Uncertainty Estimation Of Hydrological Models Under A Bayesian Framework

China is suffering from water shortage problems and frequent flood and droughtdisasters, which places high demand for hydrological forecasting and prediction.Hydrological models are the major tool of hydrological forecasting and prediction, aswell as other water-related problems. However, uncertainties of parameters, inputs andmodel structures involved in hydrological modeling have undermined its applicationvalue. The objective of this dissertation is to develop a Bayesian framework ofhydrological model system to estimate and diagnose the uncertainties involved inhydrological models.A hierarchical Bayesian model is first developed for the hydrological model system.A hybrid sampling strategy that employs Markov chain Monte Carlo methods is thendeveloped to explore the Bayesian model. We introduced the hierarchical Bayesianmodel for the hierarchical characters of input uncertainty, and specified inputuncertainty as relative errors in rainfall measurement at the gauges. To conduct thelikelihood function of observed discharge data, we divided the data into low and highflow dataset to reduce the heteroscedasticity, and adopted the first order autoregressivemodel to describe the autocorrelation of the time series. The hybrid sampling strategyfor exploration of the Bayesian model employs Metropolis-Hastings, delay rejectionadaptive Metropolis, and Gibbs sampling methods to improve the sampling efficiency.To evaluate the validity of the Bayesian model, we applied it to the dataset in anagricultural land in North China to estimate the uncertainty associated with onedimension soil hydraulic parameters. Multilayer parameters of soil water retention andhydraulic conductivity functions were estimated from in situ measurements of soil watercontent at several depths. The medians of posterior distributions of soil hydraulicparameters led to higher accuracy in simulation of soil moisture variation than theparameters obtained by laboratory test did.The developed hierarchical Bayesian model was adopted to estimate theparameters associated with a geomorphology-based hydrological model (GBHM) formountainous flood forecasting. Synthetic case study and field data applicationdemonstrated the effectiveness of the Bayesian model in estimating the uncertainty ofGBHM parameters and in giving reasonable predictive uncertainty for flood period. Jointly estimating input uncertainty with hydrological model parameters led to a lowererror criterion of probabilistic forecasting and higher consistency of the predictivedistribution with the observed data compared with estimating parameter uncertaintyseparately. The negative spatial correlation of estimated input errors suggested thatfurther information was required to improve input uncertainty estimation of distributedmodels.To analyze the model structure uncertainty of hydrological models, we developedan informal Bayesian model under the Bayesian framework by introducing a residualindependence coefficient (RIC) with a feasible zone of [0,1]. Case study result showedthat the best RIC coefficient was related to model structure errors and was determined toavoid both overfitting and underfitting. When systematic errors of a hydrological modelincreased, the best RIC coefficient declined. The developed Bayesian model wasapplied separately to a Xinanjiang model of Chuzhou catchment and a GBHM model ofGanjiang catchment for probabilistic flood forecasting. The predictive distributions arewell consistent with the observed data.The major innovation points of this dissertation lie in the development of thehierarchical Bayesian model and the empirical Bayesian model, and the application ofthe Bayesian models to the parameter estimation of hydrological models and to thehydrological flood forecasting. The dissertation demonstrates a theoretical base for thewidely application of Bayesian models in hydrological models.