Modeling Height—Diameter Relationship Using Artificial Neural Networks for Durango Pine Species in Mexico

The total tree height (h) and diameter at breast height (dbh) relationship is an essential tool in forest management and planning. The height—diameter (h-dbh) relationship had been studied with several approaches and for several species worldwide. The nonlinear mixed effect modeling (NLMEM) has been extensively used and lately the resilient backpropagation artificial neural network (RBPANN) approach has been a trend topic for modeling this relationship. The artificial neural network (ANN) is a computing system based in artificial intelligence and inspired in biological neural network for supervised learning. In this study the NLMEN and RBPANN approaches were used for modeling the h—dbh relationship for Durango pine species (Pinus durangensis Martínez) in mixed-species forest from Mexico. The total dataset considered 1,000 (11,472 measured trees) randomly selected from 14,390 temporary forest inventory plots and the dataset was randomly divided into two parts; 50% for training and 50% for testing. An unsupervised clustering analysis was used to grouped the dataset into 10 clusters based on k-means clustering method and plot-variables like density, basal area, mean dbh, mean h, quadratic mean diameter, altitude and aspect. The RBPANN was performed for tangent hyperbolicus (RBPANN-tanh), softplus (RBPANN-softplus), and logistic (RBPANN-logistic) activation functions for functions in cross product of the covariate or neurons and the weights for the ANN analysis. For both training and testing, 10 classical statistics (e.g., RMSE, R2, AIC, BIC, logLik) were computed for the residual values and assess the approaches for h—dbh relationship. For training and testing, the ANNs approach outperformed the NLMEM approach, and the RBPANN-tanh has the best performance in both training and testing phases.