COMPARISON OF THE THEORY, APPLICATION, AND RESULTS OF ONE AND
TWO DIMENSIONAL FLOW MODELS
Except where reference is made to the work of others, the work described in this thesis is
my own or was done in collaboration with my advisory committee. This thesis does not
include proprietary or classified information.
__________________________________
Kathryn Green Lee
Certificate of Approval:
________________________ ________________________
Frazier Parker, Jr. Joel G. Melville, Chair
Professor Professor
Civil Engineering Civil Engineering
________________________ ________________________
Prabhakar Clement Stephen L. McFarland
Associate Professor Dean
Civil Engineering Graduate School
COMPARISON OF THE THEORY, APPLICATION, AND RESULTS OF ONE AND
TWO DIMENSIONAL FLOW MODELS
Kathryn Green Lee
A Thesis
Submitted to
the Graduate Faculty of
Auburn University
in Partial Fulfillment of the
Requirements for the
Degree of
Masters of Science
Auburn, Alabama
August 7, 2006
iii
COMPARISON OF THE THEORY, APPLICATION, AND RESULTS OF ONE AND
TWO DIMENSIONAL FLOW MODELS
Kathryn Green Lee
Permission is granted to Auburn University to make copies of this thesis at its discretion,
upon request of individuals or institutions and at their expense. The author reserves all
publication rights.
________________________
Signature of Author
________________________
Date of Graduation
iv
VITA
Kathryn Green Lee, daughter of James R. Green and Janice (Barrentine) Green,
was born on March 14, 1981, in Brewton, Alabama. She graduated from Flomaton High
School in 1999. She then graduated suma cum laude from Jefferson Davis Community
College with an Associates of Science degree, in May 2001. She entered Auburn
University in September 2001 and graduated suma cum laude with a Bachelor of Science
degree in Civil Engineering in August, 2004. She also completed the cooperative
education program, working under Hydrologists at the U.S. Geological Survey, where
she is currently employed. She married Benjamen Paul Lee, son of Timothy Paul Lee
and Elizabeth (Stewart) Lee, on August 28, 2004. She then entered Graduate School,
Auburn University, in September 2004.
v
THESIS ABSTRACT
COMPARISON OF THE THEORY, APPLICATION AND RESULTS OF ONE AND
TWO DIMENSIONAL FLOW MODELS
Kathryn Green Lee
Master of Science, August 7, 2006
(B.C.E., Auburn University, 2004
129 Typed Pages
Directed by Joel Melville
The accurate simulation of flooding is crucial in the design of safe, costeffective
hydraulic structures. Hydraulic engineers are faced with several difficult decisions that
will determine the accuracy of any modeling scenario. The foremost decision is the
selection of the hydraulic model. Once the model has been selected the input parameters
must be chosen, the model executed, and the results interpreted.
This study is a comparison of two flow models to determine their applicability to
specific river reaches. The two models selected for comparison were Hydraulic
Engineering Center?s River Analysis System and Finite Element Surface Water Modeling
System. The respective one and twodimensional models were used in conjunction with
calibration data for flood flow simulation.
vi
Two river reaches with varying basin characteristics were modeled. The
roughness values required to simulate the highwater profiles were less for the two
dimensional model than for the onedimensional model. Comparison of the two reaches
indicated that the roughness values for one and two dimensional flow are not
considerably different for basins with very flat slopes. It was also determined, for two
dimensional flow, a reasonable range of values; the base kinematic eddy viscosity has
little effect on the resulting watersurface profile.
The high water profiles predicted by the one and twodimensional models were
examined and the hydraulic properties within the reach were investigated. The results
showed that assumptions of onedimensional flow are valid for a standard reach and a
skewed roadway crossing up to approximately thirty degrees. The flow distribution and
correlating velocities were compared to measured values, for the second river reach. It
was found that the flow distribution for both models matched the measured value within
three percent. The velocity profiles created within the twodimensional model were
found to overall provide a closer match to the calibration data.
vii
ACKNOWLEDGEMENTS
The author would like to thank Dr. Joel Melville for guidance and assistance in
the completion of this report. The author would also like to thank T.S. Hedgecock for
direction in the development and execution of the flow models and lessons in ?being the
water?. Thanks are also due to a very supportive family.
viii
Style manual used: Guide to Preparation and Submission of Theses and Dissertations
2005.
Computer Software used: Surfacewater Modeling System (SMS) 8.0 by Boss
International, Inc and Brigham Young University; HECRAS River Analysis System by
U.S. Army Corps of Engineers Hydrologic Engineering Center; Microsoft Word 2003,
Excel 2003, WordPad; Adobe Illustrator; Arc Info by ESRI; TDS Survey Link;
Terramodel by Trimble Navigation Limited; Terrain Navigator Pro by Maptech.
ix
TABLE OF CONTENTS
LIST OF TABLES............................................................................................................ xii
LIST OF FIGURES ......................................................................................................... xiv
I. INTRODUCTION.......................................................................................................... 1
II. LITERATURE REVIEW.............................................................................................. 4
III. STATEMENT OF RESEARCH OBJECTIVES ......................................................... 6
IV. DESCRIPTION OF THE PRIMARY STUDY REACH ............................................ 7
Area of Study ...................................................................................................................... 8
Flood History ...................................................................................................................... 8
V. DATA USED .............................................................................................................. 10
Survey Data....................................................................................................................... 10
Drainage Area ................................................................................................................... 11
Landuse Determination.................................................................................................... 14
Hydrologic Determinations............................................................................................... 16
VI. ONEDIMENSIONAL ANALYSIS ......................................................................... 19
History............................................................................................................................... 19
Theoretical Basis............................................................................................................... 21
Cross Section Subdivision for Conveyance Calculations......................................... 23
Composite Manning?s Roughness Coefficient for the Main Channel...................... 25
Evaluation of the Mean Kinetic Energy Head .......................................................... 26
x
Contraction and Expansion Loss Evaluation ............................................................ 27
Computation Procedure ............................................................................................ 28
Critical Depth Determination.................................................................................... 29
Application of the Momentum Equation .................................................................. 30
Steady Flow Program Limitations ............................................................................ 31
Variables ................................................................................................................... 32
Applications ...................................................................................................................... 34
Calibration......................................................................................................................... 42
Results............................................................................................................................... 42
VII. TWO DIMESNIONAL ANALYSIS...................................................................... 45
History............................................................................................................................... 45
Theoretical Basis............................................................................................................... 46
DepthAveraged Momentum Equations ................................................................... 46
Momentum Correction Factor................................................................................... 49
Coriolis Effect........................................................................................................... 50
Bottom Shear Stress.................................................................................................. 51
Surface Shear Stress.................................................................................................. 52
Stress Caused by Turbulence.................................................................................... 52
DepthAveraged Continuity of Mass........................................................................ 54
Variables ................................................................................................................... 54
Applications ...................................................................................................................... 56
Calibration......................................................................................................................... 71
Results............................................................................................................................... 74
xi
VIII. COMPARISON OF ONE AND TWO DIMENSIONAL MODELS .................. 78
IX. SECONDARY STUDY............................................................................................. 80
Description of the Reach................................................................................................... 80
Hydrology ......................................................................................................................... 81
Hydraulics......................................................................................................................... 83
OneDimensional Results ................................................................................................. 83
TwoDimensional Results................................................................................................. 83
X. COMPARISON OF SECONDARY STUDY RESULTS .......................................... 87
Flow Distribution and Velocity ........................................................................................ 87
Skewed Crossing............................................................................................................... 91
Manning?s Roughness Coefficient Reduction .................................................................. 92
XI. CONCLUSION AND ENDING REMARKS ........................................................... 97
REFERENCES.................................................................................................................. 100
APPENDIX..................................................................................................................... 102
xii
LIST OF TABLES
Table 1 Variable parameters within one and two dimensional flow models. ................ 3
Table 2. Cross sections locations for the Fivemile Creek study reach. .......................... 11
Table 3. Geographic location of significant changes in drainage area in the Fivemile
Creek study. .............................................................................................................. 12
Table 4. Flood Frequency Relations for Urban Streams in Alabama (Olin and
Bingham, 1982)......................................................................................................... 17
Table 5. Peak flow at various locations for the May 07, 2003 flood on Fivemile
Creek......................................................................................................................... 18
Table 6. Peak flow at various locations reflective of the current conditions within the
Fivemile Creek study reach ...................................................................................... 18
Table 7. Geographic location of hydraulic structures in the Fivemile Creek study
reach.......................................................................................................................... 40
Table 8. Resulting profiles using the hydraulic model HECRAS for the
May 07, 2003 flood on Fivemile Creek.................................................................... 44
Table 9. Coriolis correction factors for various geographic locations............................ 50
Table 10. Resulting watersurface profile using onedimensional Manning?s
roughness coefficients in the hydraulic model FESWMS2DH for the Fivemile
Creek study reach...................................................................................................... 72
xiii
Table 11. Resulting watersurface profile with calibrated Manning?s roughness
coefficients for the hydraulic model FESWMS2DH............................................... 75
Table 12. Stagedischarge relationship for select recurrence intervals for the
Sucarnoochee River reach......................................................................................... 82
Table 13. Correlation between watersurface elevation and Manning?s roughness
coefficients for the Sucarnoochee River reach. ........................................................ 94
Table 14. Weighting factors used to determine degree of urbanization. ........................ 109
xiv
LIST OF FIGURES
Figure 1. Fivemile Creek study reach, Tarrant City, Jefferson County, Alabama. .......... 9
Figure 2. Location of significant changes in drainage area in the Fivemile Creek study
reach.......................................................................................................................... 12
Figure 3. Location map of the Fivemile Creek basin and associated development........ 13
Figure 4. Binary map of urbanization for the Fivemile Creek basin. ............................. 15
Figure 5. Schematic used in the application of the Energy Equation. ............................ 22
Figure 6. HECRAS input deck. ..................................................................................... 23
Figure 7. Typical channel sketch. ................................................................................... 25
Figure 8. Specific energy diagram.................................................................................. 29
Figure 9. Specific energy curve with a local minimum critical depth............................ 30
Figure 10. Illustration of pressure head and depth........................................................... 32
Figure 11. Location of hydraulic structures within the Fivemile Creek study reach....... 39
Figure 12. Slope computations for the Fivemile Creek basin.......................................... 41
Figure 13. Control volume schematic.............................................................................. 48
Figure 14. Velocity profile............................................................................................... 49
Figure 15. Study reach for twodimensional flood flow simulations on Fivemile Creek 57
Figure 16. Finiteelement grid used in flood flow simulations for the May 07, 2003
flood on Fivemile Creek ........................................................................................... 58
Figure 17. Illustration of mesh generation through the use of feature arcs. .................... 60
xv
Figure 18. Mesh generation tools in SMS. ...................................................................... 61
Figure 19. Illustration of the bending of elements to represent triangular channel
geometry ................................................................................................................... 63
Figure 20. Illustration of the bending of elements to represent trapezoidal channel
geometry. .................................................................................................................. 64
Figure 21. Landsurface elevations for the Fivemile Creek study reach ......................... 65
Figure 22. Initial Manning?s roughness coefficients for the Fivemile Creek study
reach.......................................................................................................................... 73
Figure 23. Location map of the Sucarnoochee River reach............................................. 82
Figure 24. Finiteelement grid used in flood flow simulations for the 1979 flood on
the Sucarnoochee River. ........................................................................................... 85
Figure 25. Land surface elevations for the Sucarnoochee River study reach.................. 86
Figure 26. Computed velocity vectors for the main structure on the Sucarnoochee
River for the April 1979 flood. ................................................................................. 89
Figure 27. Computed velocity vectors for the relief structure on the Sucarnoochee
River for the April 1979 flood .................................................................................. 90
Figure 28. Manning?s roughness coefficients used for the flood flow simulation of
Sucarnoochee River. ................................................................................................. 96
Figure 29. Section A, outlet of the box culvert at the L and N Railroad. ....................... 102
Figure 30. Section B, looking downstream..................................................................... 103
Figure 31. Alabama Power Company Bridge, looking upstream. .................................. 103
Figure 32. Section C, looking upstream.......................................................................... 104
Figure 33. Section D, looking downstream. ................................................................... 104
xvi
Figure 34. Railroad Bridge, looking upstream................................................................ 105
Figure 35. Section E, looking downstream..................................................................... 105
Figure 36. Section F, looking west. ................................................................................ 106
Figure 37. Section H, looking downstream. ................................................................... 106
Figure 38. Highway 79 Bridge, looking upstream.......................................................... 107
Figure 39. Section I, looking downstream...................................................................... 107
Figure 40. Section J, looking upstream.......................................................................... 108
Figure 41. Section K, looking downstream. .................................................................. 108
Figure 42. Fivemile Creek study reach approximate location of cross sections A
through G. ............................................................................................................... 110
Figure 43. . Fivemile Creek study reach approximate location of cross sections F
through K. ............................................................................................................... 111
Figure 44. Results of the Indirect Calculations at Lawson Road by USGS. .................. 112
Figure 45. Comparison of computed and actual flood profiles for the May 2003 flood on
Fivemile Creek........................................................................................................ 113
1
I. INTRODUCTION
For many years engineers and scientist have made idealized assumptions to aid in
the analysis of complex problems. An example of this idealization is hydraulic modeling
of river reaches and its application to the design and evaluation of hydraulic structures.
Many situations can be simulated with onedimensional flow models. In more complex
situations two and even three dimensional models are needed to reasonably depict the
hydraulics of a reach. As modeling technology has advanced, hydraulic engineers are
faced with the problem of model selection. It has been observed, in practice, that a two
dimensional model is not merited unless there are unusual circumstances. A few of these
circumstances include severe skew of the road crossing, multiple structures, and large
rivers. Twodimensional models are also useful when lateral variations in water surface
and flow distribution are significant.
This study, through the modeling of specific river reaches, is intended to provide
insight on the applicability of the onedimensional model. It also serves to provide
comparisons of the necessary input, limitations, expected results, and one and two
dimensional modeling approaches.
The construction, execution, and results of one and twodimensional models
were investigated to provide insight into their differences and applicable scenarios. It is
known that every reach has its own characteristics that affect flood flow simulation. This
2
uniqueness is something that a modeler must learn to adapt to. Two reaches were chosen
to provide optimal points of investigation. Each reach has valuable calibration data, from
field measurement and observation, which will be used to compare the results of the one
and two dimensional models. In order to properly compare one and two dimensional
flow analyses, there has to be a standard for comparison. Unless there is a stage
discharge relationship (gaging station) or documented flood there are few opportunities
for this. In the case of these study sites both were available.
