Description

This project is concerned with the relationship between rainfall and stream flow. There is considerable uncertainty as to the nature of this relationship and the way in which it changes with time and location. Understanding and quantifying this relationship is important for assessing the potential for flooding and the impact on flooding of changes in land use.

One of the major sources of information in assessing such uncertainty is by the analysis of computer simulators based on mathematical models of stream flow, based on the solution of equations describing the relevant hydrology. There are many approximations and uncertainties involved in matching the output of such simulators with actual stream flow. For example, to evaluate a hydrological model requires the specification of a collection of input parameters, whose true values are unknown. There are many choices of model form and input parameters and so there are practical difficulties in identifying sensible choices of model form and input parameters, quite apart from all of the other uncertainties involved in matching the computer model to the real system.

Members of the Durham Mathematics department (Michael Goldstein and Nathan Huntley), are part of a PURE (Probability, uncertainty and risk in the environment) consortium which is concerned with issues related to uncertainties associated with natural hazards. One aspect of this work involves working on problems related to rainfall runoff models, in collaboration with hydrologists at Imperial College. Our collaborators have implemented a particular rainfall runoff model, which runs in R. In addition, we have several time series of rainfall, stream flow and related quantities at various locations.

This project will be concerned with uncertainty analysis for computer models in hydrological analysis and in particular with the practical issues that are raised when analysing an ensemble of model evaluations for a physical system and comparing the output to a collection of spatio-temporal data. A basic tool that we use is the statistical modelling of the relationship between the inputs and the outputs of the computer simulator, by means of a statistical emulator. Therefore, this project draws on methods described in 2H Statistical Concepts and 3H Statistical Methods.

Prerequisites

Resources

Details about the flood model that we will be using are given in this document

Some details of the kind of analysis that we might carry out, in the context of a different but related rainfall-runoff model, are given in this document

More details about the PURE project are given at

the home-page for the PURE research programme

A good web-site which is related to the general types of analyses which this project gives an introduction to is

The MUCM Web-site

This is the web-site for the Managing Uncertainty in Complex Models (MUCM) project, another consortium in which we are involved, (with the Universities of Sheffield, Aston, LSE and Southampton). There are a variety of interesting links to follow at this site.