Prediction of Distribution for Total Height and Crown Ratio Using Normal Versus Other Distributions

Abstract

Relative to the other southern pine species, many aspects of longleaf pine (Pinus palustris Mill.) growth are poorly understood due to the lack of detailed studies and modeling efforts. With changes occurring in the ecosystem and even the climate, there is a need for flexible models. One such area is the crown shape and leaf area. This thesis is part of a larger research project based at Eglin Air Force Base in Florida entitled “crown shape and leaf area distribution models for naturally regenerated longleaf pine trees at Eglin Air Force Base in Florida”. Crown shape and leaf area distribution models can also be used as an initialization model to develop biologically-based, resource driven mixed models (individual tree model between empirical growth and yield models and process models) to get more precise growth estimates of longleaf. This thesis includes three chapters. Chapter 1 explains about the larger research project at Eglin including the sections of in-depth literature review for chapters 2 and 3. Chapter 2 explores the models which can predict the entire distribution of total height rather than just the mean total height (H) given diameter at the breast height (DBH). Three different models with a normal error term were compared. In the first model (Model A) total height was used as a function of DBH with a constant variance. The weighted least square approach was applied to model the distribution of H in the second model to correct the problem of increasing variance. The third model (Model C) used H as a function of DBH and variance was also used as a function of DBH. All three models have some probability of predicting negative total height which is not realistic, however, the probability of predicting negative height from the third model was very low. Finally, a gamma model was used to predict the distribution of H, this model never predicts negative height. Cross validation indicated that the gamma model was the best model to predict the distribution of total height among all the models compared in this study. Chapter 3 explores the models which can predict the entire distribution of crown ratio rather than just the mean crown ratio (CR) given H. Similar model forms using the assumption that the errors are normally distributed versus beta distributed errors were compared. Two different model forms were used in both the cases. The first model had mean crown ratio as a logistic function of H with a constant variance, whereas, the second model had a mean crown ratio as a logistic function of H and variance also as a function of H. The second model form with beta distributed error was found to be the best model among the models used in the study. Cross validation indicated that the beta model is capable of predicting the distribution of CR correctly. This model never suffers from the problem of predicting the CR beyond the logical range of 0 and 1.