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

The study investigates the properties of residuals from 78 hydrological models applied to 419 distinct catchments over the contiguous United States in a large multi-catchment, multi-model approach. Such dataset provides a foundation for a robust analysis, allowing for an in-depth investigation of residual characteristics. The research focuses on key properties such as sample shape properties (L-skewness and L-kurtosis) investigated with conventional L-moment diagrams (λ 4 /λ 2 vs λ 3 /λ 2 ) and L-moment diagrams adapt for symmetric distributions (λ 6 /λ 2 vs λ 4 /λ 2 ). Other investigated characteristics are residuals heteroscedasticity, and residual correlation. Additional focus of the study is how these characteristics vary across the different models, hydrological regimes, and under the application of different residual transformations. Specifically, the impact of two transformations (Box-Cox and logarithmic) is evaluated on stabilizing such properties. Additionally, the removal of seasonality is analyzed as a separate process, revealing significant effects in stabilizing higher-order moments, greatly reducing heavy-tails in residuals, even in the absence of any transformation. While the removal of seasonality has notable effects on the statistical properties of the residuals, its effect alone is limited in reducing heteroskedasticity, where transformations play instead a key role, effectively approximating a homoscedastic distribution. Upper and lower tails correlations are also investigated, showing distinct patterns different from general correlation behaviors. The findings of this study lays the groundwork for a conscious and informed construction of stochastic error models for uncertainty estimation in hydrological modelling, as well as for the development of new metrics for model calibration.