A hybrid time- and signature-domain Bayesian inference framework for calibration of hydrological models: a case study in the Ren River basin in China

The Approximate Bayesian Computation (ABC) provides a powerful tool for signature-domain calibration of hydrological models where hydrological signatures are incorporated into calibration objectives. However, the efficiency of ABC relies strongly on the use of a vector of sufficient signatures that can fully represent relevant information in raw data. The application of ABC with randomly chosen signatures can result in inaccurate calibration results. To fill this gap, a hybrid time- and signature-domain Bayesian inference framework for calibration of hydrological models is proposed. In this framework, a set of approximately sufficient signatures is pursued through simultaneous consideration of the information redundancy analysis (IRA) and discriminatory power analysis (DPA) procedures. While the IRA deals with the information redundancy inherent in the pool of available signatures, DPA quantifies the discriminatory power of a given signature as the reliability and sharpness of the associated probabilistic predictions generated by ABC. The verified residual error scheme in time-domain inference is approximated as the probabilistic model in the acceptance test of ABC. The proposed framework is then tested on the Xin'anjiang rainfall-runoff model applied to the Ren River basin (RRB) of China. The use of IRA and DPA provides a probabilistic model prediction statistically equivalent to that of classical time-domain inference in terms of the reliability and sharpness. The comparison to signature-domain inference using the complete set of hydrological signatures further demonstrates the importance of IRA and DPA in improving the quality of Bayesian model calibration in the signature domain and reducing the total predictive uncertainty. The framework makes it practically possible to maintain adequate accuracy of model predictions produced by signature-domain inference, improving the efficiency of ABC in solving the model calibration problems and consequently promotes the use of ABC in signature-domain model calibration.

Automated summary

This study proposes a time- and signature-domain Bayesian inference framework for calibration of hydrological models, which aims to improve the efficiency of Approximate Bayesian Computation (ABC) in solving model calibration problems. Information redundancy analysis (IRA) and discriminatory power analysis (DPA) are used to obtain a set of approximately sufficient signatures. The framework is tested on a rainfall-runoff model for the Ren River basin in China, and the results show that utilizing relevant signatures can enhance the quality of Bayesian model calibration and reduce predictive uncertainty.