Improved estimates of incident radiation and heat load using non-parametric regression against topographic variables

Question: Can non-parametric multiplicative regression (NPMR) improve estimates of potential direct incident radiation (PDIR) and heat load based on topographic variables, as compared to least-squares multiple regression against trigonometric transforms of the predictors? Methods: We used a multiplicative kernel smoothing technique to interpolate between tabulated values of PDIR, using a locally linear model and a Gaussian kernel, with slope, aspect, and latitude as predictors. Heat load was calculated as a 45 degree rotation of the PDIR response surface. Results: This method yielded a fit to a complex response surface with R2 > 0.99 and eliminated the areas of poor fit given by a previously published method based on least squares multiple regression with trigonometric functions of the predictors. Conclusions: Improved estimates of PDIR and heat load based on topographic variables can be obtained by using non-parametric multiplicative regression (NPMR). The main drawback to the method is that it requires reference to the data tables, since those data are part of the model.