Comparison of linear mixed effects model and generalized model of the tree height-diameter relationship

Abstract

Models of height curves generated using a linear mixed effects model and generalized model were compared. Both tested models were also compared with local models of height curves, which were fitted using a nonlinear regression. In the mixed model two versions of calibration were tested. The first calibration approach was based on measurement of heights only in trees of the mean diameter interval, while the second calibration approach was based on measurement of tree heights in three diameter intervals. Generalized model is the mathematical formulation of a system of uniform height curves, which is commonly used in the Czech Republic. The study took place at Training Forest Enterprise called Masaryk Forest at Křtiny and was carried out for Norway spruce (Picea abies [L.] Karst.). It was found that the mixed model behaves correctly only in the case of calibration based on selection of trees in three diameter intervals. Selection of a total of nine trees was confirmed as the most suitable to calibrate the model. In most of the calculated quality criteria, the mixed model achieved better results than the generalized model, even with a smaller number of measured heights. The bias of both models from the local model was very similar (0.54 m for the mixed model and 0.44 m for the generalized model). The mixed model can therefore fully replace the commonly used generalized model even with a smaller number of measured heights.

Keywords

• height function
• mean height
• michailoff function
• norway spruce
• mean diameter
• uniform height curve