Nonlinear mixed effect height-diameter model for mixed species forests in the central part of the Czech Republic

Abstract

Various forest models that estimate volume, site index, growth and yield, biomass, and sequestrated carbon amounts are based on the information of the tree heights. The tree heights are obtained either directly from measurements or indirectly estimated using height-diameter models. We developed a nonlinear mixed effect height-diameter model applicable to both conifer and broadleaved tree species through the introduction of dummy variable that accounts for the variations in the height-diameter relationship, caused by the effects of species-specific differences. Data from 255 sample plots located within the multi-layered mixed species forests in the central part of the Czech Republic were used. Based on the fit statistics of twelve bi-parametric models, the Näslund's model, which best fits height-diameter data of various species, was selected for expansion by incorporating height of the tallest tree per sample plot, dummy variable, and sample plot-level random effects. As compared to the ordinary least square model, the mixed effect model described significantly a larger part of the variations in the height-diameter relationship and showed a higher prediction accuracy. Large prediction errors still occurred for the mixed species stands when all measured heights other than the focused species (species used in species group-specific model) per sample plot were used to predict random effects and localize the mixed effect model. But those errors were significantly reduced when all measured heights per sample plot, regardless of species were used to predict random effects. We therefore recommend a mixed effect model with random effects predicted using all measured heights per sample plot, regardless of species, to accurately predict the missing height measurements.

Keywords

• height-diameter relationship
• multi-layered forest stand
• model localization
• näslund's model
• prediction error