Thin-Plate Smoothing Spline Modeling of Spatial Climate Data and Its Application to Mapping South Pacific Rainfalls

Abstract

The thin-plate smoothing spline model is a mathematically elegant method for surface estimations that has been progressively developed over the last decade. A summary description of the method is given. The model smooths the data according to the criterion of minimizing a functional combining the mean-square residuals and the roughness of a signal surface. In the traditional use of the model, the trade-off between the mean-square residuals and the signal roughness is internally estimated by minimizing the general cross validation. However, in the case of meterological and climatological datasets, which are often sparse and noisy, the traditional fitting approach can result in unrealistically smooths maps. To address this, a practical method is proposed here by which the above-mentioned trade-off can incorporate the user's prior knowledge of the spatial characteristics and error characteristics of the signal surface. The approach is illustrated by application to island rainfall datasets for the tropical southwest Pacific, ranging from spatially smooth long-term mean annual data to highly spatially variable individual monthly data. The issue of data sparseness and its impact on the trade-off is considered. The examples suggest that the thin-plate smoothing spline model, with the proposed enhancement, may have advantages for mapping sparse and noisy data, and that in general it may have wider applicability in meteorology than current use indicates.