Regularized calibration of conceptual hydrological models

This paper applies recent results of risk bounds for time series forecasting to identify optimal complexity of conceptual models and complexity regularised streamflow predictions based on Vapnik-Chervonenkis generalization theory. Earlier reported similar study with SAC-SMA and SIXPAR conceptual models but on two large regions from CAMELS data set is extended to more basins in CONUS to demonstrate the effect of regularizing hydrological model calibration on streamflow prediction over unseen data. SAC-SMA and SIXPAR (conceptual simplification of SAC-SMA) are used as model examples. Results show that the effect of complexity regularization more visible on SIXPAR than SAC-SMA. Results further suggest that when basins itself are complex, regularizing complexity of models does not help and depends on hydrological characteristics of the basins. The benefits of complexity regularization are more evident when assessed based on variance based performance metrices such as correlation coefficient and the slope of observed vs predicted fit than bias and mean absolute error metrices. The paper therefore offers a novel, though computationally intense, method to calibrate conceptual models while controlling for their model complexity.