SITE QUALITY ESTIMATIONS BASED ON THE GENERALIZED ALGEBRAIC DIFFERENCE APPROACH: A CASE STUDY IN ÇANKIRI FORESTS

ABSTRACT In this study, it is aimed that the dynamic site index models were developed for Crimean Pine stands in Sarikaya-Cankiri forests located in middle northern Turkey. The data for this study are 153 sample trees obtained from the Crimean Pine stands. In modeling relationships between height and age of dominant or co-dominant trees, some dynamic site index equations such as Chapman-Richards (M1, M2, M3), Lundqvist (M4 and M6), Hossfeld (M5), Weibull (M7) and Schumacher (M8) based on the Generalized Algebraic Difference Approach (GADA) were used. The estimations for these eight-dynamic site index model parameters with well as various statistical values were obtained using the nonlinear regression technique. Among these equations, the Chapman-Richards’s equation, M3, was determined to be the most successful model, with accounted for 89.03 % of the total variance in height-age relationships with MSE: 1.7633, RMSE: 1.3279, SSE: 1165.6, Bias: -0.0380. After determination of the best predictive model, ARMA (1, 1) autoregressive prediction technique was used to account autocorrelation problems for time-series height measurements. When ARMA autoregressive prediction technique was applied to the Chapman-Richards function for solving autocorrelation problem, these success statistics were improved as SSE: 868.7, MSE: 1.3183, RMSE: 1.1482, Bias: -0.06369, R2: 0.918. Also, Durbin-Watson statistics displayed that autocorrelation problem was solved by the use of ARMA autoregressive prediction technique; DW test value=1.99, DWP=0.4378. The dynamic site index model that was developed has provided results compatible with the growth characteristics expected in the modeling of height-age relations, such as polymorphism, multiple asymptote, and base-age invariance.

摘要 本研究旨在为土耳其中北部萨勒卡亚-昌克尔(Sarikaya-Cankiri)林区的克里米亚松(Crimean Pine)林分构建动态地位指数模型。本研究的数据取自该克里米亚松林分，共包含153株样木。在构建优势木或亚优势木的树高与年龄关系模型时，本研究采用了基于广义代数差分法(Generalized Algebraic Difference Approach, GADA)的多款动态地位指数方程，包括Chapman-Richards(M1、M2、M3)、Lundqvist(M4、M6)、Hossfeld(M5)、Weibull(M7)及Schumacher(M8)。本研究采用非线性回归技术，对上述8个动态地位指数模型的参数以及各类统计量进行了估计。在所有方程中，Chapman-Richards方程M3表现最优，其树高-年龄关系的总方差解释率达89.03%，对应均方误差(Mean Squared Error, MSE)为1.7633、均方根误差(Root Mean Squared Error, RMSE)为1.3279、残差平方和(Sum of Squared Errors, SSE)为1165.6、偏差(Bias)为-0.0380。确定最优预测模型后，本研究采用ARMA(1,1)自回归移动平均模型(AutoRegressive Moving Average, ARMA)自回归预测技术以校正树高时序测量中的自相关问题。将该ARMA技术应用于Chapman-Richards模型以解决自相关问题后，各项拟合优度统计量均得到改善：残差平方和为868.7、均方误差为1.3183、均方根误差为1.1482、偏差为-0.06369、决定系数(R-squared, R²)为0.918。此外，德宾-沃森(Durbin-Watson)检验结果显示，采用ARMA自回归预测技术后，自相关问题已得到解决：DW检验值为1.99，德宾-沃森检验p值(DWP)为0.4378。本研究构建的动态地位指数模型，其拟合结果符合树高-年龄关系建模中预期的生长特性，包括多态性、多重渐近性及基龄不变性。