Uncertainty Modelling in Hydrological Applications - Error Propagation Properties of Random Linear Systems

Sammanfattning: In hydrological models for water resources management and planning, the model output or design quantities are functions of the input data and a number of parameters that are essentially stochastic processes or random variables. The task of uncertainty analysis is to estimate the uncertainty characteristics of the model output in terms of the uncertainties in the input, model parameters and initial conditions. Uncertainty analysis provides a formal and systematic framework to quantify those uncertainties. Furthermore, it offers the hydrologist a valuable insight regarding the contribution of each random component to the overall uncertainty of the model output. Such knowledge is essential to identify the parameters and input variables that most need attention in order to better assess their values and, accordingly, to increase the overall model reliability. The thesis consist of two parts. Part one is concerned with calculus of uncertain quantities and various methods for modelling uncertainty. The applicability of these methods is illustrated with various relevant hydrological problems. Part two contains five papers. The two first papers deal with water quality modelling and the relationship between input and parameter uncertainties and their effect on model prediction reliability. The third paper addresses the problem of peak flow prediction using frequency analysis and extreme value distributions. It was clear from the reported analyses that uncertainties in probability based flood estimates are large, and severely influenced by human activities in the basin such as the construction of dams and detention basins and river dredging. The weighty problem of design rainfall estimation is touched upon in the fourth paper. Design rainfall is an important concept in rainfall-runoff modelling and flood protection. The paper presents a method for relating extreme value distributions from point rainfall data directly to an extreme value distribution for the average spatial rainfall for a catchment. The method also gives an estimate of the average spatial rainfall variance as a function of the point rainfall variance. The fifth paper deals with uncertainties in rainfall-runoff modelling, especially in the estimation of peak flows using design rainfall events. The fifth paper presents a simple yet powerful stochastic rainfall-runoff model to simulate the flood peak given design rainfall as input. The model is based on a stochastic differential equation (SIUH) which describes the catchment as a single linear reservoir and includes an estimate of the uncertainty of the simulated flood peak. The method was tested on 34 rainstorm events in a Chinese catchment, these represented varying rainfall intensities and durations; single and multiple peak runoff events; and antecedent catchment soil moisture conditions. The simulations showed that the SIUH method gives a robust and reliable estimate of the flood peak and volume as well as the associated uncertainty of prediction.