Abstract
Aim of the study: The main objective of this study was to test Geographically Weighted Regression (GWR) for developing height-diameter curves for forests on a large scale and to compare it with Linear Mixed Models (LMM).Area of study: Monospecific stands of Pinus halepensis Mill. located in the region of Murcia (Southeast Spain).Materials and Methods: The dataset consisted of 230 sample plots (2582 trees) from the Third Spanish National Forest Inventory (SNFI) randomly split into training data (152 plots) and validation data (78 plots). Two different methodologies were used for modelling local (Petterson) and generalized height-diameter relationships (Cañadas I): GWR, with different bandwidths, and linear mixed models. Finally, the quality of the estimated models was compared throughout statistical analysis. Main results: In general, both LMM and GWR provide better prediction capability when applied to a generalized height-diameter function than when applied to a local one, with R2 values increasing from around 0.6 to 0.7 in the model validation. Bias and RMSE were also lower for the generalized function. However, error analysis showed that there were no large differences between these two methodologies, evidencing that GWR provides results which are as good as the more frequently used LMM methodology, at least when no additional measurements are available for calibrating.Research highlights: GWR is a type of spatial analysis for exploring spatially heterogeneous processes. GWR can model spatial variation in tree height-diameter relationship and its regression quality is comparable to LMM. The advantage of GWR over LMM is the possibility to determine the spatial location of every parameter without additional measurements. Keywords: Spatial analysis; Pinus halepensis Mill; forest modelling.Abbreviations: GWR (Geographically Weighted Regression); LMM (Linear Mixed Model); SNFI (Spanish National Forest Inventory).
Highlights
In forestry, spatial heterogeneity is theorized as one of the major drivers of biological diversity (Wiens, 1976)
The spatial heterogeneity of a tree variable in a forest stand results from the complex historical and environmental mosaic imposed by competition and systematic environmental heterogeneity (Zhang et al, 2004); which implies a spatio-temporal heterogeneity
The main aim of this paper is to analyse the suitability of Geographically Weighted Regression (GWR) for modelling height-diameter relationships in a large area and to compare it with Linear Mixed Models (LMM), which is one of the most frequently used methods for including spatial heterogeneity in these models
Summary
In forestry, spatial heterogeneity is theorized as one of the major drivers of biological diversity (Wiens, 1976). Spatial heterogeneity results from the spatial interactions between a number of biotic and abiotic factors and the differential responses of organisms to these factors (Milne, 1991) It may have significant influences on many ecosystem processes at multiple spatial scales (Turner, 1989). The spatial heterogeneity of vegetation patterns (i.e., landscape heterogeneity) is a structural property of landscapes (Li & Reynolds, 1994) that can be defined by the complexity and variability of ecological system properties in space. The spatial heterogeneity of a tree variable (height, diameter, etc.) in a forest stand results from the complex historical and environmental mosaic imposed by competition and systematic environmental heterogeneity (Zhang et al, 2004); which implies a spatio-temporal heterogeneity.
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