An argument for parsimony in differentiable hydrologic models

Abstract. Differentiable hydrologic models that use machine learning to infer parameters for process-based models show promise for both prediction and inference. However, these models are often developed with time-varying parameters, despite evidence that such flexibility can undermine physical consistency and yield only marginal predictive improvements over simpler static approaches. In this study, we revisit the comparison between static and dynamic differentiable models across 531 CAMELS-US basins, evaluating key architectural choices: (1) neural network type (multi-layer perceptron (MLP) vs. long short-term memory network (LSTM)); (2) process model configuration (single- versus ensemble-parameter estimation); and (3) comprehensive versus alternative input feature sets. Using the Hydrologiska Byråns Vattenbalansavdelning (HBV) conceptual model, we find that ensemble parameterizations consistently outperform single-parameter configurations, and that static, MLP-based ensembles achieve performance comparable to dynamic, LSTM-based ensembles despite their simpler structure. Additionally, we find that LSTM-estimated parameters rarely exhibit meaningful temporal variability despite their time-varying inputs, and when they do, this temporal variability may reflect hydrologic model equifinality rather than process dynamics. We further show that models using only latitude and longitude as static inputs achieve spatial generalization comparable to models using comprehensive feature sets describing climate, topography, geology, soils, and land cover. Similarly, temporal generalization is retained even when comprehensive features are replaced with physically meaningless values. This indicates static inputs are primarily used as spatial proxies to generalize in space and for site memorization when generalizing in time, rather than representations of physical basin processes. Overall, our results support reduced complexity in differentiable hydrologic modeling to provide greater transparency while retaining predictive performance.