Residual dynamics in hydrological models: insights from a large sample of catchments and models

Residual analysis is a cornerstone of hydrological modelling, providing the basis for assessing model performance, diagnosing structural deficiencies, and building stochastic error models for uncertainty quantification. This study investigates the properties of residuals from 78 hydrological models applied to 422 catchments spanning the contiguous United States offering an unprecedented multi-catchment, multi-model perspective. Key aspects examined include shape properties (L-skewness and L-kurtosis) assessed through both conventional L-moment diagrams and diagrams adapted for symmetric distributions. Residual heteroscedasticity, and temporal correlation are also analyzed, together with their variability due to model selection, hydrological regimes, and under different discharge transformations (Box-Cox and logarithmic). In addition, we evaluated the impact of seasonality removal, showing that while it substantially stabilizes higher-order moments and reduces heavy tails, it is less effective in mitigating heteroskedasticity, for which transformations play a crucial role. Finally, upper and lower temporal tails correlations are explored, revealing distinct behaviors that differ from general temporal correlation patterns. Collectively, these results provide a robust empirical foundation for the design of generalizable stochastic error models, with direct implications for predictive accuracy and uncertainty quantification in hydrology.