribution with an
unknown density function  can be determined from:
( ) = 1 ( ) = 1 ( )                    (4.3)
where , also called ), is the kernel function or weight function, and h is a
smoothing parameter or bandwidth.
Selecting the appropriate bandwidth and kernel function are the important factors for
applying kernel density estimation successfully (Wang et al. 2007; Sharma et al. 1997).
Figure 4.1 displays a kernel density estimate and a histogram created from the same data.
Some of the common kernel functions are triangular, Epanechnikov, rectangular,
biweight, and normal. Table 4-1 shows the kernel function for these examples (Bergman
2009, Zucchini 2003). The normal kernel is usually used as the kernel function, and it
was applied to this study as well.
90
Table 4-1 Examples of kernel functions
Kernel function K(t)
Triangular 1 | | | | < 10
Epanechnikov
3
4 1
1
5 | | < 5
0
Rectangular
1
2 | | < 1
0
Biweight
15
16 (1 ) | | < 1
0
Normal 12 ( )
Figure 4.1 Comparison of kernel density estimate (right) and histogram (left). The individual kernels are the red
dashed curves and the kernel density estimate the blue curves.
 (From http://en.wikipedia.org/wiki/File:Comparison_of_1D_histogram_and_KDE.png retrieved on 03/12/2013
91
Kernel bandwidth has a strong effect on the kernel estimate. Many studies have
investigated the selection of a smoothing parameter or bandwidth and found that it is
even more important than the selection of the kernel function (Wang et al. 2007, Scott
2009, Sheather et al. 1991, Marron et al. 1987). A change in bandwidth can greatly
change the shape of the kernel estimate (Sheather et al. 1991, Marron et al. 1987).
Various methods have been used to quantify the estimator. One method is the Mean
Squared Error (MSE) and its two components: bias and standard error (or variance)
(Scott 2009, Zucchini 2003, Sheather et al. 1991, Marron et al. 1987). MSE can be
measured using:
( ) ( ) ( )
=[ ( ) ( )] ( ) ( ))
( ) ( ))                 (4.4)
There is usually a trade-off between the variance and bias of the estimator in
equation 4.4. Bias can be reduced by increasing variance, and vice versa, by changing the
smoothing parameter.
The most common global measure of accuracy is the Mean Integrated Squared
Error (MISE) (Rosenbalt 1956, Scott 2009, Zucchini 2003, Sheather et al. 1991,
Adamowski 1985), given by:
( ) ( )
92
= ))
= ( ) + ( )                     (4.5)
4.3.3.1. Bias, Variance and MSE
The bias is given by (Scott 2009, Zucchini 2003):
( ) = 1 1 ( )
= 1 1 ( )
= 1 ( )                        (4.6)
If =  , , =
( ) = ( ) ( )
Using the Taylor series to expand the ( ) yields:
( ) ( ) ( ) + 12 ) " ( ) )
where ( ) represents terms that converge to zero faster than  as  approaches zero.
Thus:
93
( ) = ( ) ( ) ( ) ( ) + ( ) )2 "( ) )
( ) + 2 "( ) + ( )                     (4.7)
( ) 2 "( )                               (4.8)
where  is the variance of the kernel, is the smoothing parameter or bandwidth, and
"( ) is density curvature at .
The variance is given by (Scott 2009, Zucchini 2003):
( ) 1
= 1
Therfore, since ,?  are distributed independently:
= ( ) ( )
94
( ) = 1 1 ( ) 1 1 ( )
= 1 1 ( ) 1 ( ) ( )
Using Taylor approximation and substituting z= , when n becomes large and
h becomes small, the approximation of above equation will be:
( ) 1 ( ) ( )                           (4.9)
It is clear that  increases as variance decreases. Combining equations 4.8 and 4.9
leads to:
( ) ( ) ( )
1
4
" ) + 1 ( )                         (4.10 )
where = ( )  and = )
Integrating equation 4.10a leads to:
1
4 )+
1                         (4.10 )
where ( ) = " ) .
95
As shown in equation 4.10b, MISE is a function of the bandwidth. The first term
in equation 4.10 becomes large when  values are large, and the second term becomes
large when  decreases. There is a value for  that minimizes the MISE, and that is the
optimal bandwidth (Rosenbalt 1956, Scott 2009, Zucchini 2003, Sheather et al. 1991,
Adamowski 1985, Jones et al. 1996). Equation 4.10 is the measure of the estimator?s
performance. By minimizing equation 4.10, the optimal bandwidth can be calculated
using the following equation:
) ( ) 1
Setting above equation equal to zero will give the optimal bandwidth, .
= 1 ( )                   (4.11)
Substituting equation 4.11 in 4.10, the minimum MISE for the given PDF and kernel can
be calculated using:
= 54 ( )               (4.12)
Finding the optimal bandwidth depends on the sample size, kernel function, and
an unknown PDF. A variety of methods have been developed to simplify equation 4.11
based on the selected kernel function, methods such as rule of thumb, cross-validation
methods, the plug-in approach, and the smoothed bootstrap approach (Silverman 1986,
Rudemo 1982, Bowman 1984, Hall 1992, Sheather 1986, 1983, Sheather et al. 1991,
Polansky and Baker 2000). Considering a standard normal density as a kernel function,
96
Polansky and Baker (2000) proposed an equation for optimal bandwidth selection. The
optimal bandwidth is given by the following equation and was used in this study
(Polansky and Baker 2000):
= 1.587                       (4.13)
where is the sample size and ,  (Silverman 1986), where is the
sample standard deviation and  is the interquartile range.  is a measure of
statistical dispersion. It is defined as the difference between the upper and lower quartiles
( 1).
4.3.4. Probability-based IDF Curves
The results of the created IDFs from the previous chapters were used to develop the
probability-based IDF curves. The kernel density estimator was applied to the projected
rainfall depths for each return period, and each rainfall duration and probability versus
rainfall depth was plotted. To develop the IDF curves, the median of the distribution
(probability: 0.5) was selected as the most likely outcome, and the results are presented in
the form of IDF graphs.
Probability-based IDF curves were developed from the results of rainfall intensities
estimated by the stochastic method (for 15-, 30-, 45-,min, 1-hr and 2-hr) in combination
with NARCCAP projections (for 3-,6-,12-,24- and 48-hr) and estimated rainfall
intensities using the ANN model (for 15-, 30-, 45-min, 1-hr and 2-hr).
4.4.Results and Discussion
4.4.1. Optimal bandwidth selection
97
The equation proposed by Polansky and Baker (2000) was used to calculate the
optimal bandwidth. Rainfall intensities for 10 rainfall durations (e.g. 15-min, 30-min) and
6 return periods (e.g. 2-yr, 5-yr) were estimated using six different climate model
projections (Chapter 2). Selecting 15-min rainfall duration for Auburn as an example,
Table 4-2 shows calculated bandwidth when stochastic method was used as a
disaggregation method.
Table 4-2 Optimal bandwidth selection for Auburn, 15-min rainfall duration
Climate Models 15-min rainfall (mm)2-yr 5-yr 10-yr 25-yr 50-yr 100-yr
CRCM-CCSM 10.19 13.73 16.17 19.39 21.89 24.49
CRCM-CGCM3 8.50 11.16 12.77 14.63 15.91 17.09
HRM3-GFDL 14.88 20.39 23.86 28.06 31.05 33.91
RCM3-GFDL 16.58 22.28 25.55 29.17 31.54 33.65
HRM3-HadCM3 12.53 18.40 22.46 27.81 31.94 36.17
GFDL-ECP2 11.76 15.46 17.85 20.79 22.91 24.98
sample size (n)= 6
Standard deviation(S) 2.97 4.20 4.96 5.90 6.63 7.39
IQR/1.349 3.48 4.93 5.70 6.43 7.15 6.98
Min{S,IQR/1.349} 2.97 4.20 4.96 5.90 6.63 6.98
hopt (Equ. 4.13) 2.59 3.67 4.33 5.16 5.79 6.10
The same procedure was applied to calculate the bandwidth for the remaining rainfall
durations for all 34 stations in Alabama. Optimal bandwidths were also calculated to
develop the probability-based IDF curves when ANN model was used for rainfall
disaggregation.
4.4.2. Probability-based IDF Curves
4.4.2.1 Stochastic Method
Probability-based IDF curves were developed for 34 stations in Alabama (Figure 2.1).
The results of the developed probability-based IDFs when the stochastic method was
98
used for disaggregation are shown in Figure 4.2 for Auburn. The remaining graphs for
other stations in Alabama are presented in Appendix E.
15-min
Rainfall depth (mm)
0 10 20 30 40 50 60
Pro
ba
bil
ity
0.0
0.2
0.4
0.6
0.8
1.0
2-yr
5-yr
10-yr
25-yr
50-yr
100-yr
30-min
Rainfall depth (mm)
0 20 40 60 80 100
Pro
ba
bil
ity
0.0
0.2
0.4
0.6
0.8
1.0
2-yr
5-yr
10-yr
25-yr
50-yr
100-yr
45-min
Rainfall depth (mm)
0 20 40 60 80 100 120
Pro
ba
bil
ity
0.0
0.2
0.4
0.6
0.8
1.0
2-yr
5-yr
10-yr
25-yr
50-yr
100-yr
1-hr
Rainfall depth (mm)
0 20 40 60 80 100 120 140 160
Pro
ba
bil
ity
0.0
0.2
0.4
0.6
0.8
1.0
2-yr
5-yr
10-yr
25-yr
50-yr
100-yr
2-hr
Rainfall depth (mm)
0 20 40 60 80 100 120 140 160
Pro
ba
bil
ity
0.0
0.2
0.4
0.6
0.8
1.0
2-yr
5-yr
10-yr
25-yr
50-yr
100-yr
3-hr
Rainfall depth (mm)
0 50 100 150 200
Pro
ba
bil
ity
0.0
0.2
0.4
0.6
0.8
1.0
2-yr
5-yr
10-yr
25-yr
50-yr
100-yr
99
Figure 4.2 provides additional probability information compared to a typical IDF
graph, which allows designers and decision-makers to use the IDF curve with more
confidence. For example, for a 10-yr return with one-hour rainfall duration, there is a
probability of 0.6 that rainfall amount will be less than or equal to 35 mm.
6-hr
Rainfall depth (mm)
0 50 100 150 200 250 300
Pro
ba
bil
ity
0.0
0.2
0.4
0.6
0.8
1.0
2yr
5-yr
10-yr
25-yr
50-yr
100-yr
12-hr
Rainfall depth (mm)
0 100 200 300 400
Pro
ba
bil
ity
0.0
0.2
0.4
0.6
0.8
1.0
2yr
5-yr
10-yr
25-yr
50-yr
100-yr
24-hr
Rainfall depth (mm)
0 200 400 600
Pro
ba
bil
ity
0.0
0.2
0.4
0.6
0.8
1.0
2yr
5-yr
10-yr
25-yr
50-yr
100-yr
48-hr
Rainfall depth (mm)
0 200 400 600 800
Pro
ba
bil
ity
0.0
0.2
0.4
0.6
0.8
1.0
2yr
5-yr
10-yr
25-yr
50-yr
100-yr
Figure 4.2 Probability-based IDFs when stochastic method used for disaggregation for 15-, 30-, 45-
min,1- ,2-, 3-, 6-, 12-, 24- and 48-hr rainfall duration-graphs are presented for Auburn, AL.
100
Considering the median of distribution as the most likely outcome, typical IDF curves
were developed for all stations in Alabama. Figure 4.3 shows how the resultant IDF was
created for Auburn. A probability-based IDF for 15-min rainfall duration is presented as
an example to explain the process.
Figure 4.3 Resultant IDF curves for Auburn, AL using the stochastic method
Auburn IDF curves
Duration (hr)
0.1 1 10 100
Ra
inf
all
int
en
sit
y(
mm
/h
r)
1
10
100
1000
2-yr
5-yr
10-yr
25-yr
50-yr
100yr
15-min
Rainfall depth (mm)
0 10 20 30 40 50 60
Pro
ba
bil
ity
0.0
0.2
0.4
0.6
0.8
1.0
2-yr
5-yr
10-yr
25-yr
50-yr
100-yr
101
The dashed line presents the rainfall depths (mm) with a probability of 0.5 for 15-min
rainfall durations and for all the return periods. Rainfall depths for the remaining rainfall
durations (Figure 4.2) were also derived from the probability-based IDF curves. These
values were then used to create the resultant IDF curves. IDF curves for the remaining
stations (33 stations) are presented in Appendix F.
To discuss the magnitude of uncertainty using a particular GCM projection on
deriving IDF curves, Table 4-3 presents rainfall depths for 15-min rainfall durations. The
upper section of the table is similar to Table 4-2. The lower section summarize the
rainfall depths with a most likely probability of 0.5  derived from probability-based IDF
curve (Figure 4.3), minimum and maximum of the rainfall depths that presents the
rainfall depth range.
Table 4-3 Uncertainty quantification for 15-min rainfall duration, Auburn, AL
Climate Models 15-min rainfall (mm)2-yr 5-yr 10-yr 25-yr 50-yr 100-yr
CRCM-CCSM 10.19 13.73 16.17 19.39 21.89 24.49
CRCM-CGCM3 8.50 11.16 12.77 14.63 15.91 17.09
HRM3-GFDL 14.88 20.39 23.86 28.06 31.05 33.91
RCM3-GFDL 16.58 22.28 25.55 29.17 31.54 33.65
HRM3-HadCM3 12.53 18.40 22.46 27.81 31.94 36.17
GFDL-ECP2 11.76 15.46 17.85 20.79 22.91 24.98
Rainfall depth from
probability based-IDF 12.34 16.94 19.93 23.64 26.30 28.93
Min 8.50 11.16 12.77 14.63 15.91 17.09
Max 16.58 22.28 25.55 29.17 31.94 36.17
Percentage
difference (%)
-31.10 -34.12 -35.93 -38.12 -39.52 -40.93
34.40 31.52 28.19 23.38 21.42 25.02
102
Table 4-3 shows that rainfall depths for 2-yr return period range from 8.5 mm
(projection from CRCM-CGCM3) to 16.58 mm (projection from RCM3-GFDL). Using
50% as most likely probability, 2-yr, 15-min rainfall is projected as 12.34 mm. Therefore,
8.5 mm projection from CRCM-CGCM3 is 31% underestimated but 16.58 mm projection
from RCM-GFDL is about 34% overestimated. Results for the remaining return periods
(5-, 10-, 25-, 50- and 100-yr) are presented in Table 4-3. Figure 4.4 also displays the
rainfall depth range and the resulting rainfall depth derived from probability-based IDF
curve.
Figure 4.4 shows that rainfall depth range (difference between max and min)
increases for longer return periods. For example, for 100-yr return period, rainfall depth
derived from the probability-based IDF projects this amount to be about 29 mm.
15-min
Return Period(yr)
2-yr 5-yr 10-yr 25-yr 50-yr 100-yr
Ra
inf
all
de
pt
h(
mm
)
5
10
15
20
25
30
35
40
Figure 4.4 Projected rainfall depth range from six climate models (bars show minimum and
maximum) and the red dot represents the rainfall depth derived from the probability-based IDF.
103
Projected rainfall depth from HRM3-HadCM is 36.17 mm which is 25% overestimated
compared with rainfall depth derived from the probability-based IDF. CRCM-CGCM3
projection for the same return period and same duration is 17.09 mm that shows about
41% underestimation.
Solaiman and Simonovic (2011) developed probability-based IDF curves using 27
climate change scenarios for the city of London, Ontario, Canada. To compare the results
of their study with this one, Figure 4.5 shows projected rainfall depth range (bars) and
rainfall depth derived from probability-based IDF (red dots) for Auburn and London.
Results are presented for 1-, 2-, 6-, 12- and 24-hr rainfall durations.
1-hr, London
Return Period (yr)
2-yr 5-yr 10-yr 25-yr 50-yr 100-yr
Ra
inf
all
de
pt
h(
mm
)
0
20
40
60
80
100
120
2-hr, London
Return Period (yr)
2-yr 5-yr 10-yr 25-yr 50-yr 100-yr
Ra
inf
all
de
pt
h(
mm
)
20
40
60
80
100
120
140
160
1-hr, Auburn
Return Period (yr)
2-yr 5-yr 10-yr 25-yr 50-yr 100-yr
Ra
inf
all
de
pt
h(
mm
)
0
20
40
60
80
100
120
2-hr, Auburn
Return Period (yr)
2-yr 5-yr 10-yr 25-yr 50-yr 100-yr
Ra
inf
all
de
pt
h(
mm
)
0
20
40
60
80
100
120
140
160
104
Figure 4.5 Projected rainfall depth range (bars show minimum and maximum and the red dot represent s
the rainfall depth derived from the probability-based IDF) for Auburn, AL (left side) and London,
Ontario, Canada (right side).
12-hr, Auburn
Return Period (yr)
2-yr 5-yr 10-yr 25-yr 50-yr 100-yr
Ra
inf
all
de
pt
h(
mm
)
0
50
100
150
200
250
300
350
24-hr, Auburn
Return Period (yr)
2-yr 5-yr 10-yr 25-yr 50-yr 100-yr
Ra
inf
all
de
pt
h(
mm
)
0
100
200
300
400
500
600
12-hr, London
Return Period (yr)
2-yr 5-yr 10-yr 25-yr 50-yr 100-yr
Ra
inf
all
de
pt
h(
mm
)
0
50
100
150
200
250
300
350
24-hr, London
Return Period (yr)
2-yr 5-yr 10-yr 25-yr 50-yr 100-yr
Ra
inf
all
de
pt
h(
mm
)
0
100
200
300
400
500
600
6-hr, Auburn
Return Period (yr)
2-yr 5-yr 10-yr 25-yr 50-yr 100-yr
Ra
inf
all
de
pt
h(
mm
)
0
20
40
60
80
100
120
140
160
180
200
220
6-hr,London
Return Period (yr)
2-yr 5-yr 10-yr 25-yr 50-yr 100-yr
Ra
inf
all
de
pt
h(
mm
)
20
40
60
80
100
120
140
160
180
200
220
105
Table 4-4 shows the rainfall depths derived from probability-based IDF, ranges of the
rainfall depths projected by different future climate models for Auburn, AL and London,
ON. Results are presented for 1-, 2-, 6-, 12- and 24-hr rainfall duration. Percentage
differences (Table 4-4) were calculated between minimum or maximum rainfall depths
projected by different future climate models and rainfall depth derived from probability-
based IDF for each duration. The percent differences between minimum rainfall depths
and the rainfall depths derived from probability-based IDF for five durations from only
six future climate models from Auburn range from -33.5% to -43.5% with an average of -
37.2%. These percent differences are comparable to ones obtained from 27 future climate
models for London, Ontario, i.e. ranging from -18.3% to -22.1% with average of -20.6%.
The percent differences of maximum rainfall depths are also comparable to ones obtained
from Solaiman and Simonovic (2011).
Figure 4.5 and data in Table 4-5 show that rainfall depth ranges for Auburn using six
climate models are comparable to the ones for London while using 27 climate change
scenarios. Using more GCMs to develop the probability-based IDFs will lead to obtain
more accurate results but Figure 4.5 shows that even though only six GCM projections
were used, the IDF curves developed using the probability method are more
representative than only one model to what it would happen in the future.  Analyzing the
results from Table 4-3 and the remaining rainfall durations (not shown in the table) for
Auburn shows that projections from CRCM-CGCM3 are likely to be underestimated but
RCM3-GFDL and in some cases HRM3-GFDL most likely overestimates rainfall in
Alabama, and projections from HRM3-HadCM3 are the most representative.
106
Table 4-4 Uncertainty quantification of rainfall depths (mm) projected from different climate
models for Auburn, AL and London, ON
City Auburn, AL London, ON
Duration 1-hr
Return
period 2-yr 5-yr 10-yr 25-yr 50-yr 100-yr 2-yr 5-yr 10-yr 25-yr 50-yr 100-yr
50%* 18.0 25.6 30.9 37.8 43.1 48.5 33.0 43.0 52.0 62.0 67.0 77.0
Min 10.4 14.1 17.0 21.0 24.5 28.3 24.1 33.1 38.8 46.0 51.4 56.7
Max 29.1 40.4 47.6 56.3 62.4 71.1 42.1 59.6 71.2 85.9 96.8 107.6
Range 18.7 26.3 30.6 35.2 38.0 42.8 18.0 26.6 32.4 39.9 45.4 50.9
Percentage
diff (%)**
-42.0 -44.9 -45.2 -44.3 -43.2 -41.7 -26.9 -23.1 -25.4 -25.8 -23.3 -26.4
61.7 57.7 53.9 48.8 44.8 46.6 27.5 38.7 37.0 38.5 44.4 39.7
Duration 2-hr
50% 26.0 35.2 41.3 49.2 55.2 61.2 40.0 55.0 67.0 81.0 91.0 101.0