The process of calibration and validation is an important step in surfacewater
modeling where so many factors are unknown. The practice of calibration is the
adjustment of input parameters, within reason, until the results compare closely with a
measured value. Once a model has been calibrated it can be validated with a separate
flooding event. If the results of model simulation compare to the second flooding
scenario without major adjustments to input variables, the model is considered valid over
the range of flood flows.
The results of the two reaches chosen for this study were compared based on the
calibration data. The primary reach investigated was Fivemile Creek. In order to
investigate topics not explored in the Fivemile Creek study a second reach was examined.
The second study site was on the Sucarnoochee River. It provided the opportunity to
examine a roadway with multiple bridges that crossed the floodplain at an angle (skew)
and the effects this has on the computed velocity profiles, and flow distribution.
The fundamental issue with the comparison of one and twodimensional models
is the adjustment of input parameters. These adjustments, over a reasonable range of
values, based on site topography, land cover variability, limited flood flow and stage
3
information can make significant changes in model predictions. Table 1 outlines some of
the input parameters that must be determined for both models. One of the major
differences in the one and twodimensional models is the representation of energy losses
and how they are calculated based on the input parameters. The results of this study is
intended to provide insight on the variability of the input parameters and interpretation of
results within surfacewater modeling and guidance for determining when a more
complex model may be needed.
OneDimensional Input Parameters TwoDimensional Input Parameters
Manning?s Roughness Coefficient Manning?s Roughness Coefficient
 Base Kinematic Eddy Viscosity
Location of Control ( Friction Slope) Location of Control ( Tailwater Elevation)
Ground Slope Grid Adjustments
Peak Flow Assumptions Location of Inflow (Sources, Nodestrings)
Table 1 Variable parameters within one and two dimensional flow models.
4
II. LITERATURE REVIEW
Currently quantitative comparison of one and two dimensional flow models is
limited. The majority of surfacewater modelers base their judgment on experience and
their own analyses. Engineers are often faced with the dilemma of improved accuracy
versus time constraints. The costtobenefits ratio often dictates the type of model used
in every day practice.
The few published articles that provide insight into these comparisons are
inconclusive or very site specific. ?Development of a Methodology for incorporating
FESWMS2DH Results? (Parr and Zou 2000), provided a detailed comparison of various
models. The University of Kansas investigators presented the methodology and results
for a multiple bridge crossing near Neodesha, Kansas. The crossing consists of 3 bridges,
one main and two relief structures. The site was previously investigated to determine the
resulting backwater using Water Surface Profiler (WSPRO) [a onedimensional step
backwater model used for computing watersurface profiles (Sherman, 1976)]. These
computations resulted in 66% of the flow in the main channel bridge and 16% and 18%
in the relief structures, for the 50year flood. Using the same tailwater and roughness
coefficients documented for the WSPRO computations a twodimensional model was
constructed and the computational program FESWMS2DH was used. The results
indicated the main channel bridge carried 69% of the flow and the relief structures carried
5
8% and 23 %. The conclusions were that the use of the twodimensional model, in the
design analysis, suggested no need for one or both of the relief structures. This raises
several questions. Was the difference in the calculated flow distribution great enough to
merit the use of a twodimensional model? The mere 16% in the relief structure,
indicated by the WSPRO analysis, was a good indicator that the relief structure only
carries a small portion of the total flow. This specific investigation does show merit in
the use of a twodimensional model for multiple bridge crossings; however the only
results presented are the flow distributions. Typically when bridges are designed, based
on the hydraulics of the crossing, the primary indicators of a good bridge design, for a
state highway crossing, are the 50year mean velocity and the 100year backwater. The
numerical criteria of these values vary from state to state and are based on geographic,
geological, and physiological characteristics of the area. This information was not
presented in the report. Another point worth mentioning is the use of onedimensional
roughness coefficients in a twodimension model. This assumption is presumed to
present some error in the computations of the watersurface profile.
When comparing the results of two models such as these, field calibration data is
a necessity. The models could be constructed and executed, and the onedimensional
model said not to be valid when the deviance from the twodimensional model is
significant. The actual value may be somewhere between the estimated values. Without
the calibration data one would assume the onedimensional model failed when in
actuality it may have provided results that are just as close to the real value as the two
dimensional model. Without calibration data it is hard to draw a conclusion on the
improved accuracy of the twodimensional model.
6
III. STATEMENT OF RESEARCH OBJECTIVES
Due to the lack of documented results on the comparison of one and two
dimensional flow models, this study is intended to compare the results of a typical site
with no unusual characteristics and a site that would be considered a candidate for two
dimensional analysis. The models were constructed and executed based on field data and
site inspection. The variation of the input data and the resulting hydraulic data were
documented. The models were calibrated through the use of a documented flood event
and gaging station data. Based on this information, conclusions can be drawn on the
assumption that the cost to benefits ratio of a onedimensional model surpasses that of a
twodimensional model. The effects of skewed crossings on flow distribution were also
investigated. The results also provide a base line to use in the transition of picking
roughness values for a twodimensional model.
7
IV. DESCRIPTION OF THE PRIMARY STUDY REACH
The area selected for primary observation is the city of Tarrant, Alabama. Tarrant
is located in north central Alabama, approximately 1.5 miles northeast of Birmingham, in
Jefferson County, Alabama. A location map of the area can be viewed in Figure 1. The
population of Tarrant is approximately 8,000. The city?s area consists of 6.4 square miles
with 0.6% being surface water. The average elevation to mean sea level is 546 feet.
Tarrant is a primarily industrial town and is located in the Fivemile Creek basin.
Currently the city planning is based on Federal Emergency Management Agency?s
(FEMA) flood insurance study. Anthropogenic changes in the Fivemile Creek basin have
significantly altered the hydrologic and hydraulic conditions of the basin. On March 10,
2000 and May 7, 2003 the flood stage as recorded by the U.S. Geological Survey?s
stream gage (02457000) exceeded FEMA?s 100year flood stage significantly (2.9 feet
and 4.7 feet, respectively). Both of these floods caused a considerable amount of damage
in the Tarrant City community. The revision of the onedimensional study with FEMA
mandated Hydraulic Engineering Center?s River Analysis System (HECRAS) would
suffice the needs of Tarrant, however since this basin has recently experienced two major
floods the availability of data made this site a prime candidate for the comparison of a
one and two dimension model.
8
Area of Study
The reach of the stream evaluated extends from about 300 feet upstream of
Lawson Road to just below the L&N Railroad (about 5,000 feet upstream, of U.S.
Highway 31). The total reach length of the study is approximately 20,000 feet. The
average slope of the basin, in the study reach, is 18.5 ft/mi. The stream flows in a
southwesterly direction and has an average top width of 85 feet with a minimum and
maximum value of 50 and 130 feet, respectively. The average flood plain width was
1,000 feet and varied between 200 and 2,000 feet. The land cover of the reach is
characterized by grassy fields and some wooded areas with moderate vegetative growth.
The reach extends through some areas of residential and industrial land use. These areas
typically have minimal or maintained vegetative growth and areas of ineffective flow.
The ineffective flow areas, for this study reach, consisted primarily of warehouses,
homes, and large equipment lots.
Flood History
This reach was selected because of the availability of data. It has experienced two
major floods in 2001 and 2003, and over a period of time has had two stream flow gages.
Located at the upper end of the reach is the Fivemile Creek at Lawson Road gage (USGS
gage 02456980). This gage was active until April 2001. Based on highwater marks a
peak was calculated indirectly for the 2003 flood. Shortly after the 2003 flood the gage
was reactivated. The other gage is located at the Ketona Lakes.
9
LOCATION OF JEFFERSON COUNTY
IN ALABAMA
86?47'30"
86?45'
33?34'
33?36'
Figure 1. Fivemile Creek study reach, Tarrant, Jefferson County, Alabama.
0 1 2 MILES
1 2 3 KILOMETERS0
10
V. DATA USED
The objective of this project will be accomplished through these steps: field data
collection surveys, landuse (impervious cover) determinations, hydrologic
determinations, and hydraulic modeling.
Survey Data
In order to accurately represent the geometry of the reach the elevation was
defined using an electronic total station. This was accomplished by surveying eleven
flood plain cross sections and the geometry of all significant drainage structures (with
adjacent roadways). The reach consisted of six hydraulic structures, one culvert and five
bridges. In efforts to calibrate the hydraulic model, eleven highwater marks, from the
2003 flood, were also surveyed. The river stations were computed working upstream
with the furthermost downstream section being zero. Each section was also given an
alphabetical identifier. The furthermost downstream section was labeled (A). The
alphabetical identifiers and the river stations can be viewed in Table 2. Land cover
(roughness) characteristics for the reach were assessed from field investigations of the
site. Manning?s roughness coefficient was selected to reflect current conditions and the
conditions that existed during the 2003 flood. Photographs of the cross sections and the
surrounding areas can be viewed in the Appendix in Figures 29 through 41.
11
Alphabetical Section
Identifier
River Station
(ft)
A 0
B 1,077
C 3,280
D 5,206
E 6,863
F 8,692
G 11,357
H 13,168
I 14,986
J 16,798
K 18,068
Table 2. Cross sections locations for the Fivemile Creek study reach.
Drainage Area
There were three areas that were determined to have significant changes in
drainage area. These locations can be seen in Figure 2 and Table 3. The drainage areas
for gaged locations are published by USGS and other areas can be delineated using a
contour map or previously delineated drainage area maps. The drainage area was
delineated (Figure 3) for the downstream most cross section. This area is known as
Boyle?s Gap.
12
Figure 2. Location of significant changes in drainage area in the Fivemile Creek study
reach.
Identifier State Plane Coordinates
NAD 1927
Location Drainage Area
(sq. miles)
1 1304781 N, 716295 E Boyles Gap 28.4
2 1310471 N, 726288 E Ketona Gage 23.9
3 1310535 N, 726340 E Lawson Road Gage 18.6
Table 3. Geographic location of significant changes in drainage area in the Fivemile
Creek study reach.
N
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14
Landuse Determination
Due to industrial and residential growth in the Fivemile Creek basin the
hydrology has drastically changed. As described in later chapters, factors used to
determine the peak flow are drainage area and impervious area. In order to determine the
peak flows, that reflect current conditions, the impervious area was computed. Landuse
and impervious cover for the basin were calculated using the most recent aerial
photographs available for the reach. These photographs were supplemented with surveys
and field reconnaissance in the newer sections of development. Impervious area is
described by Stamper as, ?The impervious cover of a basin is that part of the total area
that is covered by either buildings or pavement that are impenetrable by infiltration from
rainfall. The percentage of impervious cover is an indication of the degree of
development or urbanization of a basin?. There are several methods of determining the
percentage of impervious cover.
Aerial photography from 2004 was made available for the entire drainage basin.
The areas of development, determined from aerial photography and field reconnaissance,
were tabulated. The resulting areas were weighted based on the type of land use and an
additional five percent was added to allow for future growth. The weighting factors and
their descriptions can be seen in the Appendix in Table 14. The resulting value of
percent impervious used in the hydrologic model was 25%. Upon inspection of Figure 3
it can be observed that the basin has little room for future growth.
As mentioned earlier, the most recent floods greatly exceeded the 100year flood
profile developed by FEMA. This is due to the growth experienced in the basin. In order
to understand the magnitude of the modifications the basin has experienced the percent
15
impervious was calculated for 1992. This date was chosen due to the availability of data.
The National Map publishes the National Land Cover Data Set in Geographic
Information System (GIS) form. The land cover data is categorized in codes that
correspond to a land use type. The land use types were digitized using aerial
photography and field reconnaissance. The National Land Cover Data Set was clipped
based on the drainage area and the resulting shape was transformed into a binary map
(Figure 4) to isolate the land cover categories of interest.
Figure 4. Binary map of urbanization for the Fivemile Creek basin.
N
16
The area of the remaining grid cells was tabulated, and the results were used to
calculate the percent urbanization. The resulting percent impervious calculated was 12%.
The results of the calculations, without a growth factor, show that in 1992 the basin
would have been rated as 12% urban whereas current conditions show the basin being
20% urban. In a matter of 12 years the percent urbanization has almost doubled.
Hydrologic Determinations
Hydrologic conditions were analyzed using the USGS urban regression equations
and procedures outlined in ?Magnitude and Frequency of Floods in Alabama? by J.B.
Atkins. The equations were developed in a previous study, Olin and Bingham (1982),
and recounted in Atkins 1996. The methodology is recapitulated by Atkins as, ?The
urban equations were derived by multiple regression analyses of peak flows obtained
from synthetic flow generated with calibrated rainfallrunoff model and basin
characteristics for 23 urban stations in Alabama?. The equations were developed for the
2, 5, 10, 25, 50, and100year recurrence intervals and can be seen in Table 4.
Recurrence interval is defined as the ?average interval of time between exceedance of the
indicated flood magnitude? (Stamper 1975). This can be explained as a there being a 1 in
100 chance that the 100year recurrence interval stage will occur in any given year. As
with most equations, these are not without limitations. The equations in Table 4 should
only be applied to basins with a drainage area of 0.16 to 83.5 square miles with greater
than five percent urbanization.
In May 07, 2003, the city of Tarrant experienced a major flood that incited further
inspection of the flood profiles computed and published by FEMA. In order to define the
17
upper end of the stagedischarge relation, for the flood gage at Lawson Road, an indirect
measurement was computed by the USGS for the 2003 flood, using the contracted
opening method. The results of the indirect measurement can be seen in the Appendix in
Figure 44. As seen in Table 5, the computed total flow is 14,100 ft
3
/s. In order to
transfer the computed peak to other areas of interest, the methods outlined in Atkins 1996
were applied. The peak at a gaged site can be transferred to an ungaged site on the same
creek.
Recurrence Interval
(years)
Regression Equation
for Streams in Urban Areas
Standard Error
Of Estimate (percent)
2 Q(u) = 150A
0.70
IA
0.36
26
5 Q(u) = 210A
0.70
IA
0.39
24
10 Q(u) = 266A
0.69
IA
0.39
24
25 Q(u) = 337A
0.69
IA
0.39
24
50 Q(u) = 396A
0.69
IA
0.38
24
100 Q(u) = 444A
0.69
IA
0.39
25
Table 4. Flood Frequency Relations for Urban Streams in Alabama (Olin and Bingham,
1982). [Q (u), flood flow in cubic feet per second; A, drainage area in square miles; IA,
impervious area in percent]
18
Location Drainage Area
(sq. miles)
May 07, 2003 Flood
(ft
3
/s)
Boyles Gap 28.4 18,800
Ketona Gage 23.9 16,700
Lawson Road Gage 18.6 14,100
Table 5. Peak flow at various locations for the May 07, 2003 flood on Fivemile Creek.
