Flow Prediction in Ungauged Catchments Using Probabilistic Random Forests Regionalization and New Statistical Adequacy Tests

Abstract

Flow prediction in ungauged catchments is a major unresolved challenge in scientific and engineering hydrology. This study attacks the prediction in ungauged catchment problem by exploiting advances in flow index selection and regionalization in Bayesian inference and by developing new statistical tests of model performance in ungauged catchments. First, an extensive set of available flow indices is reduced using principal component (PC) analysis to a compact orthogonal set of ?flow index PCs.? These flow index PCs are regionalized under minimal assumptions using random forests regression augmented with a residual error model and used to condition hydrological model parameters using a Bayesian scheme. Second, ?adequacy? tests are proposed to evaluate a priori the hydrological and regionalization model performance in the space of flow index PCs. The proposed regionalization approach is applied to 92 northern Spain catchments, with 16 catchments treated as ungauged. It is shown that (1) a small number of PCs capture approximately 87% of variability in the flow indices and (2) adequacy tests with respect to regionalized information are indicative of (but do not guarantee) the ability of a hydrological model to predict flow time series and are hence proposed as a prerequisite for flow prediction in ungauged catchments. The adequacy tests identify the regionalization of flow index PCs as adequate in 12 of 16 catchments but the hydrological model as adequate in only 1 of 16 catchments. Hence, a focus on improving hydrological model structure and input data (the effects of which are not disaggregated in this work) is recommended.