Min 14.9 18.3 20.8 24.3 27.2 30.4 30.4 40.3 46.9 55.2 61.3 67.5
Max 41.4 53.6 60.7 71.1 79.5 87.6 55.9 78.7 93.8 113.6 129.1 144.5
Range 26.5 35.3 39.9 46.8 52.2 57.2 25.5 38.4 46.9 58.4 67.8 77.0
Percentage
diff (%)
-42.9 -48.1 -49.7 -50.6 -50.7 -50.3 -24.1 -26.7 -30.0 -31.9 -32.6 -33.2
59.1 52.4 46.9 44.6 43.9 43.2 39.7 43.1 40.0 40.3 41.9 43.0
Duration 6-hr
50% 48.9 68.3 81.5 98.7 111.9 124.4 52.0 72.0 84.0 101.0 113.0 125.0
Min 27.9 35.6 41.4 49.7 56.6 64.2 40.3 53.5 62.1 73.0 81.0 89.0
Max 81.8 103.4 117.7 146.3 169.0 204.5 71.9 101.4 120.9 145.6 163.8 182.0
Range 53.9 67.8 76.3 96.6 112.4 140.3 31.6 47.9 58.8 72.6 82.8 93.0
Percentage
diff (%)
-42.9 -47.8 -49.2 -49.7 -49.4 -48.4 -22.5 -25.8 -26.1 -27.8 -28.3 -28.8
67.2 51.5 44.5 48.1 51.0 64.4 38.3 40.8 43.9 44.1 45.0 45.6
Duration 12-hr
50% 67.8 95.7 114.5 138.4 155.1 167.5 62.0 83.0 97.0 114.0 128.0 141.0
Min 41.5 54.9 65.0 79.6 91.9 99.6 49.4 66.6 77.4 90.2 99.7 109.2
Max 110.0 141.2 178.6 233.6 280.8 333.9 85.8 117.2 138.0 164.3 183.8 203.2
Range 68.5 86.4 113.6 154.0 188.9 234.2 36.4 50.6 60.6 74.0 84.1 94.0
Percentage
diff (%)
-38.8 -42.7 -43.2 -42.5 -40.7 -40.5 -20.3 -19.8 -20.2 -20.8 -22.1 -22.6
62.2 47.6 56.0 68.8 81.1 99.3 38.4 41.3 42.3 44.1 43.6 44.1
Duration 24-hr
50% 87.1 121.0 144.7 177.2 202.4 232.1 71.0 94.0 110.0 129.0 144.0 158.0
Min 57.9 77.7 92.7 114.2 123.7 131.1 56.4 76.8 87.8 102.0 112.6 123.1
Max 124.9 184.6 241.4 328.1 405.2 494.7 98.2 133.0 156.0 185.0 206.6 228.2
Range 67.0 106.9 148.7 213.9 281.5 363.6 41.8 56.2 68.2 83.0 94.1 105.1
Percentage
diff (%)
-33.5 -35.8 -36.0 -35.6 -38.9 -43.5 -20.6 -18.3 -20.1 -20.9 -21.8 -22.1
43.4 52.6 66.8 85.1 100.2 113.1 38.3 41.4 41.8 43.4 43.5 44.5
* 50%: rainfall depth derived from the probability-based IDF, considering50% probability as a most
likely outcome.
** Percentage diff (%): percentage difference of min or max from 50%.
107
A comparison of the resultant IDF curves with the current IDFs is presented in Figure
4.6. Figure 4.6a shows that, for a 2-yr return period, rainfall intensity is reduced by 39%
for durations of less than 12 hours. A 14% increase is expected for durations of more than
12 hours. Figure 4.6b displays a 36% decrease for a 5-yr return period for durations of
less than eight hours and a 17% increase for durations longer than 8 hours. For a 10-yr
return period, a 34% decline for durations of less than 8 hours and an 18% increase in
rainfall intensities are expected (Figure 4.6c).
Figure 4.6d depicts the results for a 50-yr return period. It shows that the projected
rainfall intensity tends to decrease by 31% for durations of less than 6 hours and is
expected to increase by 19% for rainfall durations of more than six hours.
108
a) Auburn, 2-yr
Duration (hr)
0.1 1 10 100
Ra
inf
all
int
en
sit
y(
mm
/h
r)
1
10
100
1000
Stochastic
Current
-39%
14%
b) Auburn, 5-yr
Duration (hr)
0.1 1 10 100
Ra
inf
all
int
en
sit
y(
mm
/h
r)
1
10
100
1000
Stochstic
Current
-36%
17%
c) Auburn, 10-yr
Duration (hr)
0.1 1 10 100
Ra
inf
all
int
en
sit
y(
mm
/h
r)
1
10
100
1000
Stochastic
Current
-34%
18%
d) Auburn, 50-yr
Duration (hr)
0.1 1 10 100
Ra
inf
all
int
en
sit
y(
mm
/h
r)
1
10
100
1000
Stochastic
Current
-31%
19%
e) Auburn, 100-yr
Duration (hr)
0.1 1 10 100
Ra
inf
all
int
en
sit
y(
mm
/h
r)
1
10
100
1000
Stochastic
Current
-29%
19%
Figure 4.6 Resultant IDF curves under future and current climate for Auburn, AL when the stochastic
method was used for rainfall disaggregation
109
4.4.2.2 ANN Model
Figure 4.7 displays probability-based IDFs when the ANN model was used to
disaggregate rainfall. For example, if the rainfall depth of a one-hour storm for a 10-yr
return period is 30 mm, the maximum probability of this specific rainfall is about 0.6
(Figure 4.7). The resultant IDF curves created using the probability of 0.5 as the most
likely probability are presented in Figure 4.8. The results were also compared to current
IDF curves. Figure 4.9 shows the IDF curves under the future and current climate for
different return periods and compares the result of the ANN model with the stochastic
method for durations of less than two hours.
Figure 4.9a shows a 48% decrease for a 2-yr return period for durations less than two
hours. The stochastic method shows almost the similar results. There was a 50% decrease
for a 5-yr return period. The stochastic method estimates a 46% decrease for the same
return period (Figure 4.9b). Figure 4.9c displays the IDF curves under the future and
current climate for a 10-yr storm. It shows that the rainfall intensity is expected to
decrease by 51%. A 44% decrease is projected when the stochastic method is used.
Figure 4.9d shows that the rainfall intensity in expected to decrease by 52% for a 50-yr
return period. The stochastic method shows a decrease of 40%. A 52% decrease in
rainfall intensities is expected for a 100-yr return period (Figure 4.9e). A 38% decrease is
estimated by the stochastic method.
110
15-min
Rainfall depth (mm)
0 10 20 30 40
Pro
ba
bil
ity
0.0
0.2
0.4
0.6
0.8
1.0
2-yr
5-yr
10-yr
25-yr
50-yr
100-yr
30-min
Rainfall depth (mm)
0 10 20 30 40 50 60
Pro
ba
bil
ity
0.0
0.2
0.4
0.6
0.8
1.0
2-yr
5-yr
10-yr
25-yr
50-yr
100-yr
45-min
Rainfall depth (mm)
0 20 40 60 80 100 120
Pro
ba
bil
ity
0.0
0.2
0.4
0.6
0.8
1.0
2-yr
5-yr
10-yr
25-yr
50-yr
100-yr
2-hr
Rainfall depth (mm)
0 20 40 60 80 100 120 140 160
Pro
ba
bil
ity
0.0
0.2
0.4
0.6
0.8
1.0
2-yr
5-yr
10-yr
25-yr
50-yr
100-yr
Figure 4.7 Probability-based IDFs when ANN model used for disaggregation for 15-, 30-, 45-min,1- and
2-hr rainfall duration-graphs are presented for Auburn, AL.
1-hr
Rainfall depth (mm)
0 20 40 60 80 100
Pro
ba
bil
ity
0.0
0.2
0.4
0.6
0.8
1.0
2-yr
5-yr
10-yr
25-yr
50-yr
100-yr
111
The results of both the ANN model and the stochastic method suggest that future
rainfall intensities for rainfall durations of less than two hours are expected to decrease.
They estimate almost the same decrease for two-, five-, and ten-year return periods.
Auburn IDF curves
Duration (hr)
0.1 1
Ra
inf
all
int
en
sit
y(
mm
/h
r)
10
100
2-yr
5-yr
10-yr
25-yr
50-yr
100yr
Figure 4.8 Resultant IDF curves for Auburn, AL using ANN model
112
Figure 4.9 Resultant IDF curves under future and current climate for Auburn, AL
a) Auburn, 2-yr
Duration (hr)
0.1 1
Ra
inf
all
int
en
sit
y(
mm
/h
r)
10
100
1000
ANN model
Current
Stochastic
-48%
-49%
b) Auburn, 5-yr
Duration (hr)
0.1 1
Ra
inf
all
int
en
sit
y(
mm
/h
r)
10
100
1000
ANN model
Current
Stochastic
-50%
-46%
c) Auburn, 10-yr
Duration (hr)
0.1 1
Ra
inf
all
int
en
sit
y(
mm
/h
r)
10
100
1000
ANN model
Current
Stochastic
-51%
-44%
d) Auburn, 50-yr
Duration (hr)
0.1 1
Ra
inf
all
int
en
sit
y(
mm
/h
r)
10
100
1000
ANN model
Current
Stochastic
-52%
-40%
e) Auburn, 100-yr
Duration (hr)
0.1 1
Ra
inf
all
int
en
sit
y(
mm
/h
r)
10
100
1000
ANN model
Current
Stochastic
-52%
-38%
113
4.5.Summary and Conclusions
Developing the IDF curves under the future climate for the state of Alabama was
investigated in the previous chapters, and the results showed that, due to the uncertainty
associated with climate models, these models are unable to project identical results.
Because all of the investigated climate models in this study provided different results,
developing probability-based IDF curves offered a more reliable approach. Therefore,
this chapter presented a methodology to develop probability-based IDF curves using non-
parametric kernel density estimation. A probability-based IDF curve provides additional
probability information that allows designers and decision-makers to use IDF curves with
more confidence.
The resultant IDF curves were also created by selecting the median of the distribution
as the most likely outcome. Analyzing the results of the ANN model and the stochastic
method for durations of less than two hours indicated that they both agree that the
precipitation pattern for Alabama veers toward less intense rainfalls for the investigated
durations and for all the return periods. The results indicated that, for small duration
events, future rainfall intensity is expected to decrease by 54% on average for the State.
The result is not exactly the same when stochastic method was use but still indicates a
decline in future rainfall intensities. A 47% decrease on average is expected for durations
of less than 2 hours.
A comparison of the results with the current IDF curves for Alabama indicated that,
when the stochastic method was used for rainfall disaggregation, future rainfall intensity
114
could decreases or increases depending on the return period. Results displays a 35%
decrease on an average for Alabama. This decline mostly is expected for durations of less
than six hours and 12 hours, depending on the location and return period. For longer
durations, an 11% increase is projected.
The results of this study indicated that incorporating all six NARCCAP projections to
develop the resultant IDF curves project that future rainfall intensities mostly for rainfall
durations of less than six hours is expected to decrease, and this finding is independent of
the temporal downscaling method used.
115
Chapter 5
5. Conclusions
5.1. Summary and Conclusions
Many hydrologic designs of water management infrastructures are based on specific
design storms derived from historic rainfall events available in the form of intensity-
duration-frequency (IDF) curves. However, it is expected that the frequency and
magnitude of future extreme rainfalls will change due to increase in greenhouse gas
concentrations in earth?s atmosphere (Prodanovic et al. 2007). There is scientific
agreement that there will be an increase in the average precipitation around the world.
However, this does not imply that more precipitation will occur everywhere. Extreme
events can present great challenges for water management utilities. Degradation of water
quality, forcing additional costs for treatment, property damage and potential loss of life
due to flooding are some of the things that are caused by extreme events (Miller and
Yates 2006). On the other hand, drought can decrease the capability of water utilities to
meet water demands and enforce emergency restrictions (Miller and Yates 2006).
Changes in precipitation characteristics may require revision of existing standards for
designing civil engineering infrastructures. It can also require the rebuilding and/or
upgrading of existing infrastructures. One way to be prepared for possible changes, and
to decrease vulnerability of hydraulic infrastructures to climate change, is to predict
potential effects (as manifested by IDF curves) and adapt to them. Therefore, the overall
116
objective of this study was to evaluate the impact of climate change on rainfall IDF
curves for Alabama. Three objectives were presented in the beginning of this dissertation.
For each of the objectives, major findings are summarized below.
5.1.1. Objective 1
 To develop rainfall IDF curves for Alabama under future climate change scenario;
using a stochastic method to disaggregate three-hourly precipitations into 15-minute
precipitations.
Six high-resolution projections (for 2038-2070) derived from dynamical
downscaling of General Circulation Models (GCMs) by Regional Climate Models
(RCMs) were used in this study. Three-hourly projected precipitations were
disaggregated using a stochastic method and rainfall IDF curves under future climate
scenario were created. Major conclusions were:
1. The rainfall pattern for Alabama will change in future due to climate change.
2. Results of the six NARCCAP projections were not identical. A variety of factors
can be responsible for differing results; a likely reason is the difference in
physical parameterizations, especially of radiative and precipitation-forming
processes, amongst different GCMs and RCMs, as well as the difference in initial
and boundary conditions for each climate projection.
3. Four of these models  HRM3-HadCM3, HRM3-GFDL, RCM3-GFDL and
ECP2-GFDL  showed both increase and decrease in predicted rainfall intensity.
This increase/decrease depends on the rainfall duration and return period of the
storm.
117
4. The remaining two model projections  CRCM-CGCM3 and CRCM-CCSM
indicated a reduction in future rainfall intensity for all return periods and all
rainfall durations for Alabama.
5. There is a large uncertainty on the projected rainfall intensity of these six climate
models for long durations (i.e., larger than 4 hours).
6. Precipitation pattern for Alabama veers toward less intense rainfalls for short
rainfall durations.
5.1.2. Objective 2
 Use Artificial Neural Network (ANN) to estimate the maximum 15-, 30-, 45-, 60-,
and 120-min rainfall depths from three-hourly precipitations for the creation of future
IDF curves for Alabama.
A feed-forward, back-propagation model was developed to estimate maximum
precipitations for different rainfall durations. The performance measures for evaluation of
the ANN model were Nash-Sutcliffe Efficiency coefficient (NSE) and correlation
coefficient (R). Normalized Mean Square Error (NMSE) and Akaike Information
Criterion (AIC) were used to find the optimum input data. The results of the ANN model
were also compared to the results of the rainfall disaggregation using stochastic method
from the previous chapter and it was found that:
1. Scatter plots created to evaluate the performance of the ANN model suggest that
the predictions of the ANN model more closely approximated the perfect
prediction line.
118
2. The ANN model provided a superior performance in estimating maximum rainfall
depths, while the stochastic method under-predicted maximum rainfall depths.
3. Analyzing the developed IDF curves for Auburn indicated that future rainfall
intensities for the studied duration (< 2 hours) events are expected to decrease by
33% to 74% from current ones.
4. Comparison of the developed ANN model and the stochastic method showed that
both methods are in agreement that future rainfall intensities (for duration less
than 2 hours) are expected to decrease.
5. ANN model and the stochastic method estimated almost similar decreases in
rainfall intensities when CRCM-CGCM3 and CRCM-CCSM models were used to
create IDF curves under the future climate.
6. The ANN model displayed more declines in rainfall intensities compared to the
stochastic method when HRM3-HadCM3, HRM3-GFDL, and RCM3-GFDL
projections were used.
5.1.3. Objective 3
To develop probability-based IDF curves incorporating climate projections from six
different climate models.
 Results of the developed IDF curves clearly indicated that due to the uncertainty
associated with climate models, these models are unable to project identical results.
Therefore, developing probability-based IDF curves seemed to offer a more reliable
approach to incorporate all the models. Non-parametric kernel density estimator was used
to develop probability-based IDF curves that provides additional probability information
and allows designers and decision-makers to use IDF curves with more confidence.
119
Major findings of this study were:
1. With the presence of significant uncertainties associated with climate models,
using one single GCM provides one of many possible realizations and may not be
representative of the future. Utilizing a collection of models can provide more
realistic information about the possible changes in future.
2. Using the ANN model to disaggregate rainfall, the resultant IDF curve for
Alabama indicated that future rainfall intensity is expected to decrease by 54% on
average for durations less than two hour.
3. A decline by 47% on average for durations less than 2 hours was estimated for
Alabama when stochastic method was used.
4. For durations more than 2 hours, changes in rainfall intensity depends on the
rainfall duration and return period. It could decrease or increase for a given
duration and return period.
5. Probability-based IDF curves developed using the kernel density estimator provide
very useful information that can help decision-makers to use IDF curves with
more confidence.
6. Although the results derived from different climate projections shows large
uncertainty associated with climate models, all of them indicate decrease in future
rainfall intensity for short durations, especially durations of less than 2 hours.
120
Chapter 6
6. Future research
This study offers two temporal downscaling methods to disaggregate precipitation
and develop the IDF curves. It also presented a framework for uncertainty quantification
associated with six NARCCAP climate models. This chapter provides some
recommendations for future research.
1. Using a collection of models can provide more realistic information about the
possible changes in future than only one model. Six climate models were used in
this study, but incorporating more models will improve the results and allows us
to use the information of IDF curves with higher level of confidence.
2. The NARCCAP modelers used only one emission scenario for simulation. In
addition to using more climate models, considering more scenarios can also lead
to improvements in IDF curves.
3. Spatial and temporal resolution of the projections used in this study was 50 km
and 3 hour, respectively. Incorporating models with higher spatial and temporal
resolution could significantly improve the results.
4. Uncertainties resulting from different downscaling methods were not considered
in this study. Therefore, future research may include uncertainty investigation of
the disaggregation method.
121
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Appendix A 
Monthly Cumulative Distribution Functions (CDF) To Perform Bias 
Correction 
A.1. HRM3-GFDL 
 
