The different schemes tested are variations on the general idea of spatial composition. The goal is to improve the estimate of the regression parameters by shortening the time window used for training (i.e., since one hundred days cover a potentially heterogeneous period in terms of seasonal dynamics), and to maintain the representativeness and degrees of freedom in the sample (i.e., number of observations). The relation between length of the training set and number of neighbors is specifically addressed.
Three approaches for compositing stations are considered: 1) Stations are "neighbors" if they are located within a maximum distance of the target station. This strictly local aggregation raises issues of spatial correlation among observations -- which will make the actual number of degrees of freedom in the sample lower than the number of data points -- and of optimal choice of the radius parameter, that we attempt to address. 2) Stations are "neighbors" if they are within a short range of degrees of latitudes and elevation. 3) Stations are "neighbors" if they have similar climatology. The second and third methods of aggregation potentially produce groups whose members are geographically distant but similar in the weather dynamics. In this respect they should resolve the issue of high spatial correlation implicitly by providing a higher number of degrees of freedom per sample than the first method.
Out-of-sample predictions are constructed by cronologically separated training and test samples or by leaving one station out of the training set and then predicting at its location (this latter exercise being useful as an alternative to spatial interpolation of forecasts at locations whose data are missing). The forecasts of the different systems are evaluated over a number of sites scattered across Midwest-to-Western states. The varied topography in the region (flat vaste plains and mountain areas) is very likely responsible for interesting differentials in the relative skills of the alternative methods.