Defining the hundred year flood: A Bayesian approach for using historic data to reduce uncertainty in flood frequency estimates

Brandon Parkes,David Demeritt

doi:10.1016/j.jhydrol.2016.07.025

Abstract

This paper describes a Bayesian statistical model for estimating flood frequency by combining uncertain annual maximum (AMAX) data from a river gauge with estimates of flood peak discharge from various historic sources that predate the period of instrument records. Such historic flood records promise to expand the time series data needed for reducing the uncertainty in return period estimates for extreme events, but the heterogeneity and uncertainty of historic records make them difficult to use alongside Flood Estimation Handbook and other standard methods for generating flood frequency curves from gauge data. Using the flow of the River Eden in Carlisle, Cumbria, UK as a case study, this paper develops a Bayesian model for combining historic flood estimates since 1800 with gauge data since 1967 to estimate the probability of low frequency flood events for the area taking account of uncertainty in the discharge estimates. Results show a reduction in 95% confidence intervals of roughly 50% for annual exceedance probabilities of less than 0.0133 (return periods over 75 years) compared to standard flood frequency estimation methods using solely systematic data. Sensitivity analysis shows the model is sensitive to 2 model parameters both of which are concerned with the historic (pre-systematic) period of the time series. This highlights the importance of adequate consideration of historic channel and floodplain changes or possible bias in estimates of historic flood discharges. The next steps required to roll out this Bayesian approach for operational flood frequency estimation at other sites is also discussed.

Highlights

On 5–6 December 2015 Storm Desmond swept across northern Britain, leaving record rainfall and widespread flooding in its wake (Priestly, 2016)
Long and reliable time series of annual maximum (AMAX) records from river gauges are uncommon in the UK; the 46 years recorded at Sheepmount is comparatively long, the average record length being roughly 35 years (Kjeldsen et al, 2008)
The results presented so far have only included data up to 2012, which at the time of writing was the extent of the AMAX time series available from CEH (2014)

Summary

Introduction

On 5–6 December 2015 Storm Desmond swept across northern Britain, leaving record rainfall and widespread flooding in its wake (Priestly, 2016). One of the worst affected places was Carlisle, where thousands of homes were flooded after newly completed flood defences were overtopped by rising flood waters (BBC, 2015a). While ministers insisted the defences could not be expected to cope with the ‘‘completely unprecedented and unpredicted levels of rainfall” (ITV News, 2015) from Storm Desmond, local residents wondered why a £38million defence scheme had failed barely five years after it was built (BBC, 2010). The Carlisle case illustrates many of the central challenges of quantifying the risk of flooding. The design of individual schemes, like the wider system for allocating resources for flood defence in England, requires estimates of the probability of flooding to support risk-based management (Lane et al, 2011).

Results

Discussion

Conclusion