Comparison of different non-linear models for prediction of the relationship between diameter and height of velvet maple trees in natural forests (Case study: Asalem Forests, Iran)

Abstract

Velvet maple (Acer velutinum) is one of the woody species in the Hyrcanian forests. In this study, the relationship between height and diameter of velvet maple was surveyed. A complete list of the selected height-diameter models was used and nineteen candidate models were considered. Various criteria were chosen and applied to evaluate the predictive performance of the models. These criteria include Akaike information criterion (AIC), Bayesian information criterion (BIC), root mean square error (RMSE), mean error (ME), and adjusted coefficient of determination (R2adj). Fitting of nineteen height-diameter models using nonlinear least square regression showed that all of the parameters in models were significant (P < 0.01). The results of goodness of fit for the calibration and k-fold validation and the performance criteria (RMSE, ME, AIC, R2adj and BIC) showed that R2adj ranged from 0.743 (model 8) to 0.8592 (model 11) and RMSE from 2.6983 (model 11) to 10.1897 (model 9). The range of ME among the models is from -7.0787 (model 9) up to 0.063m (model 7). By considering the AICfor each model it is evident that model (11) and model (9) have the lowest and highest values, respectively. Plotting the residuals showed that for all these models the residuals were randomly distributed and the models had heterogeneous residuals. According to the results, models (11), (14), (13), (15) and (12) had a better fitness compared to other models. Among these models, model (11) was the best model for predicting total height of Acer velutinum trees in this region.

Keywords

• height-diameter model
• acer velutinum
• north of iran