Nonstationary models for exploring and mapping monthly precipitation in the United Kingdom

Spatial statistical algorithms are used widely for both the exploration and mapping of environmental variables such as precipitation amount. One limitation of standard approaches to characterization and spatial interpolation is the usual assumption of stationarity. In short, spatial variation is assumed to be constant across the region of interest. Much research effort has been extended in developing approaches that allow for local variation in spatial structure. Simple moving window approaches are examples of such developments. The purpose of this paper is to apply selected methods for exploring and mapping monthly precipitation amount in the UK. Global regression, moving window regression (MWR) and geographically weighted regression (GWR) are used to explore the relationship between altitude and precipitation amount. Inverse distance weighting (IDW) is used as a basic approach to spatial prediction. Global and local variogram models are estimated and modelled to assess variation in spatial structure of precipitation amount and to inform spatial prediction using ordinary kriging (OK), kriging with an external drift (KED) and simple kriging with local means (SKlm). In the latter case, local means are derived using global regression, MWR (using ordinary least squares (OLS) and generalized least squares (GLS)) and GWR. The importance of choice of algorithm for the estimation of the variogram and for spatial prediction is assessed. The benefits of local as against global approaches and multivariate as against univariate prediction procedures are considered. It is demonstrated that use of elevation data to inform the prediction process reduces prediction errors and that there is also a small reduction in prediction errors when local variogram models are used. In this study, KED based on local variogram models provides more accurate predictions (as judged by cross‐validation statistics) than any other approach. The paper concludes by considering some key issues and possible avenues for future work.