Amplification factors for extreme sea level frequency have problematic features as a metric of coastal hazard

Abstract

Abstract The future projected frequency of a specified baseline extreme sea level (ESL), often called the amplification factor (AF), is extensively used as a metric of evolving coastal flood hazard with sea level rise (SLR). The baseline ESL is typically analyzed using extreme value analysis, and the SLR is added to the resulting distribution. In the presence of SLR uncertainty, it is natural to analyze AFs probabilistically. I derive probability density functions (PDFs) of AF, given uncertainty distributions of SLR. If the ESL distribution is modeled as Gumbel and the SLR distribution as normal, then the AF distribution is log normal. However, in active tropical cyclone regions, ESL often has a longer tail than Gumbel, and a Frechet (Type-II) Generalized Extreme Value (GEV) is more appropriate. In this case, I show that the AF distribution has a divergent mean, preventing its use as a hazard metric. In addition, I show that for Frechet ESL, the AF cannot even be defined for SLR above a threshold β / ξ f 0 − ξ , where f 0 is the specified baseline frequency (e.g., f 0 = 0.01 yr−1 for the 100-year exceedance), β is the GEV scale parameter and ξ the shape parameter. This SLR threshold can be as low as 0.5 m in the southeast US and Caribbean, within reach mid to late century. Above the threshold, ESL at all frequencies exceeds the baseline reference frequency, preventing the calculation of AF. The resulting probabilistic distribution of AF is insensitive to SLR above the threshold. These features detrimentally impact the utility of AF as a hazard metric. Frechet distributions are appropriate and commonly used for ESL in tropical cyclone regions, but AFs applied to such distributions must interpreted with caution. In such regions, coastal risk managers should consider other flood hazard metrics, such as probabilistic estimates of flood depth.