January
Rainfall (m m )
0 100 200 300 400 500 600 700
F(x)
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
O bs e r ve d
Mod e l
Fe br uar y
Rainfall (m m )
0 100 200 300 400 500
F(x)
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
O bs e r ve d
Mod e l
M ar c h
Rainfall (m m )
0 100 200 300 400 500 600
F(x)
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
O bs e r ve d
Mod e l
A pr il
Rainfall (m m )
0 100 200 300 400 500
F(x)
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
O bs e r ve d
Mod e l
M ay
Rainfall (m m )
0 100 200 300 400 500
F(x)
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
O bs e r ve d
Mod e l
June
Rainfall (m m )
0 100 200 300 400 500
F(x)
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
Obse rved
M od el
135 
 
 
July
Rainfall (m m )
0 100 200 300 400 500 600 700
F(x)
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
O bs e r ve d
Mod e l
A ugust
Rainfall (m m )
0 100 200 300 400 500 600
F(x)
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
O bs e r ve d
Mod e l
Se pte mbe r
Rainfall (m m )
0 200 400 600 800
F(x)
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
O bs e r ve d
Mod e l
Oc tobe r
Rainfall (m m )
0 100 200 300 400 500
F(x)
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
O bs e r ve d
Mod e l
Oc tobe r
Rainfall (m m )
0 100 200 300 400 500
F(x)
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
O bs e r ve d
Mod e l
D e c e mbe r
Rainfall (m m )
0 100 200 300 400 500 600
F(x)
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
O bs e r ve d
Mod e l
136 
 
A.2.RCM3-GFDL 
 
 
January
Rainfall (m m )
0 100 200 300 400 500
F(x)
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
O bs e r ve d
Mod e l
Fe br uar y
Rainfall (m m )
0 100 200 300 400 500
F(x)
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
O bs e r ve d
Mod e l
M ar c h
Rainfall (m m )
0 100 200 300 400 500
F(x)
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
O bs e r ve d
Mod e l
A pr il
Rainfall (m m )
0 100 200 300 400 500
F(x)
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
O bs e r ve d
Mod e l
M ay
Rainfall (m m )
0 100 200 300 400 500
F(x)
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
O bs e r ve d
Mod e l
June
Rainfall (m m )
0 100 200 300 400 500 600 700
F(x)
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
Obse rved
M od el
137 
 
 
July
Rainfall (m m )
0 100 200 300 400 500 600 700
F(x)
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
O bs e r ve d
Mod e l
A ugust
Rainfall (m m )
0 100 200 300 400 500 600
F(x)
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
O bs e r ve d
Mod e l
Se pte mbe r
Rainfall (m m )
0 200 400 600 800 1000
F(x)
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
O bs e r ve d
Mod e l
Oc tobe r
Rainfall (m m )
0 100 200 300 400 500 600
F(x)
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
O bs e r ve d
Mod e l
N ove mbe r
Rainfall (m m )
0 100 200 300 400 500 600
F(x)
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
O bs e r ve d
Mod e l
D e c e mbe r
Rainfall (m m )
0 100 200 300 400 500
F(x)
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
O bs e r ve d
Mod e l
138 
 
A.3. ECP2-GFDL 
 
January
Rainfall (m m )
0 100 200 300 400 500
F(x)
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
O bs e r ve d
Mod e l
Fe br uar y
Rainfall (m m )
0 100 200 300 400 500
F(x)
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
O bs e r ve d
Mod e l
M ar c h
Rainfall (m m )
0 100 200 300 400 500
F(x)
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
O bs e r ve d
Mod e l
A pr il
Rainfall (m m )
0 100 200 300 400 500 600
F(x)
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
O bs e r ve d
Mod e l
M ay
Rainfall (m m )
0 100 200 300 400 500
F(x)
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
O bs e r ve d
Mod e l
June
Rainfall (m m )
0 100 200 300 400 500
F(x)
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
Obse rved
M od el
139 
 
 
July
Rainfall (m m )
0 100 200 300 400 500 600 700
F(x)
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
O bs e r ve d
Mod e l
A ugust
Rainfall (m m )
0 100 200 300 400 500 600 700
F(x)
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
O bs e r ve d
Mod e l
Se pte mbe r
Rainfall (m m )
0 100 200 300 400 500 600 700
F(x)
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
O bs e r ve d
Mod e l
Oc tobe r
Rainfall (m m )
0 100 200 300 400 500 600 700
F(x)
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
O bs e r ve d
Mod e l
N ove mbe r
Rainfall (m m )
0 100 200 300 400 500
F(x)
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
O bs e r ve d
Mod e l
D e c e mbe r
Rainfall (m m )
0 100 200 300 400 500
F(x)
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
O bs e r ve d
Mod e l
140 
 
A.4.CRCM-CGCM3 
 
January
Rainfall (m m )
0 100 200 300 400 500
F(x)
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
O bs e r ve d
Mod e l
Fe br uar y
Rainfall (m m )
0 100 200 300 400 500
F(x)
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
O bs e r ve d
Mod e l
M ar c h
Rainfall (m m )
0 100 200 300 400 500
F(x)
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
O bs e r ve d
Mod e l
A pr il
Rainfall (m m )
0 100 200 300 400 500
F(x)
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
O bs e r ve d
Mod e l
M ay
Rainfall (m m )
0 100 200 300 400 500
F(x)
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
O bs e r ve d
Mod e l
June
Rainfall (m m )
0 100 200 300 400 500
F(x)
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
Obse rved
M od el
141 
 
July
Rainfall (m m )
0 100 200 300 400 500 600 700
F(x)
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
O bs e r ve d
Mod e l
A ugust
Rainfall (m m )
0 50 100 150 200 250 300 350
F(x)
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
O bs e r ve d
Mod e l
Se pte mbe r
Rainfall (m m )
0 100 200 300 400 500 600
F(x)
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
O bs e r ve d
Mod e l
Oc tobe r
Rainfall (m m )
0 100 200 300 400 500
F(x)
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
O bs e r ve d
Mod e l
N ove mbe r
Rainfall (m m )
0 100 200 300 400 500
F(x)
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
O bs e r ve d
Mod e l
D e c e mbe r
Rainfall (m m )
0 100 200 300 400 500
F(x)
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
O bs e r ve d
Mod e l
142 
 
A.5. CRCM-CCSM 
 
January
Rainfall (m m )
0 50 100 150 200 250 300 350
F(x)
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
O bs e r ve d
Mod e l
Fe br uar y
Rainfall (m m )
0 100 200 300 400 500
F(x)
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
O bs e r ve d
Mod e l
M ar c h
Rainfall (m m )
0 100 200 300 400 500
F(x)
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
O bs e r ve d
Mod e l
A pr il
Rainfall (m m )
0 100 200 300 400 500
F(x)
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
O bs e r ve d
Mod e l
M ay
Rainfall (m m )
0 100 200 300 400 500
F(x)
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
O bs e r ve d
Mod e l
June
Rainfall (m m )
0 100 200 300 400 500
F(x)
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
Obse rved
M od el
143 
 
 
July
Rainfall (m m )
0 100 200 300 400 500 600 700
F(x)
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
O bs e r ve d
Mod e l
A ugust
Rainfall (m m )
0 50 100 150 200 250 300 350
F(x)
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
O bs e r ve d
Mod e l
Se pte mbe r
Rainfall (m m )
0 100 200 300 400 500 600
F(x)
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
O bs e r ve d
Mod e l
Oc tobe r
Rainfall (m m )
0 100 200 300 400 500
F(x)
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
O bs e r ve d
Mod e l
N ove mbe r
Rainfall (m m )
0 100 200 300 400 500
F(x)
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
O bs e r ve d
Mod e l
D e c e mbe r
Rainfall (m m )
0 100 200 300 400 500
F(x)
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
O bs e r ve d
Mod e l
144 
 
Appendix B 
Rainfall Intensity-Duration-Frequency Maps 
B.1. HRM3-HadCM3 
 
 
145 
 
 
146 
 
 
147 
 
 
148 
 
 
149 
 
 
150 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
151 
 
B.2. HRM3-GFDL 
 
152 
 
 
153 
 
 
154 
 
 
155 
 
 
156 
 
 
157 
 
 
158 
 
B.3. RCM3-GFDL 
 
159 
 
 
160 
 
 
161 
 
 
162 
 
 
163 
 
 
164 
 
 
165 
 
B.4. ECP2-GFDL 
 
 
166 
 
 
167 
 
 
168 
 
 
169 
 
 
170 
 
 
171 
 
 
 
172 
 
B.5. CRCM-CGCM3 
 
173 
 
 
174 
 
 
175 
 
 
176 
 
 
177 
 
 
178 
 
 
179 
 
B.6. CRCM-CCSM 
 
180 
 
 
181 
 
 
182 
 
 
183 
 
 
184 
 
 
185 
 
 
186 
 
 
 
Appendix C 
Scatter plots of observed and modeled rainfall depths using the ANN model 
and the stochastic method 
C.1. 15-min, Jan-Dec 
 
 AN N mo d e l-J a n
Pre d ict e d  max  15 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5
Ob
s
e
rve
d
 max
 15
-min rain
fa
ll
             d
e
p
th
 (in
) 
0.0
0.5
1.0
1.5
2.0
2.5
Over prediction
Unde rprediction
P erfect pred ictio n
 Sto c h a s tic  mod e l-J a n
Pre d ict e d  max  15 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5
Ob
s
e
rve
d
 max
 15
-min rain
fa
ll
             d
e
p
th
 (in
) 
0.0
0.5
1.0
1.5
2.0
2.5
Over prediction
Unde rprediction
P erfect pred ictio n
 AN N mo d e l-F e b
Pre d ict e d  max  15 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5
Ob
s
e
rve
d
 max
 15
-min rain
fa
ll
             d
e
p
th
 (in
) 
0.0
0.5
1.0
1.5
2.0
2.5
Over prediction
Unde rprediction
P erfect pred ictio n
Sto c h a s tic  mod e l-F e b
Pre d ict e d  max  15 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5
Ob
s
e
rve
d
 max
 15
-min rain
fa
ll
             d
e
p
th
 (in
) 
0.0
0.5
1.0
1.5
2.0
2.5
Over prediction
Unde rprediction
P erfect pred ictio n
 AN N mo d e l-Ma r
Pre d ict e d  max  15 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5
Ob
s
e
rve
d
 max
 15
-min rain
fa
ll
             d
e
p
th
 (in
) 
0.0
0.5
1.0
1.5
2.0
2.5
Over prediction
Unde rprediction
P erfect pred ictio n
 Sto c h a s tic  mod e l-Ma r
Pre d ict e d  max  15 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5
Ob
s
e
rve
d
 max
 15
-min rain
fa
ll
             d
e
p
th
 (in
) 
0.0
0.5
1.0
1.5
2.0
2.5
Over prediction
Unde rprediction
P erfect pred ictio n
187 
 
 
 AN N mo d e l-Ap r
Pre d ict e d  max  15 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5
Ob
s
e
rve
d
 max
 15
-min rain
fa
ll
             d
e
p
th
 (in
) 
0.0
0.5
1.0
1.5
2.0
2.5
Over prediction
Unde rprediction
P erfect pred ictio n
 Sto c h a s tic  mod e l-Ap r
Pre d ict e d  max  15 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5
Ob
s
e
rve
d
 max
 15
-min rain
fa
ll
             d
e
p
th
 (in
) 
0.0
0.5
1.0
1.5
2.0
2.5
Over prediction
Unde rprediction
P erfect pred ictio n
 AN N mo d e l-Ma y
Pre d ict e d  max  15 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5
Ob
s
e
rve
d
 max
 15
-min rain
fa
ll
             d
e
p
th
 (in
) 
0.0
0.5
1.0
1.5
2.0
2.5
Over prediction
Unde rprediction
P erfect pred ictio n
 Sto c h a s tic  mod e l-Ma y
Pre d ict e d  max  15 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5
Ob
s
e
rve
d
 max
 15
-min rain
fa
ll
             d
e
p
th
 (in
) 
0.0
0.5
1.0
1.5
2.0
2.5
Over prediction
Unde rprediction
P erfect pred ictio n
 AN N mo d e l-J u n
Pre d ict e d  max  15 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5
Ob
s
e
rve
d
 max
 15
-min rain
fa
ll
             d
e
p
th
 (in
) 
0.0
0.5
1.0
1.5
2.0
2.5
Over prediction
Unde rprediction
P erfect pred ictio n
 Sto c h a s tic  mod e l-J u n
Pre d ict e d  max  15 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5
Ob
s
e
rve
d
 max
 15
-min rain
fa
ll
             d
e
p
th
 (in
) 
0.0
0.5
1.0
1.5
2.0
2.5
Over prediction
Unde rprediction
P erfect pred ictio n
188 
 
 
AN N mo d e l-J u l
Pre d ict e d  max  15 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5
Ob
s
e
rve
d
 max
 15
-min rain
fa
ll
             d
e
p
th
 (in
) 
0.0
0.5
1.0
1.5
2.0
2.5
Over prediction
Unde rprediction
P erfect pred ictio n
Sto c h a s tic  mod e l-J u l
Pre d ict e d  max  15 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5
Ob
s
e
rve
d
 max
 15
-min rain
fa
ll
             d
e
p
th
 (in
) 
0.0
0.5
1.0
1.5
2.0
2.5
Over prediction
Unde rprediction
P erfect pred ictio n
 AN N mo d e l-Au g
Pre d ict e d  max  15 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5
Ob
s
e
rve
d
 max
 15
-min rain
fa
ll
             d
e
p
th
 (in
) 
0.0
0.5
1.0
1.5
2.0
2.5
Over prediction
Unde rprediction
P erfect pred ictio n
 Sto c h a s tic  mod e l-Au g
Pre d ict e d  max  15 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5
Ob
s
e
rve
d
 max
 15
-min rain
fa
ll
             d
e
p
th
 (in
) 
0.0
0.5
1.0
1.5
2.0
2.5
Over prediction
Unde rprediction
P erfect pred ictio n
 AN N mo d e l-Se p
Pre d ict e d  max  15 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5
Ob
s
e
rve
d
 max
 15
-min rain
fa
ll
             d
e
p
th
 (in
) 
0.0
0.5
1.0
1.5
2.0
2.5
Over prediction
Unde rprediction
P erfect pred ictio n
 Sto c h a s tic  mod e l-Se p
Pre d ict e d  max  15 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5
Ob
s
e
rve
d
 max
 15
-min rain
fa
ll
             d
e
p
th
 (in
) 
0.0
0.5
1.0
1.5
2.0
2.5
Over prediction
Unde rprediction
P erfect pred ictio n
189 
 
  
 AN N mo d e l-Oc t
Pre d ict e d  max  15 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5
Ob
s
e
rve
d
 max
 15
-min rain
fa
ll
             d
e
p
th
 (in
) 
0.0
0.5
1.0
1.5
2.0
2.5
Over prediction
Unde rprediction
P erfect pred ictio n
Sto c h a s tic  mod e l-Oc t
Pre d ict e d  max  15 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5
Ob
s
e
rve
d
 max
 15
-min rain
fa
ll
             d
e
p
th
 (in
) 
0.0
0.5
1.0
1.5
2.0
2.5
Over prediction
Unde rprediction
P erfect pred ictio n
 AN N mo d e l-No v
Pre d ict e d  max  15 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5
Ob
s
e
rve
d
 max
 15
-min rain
fa
ll
             d
e
p
th
 (in
) 
0.0
0.5
1.0
1.5
2.0
2.5
Over prediction
Unde rprediction
P erfect pred ictio n
 Sto c h a s tic  mod e l-No v
Pre d ict e d  max  15 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5
Ob
s
e
rve
d
 max
 15
-min rain
fa
ll
             d
e
p
th
 (in
) 
0.0
0.5
1.0
1.5
2.0
2.5
Over prediction
Unde rprediction
P erfect pred ictio n
 AN N mo d e l-De c
Pre d ict e d  max  15 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5
Ob
s
e
rve
d
 max
 15
-min rain
fa
ll
             d
e
p
th
 (in
) 
0.0
0.5
1.0
1.5
2.0
2.5
Over prediction
Unde rprediction
P erfect pred ictio n
Sto c h a s tic  mod e l-De c
Pre d ict e d  max  15 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5
Ob
s
e
rve
d
 max
 15
-min rain
fa
ll
             d
e
p
th
 (in
) 
0.0
0.5
1.0
1.5
2.0
2.5
Over prediction
Unde rprediction
P erfect pred ictio n
190 
 
