Testing the shape of distributions of weather data

The characterization of the statistical distributions of observed weather data is of crucial importance both for the construction and for the validation of weather models, such as weather generators (WGs). An important class of WGs (e.g., the Richardson-type generators) reduce the time series of each variable to a time series of its residual elements, and the residuals are often assumed to be normally distributed. In this work we propose an approach to investigate if the shape assumed for the distribution of residuals is consistent or not with the observed data of a given site. Specifically, this procedure tests if the same distribution shape for the residuals noise is maintained along the time. The proposed approach is an adaptation to climate time series of a procedure first introduced to test the shapes of distributions of growth rates of business firms aggregated in large panels of short time series. We illustrate the procedure by applying it to the residuals time series of maximum temperature in a given location, and investigate the empirical consistency of two assumptions, namely i) the most common assumption that the distribution of the residuals is Gaussian and ii) that the residuals noise has a time invariant shape which coincides with the empirical distribution of all the residuals noise of the whole time series pooled together