Modeling the tree height-diameter relationship in natural forests of Cedrus deodara in the Pakistani Himalayas

Tree modeling is a common technique used in forestry where tree biometrics are linked to one another to predict the value of a difficult parameter such as biomass as a function of an easier parameter, commonly the diameter at breast height (DBH) and/or height. The present study was conducted in Swat District, a moist temperate mountainous Himalayan region of Pakistan where 5 sampling plots were installed to collect data. The primary purpose of this study was to develop a tree height-estimating model as a function of DBH for Cedrus deodara (deodar) in its natural habitat. The second purpose, which was linked to the primary purpose, was to evaluate model accuracy by comparing predicted tree heights (H) given by the H-DBH model with actual heights of the species measured in field surveys. This study employed 5 functions in an attempt to develop an H-DBH model. These functions were a linear regression (LR) function, logarithmic function (LF), power function (PF), quadratic function (QF), and exponential function (EF). Parameters for the regression models were obtained through the least squares method. The power function outperformed all other functions with the highest adjusted R^2 value (0.894) and lowest residual standard error (0.086) and was considered to be the model with the highest goodness of fit with the highest accuracy of tree height predictions. The selected PF model was applied to the DBH of field data to predict tree heights which were then compared to actual tree heights using t-test statistics. Respective field-measured height values of plots 1 thru 5 were 19.335 ± 3.388, 18.475 ± 3.690, 26.503 ± 6.355, 26.783 ± 4.866, and 27.849 ± 2.806 m, while respective predicted height values for plots 1 thru 5 were 19.165 ± 3.114, 18.500 ± 3.178, 26.497 ± 5.177, 26.558 ± 3.803, and 27.751 ± 2.411 m. Comparing actual and model heights using a t-test (p value ≥ 0.832 for all plots) showed that height values for each corresponding plot did not significantly differ.

關鍵字

allometric models ； Cedrus deodara ； tree height ； Himalayan moist temperate forest

並列摘要

樹木建模是林業中常用的技術，其中樹木生物學特性相互關聯以預測生物量等困難參數的值作為更簡單參數（通常是胸徑（DBH）和樹高（H））的函數。本研究是在巴基斯坦濕潤溫帶喜馬拉雅山的斯瓦特地區進行的，共設置五個採樣點收集數據。本研究主要目的在於建立模型，用於估計樹高（H）與自然棲息地中雪松（deodar）的胸徑（DBH）的函數關係，另與主要目標相關的第二個目標是通過比較H-DBH模型給出的預測H與實地調查中測量的物種的實際高度來評估模型的準確性。本研究使用五個函數來開發H-DBH模型。這些函數是線性回歸函數（LR）、對數函數（LF）、冪函數（PF）、二次函數（QF）和指數函數（EF）。回歸模型的參數通過最小二乘法獲得。冪函數優於所有其他具有最高R^2值（0.894）和最低殘差標準誤差（0.086）的函數，被認為是具有高擬合度和高準確度的模型。將選定的PF模型應用於現場數據的DBH以預測樹高，然後使用t檢驗統計將其與實際樹高進行比較。樣點1至樣點5的現場實測高度值分別為19.335±3.388、18.475±3.690、26.503±6.355、26.783±4.866、27.849±2.806 m、而樣點1至樣點5的預測高度值為19.165±3.114、18.500±3.170、26.497±5.177、26.558±3.803、27.751±2.411 m。t檢驗結果顯示使用模型做出的預測與實際樹高沒有顯著差異（p-value ≥ 0.832）。

並列關鍵字

異速生長模型；雪松；樹高；喜馬拉雅濕潤溫帶森林

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