Using the drainage areas, impervious area, and the equations (Table 4) the flood
flows (Table 6) representative of the current land use conditions were computed for
selected recurrence intervals. This was done to estimate the recurrence interval of the
2003 flood. Based on the estimated current hydrologic conditions the computed peaks
for the May 07, 2003 flood rank between a 200 and 500year flood event.
Location Drainage Area
(sq. miles)
25% Impervious
10
year
(ft
3
/s)
50
year
(ft
3
/s)
100
year
(ft
3
/s)
500
year
(ft
3
/s)
Boyles Gap 28.4 9,390 13,500 15,700 20,700
At Ketona Gage 23.9 8,340 12,000 13,900 18,300
At Lawson Road Gage 18.6 7,020 10,100 11,700 15,400
Table 6. Peak flow at various locations reflective of the current conditions within the
Fivemile Creek study reach..
19
VI. ONEDIMENSIONAL ANALYSIS
History
In order to understand the applicability of the models chosen for this reach, it is
important to look at the historical development of one and two dimensional models.
Initially any hydraulic computations made were computed by hand. After World War II
hand calculations continued as a routine process for hydraulic engineers. The first
automated process was released in the early 1960s. In 1966, Hydrologic Engineering
Center (HEC), a division of the Institute of Water Resources (IWR), U.S. Army Corps of
Engineers released a FORTRAN based program titled ?Backwater, Any Cross Section?.
This program was later revised and released in 1968 with the title of HEC2(Haestad
Methods).
The program, written by D.G. Anderson and W.L. Anderson, served as the basis
for most processes of onedimensional modeling (Shearman 1976). Through use and
observations the model was improved. With refinements, and additions E431 ?Step
Backwater and Floodway Analysis? was created. This model was developed by the
USGS in 1976 and written by James O. Shearman. The major improvements over the
previous model included, complete analysis of flow through bridges, ability to compute
flow over weirs, and the special feature of analyzing the effects of encroachments
(hydraulic structures) on existing conditions (Shearman 1976).
20
Along the same time HEC2 (1968) was revised. HEC2 was written by Bill S.
Eichert. HEC2 is the second in a series of developments made my HEC. The first was
HEC1, flood hydrograph program. The HEC2 version dated 1976 featured
improvements such as encroachment analysis, summarized output tables, and five
alternatives for calculating friction losses.
Although the two models, E431 and HEC2 were superior at the time, as
technology advanced and needed improvements were noticed, the models were updated.
Different versions were released as minor changes were made. Major advancements led
to the creation of two new models.
The policy of Federal Highway Administration (FHWA) is to consider the effects
of encroachment alternatives. Through inspection of existing models FHWA found that
while each model had positive attributes likewise there were limitations. FHWA
employed USGS to create a model that was more suitable to the design needs. In
response USGS created ?A Computer Model for Water Surface Profile Computations?
known as WSPRO, also designated as HY7 in the FHWA hydraulics computer program
series. The enhancements included but are not limited to, improved bridge analysis and
input format, the addition of the analysis of combine flow (bridge and weir), multiple
bridge analysis, and selective output. The primary development was the applicability of
bridge design using the risk analysis supposition. However, the model was still
applicable for nondesign circumstances (Shearman 1976).
In response to the USGS enhancements, HEC made efforts to adjust accordingly
with their ?Next Generation? (NexGen) of hydrologic software. A part of the NexGen
projects was the development of ?River Analysis System? (HECRAS). HECRAS was
21
released in July of 1995. Subsequently HEC has released eight versions. The latest
version is 3.1 and was released in September of 2001. HECRAS was developed by Gary
W. Brunner. The major computer science advancement associated with this model is
graphical user interface (gui). This interface allows the user to have visual representation
of the input and output data which facilitates error recognition and allows the user to
visually evaluate the applicability of the results. It has also been documented that HEC
RAS surpasses HEC2 in hydraulic analysis capability which is demonstrated in the
subsequent section on the theory of onedimensional modeling (Brunner 2002).
Theoretical Basis
The theory investigated herein is that of the model applied for this study, HEC
RAS (Bruner 2002). Profiles are computed from one cross section to the next by
application of the Energy Equation (Equation 1). The process of application is the
standard step method.
e
h
g
V
ZY
g
V
ZY +
?
?
?
?
?
?
?
?
++=
?
?
?
?
?
?
?
?
++
22
2
1
111
2
2
222
?? Equation 1
22
Figure 5. Schematic used in the application of the Energy Equation.
The term (h
e
) in the Energy Equation is defined as the head loss from one section to the
next. There are two primary losses considered, friction loss and expansion or contraction
losses. The value of h
e
can be determined from Equation 2.
()()
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
+=
g
V
g
V
CSLh
fe
22
2
1
1
2
2
2
?? Equation 2
The discharge weighted reach length can be calculated from the following equation:
?
?
?
?
?
?
?
?
++
++
=
Rc
RRccLL
QQQL
QLQLQL
L Equation 3
It is shown in Figure 6 where the user enters the corresponding flow lengths for the right
and left overbanks and the main channel.
Datum
Channel Bottom
Water Surface
Energy Grade Line
Z
1
Y
1
Z
2
Y
2
?
2
V
2
2
/2g
h
e
?
1
V
1
2
/2g
23
Figure 6. HECRAS input deck.
Cross Section Subdivision for Conveyance Calculations
Conveyance, a measure of the carrying capacity of a channel section, is an
important property when computing watersurface profiles. Conveyance can be used to
determine the flow distribution between the overbanks and the channel. This distribution
is an important determination in the calculations of local scour. In order for HECRAS to
determine the total conveyance and the velocity coefficient for a cross section the flow
has to be divided into velocity tubes. HECRAS computes a conveyance for each
subsection with a different Manning?s roughness coefficient. The subsection values are
summed to give a total conveyance. The conveyance (K) is computed for each
subdivision break point using Equation 4.
24
If ()()2
1
SKQ = and ()
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
=
2
1
3
2
486.1
SRA
n
Q Then
()() ()
3/2
3/53/2
1
486.1
486.1
?
?
?
?
?
?
==
P
ARA
n
K Equation 4
This is the default method used by HECRAS, but sometime there is a need to
compute the conveyance using other methods. In the event that one is trying to duplicate
a study using HEC2 a different method is employed. HEC2 was designed to compute a
total conveyance at every geometric break point and then sum them to get the respective
left, right and channel conveyance. These methodologies were further investigated to see
the difference in the resulting numbers. Shown below is how the two methods differ
mathematically.
()()
3/2
486.1
RA
n
K =
P
A
R =
()
3/2
486.1
?
?
?
?
?
?
=
P
A
A
n
K
The difference in the wetted perimeter will outrank the difference in the
computation of the areas. Therefore, the greatest conveyance produced will be the sum
of conveyance at each individual ground point (HEC2 Method). Higher conveyance
corresponds to a lower watersurface elevation. The results of examining the equations
are further supported by actual computations. The conveyance methodology used by
25
HECRAS, for a watersurface elevation of 91.12 feet, produced a total conveyance of
296,152 ft
3
/s. Using the HEC2 method for the same watersurface elevation produced a
total conveyance of 308,498 ft
3
/s. There is a 4% error in the difference of these
solutions.
Composite Manning?s Roughness Coefficient for the Main Channel
HECRAS is programmed to check the applicability of a subdivided channel. If
the side slope is steeper than 0.02 then a composite (n) value will be computed. If the
input (Figure 7) is specified as having individual parts each with their own roughness
they will be combined to a composite roughness using the following formula.
()
3/2
1
5.1
?
?
?
?
?
?
?
?
?
?
?
?
?
?
=
?
=
P
nP
n
N
i
ii
c
Equation 5
Figure 7. Typical channel sketch.
() 8.1096
2/1
22
31
=+== PP
30
2
=P
9? n=0.08
9? n=0.08
30? n= 0.03
6?
1
2
3
26
()()()()()()
05383.0
08.08.1003.03008.08.10
3/2
321
5.15.15.1
=
?
?
?
?
?
?
++
++
=
QQQ
n
c
Evaluation of the Mean Kinetic Energy Head
The mean kinetic energy head is based on the discharge weighted average of the
velocity head of the subdivisions. The subdivisions are defined as the left and right
overbank and the main channel. The mean kinetic energy head can be computed from the
following equation:
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
++
?
?
?
?
?
?
?
?
+
?
?
?
?
?
?
?
?
+
?
?
?
?
?
?
?
?
=
?
?
?
?
?
?
?
?
321
2
3
3
2
2
2
2
1
1
2
222
2 QQQ
g
V
Q
g
V
Q
g
V
Q
g
V avg
? Equation 6
The velocity correction coefficient can be isolated and the following equation acquired:
()()
?
?
?
?
?
?
?
?
++
=
avg
total
VQ
VQVQVQ
2
2
33
2
22
2
11
? Equation 7
The equation can also be written in terms of conveyance
()
t
t
K
A
K
A
K
A
K
A
3
3
2
3
2
2
2
2
2
1
2
1
2
2
?
?
?
?
?
?
?
?
++
=? Equation 8
Friction losses are computed from the product of the length and the friction slope.
The friction slope can be obtained from Manning?s equation.
27
2
?
?
?
?
?
?
=
K
Q
S
f
Equation 9
HECRAS uses a representative average friction slope for the reach. The standard default
method is the average conveyance method, but this can be changed based on user input.
2
3
21
321
,
?
?
?
?
?
?
?
?
++
++
=
KKK
QQQ
S
favg
Equation 10
This method is used to compute the friction slope between crosssections. This is not the
beginning friction slope that is used to converge on the normal depth for subcritical flow.
Contraction and Expansion Loss Evaluation
The program determines if the channel is contracting or expanding based on the
velocity. If the velocity head increases downstream it is assumed that contraction is
occurring. If the velocity head is decreasing downstream then it is assumed that
expansion is occurring. Based on these assumptions the loss due to contraction or
expansion is computed with the following equation.
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
=
g
V
g
V
Ch
ce
22
2
2
2
2
1
1
?? Equation 11
28
Computation Procedure
The initial consideration when performing water surface profile analysis by hand
or with a computer aided model is the location of the control. The majority of the
streams in Alabama have flat slopes and are assumed to be flowing at subcritical depths.
If this is the case, the control is a downstream cross section. This section is often
assumed to be far away enough from any structures, so that the flow is at normal depth.
It is possible that the crossing of interest is affected by backwater from a downstream
structure or headwater from another stream. In some reaches the stream may be flowing
at supercritical depth and the control is located upstream.
Once the control has been determined, the model goes through a series of steps to
compute the watersurface elevation at the next cross section using the standard step
method. A watersurface elevation is assumed at the section upstream of the control
(subcritical flow) and the total conveyance, velocity head, and the energy head losses are
computed based on this assumption. All of these values are then used in the Energy
Equation (Equation 1). If both sides of the Energy Equation agree the watersurface
elevation assumed is correct. If the values are not the same the model continues to solve
this iterative process. The program will proceed through 20 iterations. If the solutions
have not converged the minimum error water surface elevation or the critical water
surface elevation will be assumed. This usually is an indicator that there is insufficient
cross section data. Either there are not enough sections, they are too far apart or coded
wrong. There is also the possibility that this could be the result of improper flow regime.
The model could be trying to calculate a subcritical depth for a section that is actually
supercritical. This can be checked by looking at the Froude number. The Froude number
29
is calculated for the main channel and the entire section. The break point for the
differentiation between subcritical and supercritical flow, for HECRAS, is a Froude
number of 0.94. This is chosen instead of 1.0 due to the inaccuracy in the calculation of
the Froude number for irregular channels.
Critical Depth Determination
There model calculates critical depth to ensure the boundary condition entered by
the user is correct. Critical depth can be defined as the point of minimum specific energy
possible at a cross section. The specific energy diagram (Figure 8) below shows this
point graphically, for a specified flow rate, Q.
Figure 8. Specific energy diagram.
The specific energy is
g
V
yE
2
2
+=
. The critical depth is determined by assuming
depths and calculating the corresponding specific energy until a minimum value is found.
In some cross sections there may be multiple points of minimum specific energy. This is
often the result of a break in the total energy curve. This can occur when the cross
(E) Specific Energy
g
V
yE
2
2
+=
Y
D
e
p
t
h
30
section has very wide flat overbanks, levees or ineffective flow areas. If this is the case,
the user should inspect the result of the critical depth. An example of a local minimum
due to the overtopping of a levee is shown in Figure 9.
Figure 9. Specific energy curve with a local minimum critical depth.
Application of the Momentum Equation
In previous sections the process for computing watersurface elevations for
gradually varied flow has been outlined. These procedures are not applicable to rapidly
varied flow. Anytime the profile passes through critical depth the energy equation is not
valid. There are several situations where the flow could pass from supercritical to
subcritical or subcritical to supercritical. These instances include but are not limited to;
significant changes in streambed slope, stream junctions, weirs, and bridges. In cases of
hydraulic jumps, low flow at bridges and stream junctions HECRAS uses the
momentum equation.
()
( )
()
( )
1,1
1
11
,
21212,2
2
22
22
ave
fave
o
ave
YA
gA
BQ
SL
AA
SL
AAYA
gA
BQ
+
?
?
?
?
?
?
?
?
=
?
?
?
?
?
?
?
?
+??
?
?
?
?
?
+++
?
?
?
?
?
?
?
?
Equation 12
Local
Minimum
(E) Specific Energy
Y
D
e
p
t
h
31
This equation assumes that the discharge is different at each section. If the reach
being analyzed is very small the external force of friction and the force due to the weight
of the water is small and can be neglected.
Steady Flow Program Limitations
In order to determine if a onedimensional or twodimensional model is needed it
is useful to look at the limitations of the one dimensional model. The fundamental
limitation is that the flow is considered to be onedimensional. This means that the
velocity components in directions other than the flow are negligible. HECRAS assumes
that the total energy head is the same for all points in the section. The second limitation
is that the flow is considered steady state (not time dependant). HECRAS will handle
unsteady flow, but a different set of equations are used and a hydrograph is needed.
