Multivariate adaptive regression splines-assisted approximate Bayesian computation for calibration of complex hydrological models

Abstract

Approximate Bayesian computation (ABC) relaxes the need to derive explicit likelihood functions required by formal Bayesian analysis. However, the high computational cost of evaluating models limits the application of Bayesian inference in hydrological modeling. In this paper, multivariate adaptive regression splines (MARS) are used to expedite the ABC calibration process. The MARS model is trained using 6,561 runoff simulations generated by the soil and water assessment tool (SWAT) model and subsequently replaces the SWAT model to calculate the objective functions in ABC and multi-objective evolutionary algorithm (MOEA). In experiments, MARS can successfully reproduce the runoff time series simulations of the SWAT model at a low time cost, with a runoff variance determination coefficient of 0.90 as compared to the Monte Carlo method. MARS-assisted ABC can quickly and accurately estimate the parameter distributions of the SWAT model. The comparison of ABC with non-Bayesian MOEAs helps in the selection of an appropriate calibration approach. HIGHLIGHTS Approximate Bayesian computation (ABC) was used to calibrate the complex hydrological model.; Multivariate adaptive regression splines (MARS) were used to expedite the ABC process.; The ability of MARS-assisted ABC for calibration of the SWAT model was demonstrated.; The calibration results of ABC and multi-objective evolutionary algorithms were compared.; MARS-assisted ABC has the potential to extend the use of ABC in hydrological modeling.;

Keywords

• approximate bayesian computation
• bayesian inference
• multi-objective evolutionary algorithms
• multivariate adaptive regression splines
• surrogate model