Technical Note: Approximate Bayesian Computation to improve long-return flood estimates using historical data

Abstract. For the Generalised Logistic distribution as used in UK flood frequency analysis, one standard approach for parameter estimation is through maximum likelihood methods. However, there can be problems with convergence to final estimates in cases where the true parameter values are extreme. This paper applies Approximate Bayesian Computation (ABC), a likelihood-free approach popularised in statistical genetics, which generates candidate parameters and compares data simulated from those candidates to the observed data. Candidates whose data have summary statistics (Partial Probability Weighted Moments, PPWM) sufficiently close to those of the observed data are accepted as draws from the posterior distribution.

The ABC-PPWM approach is applied to new historical data points to estimate the flood frequency distribution for the River Severn at the Welsh Bridge in Shrewsbury, UK to improve the estimates of magnitudes of flood events with return period longer than the length of systematic records. Level data are derived from historical sources, and discharge estimates are obtained using data from upstream discharge gauging stations. When used in the ABC-PPWM approach, the results are at least as effective as the maximum likelihood methods, showing similar point estimates, and similar levels of variance. The estimates for the shape parameter for the GLO show some discrepancies, but this is known to be the most challenging to estimate given the availability of only censored historical data. Unlike maximum likelihood methods, for which the estimate may not be obtainable, the ABC-PPWM approach is always successful.