Bayesian calibration of fluvial flood models for risk analysis

Abstract

Flood risk analysis is now fundamental to ood management decision making. It relies on the use of computer models to estimate ood depths for given hydrological conditions. The correct calculation of risks associated with di erent management options requires that the uncertainty in the computer model output is carefully estimated. There are several sources of uncertainty in flood models, including structural uncertainties in the model representation of reality, uncertainty in model parameters, and observation errors. We refer to the rst of these as "model inadequacy". The work described in this thesis concerns the calibration of computer models to describe fluvial flooding, taking into account model inadequacy and paying particular attention to the requirements of risk analysis calculations. A methodology which has had some success in other application areas is Bayesian model calibration, using Gaussian process representation both for the error arising from model inadequacy, and to emulate the computer model output. The e ectiveness of this methodology is demonstrated for steady state flood models, both of a series of laboratory experiments, and of a historical ood using a satellite image of flood outline for calibration. Extension of the methodology to calibration of dynamic models using gauged data is not straightforward, but is achieved for flood models by means of an emulator, which replaces the computationally expensive hydrodynamic model with a time-dependent transfer function. This permits calibrated prediction of floods using historical gauged data, both in the existing channel and after modelling potential modi cations to the channel. It is shown that calibration without inclusion of a model inadequacy function cannot match measured data. Finally, application of the methodology is demonstrated in the context of a calculation of probability of inundation in the channel, both with and without modi cation.