Segmentation of Model Localization Sub-areas by Getis Statistics

Models for large areas (global models) are often biased in smaller sub-areas, even when the model is unbiased for the whole area. Localization of the global model removes the local bias, but the problem is to find homogenous sub-areas in which to localize the function. In this study, we used the eCognition Professional 4.0 (later versions called Definies Pro) segmentation process to segment the study area into homogeneous sub-areas with respect to residuals of the global model of the form height and/or local Getis statistics calculated for the residuals, i.e., G(i)*-indices. The segmentation resulted in four different rasters: 1) residuals of the global model, 2) the local G(i)*-index, and 3) residuals and the local G(i)*-index weighted by the inverse of the variance, and 4) without weighting. The global model was then localized (re-fitted) for these sub-areas. The number of resulting sub-areas varied from 4 to 366. On average, the root mean squared errors (RMSEs) were 3.6% lower after localization than the global model RMSEs in sub-areas before localization. However, the localization actually increased the RMSE in some sub-areas, indicating the sub-area were not appropriate for local fitting. For 56% of the sub-areas, coordinates and distance from coastline were not statistically significant variables, in other words these areas were spatially homogenous. To compare the segmentations, we calculated an aggregate standard error of the RMSEs of the single sub-areas in the segmentation. The segmentations in which the local index was present had slightly lower standard errors than segmentations based on residuals.