High Skill, Shallow Learning: Why Hydrological Routing Is Not Learnable from Raw Time Series by LSTMs

Deep learning models are increasingly used for operational river discharge forecasting, yet it remains unclear which hydrological processes their internal representations actually encode. Here, we show that high forecast skill can arise even when hydrological routing dynamics are statistically hidden in raw discharge time series and therefore not learnable by LSTM models.

In a multi-station river network, we find that the discharge field is overwhelmingly dominated by a synchronous storage (“bathtub”) mode, while routing-related variability is confined to weak components that are masked by noise and synchrony. Inter-station delays are small relative to this dominant variability, causing propagation signals to be effectively indistinguishable in the raw time series.

We demonstrate this using a sequence of pre-model diagnostics. Principal component analysis (PCA) shows that nearly all variance is explained by the synchronous storage mode. Cross-correlation analysis and signal-to-noise ratio (SNR) diagnostics confirm that routing signals have low visibility relative to dominant low-frequency variability. When the data are transformed into an innovation representation using a vector autoregressive (VAR) model, routing-related structure becomes more apparent, indicating that it is masked rather than absent.

Consistent with these data-space constraints, LSTM models trained on raw discharge time series achieve high predictive skill by exploiting short-term correlations and high-SNR inputs rather than learning propagation dynamics. SHAP attribution analysis shows that the same correlation-driven features dominate predictions across all forecast horizons, with increasing attribution at longer lead times reflecting growing uncertainty rather than newly learned hydrological structure. More generally, this implies that claims of physical learning by data-driven models require that the relevant dynamics are statistically identifiable in the data; model complexity and interpretability cannot recover processes that are masked by dominant variability.

These results demonstrate a clear separation between predictability and learnability: when synchronous variability dominates the data, routing dynamics are statistically inaccessible to sequence models trained on raw time series. They highlight a common but often implicit assumption in recent machine-learning application, that the chosen data representation already exposes the relevant physical structure. In Earth system applications, this assumption frequently fails. Without pre-model identifiability checks, increasing architectural complexity primarily reinforces dominant shortcuts rather than revealing new process information, leading to models that are inherently sensitive to distributional shift and brittle under non-stationary conditions.