Modeling height–diameter relationship for Populus euphratica in the Tarim riparian forest ecosystem, Northwest China

Abstract

Modeling height–diameter relationships is an important component in estimating and predicting forest development under different forest management scenarios. In this paper, ten widely used candidate height–diameter models were fitted to tree height and diameter at breast height (DBH) data for Populus euphratica Oliv. within a 100 ha permanent plots at Arghan Village in the lower reaches of the Tarim River, Xinjiang Uyghur Autonomous Region of China. Data from 4781 trees were used and split randomly into two sets: 75 % of the data were used to estimate model parameters (model calibration), and the remaining data (25 %) were reserved for model validation. All model performances were evaluated and compared by means of multiple model performance criteria such as asymptotic t-statistics of model parameters, standardized residuals against predicted height, root mean square error (RMSE), Akaike’s information criterion (AIC), mean prediction error (ME) and mean absolute error (MAE). The estimated parameter a for model (6) was not statistically significant at a level of α = 0.05. RMSE and AIC test result for all models showed that exponential models (1), (2), (3) and (4) performed significantly better than others. All ten models had very small MEs and MAEs. Nearly all models underestimated tree heights except for model (6). Comparing the MEs and MAEs of models, model (1) produced smaller MEs (0.0059) and MAEs (1.3754) than other models. To assess the predictive performance of models, we also calculated MEs by dividing the model validation data set into 10-cm DBH classes. This suggested that all models were likely to create higher mean prediction errors for tree DBH classes >20 cm. However, no clear trend was found among models. Model (6) generated significantly smaller mean prediction errors across all tree DBH classes. Considering all the aforementioned criteria, model (1): $$ {\text{TH}} = 1.3 + {\text{a}}/\left( {1 + {\text{b}} \times {\text{e}}^{{ - {\text{c}} \times {\text{DBH}}}} } \right) $$ and model (6): $$ {\text{TH}} = 1.3 + {\text{DBH}}^{2} /\left( {{\text{a}} + {\text{b}} \times {\text{DBH}} + {\text{c}} \times {\text{DBH}}^{2} } \right) $$ are recommended as suitable models for describing the height–diameter relationship of P. euphratica. The limitations of other models showing poor performance in predicting tree height are discussed. We provide explanations for these shortcomings.