Otherwise the peak flow is assumed to be the flow of highest velocity and is used to
represent the worst case scenario. The third limitation is that the flow must be gradually
varied flow except in the location of bridges, weirs, and culverts. In cases such as these
the momentum equation or empirical equations are used. The forth and last assumption
is that the channels have slopes less than 0.1. Under this condition the pressure variation
at a cross section is approximately hydrostatic. The pressure head (p) is measured by the
vertical distance and the water depth (y) is measured by the perpendicular depth, as
shown in Figure 10. When the slope exceeds 0.1 the values of (p) and (y) vary
significantly.
32
Figure 10. Illustration of pressure head and depth.
Onedimensional models provide competent, efficient, and useful solutions to
many problems. However, there are certain circumstances when the need for a two
dimensional model is suggested. A few of these circumstances are:
Skewed Crossing
Large Rivers with Incised Channels
Multiple Bridges on a wide Floodplain
Superelevated Flow
Variables
A
1
,A
2
, A
3
= flow area in subdivisions 1, 2, and 3
A
t
= total flow area of cross section
A= flow area for subdivision
?
1
, ?
2
=
velocity correction coefficients
B = momentum correction coefficient
C= contraction or expansion coefficient
E = specific energy
g = acceleration due to gravity
y
p
33
h
ce
= energy head loss due to contraction or expansion
h
e
= energy head loss from one section to the next
K
1
, K
3
, K
3
, = flow conveyance for subdivisions 1, 2, and 3
K
t
= total conveyance of cross section
K = conveyance for subdivision
L= discharge weighted reach length
L
L,
L
C
, L
R
= reach lengths for flow in the left overbank, main channel and right overbank
n = Manning?s roughness coefficient
n
c
= composite roughness coefficient
n
i
= coefficient of roughness of subdivision (i)
N = number of parts the main channel is divided into
P =
wetted perimeter of entire main channel
P
i
= wetted perimeter of subdivision (i)
Q
L
, Q
C
, Q
R
= Arithmetic average of flow between sections for the left overbank, main
channel, and right overbank
Q
1
, Q
2
, Q
3
= flow in the subdivisions 1, 2, and 3
Q
total
= total flow of cross section
R = hydraulic radius for subdivisions (area/wetted perimeter)
S
f
= representative friction slope between two cross sections
S
avg, f
= average conveyance friction slope
S
o
= slope of the channel, based on mean bed elevations
V
1
, V
2
, V
3
= average velocities in subdivisions 1, 2, and 3
34
=
?
?
?
?
?
?
?
?
g
V
2
2
velocity head
=
?
?
?
?
?
?
?
?
g
V
avg
2
2
? mean kinetic energy head
Y
1
, Y
2
= depth of water at cross sections
Y
ave
= depth from the watersurface to the centroid of the area
Z
1
, Z
2
= elevation of the main channel inverts
Applications
The process of creating a HECRAS model and the adjustments made to emulate
a known flood were documented for comparison with the twodimensional model.
The initial step in HECRAS is the creation of a river reach. This can be done on
top of a topographic map or by freehand. However, it is important that the reach be
drawn from upstream to downstream. Once this is done the cross sections can be entered.
When a cross section is created the user is prompted for the river station. A list of the
section identifiers and river stations can be seen in the Table 2. The corresponding
geographic locations of these cross sections can be seen in the Appendix in Figures 42
and 43. The other data input areas are the downstream reach lengths, Manning?s
roughness coefficient, and the subdivision break points. The downstream reach length is
the distance to the section immediately downstream. In the case of the downstream most
section, the river station and the downstream reach length is zero. The Manning?s
roughness coefficient was selected through field reconnaissance and aerial photography.
This is one of the most debatable areas in surface water modeling. It is also one of the
35
major points of comparison for this study reach. In order to provide a proper
representation of the numerical value of Manning?s roughness coefficient outside sources
were consulted.
Manning?s roughness coefficient can be determined several ways. Typically,
inexperienced hydraulic engineers use tables, equations, and roughness verification
studies to choose roughness values. Once the engineer is well versed in the area of
Manning?s roughness coefficients they are more likely to rely on their experience and
personal judgment. One of the best ways to develop the art of roughness coefficient
selection is through indirect calculations of known floods, calibrating output data to
observed watersurface profiles, and training under an experienced engineer. This gives
the engineer a sense of the streams typical to their area. Most engineers would agree that
the selection of over bank roughness is easier to determine. The area that is more
subjective is the channel roughness. This is why it is a good idea to do a sensitivity
analysis in areas where there isn't any calibration data. This allows the engineer to
determine how significant the channel roughness is in the profile calculations. Typically,
if the channel is small and insignificant in capacity the channel roughness will not play a
noteworthy role in the profile calculations. It is also a good idea to inspect the 2year
flood stage. Typically the stage of a 2year flood event should be one to two feet deep in
the floodplain.
The channel roughness value is difficult to determine because it is dependant on
so many factors. These factors and how they affect roughness are outlined by Chow
(Chow 1959). An understanding of these factors should lead to a better estimate of
channel roughness. However, it should be made clear that calculated roughness
36
coefficients are not applicable for all stages and discharges. This should be taken in to
consideration and will be discussed in latter sections.
The majority of the factors influencing channel roughness are interdependent. One of
the first factors to consider is surface roughness. This primarily focuses on the shape and
grain size distribution of the material covering the streambed and side slopes. The
material within the wetted perimeter acts as a flow retardant. Typically the larger grains
retard the flow more and result in a larger roughness coefficient. The converse is true for
smaller grained particles.
The other aspect of flow impedance is vegetation. Vegetation may project from the
top of banks into the channel or grow along the side slopes. Not only does this impede
the flow but it also reduces available flow area. The density and amount of foliage
depends on seasonal conditions. During summer months it should be expected that the
vegetation would be greater than winter months. Another important aspect of the
influence of vegetation is the depth of flow. When the depth is shallow the flow will be
hindered by vegetation more than at deep depths. It should also be considered whether
the flow could push the vegetation over or up root it. This should be well thoughtout
and all aspects of the site considered. Streams with steep slopes have greater velocity and
are more likely to make vegetation lay down. This would result in lower roughness
coefficients. Typically it can be assumed that the roughness is greater for shallower
depths. A study at the University of Illinois determined that trees 68 inches in diameter,
with pruned branches, located on the side slopes of the channel, effect flow less than
small bushy growths (Chow 1959). When in doubt of the vegetative conditions of a site,
a good rule of thumb is to select the roughness coefficients based on conditions reflective
37
of a typical spring flood. Conservative roughness coefficient selection is not always the
upper range of values. When good velocity estimates are needed it would be
conservative to choose values on the lower range of possible roughness coefficients.
The next area of concern is channel irregularity. This refers to sand bars, ridges,
bends, and depressions. Anything that causes drastic changes in channel bed or changes
in cross section size and shape warrants an increase in the roughness coefficient.
The channel alignment should be examined. If the reach has smooth curves with a
large radius a lower roughness coefficient would be selected in comparison with sharp
curves with severe meanders. Streams that are sinuous warrant an increase in roughness
coefficient. Chow states that natural streams, all things being equal, a meandering stream
may increase the roughness coefficients as much as 30% over a nonmeandering stream.
In connection with vegetation and obstructions to flow, sinuous streams should also be
investigated for attack on embankments.
Another contributing factor is silting and scouring. Both of these processes can have
an effect on the area and wetted perimeter of the channel. Scour can make a uniform
channel irregular. Sandy or gravel beds will erode more uniformly where as clay will
not. Typically there is not a significant increase in roughness for scour as long as it
progresses uniformly. There is also a roughness change due to the material that is
suspended during these processes. The suspended material consumes energy and causes
head loss resulting in an increase in the apparent roughness values. Most of the time, the
effects of suspended material is negligible. Silting may transform an irregular channel
and decrease the roughness, depending on the material deposited. The addition of sand
bars and sand waves will also increase the roughness.
38
Another technique used to determine roughness estimates is the consultation of a
roughness verification study. Publications such as these are good reference tools, but
extreme care should be exercised in selection of the publication. Manning?s roughness
coefficient is dependant upon geomorphology as well as physiographic location. The
principles that are used for roughness coefficient selection in western boulderstrewn
streams with steep slopes are not the same as southern flat slopes with heavily vegetated
streams. One publication that makes an effort to cover a wide variety of geographic
locations is, ?Roughness Characteristic of Natural Channels? (1987), by Harry H. Barnes,
Jr. This study examines the hydraulic conditions of 50 different stable streams. In order
to be considered for the study the stream must had to have a bank full flood, peak flow
measured by current meter methods or a welldefined stagedischarge relationship, good
highwater marks, and a uniform reach near a stream gage. Bed material for these sites
was determined through sampling methods. Once the data was processed Manning?s
equation and the Energy equation was applied. In these computations the value of ?,
velocity head coefficient, was assumed to be 1.0. The resulting roughness coefficients
were published with pictures of the reach and cross sectional plots. Of the 50 sites, 6
were located in Georgia. The roughness coefficients for these sites ranged from 0.04 to
0.075. Although Georgia streams are similar to Alabama streams, this would be no
substitute for methods determined by experience.
The third method of roughness coefficient selection is to consult a table of typical
values for given conditions. This is a good place for a beginner to start but should not be
relied upon solely. Due to the varying geographic and physiographic factors as
mentioned above. It should also be noted that the table is based on sites that are primarily
39
less than 100 feet in top width. When dealing with wider channels a lower roughness
coefficient should be used.
The next step in creating a HECRAS project is to enter the hydraulic structures.
The Fivemile Creek study reach has six hydraulic structures in the study reach. The
bounding cross sections, for each structure, were chosen and the river station of the
bridge was entered.
Figure 11. Location of hydraulic structures within the Fivemile Creek study reach.
N
40
Identifier State Plane Coordinates
NAD 1927
Structure
1 1304781 N, 716295 E Culvert
2 1305990 N, 718376 E Power Company Bridge
3 1305981 N, 720579 E Rail Road Bridge
4 1306383 N, 722378 E Springdale Road Bridge
5 1311015 N, 726712 E State Highway 79
6 1312930 N, 730506 E Lawson Road
Table 7. Geographic location of hydraulic structures in the Fivemile Creek study reach.
After the bridges are entered the ineffective flow areas are set. The ineffective
flow areas are based on the beginning and ending stations of the bridge. These are areas
where flow is not allowed to pass. These points are also set on the bounding cross
sections. The points of ineffective flow are based on the location of the cross section and
the contraction and expansion coefficients. For this project, the values of expansion and
contraction on the bounding cross sections were 0.5 and 0.3, respectively. The
ineffective flow areas were set to the corresponding beginning and ending stations of the
bridge, because the bounding cross sections were within a few feet of the upstream and
downstream face of the structures.
Once the geometric data has been entered and saved, the boundary conditions are
entered. The boundary conditions for this project include the peak flow at various
locations and the slope used to calculate normal depth at Section A. The hydrology for
the 2003 flood was computed and transferred to different locations based on the drainage
41
areas and transfer equations from Atkins 1996. For this reach peak flows were entered at
river stations 18068 (section K), 14986 (section I), and 5206 (section E). These locations
were chosen to account for the additional inflow brought to the system by Barton Branch
and the increase in drainage area.
The second boundary condition entered was the slope. The slope was calculated
by plotting a profile of the high water marks and fitting a linear line to the profile (Figure
12). The value computed for the slope of the high water marks is 0.0032 feet per feet.
For comparison sake, the same method was used to compute the streambed slope. The
result of this was 0.0035 feet per feet.
Slope Computations
y = 0.0035x + 500.82
y = 0.0032x + 519.46
490.00
500.00
510.00
520.00
530.00
540.00
550.00
560.00
570.00
580.00
590.00
0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000
River Station (ft)
E
l
evatio
n (
ft)
Streambed Profile Highwter Marks Linear (Streambed Profile) Linear (Highwter Marks)
Figure 12. Slope computations for the Fivemile Creek basin.
42
Calibration
Subsequent to entering and checking the data, the computational component of
the model was used. After the iterations were complete the warnings were checked and
noted. The output was inspected and it showed that the resulting watersurface profile
was low in some areas. The methods used to calibrate the watersurface profile were the
addition of interpolated cross sections, changes in cross sectional geometry, and
variations of the assigned Manning?s roughness coefficient. In order to have closer
agreement between the simulated profile and the actual profile, additional cross sections
were added. These sections were developed using the ?interpolate between cross
sections? function in HECRAS. After the sections were generated they were checked
for geometric accuracy. Roughness coefficients were assigned to these sections based on
aerial photography and field observations. The original input data was also modified to
account for areas of ineffective flow. Roughness values were also slightly adjusted to
simulate the 2003 flood profiles.
Results
The final Manning?s roughness coefficients used to simulate the 2003 flood can
be seen in Figure 22. This figure represents the roughness coefficients for the entire
reach. Pictures of the channel and floodplain in the vicinity of the cross sections can be
viewed in the Appendix in Figures 29 through 41. The resulting profiles generated in
HECRAS compared closely (within 0.25 feet) to the highwater profile of the 2003
flood.
43
The coefficient of discharge and weir coefficient were based on the default
values, for these computations. The use of the default values is common practice but
does not always provide accurate results. The flow through the Lawson Road bridge was
known for the 2003 flood. This provided an excellent opportunity to compare the flow
distribution computed with a known distribution.
The default weir coefficient and coefficient of discharge, in HECRAS, is 2.6
and 0.8, respectively. With these values and the model calibrated to the 2003 highwater
profile the resulting flow distribution was 11800 ft
3
/s (84%) bridge flow and 2300 ft
3
/s
(16%) weir flow. The indirect calculations (Appendix Figure 44) showed the bridge
carried 8760 ft
3
/s (62%) and the remaining 5320 (38%) ft
3
/s was weir flow. This
indicates that the default values resulted in 35 % error in the amount of flow through the
bridge. The default values indicate that the bridge is more efficient than it actually is.
The default values were adjusted to reflect actual conditions. The coefficient of
discharge was lowered to 0.58. This value was tabulated based on the bridge
submergence ratio. The ratio was calculated using the upstream stage and the low cord of
the bridge. The weir coefficient was also adjusted to 3.4. With these values the
computations resulted in 9020 ft
3
/s (64%) in bridge flow and 5080 ft
3
/s (36%) in weir
flow. The calculated percent error reduced to only 3 %, this is a much more acceptable
value. This also slightly adjusted the watersurface profile (Table 8). The resulting
profile was calibrated within 0.25 feet of the 2003 flood profile. A graphical plot of the
measured versus computed watersurface profile can be seen in the Appendix in Figure
45.
