Modeling form factors for sal (Shorea robusta Gaertn.) using tree and stand measures, and random effects

Abstract

Form factor (FF) is widely used for the correct estimation of tree volume. Few FF models have been developed and applied to the volume estimation, however, they have failed to account for the influence of important tree and stand characteristics on the FF variations. We aimed to incorporate the effects of these characteristics into the FF models for sal (Shorea robusta Gaertn.) trees in Nepal. A comprehensive data set representative to wide variations of tree size, crown architecture, stem form, stand density, site productivity, and environmental condition was used for the purpose. We evaluated various tree and stand measures characterized by the meaningful biological explanation as predictors in the FF models. The unstructured random component accounting for the subject-specific (diameter class-specific) random effects was included into the FF model through the application of the mixed-effects modeling. Among several predictor variables evaluated, tree height (HEIGHT), crown index (ratio of crown depth to crown diameter, CI), relative diameter (ratio of the subject tree DBH to quadratic mean DBH, Dq), and basal area proportion of the species of interest (BAPRO) significantly contributed to the FF variations. The FF models described the substantial proportion of the FF variations. There was an increased FF with increasing HEIGHT and BAPRO, but decreased FF with increasing Dq and CI. The FF was influenced significantly differently by different covariate predictors with the biggest influence of Dq followed by CI, HEIGHT, and BAPRO. Calibration of the mixed-effects FF models with the random effects estimated from the complimentary FF of four sample trees per DBH class could provide the highest prediction accuracy. Inclusion of tree- and stand-level measures, and subject-specific random effects into the FF models could significantly increase the FF prediction accuracy and increase the biological robustness of the models.