Prior information and multi-objective analysis in Bayesian ecohydrological modeling

Abstract

This thesis presents a Bayesian multi-objective calibration approach associated with uncertainty analysis in ecohydrological modeling. This work focuses on three main objectives: (1) the development and extension of Bayesian inference for hydrological models focused on the evaluation of the prior distributions; (2) the application of a formal Bayesian multi-objective approach to an ecohydrological model; and (3) the analysis of observation uncertainties in ecohydrological modelling, which is subdivided to the analysis of input uncertainty and output uncertainty in a Bayesian multi-objective framework. The first part of work focuses on the investigation of the importance of prior information in Bayesian inference. A toolkit is introduced to evaluate the impact of prior distributions on the posterior distribution in a conceptual rainfall-runoff model. In the study, the Kullback-Leibler divergence is used to quantify the impact of different priors, and the prior information elasticity is introduced to evaluate the importance of prior distributions for each model parameter. Results show that the prior distribution can dramatically affect the posterior distributions for insensitive model parameters, and it is suggested that meaningful prior distributions need to be defined appropriately for model parameters. Next, this thesis focuses on the application of a Bayesian multi-objective approach in ecohydrological modeling. Ecohydrological models are more complex and parametric than conceptual hydrological models. Thus, appropriate calibration objectives and model uncertainty analyses are essential for ecohydrological modeling. A multi-objective Bayesian calibration method is introduced. Specified prior distributions for error parameters for each of the objectives are defined which represent the weight of each objective based on the information from a traditional Pareto-based multi-objective optimization approach. Results show a better estimation of both of the objectives using this approach. Finally, the impact of observation errors on model predictions is addressed by investigating: (a) the effects of precipitation error (input error) in multi-objective analysis where different precipitation error descriptions are compared; and (b) the effects of satellite errors (output error) in specifying vegetation simulations where LAI observation error is defined using data quality information about the satellite derived product. Results suggest a detailed description of observation errors needs to be included in Bayesian ecohydrologcial modeling.