The application of approximate bayesian computation in the calibration of hydrological models

Abstract

There is an increasing need to obtain proper estimates for the uncertainty associated with Conceptual Rainfall-Runoff models and their predictions. Within hydrology, uncertainty analysis is commonly conducted using Bayesian inference or Generalized Likelihood Uncertainty Estimation (GLUE). Bayesian inference is a statistically rigorous method for estimating uncertainty, but it depends upon a formal likelihood function that may not be available. GLUE utilizes a generalized likelihood function that can operate as a proxy for a formal likelihood function. While this allows GLUE to effectively calibrate hydrological models with intractable likelihood functions, the lack of statistical rigor may negatively affect the uncertainty estimations. Approximate Bayesian Computation (ABC) is a family of likelihood-free methods that have been recently introduced for calibrating hydrological models. While these methods are implemented using formal Bayesian inference for assessing uncertainty, they do not require any assumptions regarding the likelihood function. Thus they have the potential flexibility of GLUE with the statistical rigor inherent in Bayesian Inference. The studies presented within this thesis demonstrate the theoretical links between GLUE and ABC. We then assess the efficacy of an implementation of ABC utilizing a Sequential Monte Carlo sampler (ABC-SMC) for calibrating Conceptual Rainfall-Runoff models. Two components of the ABC-SMC algorithm were evaluated. These included three classes of summary statistics used for evaluating model performance and post-processing techniques to adjust the final posterior distributions of the parameters. ABC-SMC was computationally efficient in calibrating a six parameter hydrological model for one synthetic and two real world data sets. Post-processing using local linear regression generated marginal improvements to the posterior distributions. Summary statistics measuring the goodness-of-fit between the observed and predicted hydrographs performed well for the synthetic data where the total uncertainty was low. A composite summary statistic based upon matching both hydrograph and hydrological signatures of a basin were more effective for the real world data sets as total uncertainty increased. The results suggest a properly implemented ABC-SMC algorithm is an effective method for calibrating watershed models and for conducting uncertainty analysis.