Spatial prediction on river networks: comparison of top-kriging with regional regression

Top-kriging is a method for estimating stream flow-related variables on a river network. Top-kriging treats these variables as emerging from a two-dimensional spatially continuous process in the landscape. The top-kriging weights are estimated by regularising the point variogram over the catchment area (kriging support), which accounts for the nested nature of the catchments. We test the top-kriging method for a comprehensive Austrian data set of low stream flows. We compare it with the regional regression approach where linear regression models between low stream flow and catchment characteristics are fitted independently for sub-regions of the study area that are deemed to be homogeneous in terms of flow processes. Leave-one-out cross-validation results indicate that top-kriging outperforms the regional regression on average over the entire study domain. The coefficients of determination (cross-validation) of specific low stream flows are 0.75 and 0.68 for the top-kriging and regional regression methods, respectively. For locations without upstream data points, the performances of the two methods are similar. For locations with upstream data points, top-kriging performs much better than regional regression as it exploits the low flow information of the neighbouring locations. Copyright (c) 2012 John Wiley & Sons, Ltd.