31 Jan 2023
 | 31 Jan 2023
Status: a revised version of this preprint is currently under review for the journal HESS.

An improved Approximate Bayesian Computation approach for high-dimensional posterior exploration of hydrological models

Song Liu, Dunxian She, Liping Zhang, and Jun Xia

Abstract. The Approximate Bayesian computation (ABC) methods provide a powerful tool for sampling from Bayesian posteriors for cases where we can simulate samples, but we have no access to an explicit expression of the likelihood function. The Simulated Annealing ABC (SABC) algorithm has been proposed to achieve a fast convergence to an unbiased approximation to the posterior by adaptively decreasing an initially coarse tolerance value. However, this algorithm uses a rather simplistic random walk Metropolis (RWM) sampler to generate trial moves in a Markov chain and always requires an excessive number of model evaluations for approximating the posterior, which inevitably lowers the sampling efficiency and limits its applications in more complex hydrologic modelling practices. Inspired by the advances made in Markov Chain Monte Carlo (MCMC) methods, we incorporated an adaptive Differential Evolution scheme to enhance the efficiency of SABC sampling. This scheme has its roots within Differential Evolution Markov Chains (DE-MC), and additionally utilizes a self-adaptive randomized subspace sampling strategy to optimally select the dimensions of parameters to be updated each time a proposal is generated. The superiority of the modified SABC (mSABC) over the original SABC algorithm was demonstrated through a SAC-SMA application to the Danjiangkou Reservoir region (DRR). The case study results showed that mSABC was far more efficient with lower computation costs and higher acceptance rates, and achieved higher numerical accuracy than the original SABC algorithm. mSABC also resulted in a better overall prediction of streamflow time series and signatures. The introduction of more advanced MCMC sampler into SABC helps to speed up convergence to the approximate posterior while achieving better model performance, which significantly widens the applicability of SABC to complex posterior exploration problems.

Song Liu et al.

Status: final response (author comments only)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on hess-2022-414', Anonymous Referee #1, 03 Apr 2023
    • AC1: 'Reply on RC1', Song Liu, 06 Apr 2023
  • RC2: 'Comment on hess-2022-414', Anonymous Referee #2, 03 Apr 2023
    • AC2: 'Reply on RC2', Song Liu, 06 Apr 2023
  • RC3: 'Comment on hess-2022-414', Anonymous Referee #3, 04 Apr 2023
    • AC3: 'Reply on RC3', Song Liu, 06 Apr 2023

Song Liu et al.

Song Liu et al.


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Short summary
Quantifying the uncertainty in streamflow predictions is a major challenge, with research and operational significance. This study advances the field of catchment-scale hydrological modelling by developing an improved uncertainty analysis technique that provides more reliable and accurate probabilistic streamflow predictions. This finding provides hydrologists with robust modelling tools for handling hydrological modelling uncertainties in engineering practices.