MSc Defence: Uncertainty Analysis of a River Quality Model Using Differential Inequalities

CANDIDATE: Grace D'Agostino

ABSTRACT: Model parameters in environmental systems are often non-constant and may be completely unknown (or known only for some time points). Uncertainty analysis for differential equations refers to the assessment of uncertainty of a model’s output as a result of uncertainty in a model’s parameters or state variables. In this thesis, we perform uncertainty analyses of a simple river quality differential equation model using various comparison techniques. We investigate a basic river quality model: the Streeter-Phelps equations with unknown model parameters and linear and nonlinear reaction kinetics using parameter estimates, differential inequalities and comparison theorems. We consider both advection-reaction- and advection-dispersion-reaction-type equations in linear and nonlinear forms including linear biological oxygen demand (BOD) decay, and coupled oxygen-inhibition BOD decay using Monod kinetics. We perform uncertainty analyses using various comparison techniques chosen based on the model structure. We investigate how the uncertainty in solution estimates induced by uncertainty in model parameters for a single segment propagate over a simple river network for the advection-dispersion-reaction equations and we consider the effects of the choice of boundary conditions on the estimates of the solution over a network. We discuss the results of each comparison tool and their limitations.