44
River Station OBSERVED HECRAS Difference
5,206 537.22 537.25 0.03
6,863 542 542.1 0.1
8,692 544.37 544.13 0.24
11,357 557.4 557.54 0.14
13,315 565.84 565.93 0.09
14,986 567.88 568.09 0.21
16,798 573.53 573.78 0.25
17,618 576.4 576.61 0.21
18,068 580.5 580.7 0.2
Table 8. Resulting profiles using the hydraulic model HECRAS for the May 07, 2003
flood on Fivemile Creek..
45
VII. TWO DIMESNIONAL ANALYSIS
History
The twodimensional model selected for the study reach was, Finite Element
SurfaceWater Modeling System for TwoDimensional Flow in the Horizontal Plane
(FESWMS2DH) contained within Surface water Modeling System (SMS). Initially the
software of choice was FiniteElement SurfaceWater Modeling System for Two
Dimensional Flow in the Horizontal Plane (FESWMS), (Froehlich, 1989). It is made up
of a modular set of computer programs that aid in the creation and execution of the two
dimensional flow computations. The modules are; input data preparation (DINMOD),
flow model (FLOMOD), output analysis (ANOMOD), and the graphics conversion
module (HPPLOT). The major computational engine of this model was FLOMOD. This
computer software package was created through cooperation of the U.S. Geological
Survey (USGS) and the Federal Highway Administration (FHWA). As advancements in
technology were made the model was updated to provide user friendly options. The new
model was called Finite Element Model Interface (FEMI) (R.R. McDonald, U.S.
Geological Survey, 1999). It is comprised of automated grid generator (GRIDGEN),
output visualization tool (MODVIS), and flow model (FLOMOD). Currently the model
has been updated to provide the latest graphical user interfaces (gui) to minimize the time
spent on the construction and execution of the model. The current model is contained
46
within Surface Water Modeling System (SMS). SMS was created by Brigham Young
University. The program is comprehensive and enables the programmer to use several
models one of them being the FESWMS2DH.
Theoretical Basis
The partial differential equations that govern twodimensional flow are derived
from the threedimensional equation (Froehlich 1989). The governing equations are
solved using the Galerkin finite element method. In order to apply the finite element
method the boundaries of the reach are set and the reach being modeled is divided into
elements. These elements are triangular or quadrangular in shape. Each individual
element is outlined by a series of nodes. Triangular elements are outline by placing
nodes at the vertices and midside points. In the case of the quadrangles they consist of 9
nodes, having one in the center. The dependent values of these elements are determined
using a set of interpolation functions, also called shape functions.
DepthAveraged Momentum Equations
The depth average surfacewater flow equations are derived by integrating the
threedimensional form of the conservation of mass and momentum equation. In this
derivation the vertical velocities and accelerations are considered to be negligible. Hence
the consideration of analysis of flow in twodimensions.
47
XDirection:
() () () ()KHVH
x
g
z
x
HgHUV
y
HUU
x
HU
t
buvuu
??
?
?
+
?
?
+
?
?
+
?
?
+
?
?
)(
2
)(
2
??
()()0
1
=
?
?
?
?
?
?
?
?
?
?
?
??+
xyxx
s
x
b
x
H
y
H
x
????
?
Equation 13
YDirection:
() () () ()KHUH
y
g
z
y
HgHVV
y
HVU
x
HV
t
bvvvu
??
?
?
+
?
?
+
?
?
+
?
?
+
?
?
)(
2
)(
2
??
()()0
1
=
?
?
?
?
?
?
?
?
?
?
?
??+
yyyx
s
y
b
y
H
y
H
x
????
?
Equation 14
This is a very complicated equation and therefore each piece will be broken out
separately and the variables explained. The figure below denotes the orientations used.
The variable (H) is a function of position in the x and y directions. This is what allows
the model to emulate superelevated flow. Onedimensional models only allow depth
variations in the direction(x) of flow. The partial differentiation of (z
b
) would result in
the slope in the direction of flow (x) and in the perpendicular direction(y). These values
are determined through the interpolation of user entered nodal data.
48
Figure 13. Control volume schematic.
Inside the control volume the velocities are represented by their point velocity
nomenclature u and v. The orientation inside the control volume is referenced to the
velocity. The point velocity (v) and the depth averaged velocity (V) are in the y
direction, and the point velocity (u) and the depth averaged velocity (U) are the x
direction. These combine to represent the velocity in the horizontal direction.
The capital letters U and V indicate the depthaveraged values of the functions
that describe the velocity profiles. An illustration of these profiles can be seen in the
Figure 14. In order to obtain the depth average of the velocity, the function, that
describes the shape of the velocity, is integrated over the depth of the flow. This is done
by setting the boundaries to: z
b
+h, z
b
.
()
?
+
?
?
?
?
?
?
=
Hz
z
b
b
dzu
H
U
1
Equation 15
W
v
u
Z
Y
X
H
Z
b
49
()
?
+
?
?
?
?
?
?
=
Hz
z
b
b
dzv
H
V
1
Equation 16
Figure 14. Velocity profile.
Momentum Correction Factor
The momentum equation results in a several correction factors. The first
correction factor examined is the momentum correction factor (?). These correction
factors account for vertical variation of the velocity in the x and y directions. It should be
noted that ?
uv
= ?
vu
. In most cases these terms are assumed to be equaled to unity and a
uniform vertical velocity is assumed. Based on this assumption, the variables can be
removed from the original equations.
z
y
x
H
z
b
u
U
50
Coriolis Effect
The second correction factor accounts for the Coriolis effect. The Coriolis effect
accounts for the force affecting flow due to the Earth?s rotation. The variable used to
define the Coriolis effect is (?).
() ()?=? sin2 ? Equation 17
The variable (?) is measured from the equator and returns a positive value for the
northern hemisphere and a negative value for the southern hemisphere. This effect is
minimal, for reaches that have a large width to depth ratio. An example of that would be
river or flood plain flow. The default value used in FESWMS2DH is based on the
assumption that the variation of (?) is small. To test this theory, the Coriolis factor was
computed based on the average values of latitude for Auburn, Mobile, and Fort Payne.
Table 9. Coriolis correction factors for various geographic locations.
City Latitude sin(?) ? = 2?*sin(?)
Auburn 32
o
36? 34? 0.5389 0.0045
Mobile 30
o
41? 38? 0.5105 0.0043
Fort Payne 34
o
28? 38? 0.5661 0.0047
51
The results (Table 9) show that the values differ only slightly. This is due to the
small magnitude of the angular velocity of Earth (?). A constant value of 0.0045, for the
angular velocity of the Earth, is assumed within FESWMS2DH.
Bottom Shear Stress
There are three types of stress considered; bottom shear, surface shear, and stress
caused by turbulence. Bottom shear stress, is defined by the variables (?
b
x
)
and (?
b
y
).
These variables represent bottom shear stress in the x and y directions, as previously
defined. These variables are a function of the depth averaged velocity (U and V),
density, bed slope in the x and y directions and the variable (c
f
). In most cases the
density is assumed to be a constant value. The variable (c
f
) is known as the bed friction
coefficient and can be computed by the two formulas shown below.
()()
2/1
2
2
2/1
22
1
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
+?
?
?
?
?
?
?
?
++=
y
z
x
z
VUUc
bb
f
b
x
?? Equation 18
()()
2/1
2
2
2/1
22
1
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
+?
?
?
?
?
?
?
?
++=
y
z
x
z
VUVc
bb
f
b
y
?? Equation 19
?
?
?
?
?
?
=
2
C
g
c
f
Equation 20
?
?
?
?
?
?
?
?
=
3/1
2
H
gn
c
f
?
Equation 21
52
It should be noted that FESWMS2DH allows the roughness to be varied with
depth. This is a handy tool when the area being modeled has drastic changes in surface
roughness with depth. This is also an option contained within HECRAS and WSPRO.
However the Cheesy coefficient can not be specified as a function of depth.
Surface Shear Stress
The second type of stress to be considered is surface shear stress. This
component is created by the wind. Several independent studies have measured and
investigated the values used to compute this stress. Based on these findings the default
values, within FESWMS2DH, are set and do not have to be adjusted by the user.
Stress Caused by Turbulence
The final variable considered represents the stress caused by turbulence. The
Bossiness?s eddy viscosity concept is used to determine the depthaveraged stress caused
by turbulence. The stress is assumed to be proportional to the gradients of the depth
averaged velocities. The stress caused by turbulence is represented by the variables; ?
xx
,
?
xy
,?
yx,
?
yy
.
?
?
?
?
?
?
?
?
+
?
?
=
x
U
x
U
xxxx
??? ? Equation 22
?
?
?
?
?
?
?
?
?
?
+
?
?
==
x
U
y
U
xyyxxy
???? ? Equation 23
?
?
?
?
?
?
?
?
?
?
+
?
?
=
y
V
y
V
yyyy
??? ? Equation 24
53
The variables
yyyxxyxx
and????
?,?,?,? represent the depthaveraged kinematic eddy viscosity.
FESWMS2DH assumes the depthaveraged kinematic eddy viscosity is isotropic. Based
on this assumption, there is no variation directionally ( ????? ??,?,?,? =
yyyxxyxx
). The eddy
viscosity can be computed using Equation 25.
()()HUc
o *
??
?
?? += Equation 25
The eddy viscosity if related to the eddy diffusivity for heat or mass transfer by the
following equation.
t
?
??
=?? Equation 26
We are interested in steady flow based on a peak, for these purposes. This allows
the first term, ?/?t (HU) to be eliminated. This along with the simplifications previously
outlined the governing equations in the x and y directions reduce to the following
equations.
XDirection:
() () ()KHVH
x
g
z
x
HgHUV
y
HU
x
b
0045.0)(
2
)(
22
?
?
?
+
?
?
+
?
?
+
?
?
()()0
1
=
?
?
?
?
?
?
?
?
?
?
?
??+
xyxx
s
x
b
x
H
y
H
x
????
?
Equation 13
54
YDirection:
() () ()KHUH
y
g
z
y
HgHVV
y
HVU
x
b
0045.0)(
2
)(
2
?
?
?
+
?
?
+
?
?
+
?
?
()()0
1
=
?
?
?
?
?
?
?
?
?
?
?
??+
yyyx
s
y
b
y
H
y
H
x
????
?
Equation 14
DepthAveraged Continuity of Mass
The other governing equation is the continuity of mass. The conservation of mass
equation is shown below.
?H + ?(HU) + ?(HV) = 0 Equation 27
? t ?x ?y
As years have passed and computers have advanced through the use of graphical
user interfaces the every day application of flow models has been greatly simplified.
These advancements have made it easier to model complex situations. However, through
the examination of the one and twodimensional equations, it is evident that an answer is
not a competent answer without the proper knowledge of basic hydraulic principles.
Variables
c
f
= bed friction coefficient
c
?
= dimensionless coefficient, in natural channels 0.6
C = the Chezy discharge coefficient
g = acceleration rate due to gravity 32.2 ft/s
2
or 9.81 m/s
2
H= Water depth
55
n = Manning?s roughness coefficient
? = density of water
?
x
b
, ?
y
b
= bottom shear stresses acting in the x,y directions respectively
?
xx
, ?
xy
, ?
yx
, ?
yy
= shear stress caused by turbulence, where for example ?
yx
acts in the x
direction on a plane that is perpendicular to the y direction
? = eddy diffusivity for heat or mass transfer
u =horizontal velocity in the xdirection (point velocity) along the vertical coordinate
U
*
= bed shear velocity
U = depthaveraged velocity in the horizontal direction
v = horizontal velocity in the ydirection (point velocity) along the vertical coordinate
V= depthaveraged velocity in the vertical direction
?????
??
,
?
,
?
,
?
=
yyyxxyxx
= directional values of the depthaveraged kinematic eddy viscosity
o
?? = base kinematic eddy viscosity
? = angular velocity of the rotating Earth (7.27 x 10
5
rad/s or 0.00417 degrees/second)
z
b
= Bed elevation
? = Coriolis Parameter
? = mean angle of the latitude being modeled.
? = 2.208 (U.S. Customary) and 1.0 (S.I.)
?
t =
empirical constant, Prandt number (for diffusion of heat), Schmidt number (for
diffusion of mass)
56
Applications
The Finite Element SurfaceWater Modeling System for TwoDimensional Flow
in the Horizontal Plane (FESWMS2DH) is one of many computational programs within
the Surface Water Modeling System (SMS) package. As previously described it uses
three partial differential equations to represent to conservation of mass and momentum
(Froehlich 1989).
The simulation of flood flows on Fivemile Creek was represented with a finite
element grid. This grid was made up of 5,603 elements and 12,597 nodes (Figure 16).
Of the 5,603 elements 5,094 were triangular in shape primarily representing the overbank
areas. The remaining 509 elements represent the channel and weirs.
5
7
Figure 15. Study reach for twodimensional flood flow simulations on Fivemile Creek.
N
5
8
Open Boundary
Closed Boundary
N
Explanation
Figure 16. Finiteelement grid used in flood flow simulations for the May 07, 2003 flood on Fivemile Creek.
59
Prior to the construction of the grid the boundary conditions must be determined.
The boundary condition will be either closed or open. A closed boundary is one that does
not allow flow to cross it. Closed boundary conditions usually exist at high ground,
which is known to contain the flood waters, or places where the flow is obstructed. An
open boundary represents areas where the flow is introduced and where it exits. The
Fivemile Creek study reach is bound by a closed boundary determined from topographic
maps and field surveys. The upstream and downstream boundaries of the creek were
designated as open boundaries (Figure 15).
The initial step in constructing a grid network is to determine what type of image
the grid will be built on. The most common is the use of a topographic map. Once the
image is selected it needs to be georeferenced in SMS.
When modeling a large reach it is helpful to use the automated grid generator.
This is done through the use of feature arcs. Before drawing the feature arcs it is always
a good idea to do some preparatory work. As discussed in latter sections, the channel can
be made of one or more elements. Prior to construction the user should determine what
geometric shape will best represent the channel in the grid network. All roadways should
be inspected and their widths noted. The user should also ascertain how dense the
resulting grid should be. To provided insight on this matter the friction and bed slopes
should be inspected. In the case of this reach, the slope of the water surface profile, for
the 2003 flood, is 0.0032 and the streambed slope is 0.0035 or 18 feet per mile. Based on
this a dense grid is more desirable. Most guidelines suggest that FESWMS2DH should
not be used on a reach that has a slope greater than 20 to 25 feet per mile. In retrospect if
the user decides the grid should have been denser there is an option to refine the grid.
