Abstract. Spatial interpolation of precipitation data is of great importance for hydrological modelling. Geostatistical methods (krigings) are widely used in spatial interpolation from point measurement to continuous surfaces. However, the majority of existing geostatistical algorithms are available only for single-moment data. The first step in kriging computation is the semi-variogram modelling which usually uses only one variogram model for all-moment data. The objective of this paper was to develop different algorithms of spatial interpolation for daily rainfall on 1 km2 regular grids in the catchment area and to compare the results of geostatistical and deterministic approaches. In this study, we used daily rainfall data from 70 raingages in the hilly landscape of the Ourthe and Ambleve catchments in Belgium (2908 km2). This area lies between 35 and 693 m in elevation and consists of river networks, which are tributaries of the Meuse River. For geostatistical algorithms, Cressie's Approximate Weighted Least Squares method was used to fit seven semi-variogram models (logarithmic, power, exponential, Gaussian, rational quadratic, spherical and penta-spherical) to daily sample semi-variogram on a daily basis. Seven selected raingages were used to compare the interpolation performance of these algorithms applied to many degenerated-raingage cases. Spatial interpolation with the geostatistical and Inverse Distance Weighting (IDW) algorithms outperformed considerably interpolation with the Thiessen polygon that is commonly used in various hydrological models. Kriging with an External Drift (KED) and Ordinary Cokriging (OCK) presented the highest Root Mean Square Error (RMSE) between the geostatistical and IDW methods. Ordinary Kriging (ORK) and IDW were considered to be the best methods, as they provided smallest RMSE value for nearly all cases.
Novel Optimization-Based Parameter Estimation Method for the Bass Diffusion Model