Evaluation of hydrological models at gauged and ungauged basins using machine learning-based limits-of-acceptability and hydrological signatures

Hydrological models are evaluated by comparisons with observed hydrological quantities such as streamflow. A model evaluation procedure should account for dominantly epistemic errors in hydrological data such as model input precipitation and streamflow and avoid type-2 errors (rejecting a good model). This study uses quantile random forest (QRF) to develop limits-of-acceptability (LoA) over streamflows that account for uncertainties in precipitation and streamflow values. A significant advantage of this method is that it can be used to evaluate models even at ungauged basins. This method was used to evaluate a hydrological model -Sacramento Soil Moisture Accounting (SAC-SMA) - over the St. Joseph River Watershed (SJRW) for both gauged and hypothetical ungauged scenarios. QRF defined wide LoAs that yielded a large number of models as behavioral, suggesting the need for additional measures to develop a more discriminating inference procedure. The paper discusses why the LoAs defined by QRF were wide, along with some ways to define more discriminating LoAs. To further constrain the model, five streamflow-based signatures (i.e., autocorrelation function, Hurst exponent, baseflow index, flow duration curve, and long-term runoff coefficient) were used. The combination of LoAs over streamflow and streamflow-based signatures helped constrain the set of behavioral models in both the gauged and the ungauged scenarios. Among the signatures used in this study, the Hurst exponent and baseflow index were the most useful ones. All the 1-million models evaluated in this study were eventually rejected as unfit-for-purpose.