C.2. 30-min, Jan-Dec 
 
AN N mo d e l-J a n
Pre d ict e d  max  30 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5
Ob
s
e
rve
d
 max
 30
-min rain
fa
ll
             d
e
p
th
 (in
) 
0.0
0.5
1.0
1.5
2.0
2.5
Over prediction
Unde rprediction
P erfect pred ictio n
 Sto c h a s tic  mod e l-J a n
Pre d ict e d  max  30 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5
Ob
s
e
rve
d
 max
 30
-min rain
fa
ll
             d
e
p
th
 (in
) 
0.0
0.5
1.0
1.5
2.0
2.5
Over prediction
Unde rprediction
P erfect pred ictio n
 AN N mo d e l-F e b
Pre d ict e d  max  30 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5
Ob
s
e
rve
d
 max
 30
-min rain
fa
ll
             d
e
p
th
 (in
)
0.0
0.5
1.0
1.5
2.0
2.5
Over prediction
Unde rprediction
P erfect pred ictio n
Sto c h a s tic  mod e l-F e b
Pre d ict e d  max  30 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5
Ob
s
e
rve
d
 max
 30
-min rain
fa
ll
             d
e
p
th
 (in
)
0.0
0.5
1.0
1.5
2.0
2.5
Over prediction
Unde rprediction
P erfect pred ictio n
 AN N mo d e l-Ma r
Pre d ict e d  max  30 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5
Ob
s
e
rve
d
 max
 30
-min rain
fa
ll
             d
e
p
th
 (in
)
0.0
0.5
1.0
1.5
2.0
2.5
Over prediction
Unde rprediction
P erfect pred ictio n
 Sto c h a s tic  mod e l-Ma r
Pre d ict e d  max  30 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5
Ob
s
e
rve
d
 max
 30
-min rain
fa
ll
             d
e
p
th
 (in
)
0.0
0.5
1.0
1.5
2.0
2.5
Over prediction
Unde rprediction
P erfect pred ictio n
191 
 
  
 AN N mo d e l-Ap r
Pre d ict e d  max  30 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5
Ob
s
e
rve
d
 max
 30
-min rain
fa
ll
             d
e
p
th
 (in
)
0.0
0.5
1.0
1.5
2.0
2.5
Over prediction
Unde rprediction
P erfect 
p red ictio n
 Sto c h a s tic  mod e l-Ap r
Pre d ict e d  max  30 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5
Ob
s
e
rve
d
 max
 30
-min rain
fa
ll
             d
e
p
th
 (in
)
0.0
0.5
1.0
1.5
2.0
2.5
Over prediction
Unde rprediction
P erfect pred ictio n
AN N mo d e l-Ma y
Pre d ict e d  max  30 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Ob
s
e
rve
d
 max
 30
-min rain
fa
ll
             d
e
p
th
 (in
)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Over prediction
Unde rprediction
P erfect 
p red ictio n
Sto c h a s tic  mod e l-Ma y
Pre d ict e d  max  30 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Ob
s
e
rve
d
 max
 30
-min rain
fa
ll
             d
e
p
th
 (in
)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Over prediction
Unde rprediction
P erfect pred ictio n
 AN N mo d e l-J u n
Pre d ict e d  max  30 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Ob
s
e
rve
d
 max
 30
-min rain
fa
ll
             d
e
p
th
 (in
)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Over prediction
Unde rprediction
P erfect pred ictio n
Sto c h a s tic  mod e l-J u n
Pre d ict e d  max  30 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Ob
s
e
rve
d
 max
 30
-min rain
fa
ll
             d
e
p
th
 (in
)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Over prediction
Unde rprediction
P erfect pred ictio n
192 
 
 
 AN N mo d e l-J u l
Pre d ict e d  max  30 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Ob
s
e
rve
d
 max
 30
-min rain
fa
ll
             d
e
p
th
 (in
)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Over prediction
Unde rprediction
P erfect pred ictio n
 Sto c h a s tic  mod e l-J u l
Pre d ict e d  max  30 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Ob
s
e
rve
d
 max
 30
-min rain
fa
ll
             d
e
p
th
 (in
)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Over prediction
Unde rprediction
P erfect pred ictio n
AN N mo d e l-Au g
Pre d ict e d  max  30 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Ob
s
e
rve
d
 max
 30
-min rain
fa
ll
             d
e
p
th
 (in
)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Over prediction
Unde rprediction
P erfect pred ictio n
 Sto c h a s tic  mod e l-Au g
Pre d ict e d  max  30 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Ob
s
e
rve
d
 max
 30
-min rain
fa
ll
             d
e
p
th
 (in
)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Over prediction
Unde rprediction
P erfect pred ictio n
AN N mo d e l-Se p
Pre d ict e d  max  30 -min rain fa ll de p th  (in)
0 1 2 3 4
Ob
s
e
rve
d
 max
 30
-min rain
fa
ll
             d
e
p
th
 (in
)
0
1
2
3
4
Over prediction
Unde rprediction
P erfect pred ictio n
 Sto c h a s tic  mod e l-Se p
Pre d ict e d  max  30 -min rain fa ll de p th  (in)
0 1 2 3 4
Ob
s
e
rve
d
 max
 30
-min rain
fa
ll
             d
e
p
th
 (in
)
0
1
2
3
4
Over prediction
Unde rprediction
P erfect pred ictio n
193 
 
 
 
 
 
 AN N mo d e l-Oc t
Pre d ict e d  max  30 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5
Ob
s
e
rve
d
 max
 30
-min rain
fa
ll
             d
e
p
th
 (in
)
0.0
0.5
1.0
1.5
2.0
2.5
Over prediction
Unde rprediction
P erfect pred ictio n
Sto c h a s tic  mod e l-Oc t
Pre d ict e d  max  30 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5
Ob
s
e
rve
d
 max
 30
-min rain
fa
ll
             d
e
p
th
 (in
)
0.0
0.5
1.0
1.5
2.0
2.5
Over prediction
Unde rprediction
P erfect pred ictio n
 AN N mo d e l-No v
Pre d ict e d  max  30 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5
Ob
s
e
rve
d
 max
 30
-min rain
fa
ll
             d
e
p
th
 (in
)
0.0
0.5
1.0
1.5
2.0
2.5
Over prediction
Unde rprediction
P erfect 
p red ictio n
 Sto c h a s tic  mod e l-No v
Pre d ict e d  max  30 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5
Ob
s
e
rve
d
 max
 30
-min rain
fa
ll
             d
e
p
th
 (in
)
0.0
0.5
1.0
1.5
2.0
2.5
Over prediction
Unde rprediction
P erfect pred ictio n
 AN N mo d e l-De c
Pre d ict e d  max  30 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5
Ob
s
e
rve
d
 max
 30
-min rain
fa
ll
             d
e
p
th
 (in
)
0.0
0.5
1.0
1.5
2.0
2.5
Over prediction
Unde rprediction
P erfect pred ictio n
 Sto c h a s tic  mod e l-De c
Pre d ict e d  max  30 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5
Ob
s
e
rve
d
 max
 30
-min rain
fa
ll
             d
e
p
th
 (in
)
0.0
0.5
1.0
1.5
2.0
2.5
Over prediction
Unde rprediction
P erfect pred ictio n
194 
 
C.3. 45-min, Jan-Dec 
 
 AN N mo d e l-J a n
Pre d ict e d  max  45 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5
Ob
s
e
rve
d
 max
 45
-min rain
fa
ll
             d
e
p
th
 (in
) 
0.0
0.5
1.0
1.5
2.0
2.5
Over prediction
Unde rprediction
P erfect pred ictio n
 Sto c h a s tic  mod e l-J a n
Pre d ict e d  max  45 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5
Ob
s
e
rve
d
 max
 45
-min rain
fa
ll
             d
e
p
th
 (in
) 
0.0
0.5
1.0
1.5
2.0
2.5
Over prediction
Unde rprediction
P erfect pred ictio n
 AN N mo d e l-F e b
Pre d ict e d  max  45 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5
Ob
s
e
rve
d
 max
 45
-min rain
fa
ll
             d
e
p
th
 (in
) 
0.0
0.5
1.0
1.5
2.0
2.5
Over prediction
Unde rprediction
P erfect pred ictio n
Sto c h a s tic  mod e l-F e b
Pre d ict e d  max  45 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5
Ob
s
e
rve
d
 max
 45
-min rain
fa
ll
             d
e
p
th
 (in
) 
0.0
0.5
1.0
1.5
2.0
2.5
Over prediction
Unde rprediction
P erfect pred ictio n
 AN N mo d e l-Ma r
Pre d ict e d  max  45 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Ob
s
e
rve
d
 max
 45
-min rain
fa
ll
             d
e
p
th
 (in
) 
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Over prediction
Unde rprediction
P erfect pred ictio n
Sto c h a s tic  mod e l-Ma r
Pre d ict e d  max  45 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Ob
s
e
rve
d
 max
 45
-min rain
fa
ll
             d
e
p
th
 (in
) 
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Over prediction
Unde rprediction
P erfect pred ictio n
195 
 
 
 AN N mo d e l-Ap r
Pre d ict e d  max  45 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5
Ob
s
e
rve
d
 max
 45
-min rain
fa
ll
             d
e
p
th
 (in
) 
0.0
0.5
1.0
1.5
2.0
2.5
Over prediction
Unde rprediction
P erfect 
p red ictio n
 Sto c h a s tic  mod e l-Ap r
Pre d ict e d  max  45 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5
Ob
s
e
rve
d
 max
 45
-min rain
fa
ll
             d
e
p
th
 (in
) 
0.0
0.5
1.0
1.5
2.0
2.5
Over prediction
Unde rprediction
P erfect pred ictio n
AN N mo d e l-Ma y
Pre d ict e d  max  45 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Ob
s
e
rve
d
 max
 45
-min rain
fa
ll
             d
e
p
th
 (in
) 
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Over prediction
Unde rprediction
P erfect 
p red ictio n
 Sto c h a s tic  mod e l-Ma y
Pre d ict e d  max  45 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Ob
s
e
rve
d
 max
 45
-min rain
fa
ll
             d
e
p
th
 (in
) 
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Over prediction
Unde rprediction
P erfect pred ictio n
 AN N mo d e l-J u n
Pre d ict e d  max  45 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Ob
s
e
rve
d
 max
 45
-min rain
fa
ll
             d
e
p
th
 (in
) 
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Over prediction
Unde rprediction
P erfect pred ictio n
 Sto c h a s tic  mod e l-J u n
Pre d ict e d  max  45 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Ob
s
e
rve
d
 max
 45
-min rain
fa
ll
             d
e
p
th
 (in
) 
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Over prediction
Unde rprediction
P erfect pred ictio n
196 
 
 
 AN N mo d e l-J u l
Pre d ict e d  max  45 -min rain fa ll de p th  (in)
0 1 2 3
Ob
s
e
rve
d
 max
 45
-min rain
fa
ll
             d
e
p
th
 (in
) 
0
1
2
3
Over prediction
Unde rprediction
P erfect 
p red ictio n
Sto c h a s tic  mod e l-J u l
Pre d ict e d  max  45 -min rain fa ll de p th  (in)
0 1 2 3
Ob
s
e
rve
d
 max
 45
-min rain
fa
ll
             d
e
p
th
 (in
) 
0
1
2
3
Over prediction
Unde rprediction
P erfect pred ictio n
 AN N mo d e l-Au g
Pre d ict e d  max  45 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Ob
s
e
rve
d
 max
 45
-min rain
fa
ll
             d
e
p
th
 (in
) 
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Over prediction
Unde rprediction
P erfect 
p red ictio n
 Sto c h a s tic  mod e l-Au g
Pre d ict e d  max  45 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Ob
s
e
rve
d
 max
 45
-min rain
fa
ll
             d
e
p
th
 (in
) 
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Over prediction
Unde rprediction
P erfect pred ictio n
 AN N mo d e l-Se p
Pre d ict e d  max  45 -min rain fa ll de p th  (in)
0 1 2 3 4
Ob
s
e
rve
d
 max
 45
-min rain
fa
ll
             d
e
p
th
 (in
) 
0
1
2
3
4
Over prediction
Unde rprediction
P erfect pred ictio n
 Sto c h a s tic  mod e l-Se p
Pre d ict e d  max  45 -min rain fa ll de p th  (in)
0 1 2 3 4
Ob
s
e
rve
d
 max
 45
-min rain
fa
ll
             d
e
p
th
 (in
) 
0
1
2
3
4
Over prediction
Unde rprediction
P erfect pred ictio n
197 
 
 
 
 
 
 AN N mo d e l-Oc t
Pre d ict e d  max  45 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Ob
s
e
rve
d
 max
 45
-min rain
fa
ll
             d
e
p
th
 (in
) 
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Over prediction
Unde rprediction
P erfect pred ictio n
 Sto c h a s tic  mod e l-Oc t
Pre d ict e d  max  45 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Ob
s
e
rve
d
 max
 45
-min rain
fa
ll
             d
e
p
th
 (in
) 
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Over prediction
Unde rprediction
P erfect pred ictio n
 AN N mo d e l-No v
Pre d ict e d  max  45 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5
Ob
s
e
rve
d
 max
 45
-min rain
fa
ll
             d
e
p
th
 (in
) 
0.0
0.5
1.0
1.5
2.0
2.5
Over prediction
Unde rprediction
P erfect 
p red ictio n
 Sto c h a s tic  mod e l-No v
Pre d ict e d  max  45 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5
Ob
s
e
rve
d
 max
 45
-min rain
fa
ll
             d
e
p
th
 (in
) 
0.0
0.5
1.0
1.5
2.0
2.5
Over prediction
Unde rprediction
P erfect pred ictio n
 AN N mo d e l-De c
Pre d ict e d  max  45 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5
Ob
s
e
rve
d
 max
 45
-min rain
fa
ll
             d
e
p
th
 (in
) 
0.0
0.5
1.0
1.5
2.0
2.5
Over prediction
Unde rprediction
P erfect pred ictio n
Sto c h a s tic  mod e l-De c
Pre d ict e d  max  45 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5
Ob
s
e
rve
d
 max
 45
-min rain
fa
ll
             d
e
p
th
 (in
) 
0.0
0.5
1.0
1.5
2.0
2.5
Over prediction
Unde rprediction
P erfect pred ictio n
198 
 
C.4. 60-min, Jan-Dec 
  
 AN N mo d e l-J a n
Pre d ict e d  max  60 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5
Ob
s
e
rve
d
 max
 60
-min rain
fa
ll
             d
e
p
th
 (in
) 
0.0
0.5
1.0
1.5
2.0
2.5
Over prediction
Unde rprediction
P erfect 
p red ictio n
 Sto c h a s tic  mod e l-J a n
Pre d ict e d  max  60 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5
Ob
s
e
rve
d
 max
 60
-min rain
fa
ll
             d
e
p
th
 (in
) 
0.0
0.5
1.0
1.5
2.0
2.5
Over prediction
Unde rprediction
P erfect pred ictio n
AN N mo d e l-F e b
Pre d ict e d  max  60 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Ob
s
e
rve
d
 max
 60
-min rain
fa
ll
             d
e
p
th
 (in
) 
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Over prediction
Unde rprediction
P erfect 
p red ictio n
 Sto c h a s tic  mod e l-F e b
Pre d ict e d  max  60 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Ob
s
e
rve
d
 max
 60
-min rain
fa
ll
             d
e
p
th
 (in
) 
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Over prediction
Unde rprediction
P erfect pred ictio n
 AN N mo d e l-Ma r
Pre d ict e d  max  60 -min rain fa ll de p th  (in)
0 1 2 3
Ob
s
e
rve
d
 max
 60
-min rain
fa
ll
             d
e
p
th
 (in
) 
0
1
2
3
Over prediction
Unde rprediction
P erfect 
p red ictio n
 Sto c h a s tic  mod e l-Ma r
Pre d ict e d  max  60 -min rain fa ll de p th  (in)
0 1 2 3
Ob
s
e
rve
d
 max
 60
-min rain
fa
ll
             d
e
p
th
 (in
) 
0
1
2
3
Over prediction
Unde rprediction
P erfect pred ictio n
199 
 
 
 AN N mo d e l-Ap r
Pre d ict e d  max  60 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Ob
s
e
rve
d
 max
 60
-min rain
fa
ll
             d
e
p
th
 (in
) 
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Over prediction
Unde rprediction
P erfect 
p red ictio n
Sto c h a s tic  mod e l-Ap r
Pre d ict e d  max  60 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Ob
s
e
rve
d
 max
 60
-min rain
fa
ll
             d
e
p
th
 (in
) 
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Over prediction
Unde rprediction
P erfect pred ictio n
 AN N mo d e l-Ma y
Pre d ict e d  max  60 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Ob
s
e
rve
d
 max
 60
-min rain
fa
ll
             d
e
p
th
 (in
) 
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Over prediction
Unde rprediction
P erfect 
p red ictio n
Sto c h a s tic  mod e l-Ma y
Pre d ict e d  max  60 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Ob
s
e
rve
d
 max
 60
-min rain
fa
ll
             d
e
p
th
 (in
) 
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Over prediction
Unde rprediction
P erfect pred ictio n
AN N mo d e l-J u n
Pre d ict e d  max  60 -min rain fa ll de p th  (in)
0 1 2 3
Ob
s
e
rve
d
 max
 60
-min rain
fa
ll
             d
e
p
th
 (in
) 
0
1
2
3
Over prediction
Unde rprediction
P erfect pred ictio n
 Sto c h a s tic  mod e l-J u n
Pre d ict e d  max  60 -min rain fa ll de p th  (in)
0 1 2 3
Ob
s
e
rve
d
 max
 60
-min rain
fa
ll
             d
e
p
th
 (in
) 
0
1
2
3
Over prediction
Unde rprediction
P erfect pred ictio n
200 
 
