Spatio-temporal analysis of climatic data using additive regression splines

Abstract

Environmental modelling often requires knowledge of the values of certain climatic variables at locations where no such information is available. When this is the case, one must rely on interpolated values derived from climatic data recorded at surrounding locations. The accuracy of the interpolated field, however, can often be critically dependent on the inclusion of additional predictor variables in the data models used to calculate the interpolated values. This is the case with precipitation, for example, as it is often influenced by the underlying topography. When interpolating precipitation data it is therefore desirable to include predictors such as elevation and topographic slope and aspect, in addition to those quantifying the data point locations, to achieve accurate precipitation surfaces. Furthermore, studies have shown that interpolation accuracy is improved by allowing for a spatially varying dependence on these topographic variables. Additional predictors will also be appropriate when analysing temporal trends in climatic data. Interpolation procedures that incorporate additional predictors in a spatially varying way can also be useful tools for analysing how the effects of certain predictors vary across the spatial extent of the region under consideration. While it may be desirable to include several additional predictor variables in a data model, there are practical constraints that limit the feasibility of such an approach. A common problem that arises when analysing multivariate data is that interpolation methods are limited by the fact that estimating a d-variate function with no constraints on its structure, apart from smoothness, requires data sets of impractical size for larger values of d; a fact referred to as the curse of dimension. Consequently, interpolation based on higher dimensional data can be numerically expensive or completely impractical. In many cases the interpolated surface required for application is two- or three-dimensional. This being the case, unconstrained interpolation based on higher dimensional data can produce more elaborate dependencies on the predictor variables than actually needed. It is therefore natural to employ a data fitting method that allows the incorporation of multiple predictors but bypasses the curse of dimension by identifying only the underlying two- or three-dimensional (spatial) dependencies. Additive regression spline models may be thought of as extensions of linear regression models that incorporate spatially varying dependences on the predictor variables. Additive regression splines may also be thought of as special cases of tensor-product smoothing splines. As such, they enable robust spatio-temporal analysis of climatic data that depend on many variables, in a spatially varying way. Additive regression spline models also bypass the usual technical difficulties associated with interpolation of higher dimensional data sets. In this paper we discuss the application of additive regression spline models in the analysis of climatic data that depend on many variables in a spatially varying way. We illustrate their use in two applications. The first uses additional predictor variables related to topographic slope and aspect to analyse the topographic modulation of Swiss daily rainfall. Spatial patterns of the direction and extent of orographic modulation are presented along with an analysis of the short-range correlation structure within the data. The second application uses polynomial functions of time as additional predictors to analyse spatio-temporal trends in Australian pan evaporation data collected between 1970 and 2003. Unlike other methods employed in the literature to analyse temporal trends in climatic variables, the methods presented here allow use of data from all stations, not just the serially complete ones. Estimates of the spatially disaggregated linear trend in annual pan evaporation arising from the first-order and fourth-order temporal models are presented. � MODSIM 2005 - International Congress on Modelling and Simulation: Advances and Applications for Management and Decision Making, Proceedings. All rights reserved.