Modelling individual tree height–diameter relationships for multi-layered and multi-species forests in central Europe

Abstract

The proposed height–diameter model applicable to many tree species in the multi-layered and mixed stands across Czech Republic shows a high accuracy in the height prediction. This model can be useful for estimating forest yield and biomass, and simulation of the vertical stand structures. We developed a generalized nonlinear mixed-effects height–diameter (H–D) model applicable to Norway spruce (Picea abies (L.) Karst.), European beech (Fagus sylvatica L.) and other conifer and broadleaved tree species using the modelling method that includes dummy variables accounting for species-specific height differences and random component accounting for within- and between-sample plot height differences and randomness in the data. We used two large datasets: the first set (model fitting dataset) originated from permanent research sample plots and second set (model-testing dataset) originated from the Czech national forest inventory (NFI) sample plots. The former dataset comprises 224 sample plots with 29,390 trees and the latter dataset comprises 14,903 sample plots with 382,540 trees, each representing wide variabilities of tree size, ecological zone, growth condition, stand structure and development stage, and management regime across the country. Among the four versatile growth functions evaluated as base functions with diameter at breast height (DBH) included as a single predictor, the Chapman-Richards function showed the most attractive fit statistics. This function was then extended through the integration of other predictor variables, which better describe the stand density (stand basal area), stand development and site quality (dominant height), competition (ratio of DBH to quadratic mean DBH), that would act as modifiers of the original parameters of the function. The mixed-effects H–D model described a large part of the variations in the H–D relationships ( $$R_{{{\text{adj}}}}^{2}$$ = 0.9182; RMSE = 2.7786) without substantial trends in the residuals. Testing this model against model-testing dataset confirmed the model’s high accuracy. The model may be used for estimating forest yield and biomass, and therefore will serve as an important tool for decision making in forestry.