Testing the Temporal and Spatial Transferability of a Water Balance Model using a Parameter Learning Approach

Abstract. Reliable transferability of hydrological model parameters across time and space remains a challenge for large‑scale water resources assessment. In this study, we investigate whether a differentiable hybrid framework can identify robust and physically coherent parameter sets for annual streamflow modeling across a large‑sample dataset of 3,044 catchments from eight countries. To focus on temporal and spatial transferability analysis, we work at the annual time scale using what we consider to be the simplest possible model: an annual anomaly model of climate elasticities, coupled with the Turc–Mezentsev formulation for the long-term streamflow mean (MQ). A dense neural network is trained in an end‑to‑end fashion to map catchment descriptors to the four model parameters, with gradients propagated through the entire modeling chain.

We evaluate the framework using three cross‑validation settings inspired by Klemeš (1986): temporal, spatial, and combined temporal–spatial cross-validation. As a benchmark, we compare the hybrid model against local, catchment‑by‑catchment linear regressions under temporal cross-validation.

Our results show that, for temporal transferability, our parameter learning approach outperforms local calibration, yielding higher Nash-Sutcliffe efficiency (NSE) values while producing elasticity coefficients that remain within plausible physical ranges, despite lacking explicit parameter constraints. By contrast, spatial transferability reveals a marked limitation: the anomaly component extrapolates well spatially, but regionalizing MQ from descriptors proves difficult, with MQ errors dominating the loss of performance in spatial and spatiotemporal cross-validation. Experiments with random descriptors further show that our parameter learning uses attributes mainly as catchment identifiers in temporal cross-validation but relies on their physical content to sustain spatial transfer, particularly for MQ. Overall, the study demonstrates that simple differentiable hybrid annual models can learn robust and interpretable anomaly parameters, while highlighting MQ regionalization as the main remaining bottleneck for spatially transferable annual streamflow predictions.