Interpolation of Rainfall Data with Thin Plate Smoothing Splines: II Analysis of Topographic Dependence
Michael F. Hutchinson
Journal of Geographic Information and Decision Analysis, Vol. 2., No. 2, pp. 152-167, 1998.
Thin plate smoothing splines incorporating varying degrees of topographic dependence were used to interpolate 100 daily rainfall values, with the degree of data smoothing determined by minimising the generalised cross validation. Analyses were performed on the square roots of the rainfall values. Model calibration was made difficult by short range correlation and the small size of the data set. Short range correlation was partially overcome by removing one point from each of the five closest pairs of data points. An additional five representative points were removed to make up a set of 10 withheld points to assess model error. Three dimensional spline functions of position and elevation, from digital elevation models of varying resolution, were used to assess the optimum scaling of elevation and an optimum DEM resolution of 10 km. A linear sub-model, depending on the two horizontal components of the unit normal to the scaled DEM, was used to form a five dimensional partial spline model which identified a south western aspect effect. This model also had slightly smaller estimated predictive error. The model was validated by reference to the prevailing upper atmosphere wind field and by comparing predictive accuracies on 367 withheld data points. Model selection was further validated by fitting the various spline models to the 367 data points and using the 100 data points to assess model error. This verified that there were small, but significant, elevation and topographic aspect effects in the data, when calculated from a 10 km resolution DEM, providing a physical explanation for the short range correlation identified by the two dimensional analysis in the companion paper.
KEYWORDS: partial thin plate smoothing splines, digital elevation model, topographic dependence, generalised cross validation, data smoothing, short range correlation, rainfall data, square root transformation.