Uncertainty and Confidence in Estimating Flood Frequencies from Hurricanes and Northeasters at Ungaged Coast Locations — A New Methodology

Abstract

Coastal flooding along the Atlantic coast north of Cape Hatteras is caused by hurricanes and by northeasters. The best available tidal gage records are about 100 years long, so that estimation of flood levels of a 50 year return period and above is fraught with statistical error. This, together with the fact that hydrodynamically consistent flood profiles are usually required everywhere along the coastline of communities (not just at the gage), led to the development and use of the Joint Probability Method (JPM). This is a simulation based method, whereby surges are simulated via a numerical hydrodynamic model. This model, in turn, is used to derive flood level statistics (frequencies) from statistics of the meteorological cause. Two elements necessary in applying the JPM methodare a parameterization of the storm, and the extraction of statistics for these parameters from the meteorologic record. A synthetic sample of storms is then used to simulate representative surges covering the entire range of flood levels. In the 15 years of use of the JPM method the sample size of synthetic storms has been determined heuristically to vary from 300 to 800. The central question addressed in this paper is: given the required accuracy of estimation of flood levels, what is the optimal sample size of synthetic storms which will achieve the required accuracy without producing redundant information? The question is approached from the viewpoint of confidence intervals on the estimated frequency of exceedence of a given flood level. In contrast, gage analyses provide estimates of flood levels for given exceedence frequencies and the corresponding confidence intervals are given on the flood levels rather than on the frequencies. The flood frequency estimation error expressed as a confidence interval is complemented by determination of the accuracy of the estimate. This is achieved by use of a second-moment first order technique in conjunction with multiple simulations according to a stratified sampling scheme. Thus, the level of acceptable error controls the number of synthetic storms that need to be simulated (the sample size), and the required accuracy dictates which synthetic storms to simulate.