Approximate Bayesian Computation And Its Application In Hydrological Modelling Uncertainties Estimation

Catchment-scale hydrological modelling is challenged by multiple uncertainty factors including the errors and uncertainties in model input data,the equifinality in model parameters,model structural errors and the observational errors in calibration data.How to quantify and possibly reduce the uncertainty in parameter estimation and predictive use of hydrological models remains a key question in water cycle and water resources research.The likelihood-free Approximate Bayesian Computation(ABC)provides an attractive solution to the problems where the likelihood function in Bayesian uncertainty analysis is inaccessible,and is becoming a hot topic in hydrological modelling uncertainty estimation.This dissertation focuses on the application and improvement of the ABC method in uncertainty estimation of hydrological model calibration and its comparison to other state-of-the-art uncertainty estimation methods.The main research results and conclusions are summarized as follows:(1)The impact of stochastic model operators and hydrological signatures on ABCbased uncertainty estimation is evaluated for the application of HYMOD hydrological model to the Laoguan River basin of China.The results show that ABC requires the definition of a stochastic model operator.The use of deterministic hydrological models leads to underestimated predictive uncertainty and jeopardizes the reliability of probabilistic model predictions.Meanwhile,the efficiency of ABC is highly sensitive to the selection of hydrological signatures serving as summary statistics in ABC.The increase on the number of signatures does not necessarily improve probabilistic model predictions and reduce the predictive uncertainty.The ABC methods can obtain statistically equivalent model predictions to classical Bayesian methods through appropriate choice of a stochastic model operator and hydrological signatures.(2)The comparison of ABC methods to other commonly used uncertainty estimation methods(including multi-objective optimization and Limits-ofAcceptability methods)based on 16 typical catchments and 2 hydrological models suggests that ABC methods result in better performance in the reliability but worse performance in the precision of probabilistic predictions.The efficiency of ABC methods is influenced by the choice of hydrological signatures and also sampling techniques used to generate candidate parameter samples,especially when solving high-dimensional model calibration problems.(3)To relieve the sufficiency issue of ABC in defining summary statistics,the information redundancy analysis and discriminatory power analysis of prespecified signatures are subsequently utilized by using classical Bayesian methods as a benchmark.A sufficient set of signatures is assumed to obtain comparable performance in the reliability and sharpness(precision)of probabilistic predictions simultaneously when served as summary statistics in ABC.The application of Xin’anjiang hydrological model to daily streamflow simulation of the Ren River basin of China confirms that the proposed exploratory analysis of signatures helps to objectively screen out a reduced set of sufficient signatures and improve the accuracy of ABC.(4)To improve the sampling efficiency of ABC in dealing with high-dimensional parameter estimation problems,inspired by the development of DREAM(ABC)(Differential Evolution Adaptive Metropolis)algorithm,we replace the simple random walk Metropolis sampling module of SABC(Simulated Annealing to ABC)algorithm with adaptive MCMC(Markov Chain Monte Carlo)sampling technique.The efficiency of the modified SABC algorithm(m SABC)to the original one is demonstrated by the application of Xin’anjiang hydrological model to daily streamflow simulation of the Ren River basin of China.The results show that the modified SABC algorithm could effectively improve the sampling efficiency of ABC and obtain consistently better model performance than SABC.The proposed SABC algorithm is well suited for highdimensional model calibration problems.(5)Finally,we explore the potential of ABC methods in solving likelihood-free Bayesian inference problems where the observational errors in streamflow data are explicitly considered.Specifically,the 95% confidence intervals of daily streamflow are derived using BaRatin and VPM(Voting Point Likelihood Method)approaches respectively.The ABC distance metric is re-defined by calculating the distance between the model outputs and the corresponding 95% confidence intervals,and the proposed SABC algorithm is utilized to solve the ABC inference problem.The experiment in the Ren River basin of China suggests that compared to traditional Bayesian methods based on error-free streamflow data,ABC inference that explicitly accounts for streamflow errors can efficiently reduce the predictive uncertainty and obtain significantly better probabilistic prediction for the validation period.The ABC methods conveniently overcomes the obstacle of formal Bayesian inference in solving likelihood-free inference problems while maintaining sufficient computation accuracy.