Statistical Learning and Topkriging Improve Spatio-Temporal Low-Flow Estimation

Abstract

This study evaluates the potential of a novel hierarchical space-time model for predicting monthly low-flow in ungauged basins. The model decomposes the monthly low-flows into a mean field and a residual field, where the mean field represents the seasonal low-flow regime plus a long-term trend component. We compare four statistical learning approaches for the mean field, and three geostatistical methods for the residual field. All model combinations are evaluated using a hydrologically diverse dataset of 260 stations in Austria and the predictive performance is validated using nested 10-fold cross-validation. The best model for monthly low-flow prediction is a combination of a model-based boosting approach for the mean field and topkriging for the residual field. This model reaches a median $R^2$ of 0.73 across all stations, outperforming an XGBoost model on the same data set. Model performance is generally higher for stations with a winter regime (median $R^2$ = 0.84) than for summer regimes ($R^2$ = 0.70), and lowest for the mixed regime type ($R^2$ = 0.68). The proposed model appears to be most useful in headwater catchments and provides robust estimates not only for moderate events, but also for extreme low-flow events. The favorable performance is due to the hierarchical model structure, which effectively combines different types of information: the low-flow regime estimated from average climate and catchment characteristics, and the actual flow conditions estimated from flow records of neighboring catchments. This information is readily available for most regions of the world, making the model easily transferable to other studies.