Let the data speak: Catchments as non-autonomous dynamical systems via a modulated storage–discharge function

Physics-based hydrological models frequently estimate subsurface fluxes and storage behaviour in catchments from limited observations. As a result, simulations rely on oversimplified, static descriptors of subsurface processes. To address those limitations, data-driven approaches emerge as an alternative; nevertheless, many of these methods either rely on restrictive assumptions -such as discharge depends solely on storage derived from recession periods- or represent the internal state of the catchments implicitly, without an interpretable characterisation of the storage-discharge dynamics. Here, we introduce a data-driven framework for rainfall-runoff modelling that represents catchments as non-autonomous dynamical systems using a modulated discharge-storage sensitivity function. The approach implements the recession-based sensitivity function proposed by Kirchner (2009), which characterises the baseline drainage behaviour of groundwater-dominated catchments. In our formulation, the derived recession-based function serves as a limiting reference constraining a dynamic storage-discharge sensitivity function that is continuously modulated by net atmospheric forcing through an explicit state-forcing relationship. As a result, the storage-discharge relationship varies with different hydro-meteorological conditions and returns to the recession-based formulation when atmospheric forcings are negligible relative to the discharge. Our framework accounts for changes in the dynamical structure of watersheds during rising and recession periods without requiring calibration parameters and is primarily applicable to catchments where discharge is controlled by their storage-state dynamics. Initial tests show that our framework captures forcing-dependent variations in storage-discharge sensitivity functions and provides additional diagnostic insight into catchment behaviour during rising limbs and recession. Ongoing work evaluates the robustness of different hydro-climatic settings and explores the method’s potential to characterise storage-forcing interactions in groundwater-dominated catchments.