  
 AN N mo d e l-J u l
Pre d ict e d  max  60 -min rain fa ll de p th  (in)
0 1 2 3 4
Ob
s
e
rve
d
 max
 60
-min rain
fa
ll
             d
e
p
th
 (in
) 
0
1
2
3
4
Over prediction
Unde rprediction
P erfect 
p red ictio n
 Sto c h a s tic  mod e l-J u l
Pre d ict e d  max  60 -min rain fa ll de p th  (in)
0 1 2 3 4
Ob
s
e
rve
d
 max
 60
-min rain
fa
ll
             d
e
p
th
 (in
) 
0
1
2
3
4
Over prediction
Unde rprediction
P erfect pred ictio n
 AN N mo d e l-Au g
Pre d ict e d  max  60 -min rain fa ll de p th  (in)
0 1 2 3
Ob
s
e
rve
d
 max
 60
-min rain
fa
ll
             d
e
p
th
 (in
) 
0
1
2
3
Over prediction
Unde rprediction
P erfect 
p red ictio n
Sto c h a s tic  mod e l-Au g
Pre d ict e d  max  60 -min rain fa ll de p th  (in)
0 1 2 3
Ob
s
e
rve
d
 max
 60
-min rain
fa
ll
             d
e
p
th
 (in
) 
0
1
2
3
Over prediction
Unde rprediction
P erfect pred ictio n
 AN N mo d e l-Se p
Pre d ict e d  max  60 -min rain fa ll de p th  (in)
0 1 2 3 4 5 6
Ob
s
e
rve
d
 max
 60
-min rain
fa
ll
             d
e
p
th
 (in
) 
0
1
2
3
4
5
6
Over prediction
Unde rprediction
P erfect 
p red ictio n
 Sto c h a s tic  mod e l-Se p
Pre d ict e d  max  60 -min rain fa ll de p th  (in)
0 1 2 3 4 5 6
Ob
s
e
rve
d
 max
 60
-min rain
fa
ll
             d
e
p
th
 (in
) 
0
1
2
3
4
5
6
Over prediction
Unde rprediction
P erfect 
p red ictio n
201 
 
 
 
 
 AN N mo d e l-Oc t
Pre d ict e d  max  60 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Ob
s
e
rve
d
 max
 60
-min rain
fa
ll
             d
e
p
th
 (in
) 
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Over prediction
Unde rprediction
P erfect
 p red ictio n
Sto c h a s tic  mod e l-Oc t
Pre d ict e d  max  60 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Ob
s
e
rve
d
 max
 60
-min rain
fa
ll
             d
e
p
th
 (in
) 
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Over prediction
Unde rprediction
P erfect pred ictio n
 AN N mo d e l-No v
Pre d ict e d  max  60 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5
Ob
s
e
rve
d
 max
 60
-min rain
fa
ll
             d
e
p
th
 (in
) 
0.0
0.5
1.0
1.5
2.0
2.5
Over prediction
Unde rprediction
P erfect 
p red ictio n
 Sto c h a s tic  mod e l-No v
Pre d ict e d  max  60 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5
Ob
s
e
rve
d
 max
 60
-min rain
fa
ll
             d
e
p
th
 (in
) 
0.0
0.5
1.0
1.5
2.0
2.5
Over prediction
Unde rprediction
P erfect pred ictio n
 AN N mo d e l-De c
Pre d ict e d  max  60 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5
Ob
s
e
rve
d
 max
 60
-min rain
fa
ll
             d
e
p
th
 (in
) 
0.0
0.5
1.0
1.5
2.0
2.5
Over prediction
Unde rprediction
P erfect 
p red ictio n
Sto c h a s tic  mod e l-De c
Pre d ict e d  max  60 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5
Ob
s
e
rve
d
 max
 60
-min rain
fa
ll
             d
e
p
th
 (in
) 
0.0
0.5
1.0
1.5
2.0
2.5
Over prediction
Unde rprediction
P erfect pred ictio n
202 
 
C.5. 120-min, Jan-Dec 
 
 AN N mo d e l-J a n
Pre d ict e d  max  12 0 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5
Ob
s
e
rve
d
 max
 12
0
-min rain
fa
ll
             d
e
p
th
 (in
) 
0.0
0.5
1.0
1.5
2.0
2.5
Over prediction
Unde rprediction
P erfect 
p red ictio n
 Sto c h a s tic  mod e l-J a n
Pre d ict e d  max  12 0 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5
Ob
s
e
rve
d
 max
 12
0
-min rain
fa
ll
             d
e
p
th
 (in
)
0.0
0.5
1.0
1.5
2.0
2.5
Over prediction
Unde rprediction
P erfect pred ictio n
 AN N mo d e l-F e b
Pre d ict e d  max  12 0 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Ob
s
e
rve
d
 max
 12
0
-min rain
fa
ll
             d
e
p
th
 (in
)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Over prediction
Unde rprediction
P erfect 
p red ictio n
 Sto c h a s tic  mod e l-F e b
Pre d ict e d  max  12 0 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Ob
s
e
rve
d
 max
 12
0
-min rain
fa
ll
             d
e
p
th
 (in
)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Over prediction
Unde rprediction
P erfect pred ictio n
 AN N mo d e l-Ma r
Pre d ict e d  max  12 0 -min rain fa ll de p th  (in)
0 1 2 3
Ob
s
e
rve
d
 max
 12
0
-min rain
fa
ll
             d
e
p
th
 (in
)
0
1
2
3
Over prediction
Unde rprediction
P erfect 
p red ictio n
 Sto c h a s tic  mod e l-Ma r
Pre d ict e d  max  12 0 -min rain fa ll de p th  (in)
0 1 2 3
Ob
s
e
rve
d
 max
 12
0
-min rain
fa
ll
             d
e
p
th
 (in
)
0
1
2
3
Over prediction
Unde rprediction
P erfect pred ictio n
203 
 
 
 AN N mo d e l-Ap r
Pre d ict e d  max  12 0 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Ob
s
e
rve
d
 max
 12
0
-min rain
fa
ll
             d
e
p
th
 (in
)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Over prediction
Unde rprediction
P erfect 
p red ictio n
Sto c h a s tic  mod e l-Ap r
Pre d ict e d  max  12 0 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Ob
s
e
rve
d
 max
 12
0
-min rain
fa
ll
             d
e
p
th
 (in
)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Over prediction
Unde rprediction
P erfect pred ictio n
 AN N mo d e l-Ma y
Pre d ict e d  max  12 0 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Ob
s
e
rve
d
 max
 12
0
-min rain
fa
ll
             d
e
p
th
 (in
)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Over prediction
Unde rprediction
P erfect 
p red ictio n
Sto c h a s tic  mod e l-Ma y
Pre d ict e d  max  12 0 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Ob
s
e
rve
d
 max
 12
0
-min rain
fa
ll
             d
e
p
th
 (in
)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Over prediction
Unde rprediction
P erfect pred ictio n
 AN N mo d e l-J u n
Pre d ict e d  max  12 0 -min rain fa ll de p th  (in)
0 1 2 3
Ob
s
e
rve
d
 max
 12
0
-min rain
fa
ll
             d
e
p
th
 (in
)
0
1
2
3
Over prediction
Unde rprediction
P erfect pred ictio n
 Sto c h a s tic  mod e l-J u n
Pre d ict e d  max  12 0 -min rain fa ll de p th  (in)
0 1 2 3
Ob
s
e
rve
d
 max
 12
0
-min rain
fa
ll
             d
e
p
th
 (in
)
0
1
2
3
Over prediction
Unde rprediction
P erfect pred ictio n
204 
 
 
 AN N mo d e l-J u l
Pre d ict e d  max  12 0 -min rain fa ll de p th  (in)
0 1 2 3 4
Ob
s
e
rve
d
 max
 12
0
-min rain
fa
ll
             d
e
p
th
 (in
)
0
1
2
3
4
Over prediction
Unde rprediction
P erfect 
p red ictio n
Sto c h a s tic  mod e l-J u l
Pre d ict e d  max  12 0 -min rain fa ll de p th  (in)
0 1 2 3 4
Ob
s
e
rve
d
 max
 12
0
-min rain
fa
ll
             d
e
p
th
 (in
)
0
1
2
3
4
Over prediction
Unde rprediction
P erfect pred ictio n
e ) AN N mo d e l
AN N mo d e l-Au g
Pre d ict e d  max  12 0 -min rain fa ll de p th  (in)
0 1 2 3
Ob
s
e
rve
d
 max
 12
0
-min rain
fa
ll
             d
e
p
th
 (in
)
0
1
2
3
Over prediction
Unde rprediction
P erfect 
p red ictio n
Sto c h a s tic  mod e l-Au g
Pre d ict e d  max  12 0 -min rain fa ll de p th  (in)
0 1 2 3
Ob
s
e
rve
d
 max
 12
0
-min rain
fa
ll
             d
e
p
th
 (in
)
0
1
2
3
Over prediction
Unde rprediction
P erfect pred ictio n
 AN N mo d e l-Se p
Pre d ict e d  max  12 0 -min rain fa ll de p th  (in)
0 1 2 3 4 5 6
Ob
s
e
rve
d
 max
 12
0
-min rain
fa
ll
             d
e
p
th
 (in
)
0
1
2
3
4
5
6
Over prediction
Unde rprediction
P erfect 
p red ictio n
 Sto c h a s tic  mod e l-Se p
Pre d ict e d  max  12 0 -min rain fa ll de p th  (in)
0 1 2 3 4 5 6
Ob
s
e
rve
d
 max
 12
0
-min rain
fa
ll
             d
e
p
th
 (in
)
0
1
2
3
4
5
6
Over prediction
Unde rprediction
P erfect 
p red ictio n
205 
 
 
  
 AN N mo d e l-Oc t
Pre d ict e d  max  12 0 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Ob
s
e
rve
d
 max
 12
0
-min rain
fa
ll
             d
e
p
th
 (in
)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Over prediction
Unde rprediction
P erfect
 p red ictio n
Sto c h a s tic  mod e l-Oc t
Pre d ict e d  max  12 0 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Ob
s
e
rve
d
 max
 12
0
-min rain
fa
ll
             d
e
p
th
 (in
)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Over prediction
Unde rprediction
P erfect pred ictio n
 AN N mo d e l-No v
Pre d ict e d  max  12 0 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5
Ob
s
e
rve
d
 max
 12
0
-min rain
fa
ll
             d
e
p
th
 (in
)
0.0
0.5
1.0
1.5
2.0
2.5
Over prediction
Unde rprediction
P erfect 
p red ictio n
Sto c h a s tic  mod e l-No v
Pre d ict e d  max  12 0 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5
Ob
s
e
rve
d
 max
 12
0
-min rain
fa
ll
             d
e
p
th
 (in
)
0.0
0.5
1.0
1.5
2.0
2.5
Over prediction
Unde rprediction
P erfect pred ictio n
AN N mo d e l-De c
Pre d ict e d  max  12 0 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5
Ob
s
e
rve
d
 max
 12
0
-min rain
fa
ll
             d
e
p
th
 (in
)
0.0
0.5
1.0
1.5
2.0
2.5
Over prediction
Unde rprediction
P erfect 
p red ictio n
 Sto c h a s tic  mod e l-De c
Pre d ict e d  max  12 0 -min rain fa ll de p th  (in)
0.0 0.5 1.0 1.5 2.0 2.5
Ob
s
e
rve
d
 max
 12
0
-min rain
fa
ll
             d
e
p
th
 (in
)
0.0
0.5
1.0
1.5
2.0
2.5
Over prediction
Unde rprediction
P erfect pred ictio n
206 
 
Appendix D 
IDF Maps, using ANN model for rainfall disaggregation 
D.1. HRM3-HadCM3 
 
207 
 
 
208 
 
 
209 
 
 
 
210 
 
D.2. HRM3-GFDL 
 
211 
 
 
 
212 
 
 
213 
 
 
 
214 
 
D.3. RCM3-GFDL 
 
215 
 
 
 
216 
 
 
 
217 
 
 
218 
 
D.4. CRCM-CGCM3 
 
219 
 
 
220 
 
 
221 
 
 
222 
 
D.5. CRCM-CCSM 
 
223 
 
 
224 
 
 
225 
 
 
226 
 
Appendix E 
Probability-based IDF curves for Alabama 
E1. Stochastic Method 
1. Athens 
 
 
15-min
Rainfall dep th  (m m )
0 20 40 60 80
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
30-min
Rainfall dep th  (m m )
0 20 40 60 80 100
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
45-min
Rainfall dep th  (m m )
0 20 40 60 80 100 120
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
1-hr
Rainfall dep th  (m m )
0 20 40 60 80 100 120 140
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
2-hr
Rainfall dep th  (m m )
0 20 40 60 80 100 120 140 160
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
3-hr
Rainfall dep th  (m m )
0 20 40 60 80 100 120 140 160 180
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
227 
 
 
 
6-hr
Rainfall dep th  (m m )
0 50 100 150 200 250
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
12-hr
Rainfall dep th  (m m )
0 100 200 300
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
24-hr
Rainfall dep th  (m m )
0 100 200 300 400
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
48-hr
Rainfall dep th  (m m )
0 100 200 300 400
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
228 
 
2. Bridgeport 
 
 
 
 
15-min
Rainfall dep th  (m m )
0 10 20 30 40 50 60
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
30-min
Rainfall dep th  (m m )
0 10 20 30 40 50 60
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
45-min
Rainfall dep th  (m m )
0 20 40 60 80
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
1-hr
Rainfall dep th  (m m )
0 20 40 60 80 100
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
2-hr
Rainfall dep th  (m m )
0 20 40 60 80 100
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
3-hr
Rainfall dep th  (m m )
0 20 40 60 80 100 120
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
229 
 
 
 
6-hr
Rainfall dep th  (m m )
0 50 100 150 200
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
12-hr
Rainfall dep th  (m m )
0 50 100 150 200
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
24-hr
Rainfall dep th  (m m )
0 50 100 150 200 250 300
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
48-hr
Rainfall dep th  (m m )
0 50 100 150 200 250 300
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
230 
 
3. Boaz 
 
 
 
 
15-min
Rainfall dep th  (m m )
0 10 20 30 40 50 60
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
30-min
Rainfall dep th  (m m )
0 20 40 60 80 100
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
45-min
Rainfall dep th  (m m )
0 20 40 60 80 100 120
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
1-hr
Rainfall dep th  (m m )
0 20 40 60 80 100 120 140 160
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
2-hr
Rainfall dep th  (m m )
0 20 40 60 80 100 120 140 160 180
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
3-hr
Rainfall dep th  (m m )
0 50 100 150 200
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
231 
 
 
 
 
6-hr
Rainfall dep th  (m m )
0 100 200 300
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
12-hr
Rainfall dep th  (m m )
0 100 200 300 400
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
24-hr
Rainfall dep th  (m m )
0 100 200 300 400 500
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
48-hr
Rainfall dep th  (m m )
0 100 200 300 400 500 600
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
232 
 
4. Hanceville 
 
 
 
15-min
Rainfall dep th  (m m )
0 20 40 60 80 100
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
30-min
Rainfall dep th  (m m )
0 20 40 60 80 100 120
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
45-min
Rainfall dep th  (m m )
0 20 40 60 80 100 120 140 160
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
1-hr
Rainfall dep th  (m m )
0 50 100 150 200
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
2-hr
Rainfall dep th  (m m )
0 50 100 150 200
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
3-hr
Rainfall dep th  (m m )
0 50 100 150 200
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
233 
 
 
 
 
 
6-hr
Rainfall dep th  (m m )
0 50 100 150 200 250 300
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
12-hr
Rainfall dep th  (m m )
0 100 200 300 400
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
12-hr
Rainfall dep th  (m m )
0 100 200 300 400
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
48-hr
Rainfall dep th  (m m )
0 100 200 300 400 500
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
234 
 
5. Addison 
 
15-min
Rainfall dep th  (m m )
0 10 20 30 40 50 60
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
30-min
Rainfall dep th  (m m )
0 20 40 60 80
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
45-min
Rainfall dep th  (m m )
0 20 40 60 80 100
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
1-hr
Rainfall dep th  (m m )
0 20 40 60 80 100
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
2-hr
Rainfall dep th  (m m )
0 20 40 60 80 100 120 140
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
3-hr
Rainfall dep th  (m m )
0 20 40 60 80 100 120 140
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
235 
 
 
 
6-hr
Rainfall dep th  (m m )
0 50 100 150 200
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
12-hr
Rainfall dep th  (m m )
0 50 100 150 200 250 300
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
24-hr
Rainfall dep th  (m m )
0 100 200 300 400
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
48-hr
Rainfall dep th  (m m )
0 100 200 300 400
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
236 
 
6. Haleyville 
 
 
15-min
Rainfall dep th  (m m )
0 10 20 30 40 50 60
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
30-min
Rainfall dep th  (m m )
0 20 40 60 80 100 120
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
45-min
Rainfall dep th  (m m )
0 20 40 60 80 100 120
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
1-hr
Rainfall dep th  (m m )
0 20 40 60 80 100 120
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
2-hr
Rainfall dep th  (m m )
0 20 40 60 80 100 120 140 160
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
3-hr
Rainfall dep th  (m m )
0 50 100 150 200
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
237 
 
 
6-hr
Rainfall dep th  (m m )
0 50 100 150 200
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
12-hr
Rainfall dep th  (m m )
0 100 200 300
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
24-hr
Rainfall dep th  (m m )
0 100 200 300 400
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
48-hr
Rainfall dep th  (m m )
0 100 200 300 400 500
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
238 
 
