Generalized additive models as an alternative approach to the modelling of the tree height-diameter relationship

Abstract

Generalized additive models were tested using three types of smoothing functions as an alternative for modelling the height curve. The models were produced for 23 forest stands of Norway spruce (Picea abies [L.] Karst.) in the territory of the Training Forest Enterprise Masaryk Forest Křtiny. The results show that the best evaluated and recommended for practical use at the level of forest stand was the LOESS function (locally weighted scatterplot smooting) when using a greater width of the bandwidth. Due to the frequent overfitting and the associated unrealistic behaviour of the function, smoothing by spline functions cannot be recommended for modelling the height curve at the level of forest stand. It was validated that the resulting model must be assessed not only according to the calculated quality criteria, but also depending on the graphic pattern of the model which must ensure that the height curve pattern is realistic. The quality of the resulting models (with LOESS function) was assessed to be high, mainly due to the very precise determination of model heights.

Keywords

• loess
• nonparametric method
• norway spruce
• petterson function
• smoothing function
• spline