60
This option will break each element into four elements. This can be done for the whole
grid or select elements.
Once the necessary decisions are made the overbank can be outlined with feature
arcs. The channel elements were determined to be 80 feet top width, for this project. To
represent this, two feature arcs were drawn on either side of the channel 80 feet apart.
Each feature arc is made up of nodes connected by line segments. The distance between
the node points will determine how dense the resulting grid will be. Depending on the
topography sections of the overbank are defined by connecting feature arcs to form a
polygon. An illustration of this can be seen in Figure 17.
Figure 17. Illustration of mesh generation through the use of feature arcs.
All of the feature arcs forming the polygon are selected and the ?Feature Objects? ?
?Build Polygons? command is executed. The polygon can be selected and double clicked
on. This will bring up the window where the elements are generated. The mesh type
61
chosen is up to the user, but it has been found that the paving method results in fewer
errors and works computationally just as well. This can be viewed in Figure 18.
Figure 18. Mesh generation tools in SMS.
An important concept when inspecting the resulting grid is the density in relation
to the channel. The grid should be denser near the channel and sparse away from the
channel. The channel elements should be constructed by hand. It is preferable to stay
consistent with the shape (rectangular or triangular) of element used in the channel. This
is sometimes unavoidable and results in strange geometry within the channel.
62
The final elements to be constructed are the hydraulic structures. It is very
important to make the grid dense around bridges. The area representing the bridge
should be two elements deep. The bridge definition should be dense enough that the
model does not have a problem converging on a solution.
In order to improve the quality of the solution there are guidelines used to judge
the quality of elements within the mesh. The user can set the specifications or leave them
at the default values. In this model the specifications were left at the default values. The
minimum and maximum exterior angles should not exceed 29 and 120 degrees,
respectively. The maximum slope computed across an element should not exceed 0.1.
The model also checks the size of elements relative to adjacent elements. Element should
not have an area change greater than 0.5 or 2.0. This makes it difficult to have a dense
bridge opening with larger elements surrounding it. This is why it is suggested that the
mesh be more refined around hydraulic openings and adjacent roadways. The model also
checks for concave quadrilaterals and ambiguous gradients.
Once the grid is built the elevation of the nodes must be defined. This can be
done through numerous ways. If the user has well defined Digital Elevation Maps
(DEM) at their disposal the amount of time is greatly reduced. However, DEMs are
rarely as distinct as field surveys. In the case of this model the same field survey used in
the onedimensional model was imported and the ground points were interpolated.
It is important to consider the elevation of the points imported. The thalwegs
should be negated when importing ground points. The interpolation method is not
capable of interpolating the channel definition. If the thalwegs are imported the elevation
of the overbank areas will be skewed because of the low value of the thalweg. Another
63
concern is the definition of obscure geometric break points. High or low areas that are
not continuous from one cross section to the next should also be omitted. An example of
this is a section H. The right overbank had a large mound of dirt that did not continue all
the way to section G. These points were not imported; rather the area was defined by
hand. Once the interpolation is complete the user should always check the validity of the
points interpolated.
The typical onedimensional method of defining geometry is not applicable for
twodimensional models. A channel within a flood plain cross section is usually
represented by station and elevation. This allows the user to show every geometric break
within the channel. One draw back of FESWMS2DH is the channel is represented by
one or more elements. The elements are bent to form a simple shape of the channel.
Smaller sites are typically represented with one element, a rectangle. These rectangles
are bent to correspond to a twodimensional triangle. The mid side nodes are assigned an
elevation to represent the thalweg of the channel. The figure below shows how the
rectangles are transformed into a twodimensional triangle. The red dots represent the
midside nodes.
Figure 19. Illustration of the bending of elements to represent triangular channel
geometry.
64
The shape that was determined to best suit this reach was a trapezoid. Because
the creek was relatively small in comparison to most river reaches the channel was
constructed of two rectangles bent at their joining node and mid side nodes. The figure
shown below is a graphical representation of the channel shape modeled in this reach.
Figure 20. Illustration of the bending of elements to represent trapezoidal channel
geometry.
This shape worked geometrically, but it was found that during the course of the
modeling the midside nodes would change back to the average values in certain areas.
This did not compromise the solution; however it took added time to maintain the desired
shape. The elevations of the top of banks and thalwegs were entered by hand. It is
important to do this after the ground points are imported and interpolated between. This
was one of the major time investments.
Once all of the nodes have been programmed with the appropriate geometry the
entire reach should be inspected for any nodes that were overlooked or were assigned the
wrong elevation. This can be done by inspecting the contour plot (Figure 21) of the
mesh. The elevations ranged from 509 to 588 feet, for this project.
65
e
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v
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t
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5
.
0
5
1
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66
Once the elevations have been interpolated or entered for each node the next
logical step is to assign the material properties. The areas that need to be set are the
Manning?s roughness coefficient, base kinematic eddy viscosity, and eddy diffusivity.
The selection of Manning?s roughness can be aided by the references Chow
(1959), or Barnes (1987). However, these calculations are based on the assumption of
onedimensional flow. The depth averaged flow equations as outlined in the theory
directly account for turbulence and horizontal variations in velocity. This indicates that if
the same roughness values were used in a 2dimensional model as a 1dimensional
model, these factors would be accounted for twice and the resulting watersurface
elevation would be higher than it should be.
For the initial simulation for the 2003 flood, the same roughness values were used
as the calibrated roughness values from HECRAS. This was done in order to determine
the variation in one and two dimensional roughness values. The roughness values were
then lowered incrementally to simulate the 2003 flood event. It should be noted that it is
easier for the model to transition from lower to higher values of roughness than vice
versa. When calibrating to a known flood event it is useful to have a base line of how
much to reduce one dimensional roughness values. As stated in the discussion of HEC
RAS, when calibration data is not available, the 2year flood event is inspected. Smaller
floods are not easily modeled using FESWMS2HD, so it helps to know the range of
roughness coefficient reduction.
One of the other input material properties is the base kinematic eddy viscosity.
The base kinematic eddy viscosity is based on the Boussinesq principle. Eddy viscosity
is typically referred to as internal friction. It is created when laminar flow becomes
67
turbulent as it passes over surface irregularities. It is also described as the turbulent
transfer of momentum due to internal fluid friction. The eddy diffusivity is typically
entered as 0.8.
The model can be error free and have accurate geometry but without the proper
boundary conditions the results are not justified. The upstream boundary condition is the
introduction of flow, for this reach. If the grid represents a relatively short reach there is
little judgment involved. However if the reach is long and the drainage area varies
significantly throughout the reach, the user should consider where the additional flow
will be introduced. There are several methods of doing this.
The Fivemile Creek reach is approximately 20,000 feet long and as previously
mentioned experiences notable changes in drainage area and peak flow. The first change
in attributing area is the addition of Barton Branch. Barton Branch is introduced to the
system above the Highway 79 crossing. Because this is an external tributary it could be
represented as an inflow on the exterior of the mesh. If the flow of Barton Branch is
introduced in a relatively high area it is possible the elements will dry up and the flow
will not be introduced to the system. The other change in drainage area and peak flow is
just above the railroad crossing. This area was selected to represent a portion of the reach
where the drainage area has increased and the flow at the upstream boundary is no longer
valid. Because this is simply a case of increased drainage area it would be easier to
introduce the additional flow as a source. Both areas were represented as a source, for
this reach.
The upstream most inflow was represented with a nodestring. A value of 14,100
(ft
3
/s) was entered for the 2003 flood, for this nodestring. This is the discharge computed
68
by indirect methods, at Lawson Road, by the USGS. The peak flow computed above
Highway 79 was 16,700 ft
3
/s. This is a net gain of 2,600 ft
3
/s. This addition was
introduced as a source.
Once all of the inflow boundaries were entered the tailwater was entered by
defining a nodestring at the downstream boundary of the gird. In order to properly
calibrate the model the tailwater should be known. The most popular way of calculating
the tailwater is the use of a onedimensional model to obtain a watersurface elevation at
the downstream boundary of the grid. The twodimensional model started at section C
and extended through section K. The onedimensional model started at cross section A
and extended through cross section K. Once the onedimensional model was calibrated,
the computed watersurface elevation at section C was used as the tailwater elevation, for
the twodimensional model. If there was a documented highwater mark a section C this
elevation would have been used instead. The computed tailwater elevation for this reach
was 533.9 feet. For the initial run or ?cold start?, every element within the mesh must be
wet. In order to achieve this, the initial tailwater used was 590.0 feet. This elevation was
spun down to the boundary condition of 533.8. The process of spinning down variables
will be discussed in latter sections.
Prior to running FESWMS2DH it is important to make all necessary changes to
the grid. Elements can not be created or deleted during the spin down process. This is
why it is important to inspect all aspects of the grid. The creation of the grid is an art that
is improved with practice. The user should look at the grid and visualize the water
flowing through the elements.
69
Once the grid is determined to be satisfactory visually and computationally the
nodes should be renumbered. This is done by selecting the upstream nodestring and
selecting ?Renumber? from the ?Nodestring? menu. There are two methods of completing
this task and the band width method should be chosen.
Before FESWMS2DH can be executed the parameters must be set. The run type
should be specified as hydrodynamic and the solution types as steady state. The bottom
stresses were calculated using Manning?s Equation, for this reach. The other input
variable that is adjustable, depending on the reach modeled, is the slip condition. Either a
slip, noslip, or semislip condition is specified for the closed boundary. The tangential
stresses are assumed to be zero, for the slip condition. Under these circumstances the
velocity at the boundary nodes are required to satisfy zero flow crossing the boundary.
The noslip condition assumes the velocity is set to zero. This automatically satisfies the
condition of zero flow crossing the closed boundary. Semislip is a combination of these
conditions (Froehlich 1989). The slip condition was chosen, for this reach
One other area that should be set is the convergence parameters. The ?Unit Flow
Convergence? and the ?Water Depth Convergence? were set to a value of 0.1. Based on
this, the model will not converge on a solution until the maximum change is equal to or
less than 0.1. The ?Element Wetting and Drying Tolerance? was also set to 0.25 feet.
This is the minimum depth used to turn an element off.
FESWMS2HD is very sensitive to drastic changes and therefore it has to go
through a process called spinning down. This is where the initial values of the tailwater
and the base kinematic eddy viscosity are given a large value and stepped down
incrementally to the actual value. The same process is used for weir flow and bridge
70
girders (pressure flow). The solver within the FESWMS2HD module computes the
water surface elevation and velocity for every node. This is done through an iterative
process. In order to do this the solver has to have an initial water surface elevation. The
solver assumes a constant water surface across the boundary and a velocity of zero. The
first computation or cold start is based on the initial condition and boundary conditions
files. The tailwater was set at 590 feet and the base kinematic eddy viscosity was set at
150 ft
2
/s, for the cold start, for the Fivemile Creek study reach.
Once a cold start has been successfully executed the next step is a ?hot start?.
The hot start uses the same iterative process based on the computed results of the
previous run. For each successive run the variable being spun down is decreased until the
target value is reached.
The first parameter that needs to be spun down is the tailwater. The tailwater is
initially set high to make sure all elements are wet. During the spinning down process
the tailwater is incrementally decreased. Once the tailwater is at the desired elevation the
base kinematic eddy viscosity should be spun down. The typical starting value is 150
ft
2
/s and is spun down in increments of 25 to 50. The target value is in the range of 10
ft
2
/s to 25 ft
2
/s depending on the flow energy and depth in the channel.
The next area of concern is weir flow. If the upstream stage of the hydraulic
structures is less than the crest of the weir this is not a concern and the grid interface with
the weir can be left as a closed boundary. The twodimensional governing equations are
depth averaged and the velocity in the vertical direction is assumed to be negligible. This
is not a valid assumption for weir flow. Weirs and similar structures can have a
significant velocity in the vertical direction. To account for flow over weirs, within the
71
twodimensional model, onedimensional methods are used. This is done the through the
use of an empirical equation.
The initial construction of the Fivemile Creek grid was based on the concept of
weir segments. The model would not converge on a solution when the weir segments
were lowered. Upon consultation of other modelers, it was found that this is a common
problem. Various methods were employed to overcome this problem, but none resulted
in a converged solution. Consequently, alternative methods were used. The model was
updated to represent the weir as obstruction flow. This is an acceptable practice, but is
not without flaw. This method of modeling weir flow assumes negligible velocity in the
vertical direction. It should also be noted that obstruction flow is not as efficient as weir
flow. This will cause the model to indicate a lower value of weir flow than direct weir
methods.
The final step in the spin down process is the lowering of the ceiling values
(pressure flow) of the structures. This is done in small increments due to the instability
that it causes. This also was a source of error introduced into the model. The ceiling
values of the two structures on the upper end of the reach were not successfully set to the
actual value. If the ceiling elevations were successfully lowered the watersurface would
have been slightly higher upstream of the structure. The lower ceiling elevation would
also affect the coefficient of discharge and resulted in less flow going through the bridge.
Calibration
In order to provide a wide range of comparison FESWMS2DH was executed for
several different scenarios. The grid network was analyzed with the roughness
72
coefficients from the onedimensional study and reduced roughness values. Each method
provided insight in proper way of representing the reach with twodimensional flow
assumptions.
The first simulation was used to compare directly to the onedimensional results.
The onedimensional Manning?s roughness coefficients were used in the two
dimensional model (Figure 22). The boundary of the roughness values were estimated
from aerial photography. The results of this simulation gave a watersurface profile that
deviated from the 2003 flood profile as much as 1.9 feet and as little as 0.4 feet. As
expected the resulting water surface profile was higher than the one computed with the
one dimensional model.
Section Observed
(ft)
HECRAS
(ft)
FESWMS2DH
Average
(ft)
(ft)
D 537.22 537.25 537.65 0.4
E 542 542.1 541.3 0.8
F 544.37 544.13 546 1.9
G 557.4 557.5 556.4 1.1
I 567.88 568.09 568.9 0.8
J 573.53 573.8 574.5 0.7
K 580.5 580.55 581.55 1.0
Table 10. Resulting watersurface profile using onedimensional Manning?s roughness
coefficients in the hydraulic model FESWMS2DH for the Fivemile Creek study reach.
73
Dis
able
ob_
n=
0.1
4
ob_
n=
0.0
6
ob_
n=
.07
ob_
n=
0.0
4
ob_
n=
0.0
45
cha
nne
l_0.
05
cha
nne
l_0.
06
0.1
2
ob_
n=
0.0
5
ob_
n=
0.1
5
cha
nne
l_0.