7. Hamilton 
 
15-min
Rainfall dep th  (m m )
0 10 20 30 40 50 60
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
30-min
Rainfall dep th  (m m )
0 10 20 30 40 50 60
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
45-min
Rainfall dep th  (m m )
0 20 40 60 80 100
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
1-hr
Rainfall dep th  (m m )
0 20 40 60 80 100
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
2-hr
Rainfall dep th  (m m )
0 20 40 60 80 100 120
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
3-hr
Rainfall dep th  (m m )
0 20 40 60 80 100 120 140
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
239 
 
 
 
6-hr
Rainfall dep th  (m m )
0 50 100 150 200
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
12-hr
Rainfall dep th  (m m )
0 100 200 300
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
24-hr
Rainfall dep th  (m m )
0 100 200 300 400
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
48-hr
Rainfall dep th  (m m )
0 100 200 300 400 500
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
240 
 
8. Vernon 
 
15-min
Rainfall dep th  (m m )
0 20 40 60 80
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
30-min
Rainfall dep th  (m m )
0 20 40 60 80 100 120
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
45-min
Rainfall dep th  (m m )
0 20 40 60 80 100 120 140 160
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
1-hr
Rainfall dep th  (m m )
0 50 100 150 200
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
2-hr
Rainfall dep th  (m m )
0 50 100 150 200
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
3-hr
Rainfall dep th  (m m )
0 50 100 150 200 250
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
241 
 
 
6-hr
Rainfall dep th  (m m )
0 100 200 300 400
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
12-hr
Rainfall dep th  (m m )
0 100 200 300 400 500
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
24-hr
Rainfall dep th  (m m )
0 100 200 300 400 500 600
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
48-hr
Rainfall dep th  (m m )
0 100 200 300 400 500 600
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
242 
 
9. Berry 
 
15-min
Rainfall dep th  (m m )
0 20 40 60 80
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
30-min
Rainfall dep th  (m m )
0 20 40 60 80 100 120
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
45-min
Rainfall dep th  (m m )
0 20 40 60 80 100 120 140 160
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
1-hr
Rainfall dep th  (m m )
0 50 100 150 200
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
2-hr
Rainfall dep th  (m m )
0 50 100 150 200
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
3-hr
Rainfall dep th  (m m )
0 50 100 150 200 250
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
243 
 
 
 
6-hr
Rainfall dep th  (m m )
0 100 200 300 400
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
12-hr
Rainfall dep th  (m m )
0 100 200 300 400 500
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
24-hr
Rainfall dep th  (m m )
0 100 200 300 400 500 600
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
48-hr
Rainfall dep th  (m m )
0 100 200 300 400 500 600
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
244 
 
 
10. Warrior 
 
 
15-min
Rainfall dep th  (m m )
0 20 40 60 80 100
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
30-min
Rainfall dep th  (m m )
0 20 40 60 80 100 120
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
45-min
Rainfall dep th  (m m )
0 20 40 60 80 100 120 140 160
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
1-hr
Rainfall dep th  (m m )
0 50 100 150 200
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
2-hr
Rainfall dep th  (m m )
0 50 100 150 200
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
3-hr
Rainfall dep th  (m m )
0 50 100 150 200
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
245 
 
 
6-hr
Rainfal l dept h (m m)
0 50 100 150 200 250 300
Pr
obability
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2 yr  
5 -yr  
1 0 -yr  
2 5 -yr  
5 0 -yr  
1 0 0 -yr  
12-hr
Rainfal l dept h (m m)
0 100 200 300 400
Pr
obability
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2 yr  
5 -yr  
1 0 -yr  
2 5 -yr  
5 0 -yr  
1 0 0 -yr  
24-hr
Rainfal l dept h (m m)
0 100 200 300 400 500
Pr
obability
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2 yr  
5 -yr  
1 0 -yr  
2 5 -yr  
5 0 -yr  
1 0 0 -yr  
48-hr
Rainfal l dept h (m m)
0 100 200 300 400 500
Pr
obability
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2 yr  
5 -yr  
1 0 -yr  
2 5 -yr  
5 0 -yr  
1 0 0 -yr  
246 
 
 
11. Jacksonville 
 
15-min
Rainfall dep th  (m m )
0 10 20 30 40 50 60
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
30-min
Rainfall dep th  (m m )
0 20 40 60 80 100
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
45-min
Rainfall dep th  (m m )
0 20 40 60 80 100 120
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
1-hr
Rainfall dep th  (m m )
0 20 40 60 80 100 120 140 160
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
2-hr
Rainfall dep th  (m m )
0 20 40 60 80 100 120 140 160 180
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
3-hr
Rainfall dep th  (m m )
0 50 100 150 200
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
247 
 
 
6-hr
Rainfall dep th  (m m )
0 100 200 300
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
12-hr
Rainfall dep th  (m m )
0 100 200 300 400
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
24-hr
Rainfall dep th  (m m )
0 100 200 300 400
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
48-hr
Rainfall dep th  (m m )
0 100 200 300 400
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
248 
 
12. Birmingham 
 
 
15-min
Rainfall dep th  (m m )
0 20 40 60 80
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
30-min
Rainfall dep th  (m m )
0 20 40 60 80 100 120
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
45-min
Rainfall dep th  (m m )
0 20 40 60 80 100 120 140 160
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
1-hr
Rainfall dep th  (m m )
0 50 100 150 200
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
2-hr
Rainfall dep th  (m m )
0 50 100 150 200
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
3-hr
Rainfall dep th  (m m )
0 50 100 150 200
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
249 
 
 
6-hr
Rainfall dep th  (m m )
0 100 200 300
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
12-hr
Rainfall dep th  (m m )
0 100 200 300 400
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
24-hr
Rainfall dep th  (m m )
0 100 200 300 400 500
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
48-hr
Rainfall dep th  (m m )
0 100 200 300 400 500
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
250 
 
13. Ashland 
 
15-min
Rainfall dep th  (m m )
0 10 20 30 40 50 60
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
30-min
Rainfall dep th  (m m )
0 20 40 60 80 100
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
45-min
Rainfall dep th  (m m )
0 20 40 60 80 100 120
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
1-hr
Rainfall dep th  (m m )
0 20 40 60 80 100 120
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
2-hr
Rainfall dep th  (m m )
0 20 40 60 80 100 120 140 160 180
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
3-hr
Rainfall dep th  (m m )
0 50 100 150 200
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
251 
 
 
6-hr
Rainfall dep th  (m m )
0 100 200 300
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
12-hr
Rainfall dep th  (m m )
0 100 200 300 400
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
24-hr
Rainfall dep th  (m m )
0 100 200 300 400 500
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
48-hr
Rainfall dep th  (m m )
0 100 200 300 400 500
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
252 
 
14. Tuscaloosa 
 
15-min
Rainfall dep th  (m m )
0 20 40 60 80
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
30-min
Rainfall dep th  (m m )
0 20 40 60 80 100
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
45-min
Rainfall dep th  (m m )
0 20 40 60 80 100 120
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
1-hr
Rainfall dep th  (m m )
0 20 40 60 80 100 120 140 160
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
2-hr
Rainfall dep th  (m m )
0 50 100 150 200
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
3-hr
Rainfall dep th  (m m )
0 50 100 150 200
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
253 
 
 
 
6-hr
Rainfall dep th  (m m )
0 100 200 300
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
12-hr
Rainfall dep th  (m m )
0 100 200 300 400 500
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
24-hr
Rainfall dep th  (m m )
0 100 200 300 400 500
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
48-hr
Rainfall dep th  (m m )
0 100 200 300 400 500 600
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
254 
 
15. Thorsby 
 
15-min
Rainfall dep th  (m m )
0 20 40 60 80
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
30-min
Rainfall dep th  (m m )
0 20 40 60 80 100 120
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
45-min
Rainfall dep th  (m m )
0 20 40 60 80 100 120 140 160
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
1-hr
Rainfall dep th  (m m )
0 50 100 150 200
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
2-hr
Rainfall dep th  (m m )
0 50 100 150 200
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
3-hr
Rainfall dep th  (m m )
0 50 100 150 200
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
255 
 
 
 
6-hr
Rainfall dep th  (m m )
0 100 200 300
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
12-hr
Rainfall dep th  (m m )
0 100 200 300 400
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
24-hr
Rainfall dep th  (m m )
0 100 200 300 400 500
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
48-hr
Rainfall dep th  (m m )
0 100 200 300 400 500
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
256 
 
16. Dadeville 
 
15-min
Rainfall dep th  (m m )
0 20 40 60 80
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
30-min
Rainfall dep th  (m m )
0 20 40 60 80 100
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
45-min
Rainfall dep th  (m m )
0 20 40 60 80 100 120
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
1-hr
Rainfall dep th  (m m )
0 20 40 60 80 100 120
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
2-hr
Rainfall dep th  (m m )
0 20 40 60 80 100 120 140 160 180
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
3-hr
Rainfall dep th  (m m )
0 50 100 150 200
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
257 
 
 
 
6-hr
Rainfall dep th  (m m )
0 100 200 300
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
12-hr
Rainfall dep th  (m m )
0 200 400 600
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
24-hr
Rainfall dep th  (m m )
0 200 400 600
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
48-hr
Rainfall dep th  (m m )
0 200 400 600 800
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
258 
 
 
17. Marion 
 
15-min
Rainfall dep th  (m m )
0 20 40 60 80
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
30-min
Rainfall dep th  (m m )
0 20 40 60 80 100 120
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
45-min
Rainfall dep th  (m m )
0 20 40 60 80 100 120 140 160
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
1-hr
Rainfall dep th  (m m )
0 50 100 150 200
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
2-hr
Rainfall dep th  (m m )
0 50 100 150 200 250
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
3-hr
Rainfall dep th  (m m )
0 50 100 150 200 250 300
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
259 
 
 
6-hr
Rainfall dep th  (m m )
0 100 200 300 400
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
12-hr
Rainfall dep th  (m m )
0 100 200 300 400
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
24-hr
Rainfall dep th  (m m )
0 100 200 300 400 500
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
48-hr
Rainfall dep th  (m m )
0 100 200 300 400 500
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
260 
 
18. Warrior L&D 
 
15-min
Rainfall dep th  (m m )
0 20 40 60 80
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
30-min
Rainfall dep th  (m m )
0 20 40 60 80 100 120
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
45-min
Rainfall dep th  (m m )
0 20 40 60 80 100 120 140 160
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
1-hr
Rainfall dep th  (m m )
0 20 40 60 80 100 120 140 160
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
2-hr
Rainfall dep th  (m m )
0 50 100 150 200
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
3-hr
Rainfall dep th  (m m )
0 50 100 150 200 250
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
261 
 
 
6-hr
Rainfall dep th  (m m )
0 100 200 300
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
12-hr
Rainfall dep th  (m m )
0 100 200 300 400 500
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
24-hr
Rainfall dep th  (m m )
0 100 200 300 400 500
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
48-hr
Rainfall dep th  (m m )
0 100 200 300 400 500 600
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
262 
 
19. Alberta 
 
15-min
Rainfall dep th  (m m )
0 20 40 60 80
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
30-min
Rainfall dep th  (m m )
0 20 40 60 80 100 120
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
45-min
Rainfall dep th  (m m )
0 20 40 60 80 100 120 140 160
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
1-hr
Rainfall dep th  (m m )
0 50 100 150 200
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
2-hr
Rainfall dep th  (m m )
0 50 100 150 200 250
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
3-hr
Rainfall dep th  (m m )
0 50 100 150 200 250 300
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
263 
 
 
6-hr
Rainfall dep th  (m m )
0 100 200 300 400
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
12-hr
Rainfall dep th  (m m )
0 100 200 300 400 500
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
24-hr
Rainfall dep th  (m m )
0 200 400 600
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
48-hr
Rainfall dep th  (m m )
0 200 400 600 800
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
264 
 
20. Montgomery 
 
15-min
Rainfall dep th  (m m )
0 20 40 60 80
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
30-min
Rainfall dep th  (m m )
0 20 40 60 80 100
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
45-min
Rainfall dep th  (m m )
0 20 40 60 80 100 120
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
1-hr
Rainfall dep th  (m m )
0 20 40 60 80 100 120
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
2-hr
Rainfall dep th  (m m )
0 20 40 60 80 100 120 140 160 180
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
3-hr
Rainfall dep th  (m m )
0 50 100 150 200
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
265 
 
 
6-hr
Rainfall dep th  (m m )
0 100 200 300
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
12-hr
Rainfall dep th  (m m )
0 200 400 600
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
24-hr
Rainfall dep th  (m m )
0 200 400 600 800 1000 1200
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
48-hr
Rainfall dep th  (m m )
0 200 400 600 800 1000 1200
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
266 
 
21. Midway 
 
15-min
Rainfall dep th  (m m )
0 20 40 60 80
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
30-min
Rainfall dep th  (m m )
0 20 40 60 80 100
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
45-min
Rainfall dep th  (m m )
0 20 40 60 80 100 120
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
1-hr
Rainfall dep th  (m m )
0 20 40 60 80 100 120 140 160
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
2-hr
Rainfall dep th  (m m )
0 50 100 150 200 250
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
3-hr
Rainfall dep th  (m m )
0 50 100 150 200 250 300
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
267 
 
 
6-hr
Rainfall dep th  (m m )
0 100 200 300 400
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
12-hr
Rainfall dep th  (m m )
0 100 200 300 400
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
24-hr
Rainfall dep th  (m m )
0 100 200 300 400 500
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
48-hr
Rainfall dep th  (m m )
0 100 200 300 400 500 600
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
268 
 
22. Troy 
 
15-min
Rainfall dep th  (m m )
0 20 40 60 80
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
30-min
Rainfall dep th  (m m )
0 20 40 60 80 100 120
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
45-min
Rainfall dep th  (m m )
0 20 40 60 80 100 120 140
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
1-hr
Rainfall dep th  (m m )
0 20 40 60 80 100 120 140 160
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
2-hr
Rainfall dep th  (m m )
0 50 100 150 200 250
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
3-hr
Rainfall dep th  (m m )
0 50 100 150 200 250 300
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
269 
 
 
6-hr
Rainfall dep th  (m m )
0 100 200 300 400
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
12-hr
Rainfall dep th  (m m )
0 100 200 300 400 500
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
24-hr
Rainfall dep th  (m m )
0 150 300 450 600 750
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
48-hr
Rainfall dep th  (m m )
0 200 400 600 800
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
270 
 
23. Greenville 
 
15-min
Rainfall dep th  (m m )
0 20 40 60 80
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
30-min
Rainfall dep th  (m m )
0 20 40 60 80 100
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
45-min
Rainfall dep th  (m m )
0 20 40 60 80 100 120 140
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
1-hr
Rainfall dep th  (m m )
0 20 40 60 80 100 120 140 160
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
2-hr
Rainfall dep th  (m m )
0 50 100 150 200 250
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
3-hr
Rainfall dep th  (m m )
0 50 100 150 200 250 300
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
271 
 
 
6-hr
Rainfall dep th  (m m )
0 100 200 300 400
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
12-hr
Rainfall dep th  (m m )
0 100 200 300 400 500
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
24-hr
Rainfall dep th  (m m )
0 150 300 450 600 750
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
48-hr
Rainfall dep th  (m m )
0 200 400 600 800
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
272 
 
24. Peterman 
 
15-min
Rainfall dep th  (m m )
0 20 40 60 80
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
30-min
Rainfall dep th  (m m )
0 20 40 60 80 100 120 140
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
45-min
Rainfall dep th  (m m )
0 20 40 60 80 100 120 140
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
1-hr
Rainfall dep th  (m m )
0 20 40 60 80 100 120 140 160
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
2-hr
Rainfall dep th  (m m )
0 50 100 150 200 250
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
3-hr
Rainfall dep th  (m m )
0 50 100 150 200 250 300
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
273 
 
 
6-hr
Rainfall dep th  (m m )
0 100 200 300 400
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
12-hr
Rainfall dep th  (m m )
0 100 200 300 400 500
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
24-hr
Rainfall dep th  (m m )
0 150 300 450 600 750
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
48-hr
Rainfall dep th  (m m )
0 200 400 600 800
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
274 
 
 
25. Abbeville 
 
15-min
Rainfall dep th  (m m )
0 20 40 60 80
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
30-min
Rainfall dep th  (m m )
0 20 40 60 80 100
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
45-min
Rainfall dep th  (m m )
0 20 40 60 80 100 120 140
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
1-hr
Rainfall dep th  (m m )
0 50 100 150 200
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
2-hr
Rainfall dep th  (m m )
0 50 100 150 200 250
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
3-hr
Rainfall dep th  (m m )
0 50 100 150 200 250 300
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
275 
 
 
6-hr
Rainfall dep th  (m m )
0 100 200 300 400
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
12-hr
Rainfall dep th  (m m )
0 100 200 300 400 500 600
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
24-hr
Rainfall dep th  (m m )
0 200 400 600
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
48-hr
Rainfall dep th  (m m )
0 200 400 600 800 1000 1200
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
276 
 
26. Enterprise 
 
15-min
Rainfall dep th  (m m )
0 20 40 60 80
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
30-min
Rainfall dep th  (m m )
0 20 40 60 80 100 120
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
45-min
Rainfall dep th  (m m )
0 20 40 60 80 100 120 140
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
1-hr
Rainfall dep th  (m m )
0 20 40 60 80 100 120 140 160
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
2-hr
Rainfall dep th  (m m )
0 50 100 150 200
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
3-hr
Rainfall dep th  (m m )
0 50 100 150 200
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
277 
 
 
6-hr
Rainfall dep th  (m m )
0 50 100 150 200 250 300
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
12-hr
Rainfall dep th  (m m )
0 100 200 300 400
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
24-hr
Rainfall dep th  (m m )
0 150 300 450 600
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
48-hr
Rainfall dep th  (m m )
0 200 400 600 800
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
278 
 
 
27. Dothan 
 
15-min
Rainfall dep th  (m m )
0 10 20 30 40 50 60
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
30-min
Rainfall dep th  (m m )
0 20 40 60 80 100
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
45-min
Rainfall dep th  (m m )
0 20 40 60 80 100 120 140
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
1-hr
Rainfall dep th  (m m )
0 50 100 150 200
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
2-hr
Rainfall dep th  (m m )
0 50 100 150 200 250
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
3-hr
Rainfall dep th  (m m )
0 50 100 150 200 250 300
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
279 
 
