Modeling of stem taper model with mixed effects approach for oriental spruce

Abstract

Oriental spruce (Picea orientalis L.) is one of the most important tree species in Turkey. Therefore, the information is necessary about growth and yield of the species for developing future management and planning strategies. The one of the essential building blocks in forest growth and yield prediction models is the equations for estimating individual tree volume. One of the most accurate and reliable approaches for estimating stem total volume and merchantable volume is the use of taper models. In this study, a taper model was developed by using nonlinear mixed effects modeling approach (NLME) using data from 170 trees felled in oriental spruce stands from Ardahan-Posof Region. An NLME approach accounted for within-and between tree variations in stem form. In the first stage, all possible combinations of expansion with random effects in one and two model parameters were tested, selecting then the best one. The inclusion of random effects was not enough to account for the existing autocorrelation between the residuals and then the variance-covariance matrix of the error term was modelled through a first order autocorrelation structure AR (1). In a second step, we evaluated the response obtained by calibration (which implies estimation of random effects for a new tree) based on upper-stem diameter measurements at different points. The selected mixed-effects model produced the best results both in fitting and calibration process. It was found that an upper-stem diameter measurement at 40-80% of total height was best suited for calibrating tree-specific predictions. As a result, model calibration should be considered an essential criterion in mixed model selection.

Keywords

• picea orientalis
• gövde çapı modeli
• otokorelasyon
• kalibrasyon
• ardahan-posof
• picea orientalis
• taper model
• autocorrelation
• calibration
• ardahan-posof