Modelling Hydrologically-Conditioned Residuals For Improved Error Correction Across Different Flow Regimes

Hydrological models often fail to fully capture catchment responses, which leaves systematic residuals between modelled and observed flow. Here, we present a comprehensive state-dependent, two-stage residual modelling framework that separates residuals into modelling error, arising from structural and parametric limitation, and observation error, coming from measurement and forcing data uncertainty. The residuals are estimated conditional on hydrological states, allowing the error dynamics to vary across flow regimes rather than assuming stationarity. The residual model is trained on 124 CAMELS-AU catchments from diverse climatic regions across Australia and is tested on independent catchments from the continent. The results demonstrate improved correction across all flow regimes, specifically for high (>95th percentile) and extremely high flow (>99th percentile). To enhance the generalizability, Minimum Redundancy Maximum Relevance (mRMR) feature selection is employed to identify the most important catchment attributes, which are used as static inputs alongside the dynamic model states and hydrological forcings. The framework is applicable to fully calibrated, partially calibrated, and uncalibrated hydrological models, and remains effective under limited or absent streamflow data. By explicitly modelling residuals as separable state-dependent processes, the proposed framework provides a robust method for improved streamflow correction, with particular relevance for peak flow estimation and applications in data-scarce environments.