 
6-hr
Rainfall dep th  (m m )
0 100 200 300 400
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
12-hr
Rainfall dep th  (m m )
0 100 200 300 400 500 600
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
24-hr
Rainfall dep th  (m m )
0 150 300 450 600 750
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
48-hr
Rainfall dep th  (m m )
0 200 400 600 800
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
280 
 
28. Atmore 1 
 
15-min
Rainfall dep th  (m m )
0 20 40 60 80
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
30-min
Rainfall dep th  (m m )
0 20 40 60 80 100 120 140
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
45-min
Rainfall dep th  (m m )
0 20 40 60 80 100 120 140
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
1-hr
Rainfall dep th  (m m )
0 50 100 150 200
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
2-hr
Rainfall dep th  (m m )
0 50 100 150 200 250
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
3-hr
Rainfall dep th  (m m )
0 50 100 150 200 250 300
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
281 
 
 
6-hr
Rainfall dep th  (m m )
0 100 200 300 400
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
12-hr
Rainfall dep th  (m m )
0 100 200 300 400
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
24-hr
Rainfall dep th  (m m )
0 150 300 450 600
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
48-hr
Rainfall dep th  (m m )
0 200 400 600 800
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
282 
 
29. Atmore 2 
 
15-min
Rainfall dep th  (m m )
0 20 40 60 80
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
30-min
Rainfall dep th  (m m )
0 20 40 60 80 100 120 140
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
45-min
Rainfall dep th  (m m )
0 20 40 60 80 100 120 140
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
1-hr
Rainfall dep th  (m m )
0 50 100 150 200
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
2-hr
Rainfall dep th  (m m )
0 50 100 150 200 250
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
3-hr
Rainfall dep th  (m m )
0 50 100 150 200 250 300
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
283 
 
 
6-hr
Rainfall dep th  (m m )
0 100 200 300 400
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
12-hr
Rainfall dep th  (m m )
0 100 200 300 400 500
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
24-hr
Rainfall dep th  (m m )
0 150 300 450 600
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
48-hr
Rainfall dep th  (m m )
0 200 400 600 800
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
284 
 
30. River Falls 
 
15-min
Rainfall dep th  (m m )
0 20 40 60 80
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
30-min
Rainfall dep th  (m m )
0 20 40 60 80 100
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
45-min
Rainfall dep th  (m m )
0 20 40 60 80 100 120 140
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
1-hr
Rainfall dep th  (m m )
0 20 40 60 80 100 120 140 160
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
2-hr
Rainfall dep th  (m m )
0 50 100 150 200 250
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
3-hr
Rainfall dep th  (m m )
0 50 100 150 200 250 300
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
285 
 
 
6-hr
Rainfall dep th  (m m )
0 100 200 300 400
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
12-hr
Rainfall dep th  (m m )
0 100 200 300 400 500
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
24-hr
Rainfall dep th  (m m )
0 150 300 450 600 750
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
48-hr
Rainfall dep th  (m m )
0 200 400 600 800
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
286 
 
31. Andalusia 
 
15-min
Rainfall dep th  (m m )
0 20 40 60 80
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
30-min
Rainfall dep th  (m m )
0 20 40 60 80 100
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
45-min
Rainfall dep th  (m m )
0 20 40 60 80 100 120 140
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
1-hr
Rainfall dep th  (m m )
0 20 40 60 80 100 120 140 160
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
2-hr
Rainfall dep th  (m m )
0 50 100 150 200 250
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
3-hr
Rainfall dep th  (m m )
0 50 100 150 200 250 300
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
287 
 
 
6-hr
Rainfall dep th  (m m )
0 100 200 300 400
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
12-hr
Rainfall dep th  (m m )
0 100 200 300 400
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
24-hr
Rainfall dep th  (m m )
0 150 300 450 600
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
48-hr
Rainfall dep th  (m m )
0 100 200 300 400 500 600
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
288 
 
32. Thomasville 
 
15-min
Rainfall dep th  (m m )
0 20 40 60 80
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
30-min
Rainfall dep th  (m m )
0 20 40 60 80 100 120 140
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
45-min
Rainfall dep th  (m m )
0 20 40 60 80 100 120 140
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
1-hr
Rainfall dep th  (m m )
0 50 100 150 200
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
2-hr
Rainfall dep th  (m m )
0 50 100 150 200 250
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
3-hr
Rainfall dep th  (m m )
0 50 100 150 200 250 300
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
289 
 
 
6-hr
Rainfall dep th  (m m )
0 100 200 300 400
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
12-hr
Rainfall dep th  (m m )
0 100 200 300 400 500 600
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
24-hr
Rainfall dep th  (m m )
0 150 300 450 600
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
48-hr
Rainfall dep th  (m m )
0 200 400 600 800
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
290 
 
33. Jackson 
 
15-min
Rainfall dep th  (m m )
0 20 40 60 80
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
30-min
Rainfall dep th  (m m )
0 20 40 60 80 100
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
45-min
Rainfall dep th  (m m )
0 20 40 60 80 100 120
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
1-hr
Rainfall dep th  (m m )
0 20 40 60 80 100 120 140
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
2-hr
Rainfall dep th  (m m )
0 50 100 150 200 250
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
3-hr
Rainfall dep th  (m m )
0 50 100 150 200 250 300
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
291 
 
 
6-hr
Rainfall dep th  (m m )
0 100 200 300 400
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
12-hr
Rainfall dep th  (m m )
0 100 200 300 400 500 600
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
24-hr
Rainfall dep th  (m m )
0 150 300 450 600
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
48-hr
Rainfall dep th  (m m )
0 200 400 600 800
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
292 
 
 
E.2. ANN model 
1. Athens 
 
15-min
Rainfall dep th  (m m )
0 10 20 30 40
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
30-min
Rainfall dep th  (m m )
0 10 20 30 40 50 60
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2- y r
5- y r
10 - y r
25 - y r
50 - y r
10 0- y r
45-min
Rainfall dep th  (m m )
0 20 40 60 80 100
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2- y r
5-y r
10 - y r
25- y r
50 - y r
10 0- y r
1-hr
Rainfall dep th  (m m )
0 20 40 60 80 100
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2- y r
5- y r
10 - y r
25 - y r
50 - y r
10 0- y r
2-hr
Rainfall dep th  (m m )
0 20 40 60 80 100
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2- y r
5- y r
10 - y r
25 - y r
50 - y r
10 0- y r
293 
 
2. Bridgeport 
 
15-min
Rainfall dep th  (m m )
0 10 20 30 40
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
30-min
Rainfall dep th  (m m )
0 10 20 30 40 50
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
45-min
Rainfall dep th  (m m )
0 20 40 60 80
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
1-hr
Rainfall dep th  (m m )
0 20 40 60 80 100
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
2-hr
Rainfall dep th  (m m )
0 20 40 60 80 100
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
294 
 
3. Boaz 
 
15-min
Rainfall dep th  (m m )
0 10 20 30 40
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
30-min
Rainfall dep th  (m m )
0 20 40 60 80
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
45-min
Rainfall dep th  (m m )
0 20 40 60 80
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
1-hr
Rainfall dep th  (m m )
0 20 40 60 80 100
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
2-hr
Rainfall dep th  (m m )
0 20 40 60 80 100 120 140
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
295 
 
4. Hanceville 
 
15-min
Rainfall dep th  (m m )
0 10 20 30 40
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
30-min
Rainfall dep th  (m m )
0 10 20 30 40 50 60
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
45-min
Rainfall dep th  (m m )
0 10 20 30 40 50 60
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
1-hr
Rainfall dep th  (m m )
0 20 40 60 80
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
2-hr
Rainfall dep th  (m m )
0 20 40 60 80 100
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
296 
 
5. Addison 
 
15-min
Rainfall dep th  (m m )
0 10 20 30 40
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
30-min
Rainfall dep th  (m m )
0 10 20 30 40
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
45-min
Rainfall dep th  (m m )
0 10 20 30 40 50 60
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
1-hr
Rainfall dep th  (m m )
0 10 20 30 40 50 60
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
2-hr
Rainfall dep th  (m m )
0 20 40 60 80 100
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
297 
 
6. Haleyville 
 
15-min
Rainfall dep th  (m m )
0 10 20 30 40
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
30-min
Rainfall dep th  (m m )
0 10 20 30 40 50 60
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
45-min
Rainfall dep th  (m m )
0 20 40 60 80
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
1-hr
Rainfall dep th  (m m )
0 20 40 60 80
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
2-hr
Rainfall dep th  (m m )
0 20 40 60 80 100 120
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
298 
 
7. Hamilton 
 
15-min
Rainfall dep th  (m m )
0 10 20 30 40
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
30-min
Rainfall dep th  (m m )
0 10 20 30 40 50 60
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
45-min
Rainfall dep th  (m m )
0 20 40 60 80
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
1-hr
Rainfall dep th  (m m )
0 20 40 60 80
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
1-hr
Rainfall dep th  (m m )
0 20 40 60 80
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
299 
 
8. Vernon 
 
15-min
Rainfall dep th  (m m )
0 10 20 30 40
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
30-min
Rainfall dep th  (m m )
0 10 20 30 40 50 60
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
45-min
Rainfall dep th  (m m )
0 20 40 60 80
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
1-hr
Rainfall dep th  (m m )
0 20 40 60 80 100 120
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
2-hr
Rainfall dep th  (m m )
0 20 40 60 80 100 120 140
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
300 
 
9. Berry 
 
15-min
Rainfall dep th  (m m )
0 10 20 30 40
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
30-min
Rainfall dep th  (m m )
0 20 40 60 80
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
45-min
Rainfall dep th  (m m )
0 20 40 60 80
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
1-hr
Rainfall dep th  (m m )
0 20 40 60 80 100
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
2-hr
Rainfall dep th  (m m )
0 20 40 60 80 100 120 140 160
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
301 
 
 
10. Warrior 
 
15-min
Rainfall dep th  (m m )
0 10 20 30 40
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
30-min
Rainfall dep th  (m m )
0 10 20 30 40 50 60
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
45-min
Rainfall dep th  (m m )
0 20 40 60 80
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
1-hr
Rainfall dep th  (m m )
0 20 40 60 80
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
2-hr
Rainfall dep th  (m m )
0 20 40 60 80 100 120
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
302 
 
11. Jacksonville 
 
15-min
Rainfall dep th  (m m )
0 10 20 30 40
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
30-min
Rainfall dep th  (m m )
0 10 20 30 40 50 60
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
45-min
Rainfall dep th  (m m )
0 20 40 60 80
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
1-hr
Rainfall dep th  (m m )
0 20 40 60 80 100
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
2-hr
Rainfall dep th  (m m )
0 20 40 60 80 100 120
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
303 
 
12. Birmingham 
 
15-min
Rainfall dep th  (m m )
0 10 20 30 40
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
30-min
Rainfall dep th  (m m )
0 10 20 30 40 50 60
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
45-min
Rainfall dep th  (m m )
0 20 40 60 80
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
1-hr
Rainfall dep th  (m m )
0 20 40 60 80 100
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
1-hr
Rainfall dep th  (m m )
0 20 40 60 80 100
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
304 
 
13. Ashland 
 
15-min
Rainfall dep th  (m m )
0 10 20 30 40
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
30-min
Rainfall dep th  (m m )
0 10 20 30 40 50 60
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
45-min
Rainfall dep th  (m m )
0 20 40 60 80
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
1-hr
Rainfall dep th  (m m )
0 20 40 60 80 100
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
2-hr
Rainfall dep th  (m m )
0 20 40 60 80 100 120
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
305 
 
14. Tuscaloosa 
 
15-min
Rainfall dep th  (m m )
0 10 20 30 40
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
30-min
Rainfall dep th  (m m )
0 10 20 30 40 50 60
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
45-min
Rainfall dep th  (m m )
0 20 40 60 80
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
1-hr
Rainfall dep th  (m m )
0 20 40 60 80 100
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
2-hr
Rainfall dep th  (m m )
0 20 40 60 80 100 120
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
306 
 
15. Thorsby 
 
15-min
Rainfall dep th  (m m )
0 10 20 30 40 50 60
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
30-min
Rainfall dep th  (m m )
0 10 20 30 40 50 60
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
45-min
Rainfall dep th  (m m )
0 20 40 60 80
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
1-hr
Rainfall dep th  (m m )
0 10 20 30 40 50
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
2-hr
Rainfall dep th  (m m )
0 10 20 30 40 50 60
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
307 
 
16. Dadeville 
 
15-min
Rainfall dep th  (m m )
0 10 20 30 40 50 60
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
30-min
Rainfall dep th  (m m )
0 20 40 60 80
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
45-min
Rainfall dep th  (m m )
0 20 40 60 80
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
1-hr
Rainfall dep th  (m m )
0 20 40 60 80 100 120
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
2-hr
Rainfall dep th  (m m )
0 20 40 60 80 100 120 140 160
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
308 
 
17. Marion 
 
15-min
Rainfall dep th  (m m )
0 10 20 30 40 50 60
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
30-min
Rainfall dep th  (m m )
0 20 40 60 80
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
45-min
Rainfall dep th  (m m )
0 20 40 60 80
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
1-hr
Rainfall dep th  (m m )
0 20 40 60 80 100
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
2-hr
Rainfall dep th  (m m )
0 20 40 60 80 100 120 140 160
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
309 
 
18. Warrior L&D 
 
15-min
Rainfall dep th  (m m )
0 10 20 30 40
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
30-min
Rainfall dep th  (m m )
0 10 20 30 40 50 60
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
45-min
Rainfall dep th  (m m )
0 10 20 30 40 50 60
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
1-hr
Rainfall dep th  (m m )
0 20 40 60 80 100
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
2-hr
Rainfall dep th  (m m )
0 20 40 60 80 100 120
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
310 
 
19. Alberta 
 
15-min
Rainfall dep th  (m m )
0 10 20 30 40
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
30-min
Rainfall dep th  (m m )
0 20 40 60 80
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
45-min
Rainfall dep th  (m m )
0 20 40 60 80 100
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
1-hr
Rainfall dep th  (m m )
0 20 40 60 80 100 120
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
2-hr
Rainfall dep th  (m m )
0 50 100 150 200 250 300
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
311 
 
20. Montgomery 
 
15-min
Rainfall dep th  (m m )
0 10 20 30 40 50 60
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
30-min
Rainfall dep th  (m m )
0 20 40 60 80 100
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
45-min
Rainfall dep th  (m m )
0 20 40 60 80 100 120
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
1-hr
Rainfall dep th  (m m )
0 20 40 60 80 100 120
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
2-hr
Rainfall dep th  (m m )
0 20 40 60 80 100 120 140 160 180
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
312 
 
 
21. Midway 
 
15-min
Rainfall dep th  (m m )
0 10 20 30 40 50
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
30-min
Rainfall dep th  (m m )
0 20 40 60 80 100
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
45-min
Rainfall dep th  (m m )
0 20 40 60 80 100 120
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
1-hr
Rainfall dep th  (m m )
0 20 40 60 80 100 120 140 160
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
2-hr
Rainfall dep th  (m m )
0 50 100 150 200 250
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
313 
 
22. Troy 
 
15-min
Rainfall dep th  (m m )
0 20 40 60 80
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
30-min
Rainfall dep th  (m m )
0 20 40 60 80 100 120
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
45-min
Rainfall dep th  (m m )
0 20 40 60 80 100 120 140
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
1-hr
Rainfall dep th  (m m )
0 20 40 60 80 100 120 140 160
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
2-hr
Rainfall dep th  (m m )
0 50 100 150 200 250
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
314 
 
23. Greenville 
 
15-min
Rainfall dep th  (m m )
0 20 40 60 80
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
30-min
Rainfall dep th  (m m )
0 20 40 60 80 100
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
45-min
Rainfall dep th  (m m )
0 20 40 60 80 100 120 140
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
1-hr
Rainfall dep th  (m m )
0 20 40 60 80 100 120 140 160
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
2-hr
Rainfall dep th  (m m )
0 50 100 150 200 250
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
315 
 
24. Peterman 
  
15-min
Rainfall dep th  (m m )
0 10 20 30 40 50 60
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
30-min
Rainfall dep th  (m m )
0 20 40 60 80 100
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
45-min
Rainfall dep th  (m m )
0 20 40 60 80 100 120 140
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
1-hr
Rainfall dep th  (m m )
0 20 40 60 80 100 120 140 160
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
2-hr
Rainfall dep th  (m m )
0 50 100 150 200 250
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
316 
 
25. Abbeville 
 
15-min
Rainfall dep th  (m m )
0 10 20 30 40 50
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
30-min
Rainfall dep th  (m m )
0 20 40 60 80 100
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
45-min
Rainfall dep th  (m m )
0 20 40 60 80 100 120 140
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
1-hr
Rainfall dep th  (m m )
0 50 100 150 200
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
2-hr
Rainfall dep th  (m m )
0 50 100 150 200 250
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
317 
 
26. Enterprise 
 
15-min
Rainfall dep th  (m m )
0 20 40 60 80
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
30-min
Rainfall dep th  (m m )
0 20 40 60 80 100 120
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
45-min
Rainfall dep th  (m m )
0 20 40 60 80 100 120 140
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
1-hr
Rainfall dep th  (m m )
0 20 40 60 80 100 120 140 160
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
2-hr
Rainfall dep th  (m m )
0 50 100 150 200
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
318 
 
27. Dothan 
 
15-min
Rainfall dep th  (m m )
0 10 20 30 40 50 60
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
30-min
Rainfall dep th  (m m )
0 20 40 60 80 100
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
45-min
Rainfall dep th  (m m )
0 20 40 60 80 100 120 140
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
1-hr
Rainfall dep th  (m m )
0 50 100 150 200
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
2-hr
Rainfall dep th  (m m )
0 50 100 150 200 250
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
319 
 
