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.

Generalized nonlinear height–diameter models for a <i>Cryptomeria fortunei</i> plantation in the Pingba region of Guizhou Province, China

“…Tree height and diameter at breast height (DBH, 1.3 m above ground) are fundamental essential individual tree variables used in forest measurements and inventories (Adamec and Drápela, 2015;Misir, 2010;Subedi and Sharma, 2011). DBH can be easily and accurately measured in field inventories, whereas due to visual obstructions the estimation of tree height is less accurate and often far more difficult and time consuming, especially in tall and closed-canopy stands (Ahmadi et al, 2013;Bi et al, 2012).…”

“…Generally, the models can be divided into linear and nonlinear types, but the H-D relationship is influenced by numerous factors, particularly site quality and silvicultural treatments. In many cases, such relationships feature a complex nonlinear process, which is difficult to describe using ordinary linear models (Adamec and Drápela, 2015;Nanos et al, 2004;Watt and Kirschbaum, 2011). Thus, there is a general consensus that nonlinear models can improve measurement accuracy and reliability, leading to better predictions (Cimini and Salvati, 2011;CrecenteCampo et al, 2010;Paulo et al, 2011).…”

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

“…Besides the traditional parametric methods, also nonparametric models can be used. Examples of these methods can be found in Zhang et al (2008), Schmidt et al (2011), Kangas and Haara (2012) and Adamec and Drápela (2015).…”

Comparison of height-diameter models based on geographically weighted regressions and linear mixed modelling applied to large scale forest inventory data

“…1), which has been successfully used in similar, previously published studies (e.g. Juárez de Galíndez et al, 2007;Drápela, 2011;Adamec, 2014;Adamec & Drápela, 2015) h = 1.3+ 1…”