Modeling spatial variation in tree diameter–height relationships

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Traditionally the relationship between tree diameter and total height in a forest stand is investigated by using linear or non-linear regression models, in which the spatial heterogeneity in the relationship is largely ignored. The objective of this study is to explore and model the spatial variations in the tree diameter–height relationship in an eucalypt stand using geographically weighted regression (GWR). GWR attempts to capture spatial variations by calibrating a multiple regression model fitted at each tree, weighting all neighboring trees by a function of distance from the subject tree. GWR produces a set of parameter estimates and model statistics (e.g. model R 2) for each tree in the stand. The results indicate that GWR significantly improves model fitting over ordinary least squares (OLS). The GWR model produces smaller model residuals across diameter classes than the traditional OLS model does. The overall average (0.074) of the model absolute residual from the GWR model is 43% smaller than that (0.129) from the OLS model. Furthermore, the parameter estimates and model statistics of the GWR model can be mapped using visualization tools such as geographical information system (GIS) to illustrate local spatial variations in the regression relationship under study.