28. Atmore 1 
 
  
15-min
Rainfall dep th  (m m )
0 20 40 60 80
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
30-min
Rainfall dep th  (m m )
0 20 40 60 80 100 120 140
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
45-min
Rainfall dep th  (m m )
0 20 40 60 80 100 120 140
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
1-hr
Rainfall dep th  (m m )
0 50 100 150 200
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
2-hr
Rainfall dep th  (m m )
0 50 100 150 200 250
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
320 
 
29. Atmore 2 
 
15-min
Rainfall dep th  (m m )
0 50 100 150 200
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
30-min
Rainfall dep th  (m m )
0 50 100 150 200
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
45-min
Rainfall dep th  (m m )
0 50 100 150 200
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
1-hr
Rainfall dep th  (m m )
0 50 100 150 200
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
2-hr
Rainfall dep th  (m m )
0 50 100 150 200 250
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
321 
 
30. River Falls 
 
15-min
Rainfall dep th  (m m )
0 10 20 30 40
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
30-min
Rainfall dep th  (m m )
0 10 20 30 40 50 60
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
45-min
Rainfall dep th  (m m )
0 20 40 60 80
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
1-hr
Rainfall dep th  (m m )
0 20 40 60 80 100 120
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
2-hr
Rainfall dep th  (m m )
0 50 100 150 200 250
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
322 
 
31. Andalusia 
 
15-min
Rainfall dep th  (m m )
0 10 20 30 40
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
30-min
Rainfall dep th  (m m )
0 10 20 30 40 50 60
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
45-min
Rainfall dep th  (m m )
0 20 40 60 80
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
1-hr
Rainfall dep th  (m m )
0 20 40 60 80
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
2-hr
Rainfall dep th  (m m )
0 20 40 60 80 100 120 140
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
323 
 
32. Thomasville 
 
15-min
Rainfall dep th  (m m )
0 10 20 30 40 50 60
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
30-min
Rainfall dep th  (m m )
0 20 40 60 80
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
45-min
Rainfall dep th  (m m )
0 20 40 60 80 100
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
1-hr
Rainfall dep th  (m m )
0 20 40 60 80 100 120
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
2-hr
Rainfall dep th  (m m )
0 20 40 60 80 100 120 140
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
324 
 
33. Jackson 
 
15-min
Rainfall dep th  (m m )
0 20 40 60 80
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
30-min
Rainfall dep th  (m m )
0 20 40 60 80 100
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
45-min
Rainfall dep th  (m m )
0 20 40 60 80 100 120
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
1-hr
Rainfall dep th  (m m )
0 20 40 60 80 100
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
2-hr
Rainfall dep th  (m m )
0 20 40 60 80 100 120 140
Probab
ili
ty
0. 0
0. 2
0. 4
0. 6
0. 8
1. 0
2-y r  
5-y r  
10 -yr  
25 -yr  
50 -yr  
10 0-y r  
325 
 
Appendix F 
IDF curves for Alabama 
F.1. Stochastic Method 
 
1 -A th ens 
Duration  (h r)
0. 1 1 10 100
Rainfall inten
s
ity (m
m
/h
r)
1
10
100
1000
2-y r
5-y r
10- y r
25- y r
50- y r
100y r
2 -Bridgepo rt 
Duration  (h r)
0. 1 1 10 100
Rainfall inten
s
ity (m
m
/h
r)
1
10
100
1000
2-y r
5-y r
10- y r
25- y r
50- y r
100y r
3 -Bo a z
Duration  (h r)
0. 1 1 10 100
Rainfall inten
s
ity (m
m
/h
r)
1
10
100
1000
2-y r
5-y r
10- y r
25- y r
50- y r
100y r
4 -H a nceville 
Duration  (h r)
0. 1 1 10 100
Rainfall inten
s
ity (m
m
/h
r)
1
10
100
1000
2-y r
5-y r
10- y r
25- y r
50- y r
100y r
5 -A dd ison  
Duration  (h r)
0. 1 1 10 100
Rainfall inten
s
ity (m
m
/h
r)
1
10
100
1000
2-y r
5-y r
10- y r
25- y r
50- y r
100y r
6 -H a leyv ill e 
Duration  (h r)
0. 1 1 10 100
Rainfall inten
s
ity (m
m
/h
r)
1
10
100
1000
2-y r
5-y r
10- y r
25- y r
50- y r
100y r
326 
 
 
7 -H a milto n 
Duration  (h r)
0. 1 1 10 100
Rainfall inten
s
ity (m
m
/h
r)
1
10
100
1000
2-y r
5-y r
10- y r
25- y r
50- y r
100y r
8 -V er no n
Duration  (h r)
0. 1 1 10 100
Rainfall inten
s
ity (m
m
/h
r)
1
10
100
1000
2-y r
5-y r
10- y r
25- y r
50- y r
100y r
9 -Ber ry
Duration  (h r)
0. 1 1 10 100
Rainfall inten
s
ity (m
m
/h
r)
1
10
100
1000
2-y r
5-y r
10- y r
25- y r
50- y r
100y r
1 0 -Wa rr ior
Duration  (h r)
0. 1 1 10 100
Rainfall inten
s
ity (m
m
/h
r)
1
10
100
1000
2-y r
5-y r
10- y r
25- y r
50- y r
100y r
1 1 -J a ckso nv ill e
Duration  (h r)
0. 1 1 10 100
Rainfall inten
s
ity (m
m
/h
r)
1
10
100
2-y r
5-y r
10- y r
25- y r
50- y r
100y r
1 2 -Birming ha m
Duration  (h r)
0. 1 1 10 100
Rainfall inten
s
ity (m
m
/h
r)
1
10
100
1000
2-y r
5-y r
10- y r
25- y r
50- y r
100y r
327 
 
 
1 3 -A shla nd
Duration  (h r)
0. 1 1 10 100
Rainfall inten
s
ity (m
m
/h
r)
1
10
100
1000
2-y r
5-y r
10- y r
25- y r
50- y r
100y r
1 4 -Tusca loo sa
Duration  (h r)
0. 1 1 10 100
Rainfall inten
s
ity (m
m
/h
r)
1
10
100
1000
2-y r
5-y r
10- y r
25- y r
50- y r
100y r
1 5 -Tho rsby
Duration  (h r)
0. 1 1 10 100
Rainfall inten
s
ity (m
m
/h
r)
1
10
100
1000
2-y r
5-y r
10- y r
25- y r
50- y r
100y r
1 6 -D a dev ill e
Duration  (h r)
0. 1 1 10 100
Rainfall inten
s
ity (m
m
/h
r)
1
10
100
1000
2-y r
5-y r
10- y r
25- y r
50- y r
100y r
1 7 -M a rion
Duration  (h r)
0. 1 1 10 100
Rainfall inten
s
ity (m
m
/h
r)
1
10
100
1000
2-y r
5-y r
10- y r
25- y r
50- y r
100y r
1 8 -Wa rr ior L&D
Duration  (h r)
0. 1 1 10 100
Rainfall inten
s
ity (m
m
/h
r)
1
10
100
1000
2-y r
5-y r
10- y r
25- y r
50- y r
100y r
328 
 
 
1 9 -A lberta
Duration  (h r)
0. 1 1 10 100
Rainfall inten
s
ity (m
m
/h
r)
1
10
100
1000
2-y r
5-y r
10- y r
25- y r
50- y r
100y r
2 0 -M o nt g o mery
Duration  (h r)
0. 1 1 10 100
Rainfall inten
s
ity (m
m
/h
r)
1
10
100
1000
2-y r
5-y r
10- y r
25- y r
50- y r
100y r
2 1 -M idway
Duration  (h r)
0. 1 1 10 100
Rainfall inten
s
ity (m
m
/h
r)
1
10
100
1000
2-y r
5-y r
10- y r
25- y r
50- y r
100y r
2 2 -Troy
Duration  (h r)
0. 1 1 10 100
Rainfall inten
s
ity (m
m
/h
r)
1
10
100
1000
2-y r
5-y r
10- y r
25- y r
50- y r
100y r
2 3 -G re env ill e
Duration  (h r)
0. 1 1 10 100
Rainfall inten
s
ity (m
m
/h
r)
1
10
100
1000
2-y r
5-y r
10- y r
25- y r
50- y r
100y r
2 4 -Peterma n
Duration  (h r)
0. 1 1 10 100
Rainfall inten
s
ity (m
m
/h
r)
1
10
100
2-y r
5-y r
10- y r
25- y r
50- y r
100y r
329 
 
 
 
2 5 -A bb eville
Duration  (h r)
0. 1 1 10 100
Rainfall inten
s
ity (m
m
/h
r)
1
10
100
1000
2-y r
5-y r
10- y r
25- y r
50- y r
100y r
2 6 -Ent er prise
Duration  (h r)
0. 1 1 10 100
Rainfall inten
s
ity (m
m
/h
r)
1
10
100
1000
2-y r
5-y r
10- y r
25- y r
50- y r
100y r
2 7 -D o th a n
Duration  (h r)
0. 1 1 10 100
Rainfall inten
s
ity (m
m
/h
r)
1
10
100
1000
2-y r
5-y r
10- y r
25- y r
50- y r
100y r
2 8 -A tm o re  1
Duration  (h r)
0. 1 1 10 100
Rainfall inten
s
ity (m
m
/h
r)
1
10
100
1000
2-y r
5-y r
10- y r
25- y r
50- y r
100y r
2 9 -A tm o re  2
Duration  (h r)
0. 1 1 10 100
Rainfall inten
s
ity (m
m
/h
r)
1
10
100
1000
2-y r
5-y r
10- y r
25- y r
50- y r
100y r
3 0 -R iver Fa lls
Duration  (h r)
0. 1 1 10 100
Rainfall inten
s
ity (m
m
/h
r)
1
10
100
1000
2-y r
5-y r
10- y r
25- y r
50- y r
100y r
330 
 
 
 
3 1 -A nd a lusia
Duration  (h r)
0. 1 1 10 100
Rainfall inten
s
ity (m
m
/h
r)
1
10
100
1000
2-y r
5-y r
10- y r
25- y r
50- y r
100y r
3 2 -Tho ma sv ill e
Duration  (h r)
0. 1 1 10 100
Rainfall inten
s
ity (m
m
/h
r)
1
10
100
1000
2-y r
5-y r
10- y r
25- y r
50- y r
100y r
3 3 -J a ckso n
Duration  (h r)
0. 1 1 10 100
Rainfall inten
s
ity (m
m
/h
r)
1
10
100
1000
2-y r
5-y r
10- y r
25- y r
50- y r
100y r
331 
 
 
F.2. ANN model 
 
1 -A th ens  
Du ratio n  ( h r)
0.1 1
Rain
fall 
in
ten
s
ity
 (
m
m
/h
r)
10
100
2- yr
5- yr
10- yr
25- yr
50- yr
100yr
2 -Brid g epo rt 
Du ratio n  ( h r)
0.1 1
Rain
fall 
in
ten
s
ity
 (
m
m
/h
r)
10
100
2- yr
5- yr
10- yr
25- yr
50- yr
100yr
3 -Bo a z
Du ratio n  ( h r)
0.1 1
Rain
fall 
in
ten
s
ity
 (
m
m
/h
r)
10
100
2- yr
5- yr
10- yr
25- yr
50- yr
100yr
4 -H a ncev ille 
Du ratio n  ( h r)
0.1 1
Rain
fall 
in
ten
s
ity
 (
m
m
/h
r)
10
100
2- yr
5- yr
10- yr
25- yr
50- yr
100yr
5 -A dd iso n 
Du ratio n  ( h r)
0.1 1
Rain
fall 
in
ten
s
ity
 (
m
m
/h
r)
10
100
2- yr
5- yr
10- yr
25- yr
50- yr
100yr
6 -H a ley v ille 
Du ratio n  ( h r)
0.1 1
Rain
fall 
in
ten
s
ity
 (
m
m
/h
r)
10
100
2- yr
5- yr
10- yr
25- yr
50- yr
100yr
332 
 
 
7 -H a mil to n 
Du ratio n  ( h r)
0.1 1
Rain
fall 
in
ten
s
ity
 (
m
m
/h
r)
10
100
2- yr
5- yr
10- yr
25- yr
50- yr
100yr
8 -V erno n
Du ratio n  ( h r)
0.1 1
Rain
fall 
in
ten
s
ity
 (
m
m
/h
r)
10
100
2- yr
5- yr
10- yr
25- yr
50- yr
100yr
9 -Berry
Du ratio n  ( h r)
0.1 1
Rain
fall 
in
ten
s
ity
 (
m
m
/h
r)
10
100
2- yr
5- yr
10- yr
25- yr
50- yr
100yr
1 0 -W a rrio r
Du ratio n  ( h r)
0.1 1
Rain
fall 
in
ten
s
ity
 (
m
m
/h
r)
10
100
2- yr
5- yr
10- yr
25- yr
50- yr
100yr
1 1 -J a cks o nv ille
Du ratio n  ( h r)
0.1 1
Rain
fall 
in
ten
s
ity
 (
m
m
/h
r)
10
100
2- yr
5- yr
10- yr
25- yr
50- yr
100yr
1 2 -Birm ing ha m
Du ratio n  ( h r)
0.1 1
Rain
fall 
in
ten
s
ity
 (
m
m
/h
r)
10
100
2- yr
5- yr
10- yr
25- yr
50- yr
100yr
333 
 
 
 
 
1 3 -A sh la nd
Du ratio n  ( h r)
0.1 1
Rain
fall 
in
ten
s
ity
 (
m
m
/h
r)
10
100
2- yr
5- yr
10- yr
25- yr
50- yr
100yr
1 4 -Tu sca lo o sa
Du ratio n  ( h r)
0.1 1
Rain
fall 
in
ten
s
ity
 (
m
m
/h
r)
10
100
2- yr
5- yr
10- yr
25- yr
50- yr
100yr
1 5 -Th o rsb y
Du ratio n  ( h r)
0.1 1
Rain
fall 
in
ten
s
ity
 (
m
m
/h
r)
10
100
2- yr
5- yr
10- yr
25- yr
50- yr
100yr
1 6 -D a dev ille
Du ratio n  ( h r)
0.1 1
Rain
fall 
in
ten
s
ity
 (
m
m
/h
r)
10
100
2- yr
5- yr
10- yr
25- yr
50- yr
100yr
1 7 -M a rio n
Du ratio n  ( h r)
0.1 1
Rain
fall 
in
ten
s
ity
 (
m
m
/h
r)
10
100
2- yr
5- yr
10- yr
25- yr
50- yr
100yr
1 8 -W a rrio r L& D
Du ratio n  ( h r)
0.1 1
Rain
fall 
in
ten
s
ity
 (
m
m
/h
r)
10
100
2- yr
5- yr
10- yr
25- yr
50- yr
100yr
334 
 
 
1 9 -A lbert a
Du ratio n  ( h r)
0.1 1
Rain
fall 
in
ten
s
ity
 (
m
m
/h
r)
10
100
2- yr
5- yr
10- yr
25- yr
50- yr
100yr
2 0 -M o nt g o mery
Du ratio n  ( h r)
0.1 1
Rain
fall 
in
ten
s
ity
 (
m
m
/h
r)
10
100
2- yr
5- yr
10- yr
25- yr
50- yr
100yr
2 1 -M idwa y
Du ratio n  ( h r)
0.1 1
Rain
fall 
in
ten
s
ity
 (
m
m
/h
r)
10
100
2- yr
5- yr
10- yr
25- yr
50- yr
100yr
2 2 -Tro y
Du ratio n  ( h r)
0.1 1
Rain
fall 
in
ten
s
ity
 (
m
m
/h
r)
10
100
2- yr
5- yr
10- yr
25- yr
50- yr
100yr
2 3 -G reenv ille
Du ratio n  ( h r)
0.1 1
Rain
fall 
in
ten
s
ity
 (
m
m
/h
r)
10
100
2- yr
5- yr
10- yr
25- yr
50- yr
100yr
2 4 -P eterm a n
Du ratio n  ( h r)
0.1 1
Rain
fall 
in
ten
s
ity
 (
m
m
/h
r)
10
100
2- yr
5- yr
10- yr
25- yr
50- yr
100yr
335 
 
 
2 5 -A bb ev ille
Du ratio n  ( h r)
0.1 1
Rain
fall 
in
ten
s
ity
 (
m
m
/h
r)
10
100
2- yr
5- yr
10- yr
25- yr
50- yr
100yr
2 6 -En terp rise
Du ratio n  ( h r)
0.1 1
Rain
fall 
in
ten
s
ity
 (
m
m
/h
r)
10
100
2- yr
5- yr
10- yr
25- yr
50- yr
100yr
2 7 -D o th a n
Du ratio n  ( h r)
0.1 1
Rain
fall 
in
ten
s
ity
 (
m
m
/h
r)
10
100
2- yr
5- yr
10- yr
25- yr
50- yr
100yr
2 8 -A tm o re 1
Du ratio n  ( h r)
0.1 1
Rain
fall 
in
ten
s
ity
 (
m
m
/h
r)
10
100
2- yr
5- yr
10- yr
25- yr
50- yr
100yr
2 9 -A tm o re  2
Duration  (h r)
0. 1 1
Rainfall inten
s
ity (m
m
/h
r)
10
100
1000
2-yr
5-yr
10 - yr
25 - yr
50 - yr
10 0yr
3 0 -R iv er F a lls
Du ratio n  ( h r)
0.1 1
Rain
fall 
in
ten
s
ity
 (
m
m
/h
r)
10
100
2- yr
5- yr
10- yr
25- yr
50- yr
100yr
336 
 
 
 
3 1 -A nd a lus ia
Du ratio n  ( h r)
0.1 1
Rain
fall 
in
ten
s
ity
 (
m
m
/h
r)
10
100
2- yr
5- yr
10- yr
25- yr
50- yr
100yr
3 2 -Th o ma sv ille
Du ratio n  ( h r)
0.1 1
Rain
fall 
in
ten
s
ity
 (
m
m
/h
r)
10
100
2- yr
5- yr
10- yr
25- yr
50- yr
100yr
3 3 -J a cks o n
Du ratio n  ( h r)
0.1 1
Rain
fall 
in
ten
s
ity
 (
m
m
/h
r)
10
100
2- yr
5- yr
10- yr
25- yr
50- yr
100yr