Interpolation of Rainfall Data with Thin Plate Smoothing Splines: I Two Dimensional Smoothing of Data with Short Range Correlation
Michael F. Hutchinson
Journal of Geographic Information and Decision Analysis, Vol. 2., No. 2, pp. 139-151, 1998.
Two dimensional thin plate smoothing splines 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, permitting robust calibration of spatially distributed standard errors which are correlated with rainfall amount. Initial model calibration was made difficult by apparent short range spatial correlation in the data. This was overcome by removing one point from each of the ten closest pairs of data points, indicating that this correlation had a range of less than 10 km. A companion paper shows that the short range correlation can be associated with topographic effects. The error analyses were confirmed by comparing predictive accuracies on 367 withheld data points. The validity of using the square root transformation was also confirmed.
KEYWORDS: thin plate smoothing splines, generalised cross validation, data smoothing, standard errors, short range correlation, correlated errors, rainfall data, square root transformation