065
ob_
n=
0.1
0
ob_
n=
0.1
3
Law
son
_R
oad
_Br
idg
e
Ga
s_C
o_B
r
RR
_Br
idg
e
Hw
y_7
9_B
ridg
e
RO
AD
Dis
able
ob_
n=
0.1
4
ob_
n=
0.0
6
ob_
n=
.07
ob_
n=
0.0
4
ob_
n=
0.0
45
cha
nne
l_0.
05
cha
nne
l_0.
06
0.1
2
ob_
n=
0.0
5
ob_
n=
0.1
5
cha
nne
l_0.
065
ob_
n=
0.1
0
ob_
n=
0.1
3
Law
son
_R
oad
_Br
idg
e
Ga
s_C
o_B
r
RR
_Br
idge
Hw
y_7
9_B
ridg
e
RO
AD
Dis
able
ob_
n=
0.1
4
ob_
n=
0.0
6
ob_
n=
.07
ob_
n=
0.0
4
ob_
n=
0.0
45
cha
nne
l_0.
05
cha
nne
l_0.
06
0.1
2
ob_
n=
0.0
5
ob_
n=
0.1
5
cha
nne
l_0.
065
ob_
n=
0.1
0
ob_
n=
0.1
3
Law
son
_R
oad
_Br
idg
e
Ga
s_C
o_B
r
RR
_Br
idge
Hw
y_7
9_B
ridg
e
RO
AD
Dis
able
ob_
n=0
.14
ob_
n=0
.06
ob_
n=.
07
ob_
n=0
.04
ob_
n=0
.04
5
cha
nne
l_0.
05
cha
nne
l_0.
06
0.1
2
ob_
n=0
.05
ob_
n=0
.15
cha
nne
l_0.
065
ob_
n=0
.10
ob_
n=0
.13
Law
son
_R
oad
_Br
idg
e
Ga
s_C
o_B
r
RR
_Br
idge
Hw
y_7
9_B
ridg
e
RO
AD
F
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=
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1
3
B
r
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R
o
a
d
N
74
Results
Attempts were made to transition to lesser values of roughness in increments of 5
%, from the initial simulation. This was a difficult and unsuccessful process. This is
evidence that if the user plans to calibrate the profile to a known flood their initial
simulation should be with reduced roughness values. The question that most commonly
arises is how much to decrease the roughness.
In order to calibrate the model to the 2003 flood profile a new simulation was
created with the initial roughness values being decreased. The percent reduction was
chosen from sensitivity analysis. The base reduction factor chosen was 20% for the
overbanks and 5% for the channel roughness values. Preceding chapters outlined how
variable Manning?s roughness coefficient is. The methods used on this reach are not
applicable in all situations, because every reach is unique and has its own characteristics.
However, if enough studies are conducted and documented, relationships between the
characteristics of the reach and the percent reduction can be developed and a based line
reduction factor determined.
The decrease in roughness values alone did not ensure that the profiles accurately
emulated the 2003 flood profiles. The majority of the cross sections depicted a water
surface elevation that was within 0.8 feet of the known 2003 profile. The geometry was
then inspected. Similar to the onedimensional model areas of ineffective flow were
added were large buildings are located. This was done by disabling elements to represent
the buildings. This improved the accuracy of the profile. The profile (Table 11) created
by the twodimensional model was successfully calibrated within 0.65 feet of the known
water surface profile.
75
Section Observed
(ft)
FESWMS2DH
Average
(ft)
Difference
(ft)
D 537.22 537.15 0.07
E 542.00 541.9 0.10
F 544.37 544.85 0.48
G 557.40 557.2 0.20
I 567.88 568.4 0.52
J 573.53 573.75 0.22
K 580.50 581.15 0.65
Table 11. Resulting watersurface profile with calibrated Manning?s roughness
coefficients for the hydraulic model FESWMS2DH.
An important aspect of the twodimensional model is the ability to represent
superelevated flow. Superelevation is characterized by a higher water surface elevation
in the outer bank of a bend and a lower watersurface elevation on the inner bank. It is
created by the centrifugal force acting on the flow at the bend that causes the water to
stack up in the outside of the bend, this also results in irregular velocity profiles in the
area of the bend which corresponds to values of the coefficients ? and ? not being equal
to unity (Chow1959).
One dimensional flow models simulate the watersurface profile at a constant
elevation for the entire crosssection. However, for short radius bends with a significant
size channel or supercritical conditions the effects of superelevation should not be
neglected. This is also a condition that should be considered when locating and
documenting highwater marks. If the highwater mark is located in a bend a mark
76
should also be located on the other bank. This is a good idea for one and two
dimensional calibration. The two marks can be averaged, for onedimensional
calibration. The accuracy of superelevated results can be examined, for twodimensional
calibration. The maximum superelevation observed for the Fivemile Creek simulation
was 1.5 feet.
Another area of inspection is flow distribution and velocity profiles. Larger
flooding events often incite combination flow. Under these circumstances the model
must separate the flow into bridge flow and weir flow. In some cases the model must
determine the flow separation between multiple bridges and weir flow. Once the model
has determined the flow distribution the resulting velocities are available. This is a major
concern in the design of hydraulic structures. This reach was considered a prime
candidate for the comparison of one and twodimensional results, because of a known
flow distribution at Lawson Road. However, due to inconsistencies in the two
dimensional model it was determined that an accurate conclusion could not be drawn.
The results of the twodimensional model are considered to have sources of error near the
Lawson Road crossing. The use of obstruction flow in the place of weir flow and
difficulty in simulating pressure flow added error to the resulting flow distribution and
velocity profile.
The onedimensional model did not accurately depict the flow distribution
between weir and bridge flow, at Lawson Road. From this it can be seen that the use of a
calibrated watersurface elevation does not always produce an accurate flow distribution.
Due to the lack of accurate results this could not be investigated for the twodimensional
model.
77
Other studies were researched to provide insight into the matter. One particular
article ?Use of Velocity Data to Calibrate and Validate Two Dimensional Hydrodynamic
Models?, by Wagner investigated this topic with the use of RMA2. RMA2 is a finite
element hydrodynamic numerical model developed by the U.S. Army Corps of
Engineers. Wagner found that, ?Calibrated models that accurately matched watersurface
elevations did not necessarily guarantee an adequate match of the measured flow field?
(Wagner 2002). The study consisted of a 40 mile reach. The reach had 40 cross sections
with calibration and validation data for low and high flow. Each cross section was
calibrated to the watersurface elevation. The velocity fields were then inspected and
found to be in close agreement for low flow, but deviated from the observed values for
high flow. It was found that in order to calibrate the model to the measured field a slip
condition was used and a variance of roughness coefficients within the channel. This
further supports the conclusion that a calibrated model does not ensure that all of the
hydraulic properties will be calibrated.
78
VIII. COMPARISON OF ONE AND TWO DIMENSIONAL MODELS
The onedimensional model is a highly efficient way of representing hydraulic
conditions for flood studies and the design of hydraulic structures. However, the one
dimensional model is not suitable for all cases. It is based on several assumptions that do
not always accurately represent the watersurface profile or velocity distribution. This
includes reaches that have a high degree of sinuosity. The onedimensional model
assumes a constant water surface elevation and is not equipped to simulate superelevated
flow. Onedimensional models are not adequate to handle complex crossings with
multiple openings, especially more than four or crossings having extreme skew.
Some of the difficulties incurred in the development and execution of the two
dimensional model include ground elevation data, Manning?s roughness coefficient
selection, and construction of the grid. Often accurate ground elevations are not available
for the entire reach and interpolation introduces error. Most surfacewater modelers use
onedimensional models on a day to day basis and develop their roughness coefficient
selection skills based on the use of these models. These skills are not conducive to all
reaches modeled with twodimensional flow equations. The reduction of one
dimensional roughness values for twodimensional flow varies based on the basin?s
characteristics. It was seen that for this reach the reduction of roughness values varied
from 5% to 20%. These values are not applicable for all reaches but can serve as a base
79
line reduction for a basin with similar characteristics. More research should be done on
this topic to provide modelers with a sense of acceptable reduction factors when
calibration data is not available. The construction of the grid is also timeconsuming.
From examination of the results it can be seen that the maximum divergence of
the watersurface elevation was 0.25 feet for the onedimensional model and 0.65 feet for
the twodimensional model. The onedimensional model was easier to calibrate and
resulted in a closer match to the calibration data.
The theory, methodology and results of the one and two dimensional models
have been compared for the given reach. Upon inspection of these topics it was found
that for a standard reach, such as the one described, the benefits of the one dimensional
model far out weigh those of the twodimensional model.
80
IX. SECONDARY STUDY
Based on these results of the Fivemile Creek study it was determined that for a
standard reach the onedimensional analysis is sufficiently accurate and more cost
effective than the two dimensional analysis. It was also concluded that more research
should be done to provide correlations between roughness coefficient reductions and
reach characteristics. The one area that is still gray is the performance of one and two
dimensional analyses on velocity and flow distribution. In order to provide further
investigation on these topics a second reach was investigated.
The second reach was selected to provide as many points of investigation as
possible. The primary function of the reach was the investigation of flow distribution and
velocity profiles. However, it also provided insight on multiple bridges on a skewed
crossing and n roughness coefficient reduction for a basin with characteristics different
from the Fivemile Creek reach.
Description of the Reach
The second reach selected for flood flow simulation was the U.S. Highway 11
crossing of Sucarnoochee River at Livingston, Alabama (Figure 23). The drainage area
of this site was determined to be 607 square miles and the average streambed slope is
81
0004. This site is a prime candidate for a calibrated flood study. The USGS has operated
a stream flow gage at this site since 1938. The gage has a stable stagedischarge
relationship and an excellent high flow measurement. The measurement was taken
during the1979 flood. The bridges have recently been replaced; however the models
were based on the conditions reflective of the 1979 flood. At the time of the flood the
hydraulic structures consisted of a 850 foot long main channel bridge and 165 foot long
relief.
Hydrology
The measurement made in 1979 indicated that the total flow at the time of
the measurement was 57,207 ft
3
/s. Of this amount 48,700 ft
3
/s (85%) passed through the
main channel structure and 8,458 ft
3
/s (15%) passed through the relief structure. In order
to relate the measured value to a recurrence interval the flood frequency relation was
developed for the gage for the 10, 25, 50, 100, 200, and 500 year recurrence
intervals. The flood peak discharges (Table 12) were computed using the rural regression
equations for hydrologic area 4 and gaging station data collected for the site. Inspection
of the flood frequency indicates that the measured event is approximately a 200year
recurrence interval flood.
82
Recurrence Interval
(years)
Discharge
(ft
3
/s)
Station Weighted
Gage WaterSurface Elevation
(ft)
10 19,100 116.7
25 28,000 118.6
50 36,200 120.1
100 45,900 121.4
200 57,400 122.8
500 75,800 124.5
Table 12. Stagedischarge relationship for select recurrence intervals for the
Sucarnoochee River reach
Figure 23. Location map of the Sucarnoochee River reach.
N
83
Hydraulics
The corresponding stage on the downstream side of the bridge is 122.8 feet. The
lowest ceiling elevation for both bridges is 123.2 feet and the minimum weir elevation is
124.7 feet. This indicates that the reach will not be further complicated by pressure flow
or weir flow. Examination of the location map shows that that approximately 550 feet
downstream of the U.S. 11 crossing is Southern Railway. The Southern Railway crossing
has two hydraulic structures that convey the flow. The headwater elevation for these
bridges will serves as the downstream control for both models.
OneDimensional Results
The onedimensional model was constructed in the same manner as the Fivemile
Creek study. The roughness values were selected through a site investigation and slightly
adjusted to match the gage rating. The boundary condition was entered as a known
watersurface elevation. The geometry was based on cross sections at the bridge and
upstream and downstream of U.S. Highway 11.
TwoDimensional Results
The two dimensional reach was approximately 3,500 feet long and consisted of
6,502 elements and 13,694 nodes. The grid was constructed and then refined using tools
within SMS. The upstream extent of the reach extends just above the zone of contraction
and the downstream extent if just upstream of the railroad crossing. The same default
parameters described for the Fivemile Creek were used. The initial simulation was based
84
on the roughness coefficients used in the calibration of the onedimensional model. The
roughness coefficients were then decreased incrementally and the changes in water
surface elevation were noted. Cross sections upstream and downstream of US 11 were
imported and the elevations of the nodes were set through linear interpolation.
85
N
Open Boundary
Closed Boundary
EXPLANATION
Figure 24. Finiteelement grid used in flood flow simulations for the 1979 flood on the
Sucarnoochee River.
86
Figure 25. Land surface elevations for the Sucarnoochee River study reach
elev ation
85.0
88.0
91.0
94.0
97.0
100.0
103.0
106.0
109.0
112.0
115.0
118.0
121.0
124.0
127.0
130.0
N
87
X. COMPARISON OF SECONDARY STUDY RESULTS
Flow Distribution and Velocity
It is a rarity to have highwater marks, flow distribution, and average velocity
profiles. Highwater marks are often used to indirectly calculate discharge for areas that
do have a gage, has a stage only gage, or a gage that was destroyed by the flood. In some
instances highwater marks are located solely for calibration data. Because of this it is
rare to have highwater marks, flow distribution and velocities.
Since the watersurface elevation is the most common calibration data both
models were constructed and calibrated to the known watersurface elevation at the
downstream side of the bridge. The resulting flow distribution and velocities were then
compared with the measured values. The measured discharge indicated 85 % of the flow
passed through the main channel bridge and 15% through the relief. The one
dimensional model showed 88% of the flow in the main channel bridge and 12% in the
relief. The twodimensional model indicated 82% of the flow in the main channel and
18% in the relief. Both models were off from the measured value by 3%. Without the
use of the calibration data the comparison of the results show that the flow distribution
between the two models deviated by 6%. This would lead one to conclude that the one
dimensional model was off by 6% when in actuality it was only off by 3%. The results
indicate that both models provide an accurate representation of the flow distribution. The
88
measured velocities are an average tube velocity. This is also true for the velocities
provided by the onedimensional model. The twodimensional model provides a depth
average point velocity. The maximum velocities for the nodes and midside nodes were
documented from FESWMS2DH. The corresponding tube velocity from the
measurement and the HECRAS results were compared to this value. The results
indicated that for both bridges FESWMS2DH provided a closer estimated than HEC
RAS. However, in some areas both models deviated from the actual value significantly.
