A comparison of two statistical methods for spatial interpolation of Canadian monthly mean climate data

Abstract

Two methods for elevation-dependent spatial interpolation of climatic data from sparse weather station networks were compared. Thirty-year monthly mean minimum and maximum temperature and precipitation data from regions in western and eastern Canada were interpolated using thin-plate smoothing splines (ANUSPLIN) and a statistical method termed ‘Gradient plus Inverse-Distance-Squared’ (GIDS). Data were withheld from approximately 50 stations in each region and both methods were then used to predict the monthly mean values for each climatic variable at those locations. The comparison revealed lower root mean square error (RMSE) for ANUSPLIN in 70 out of 72 months (three variables for 12 months for both regions). Higher RMSE for GIDS was caused by more frequent occurrence of extreme errors. This result had important implications for surfaces generated using the two methods. Both interpolators performed best in the eastern (Ontario/Québec) region where topographic and climatic gradients are smoother, whereas predicting precipitation in the west (British Columbia/Alberta) was most difficult. In the latter case, ANUSPLIN clearly produced better results for most months. GIDS has certain advantages in being easy to implement and understand, hence providing a useful baseline to compare with more sophisticated methods. The significance of the errors for any method should be considered in light of the planned applications (e.g., in extensive, uniform terrain with low relief, differences may not be important).