To illustrate the output format of FESWMS2DH and show the resulting velocity vectors
Figures 26 and 27 are shown
8
9
Figure 26. Computed velocity vectors for the main structure on the Sucarnoochee River for the April 1979 flood.
velocity mag
0. 0
1. 0
2. 0
3. 0
4. 0
5. 0
6. 0
7. 0
8. 0
9. 0
10.0
N
9
0
Figure 27. Computed velocity vectors for the relief structure on the Sucarnoochee River for the April 1979 flood.
velocity mag
0. 0
1. 0
2. 0
3. 0
4. 0
5. 0
6. 0
7. 0
8. 0
9. 0
10.0
N
91
Skewed Crossing
One of the advantages of this reach is the measured angle of attack. Inspection of
the channel and road does not indicate there is a significant attack angle. However, the
roadway crosses the flood plain at a slight skew. The discharge measurement recorded
the skew varying from 12 to 25 degrees. This is an interesting topic in the comparison of
one and two dimensional flow models. Skew is one of the major complexities that
necessitates a twodimensional model. It is also an area where many engineers question
their judgment.
When the roadway crossing is skewed relative to the flood plain and multiple
structures are present the modeling techniques are subjected to engineering judgment.
Based on the flow path, for a skewed crossing one structure will be further downstream
than the other. The typical onedimensional models use conveyance and available flow
area to determine a stagnation point between the structures. Onedimensional models can
not divide flow between multiple structures on the same floodplain with different river
stations. Typically, to account for the difference in river stations between the two
structures, a river station at the half way point is selected and the openings are projected
to this location. This is thought to provide a fairly accurate flow distribution, for minimal
skew. The exact threshold of where this assumption becomes unrealistic is unknown.
This is further complicated by another factor. The distribution is not only affected by the
skew but also the spacing between the structures. This can be referenced to the flood
plain width. This particular reach has a maximum skew value of 25 degrees for the 200
year event. The average flood plain width is approximately 2,900 feet, and the spacing
between the structures is 1,200 feet. This is spacing to width ratio of 0.4. Based on the
92
results of the flow distribution it can be concluded that an attack angle of 25 degree and
spacing to width ratio of 0.4 is not great enough to warrant the use of a twodimensional
model.
Previous studies, not discussed in this publication, indicated that the flow
distribution greatly varied for the one and two dimensional models for an average skew
of 45 degrees. The study was not calibrated therefore the true distribution is unknown
and no conclusion can be drawn as to how inaccurate the onedimensional model was.
Based on these findings it can be assumed that the threshold is between 25 and 45
degrees. A safe assumption is that a roadway crossing of 30 degrees or greater
necessitates a twodimensional model for accurate flow distribution. The spacing to
width ratio deserves further investigation.
Manning?s Roughness Coefficient Reduction
Previous chapters discuss the variance between one and twodimensional
roughness coefficients. This difference is primarily due to the different methods of
accounting for bed shear stress and turbulence. These variables are directly included in
onedimensional roughness coefficients. A common way of selecting the appropriate
roughness coefficient is through a roughness verification study or references such as
Chow (1959). These calculated values directly account for the effects of turbulence and
bottom shear stresses. The depthaveraged flow equations directly account for bottom
shear stresses, surface shear stresses, and stresses caused by turbulence. Manning?s
roughness coefficient is used to determine the bottom shear stresses. The bottom shear
stress is a function of the depth averaged velocity, density, bed slope in the x and y
93
directions and the variable (c
f
). The value of (c
f
) is a function of Manning?s roughness or
the Chezy coefficient. The variables used to compute (c
f
) can be seen in Equations 20
and 21.
Froehlich documents this in the users? manual ??.[A]ssumed onedimensional
flow, implicitly accounts for the effects of turbulence and deviation from uniform
velocity in a cross section. Because the depthaveraged flow equations directly account
for horizontal variations of velocity and the effects of turbulence, values of (c
f
) computed
using coefficients based on onedimensional flow assumptions may be slightly greater
than necessary?(Froehlich 1989).
Based this it can be concluded that the reduction of the roughness coefficient will
depend on the slope, velocity, and roughness value. Equation 21 shows that lower values
of roughness will produce lower values for (c
f
). This would indicate that within the same
basin lower values of roughness would need to be reduced by a smaller factor. This was
observed within the Fivemile Creek study reach. The roughness values for the channel
were lower than the average floodplain roughness. To simulate the May 2003 flood the
channel roughness values were reduced by 5% and the floodplain values were reduced by
an average of 20%. These values are interconnected. To determine the actual reduction
in channel values low flow or bank full calibration data would be needed. Since this is
not available, the other two areas of interest, slope and velocity were further investigated.
Sucarnoochee River was chosen for the insight it would provide in this matter.
The previous study, Fivemile Creek, had a bed slope of 0.0035. The variance in
roughness for this reach ranged from 5 to 20 percent. Similar analyses were performed
for Sucarnoochee River. The approximate bed slope was calculated to be 0.0004. The
94
percent reduction used to calibrate the reach to the water surface elevation at the bridge
was 5%. This provides insight into the change of roughness coefficient reduction with
slope.
Sensitivity analysis was done to further document the changes in the water
surface elevation with the associated reduction in roughness values. The roughness
coefficients were reduced in increments of five percent and the change in watersurface
elevation noted in four locations. The four locations were chosen at the main and relief
bridges, the upstream boundary and the mid point of the reach. The watersurface was
taken at the left and right edges of water and averaged, for each location. The maximum
change was seen at the upstream boundary and the minimum change was seen at the
relief structure. Table 13 shows the change in watersurface based on the value
documented prior to the reduction of roughness.
Location WaterSurface
change for
5% Reduction
(ft)
WaterSurface
change for
10% Reduction
(ft)
WaterSurface
change for
20% Reduction
(ft)
Relief Bridge
0.006 0.011 0.0170
Upstream Boundary
0.115 0.229 0.447
Table 13. Correlation between watersurface elevation and Manning?s roughness
coefficients for the Sucarnoochee River reach.
Inspection of the table indicates that the changes of watersurface elevation in the
bridge are not noteworthy. This is a great indicator that for a flat slope the effects due to
turbulence are negligible and the onedimensional roughness values would suffice.
95
However, it should also be noted that many factors are considered when determining
roughness and how it effects the watersurface elevation. These factors should not be
over looked and the decision should not be based on slope alone.
The other area of interest in the twodimensional, depthaveraged flow equations is
turbulence. The changes in watersurface elevation were noted as the base kinematic
eddy viscosity was adjusted. It was found that large values of base kinematic eddy
viscosity had an effect on the upstream stage. Variations between reasonable values had
little effect on the stage of the reach. It should be noted that turbulence is a function of
the eddy viscosity and velocity gradients. The variance of the base kinematic eddy
viscosity indicated that the influences on the watersurface elevation are less than that of
Manning?s roughness coefficient. This confirms that the variance of roughness should be
used in calibration and the base kinematic eddy viscosity should be held constant at a
reasonable value.
96
Figure 28. Manning?s roughness coefficients used for the flood flow simulation of
Sucarnoochee River.
N_= _0.14
Bridges
N_= _0.055
N_= _0.05
N
EXPLANATION
Manning?s Roughness Coefficients
n= 0.15
n= 0.055
n=.05
Bridges
97
XI. CONCLUSION AND ENDING REMARKS
The development, theory, and results of a onedimensional stepbackwater
model and a twodimensional finiteelement surfacewater model were examined. The
creation, execution and steps taken toward calibration were documented. The theory as
documented by the respective users? manuals was explained and elaborated upon where
necessary. The results of the models were also examined for effects of superelevated
flow, variance in Manning?s roughness coefficient and base kinematic eddy viscosity,
flow distribution, and velocity profiles.
The first reach examined was Fivemile Creek. The results showed that for a
standard reach the cost to benefits ratio of a onedimensional model out weighed that of a
twodimensional model. The process of construction, execution, and calibration for the
twodimensional model was time consuming and did not yield results closer to the
measured values. It was also determined for a reach with similar characteristics the
average roughness reduction is approximately 20% to transition between a calibrated
one and twodimensional models.
The second reach, Sucarnoochee River, was examined for comparison to the first
reach and the inspection of flow distribution and velocity profiles. This reach was chosen
because it has a much flatter slope than the Fivemile Creek reach. The average roughness
reduction determined for this reach was 5%. Inspection of the twodimensional,
98
depthaveraged equations showed the effects of turbulence and bottom shear stresses are
a function of the slope, base kinematic eddy viscosity, and the roughness value. The
calibration data indicated that reaches with a flatter slope should be reduced by a smaller
percentage when transitioning from onedimensional to twodimensional flow. The
effects of varying the base kinematic eddy viscosity were also inspected. The results
indicated that for values of base kinematic eddy viscosity between 20 ft
2
/s and 40 ft
2
/s the
watersurface elevation was not greatly affected. It was also determined that for values
of base kinematic eddy viscosity greater than 40 ft
2
/s the upstream stage was affected the
most. This is the primary reason the Manning?s roughness coefficient is adjusted to
calibrate to a known watersurface elevation instead of the base kinematic eddy viscosity.
Since it was determined that onedimensional models are sufficient for standard
reaches the effects of a nonstandard reach were examined. The general restrictions on a
one dimensional model are skewed roadway crossings, large rivers with incised
channels, four or more bridges on a crossing, and superelevated flow. Of these
stipulations the one that is vague is skewed crossings. The onedimensional model can
be adjusted to account for skewed crossings; however there is a point where this no
longer provides accurate results. The variables to be considered are the angel of attack
(skew), and the bridge spacing to flood plain width ratio. Sucarnoochee River was
chosen to provide insight on this subject as well. A measurement of the 1979 flood, on
Sucarnoochee River, indicated that the angle of attack for the 200year flood event
ranged from 15 to 20 degrees. The spacing to width ratio for this reach was 0.4. It was
determined from inspection of the flow distribution between the main and relief
structures that these two values are not great enough to merit the use of a
99
twodimensional model. This in conjunction with previous studies, not documented, led
the author to the conclusion that multiple structures that cross the flood plain at an
average angle greater then 30 degrees should be analyzed with a twodimensional model.
100
REFERENCES
Atkins, J.B., 1996, Magnitude and frequency of floods in Alabama: U.S. Geological
Survey WaterResources Investigations Report 954199, 234p.
Barnes, Harry H. Jr., 1987, Roughness Characteristics of Natural Channels: U.S.
Geological Survey WaterSupply Paper 1849, 209 p.
Brunner, Gary W., 2002, HECRAS River Analysis System Hydraulic Reference
Manual: U.S. Army Corps of Engineers Hydrologic Engineering Center Report
No. 1243 p.
Chow, V.T., 1959, Openchannel hydraulics: New York, McGrawHill, 616 p.
Federal Emergency Management Agency, Flood Insurance Study: Jefferson County,
Alabama and Incorporated Areas: Vol 2, 34P.
Froehlich, David C., 2002, Finite Element Surfacewater Modeling System: Two
Dimensional Flow in a Horizontal Plane Version 2 Draft user?s Manual
FESWMS: U.S. Department of Transportation Publication No. FHWARD03
053, 710p.
Froehlich, D.A., 1989, Finite element surfacewater modeling system: Two dimensional
flow in a horizontal plainUsers manual: U.S. Department of Transportation
Publication No. FHWARD88187. 124 p.
Jansen, P.P., et al., 1979, Principles of River Engineering ? The NonTidal Alluvial
River: London, Pittman, 509 p.
Methods, Dyhouse, et al., 2003, Floodplain modeling using HECRAS. Waterbury:
Haysted Methods 658 p.
Parr, A. David and Shimin Zou, 2000, Development of a Methodology for Incorporating
FESWMS2DH Results: Kansas Department of Transportation Report No. K
Tran: KU974., 26 p.
101
Shearman, James O., 1976, Computer Applications for StepBackwater and Floodway
Analyses: U.S. Geological Survey OpenFile Report 76499, 110 p.
Stamper, William G., 1975, Flood Mapping in Charlotte and Meklenburg County, North
Carolina, U.S. Geological Survey OpenFile Report, p9.
Wagner, Chad R. and David S. Mueller, ?Use of Velocity Data to Calibrate and Validate
TwoDimensional Hydrodynamic Models?: Proceedings of the Second Federal
Interagency Hydrologic Modeling Conference, Las Vegas, NV: July 29 August
1, 2002, 12 p.
?A Brief History of Floodplain Management.? Haestad Methods Water Solutions. 11
Jan. 2006.http://www.haestad.com/library/books/fmras/floodplainonlinebook.
102
APPENDIX
Figure 29. Section A, outlet of the box culvert at the L and N Railroad.
103
Figure 30. Section B, looking downstream.
Figure 31. Alabama Power Company Bridge, looking upstream.
104
Figure 32. Section C, looking upstream.
Figure 33. Section D, looking downstream.
105
Figure 34. Railroad Bridge, looking upstream.
Figure 35. Section E, looking downstream.
106
Figure 36. Section F, looking west.
Figure 37. Section H, looking downstream.
107
Figure 38. Highway 79 Bridge, looking upstream.
Figure 39. Section I, looking downstream.
108
Figure 40. Section J, looking upstream.
Figure 41. Section K, looking downstream.
109
Type of Development Description Impervious Cover
%
Urban Core Central Business District 88.0
Arterial Commercial Commercial Strip Development 68.8
Office Shop Regional Shopping 48.9
Urban Node Neighborhood Shopping Areas 47.1
Industrial High Density Heavy Intercity Industry 56.5
Industrial Med Density Light Industry 44.0
Industrial Low Density Modern Industry Park 23.8
Residential High Density Concentrated MultiFamily Units 34.0
ResidentialMed Density Density of 36 units per acre 21.6
ResidentialLow Density Density 12 units per acre 15.0
Exurban Density of less than 1 unit per acre 1.3
100
Table 14. Weighting factors used to determine degree of urbanization.
110
B
F
G
86?47'
86?46'
33?35'
33?36'
Figure 42. Fivemile Creek study reach approximate location of cross sections A through G.
0 0.5 1 MILE
LOCATION OF JEFFERSON COUNTY
IN ALABAMA
1 KILOMETER
0
C
D
A
E
111
J
K
86?46' 86?44'
33?35'30"
33?36'30"
Figure 43. Fivemile Creek study reach approximate location of cross sections F through K.
0 0.5 10.25 MILE
F
I
H
G
1 KILOMETER
LOCATION OF JEFFERSON COUNTY
IN ALABAMA
112
Figure 44. Results of the Indirect Calculations at Lawson Road by USGS.
113

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