The amplification of flood frequencies by sea level rise (SLR) is expected to become one of the most economically damaging impacts of climate change for many coastal locations. Understanding the magnitude and pattern by which the frequency of current flood levels increase is important for developing more resilient coastal settlements, particularly since flood risk management (e.g. infrastructure, insurance, communications) is often tied to estimates of flood return periods. The Intergovernmental Panel on Climate Change's Fifth Assessment Report characterized the multiplication factor by which the frequency of flooding of a given height increases (referred to here as an amplification factor; AF). However, this characterization neither rigorously considered uncertainty in SLR nor distinguished between the amplification of different flooding levels (such as the 10% versus 0.2% annual chance floods); therefore, it may be seriously misleading. Because both historical flood frequency and projected SLR are uncertain, we combine joint probability distributions of the two to calculate AFs and their uncertainties over time. Under probabilistic relative sea level projections, while maintaining storm frequency fixed, we estimate a median 40-fold increase (ranging from 1-to 1314-fold) in the expected annual number of local 100-year floods for tide-gauge locations along the contiguous US coastline by 2050. While some places can expect disproportionate amplification of higher frequency events and thus primarily a greater number of historically precedented floods, others face amplification of lower frequency events and thus a particularly fast growing risk of historically unprecedented flooding. For example, with 50 cm of SLR, the 10%, 1%, and 0.2% annual chance floods are expected respectively to recur 108, 335, and 814 times as often in Seattle, but 148, 16, and 4 times as often in Charleston, SC.

Estimates of future flood hazards made under the assumption of stationary mean sea level are biased low due to sea-level rise (SLR). However, adjustments to flood return levels made assuming fixed increases of sea level are also inadequate when applied to sea level that is rising over time at an uncertain rate. SLR allowances-the height adjustment from historic flood levels that maintain under uncertainty the annual expected probability of flooding-are typically estimated independently of individual decision-makers' preferences, such as time horizon, risk tolerance, and confidence in SLR projections. We provide a framework of SLR allowances that employs complete probability distributions of local SLR and a range of user-defined flood risk management preferences. Given non-stationary and uncertain sea-level rise, these metrics provide estimates of flood protection heights and offsets for different planning horizons in coastal areas. We illustrate the calculation of various allowance types for a set of long-duration tide gauges along U.S. coastlines. Electronic supplementary material The online version of this article

Sea-level rise (SLR) is magnifying the frequency and severity of extreme sea levels (ESLs) that can cause coastal flooding. The rate and amount of global mean sea-level (GMSL) rise is a function of the trajectory of global mean surface temperature (GMST). Therefore, temperature stabilization targets (e.g. 1.5• C and 2.0 • C of warming above pre-industrial levels, as from the Paris Agreement) have important implications for coastal flood risk. Here, we assess, in a global network of tide gauges, the differences in the expected frequencies of ESLs between scenarios that stabilize GMST warming at 1.5• C, 2.0 • C, and 2.5• C above pre-industrial levels. We employ probabilistic, localized SLR projections and long-term hourly tide gauge records to estimate the expected frequencies of historical and future ESLs for the 21st and 22nd centuries. By 2100, under 1.5• C, 2.0 • C, and 2.5• C GMST stabilization, the median GMSL is projected to rise 48 cm (90% probability of 28-82 cm), 56 cm (28-96 cm), and 58 cm (37-93 cm), respectively. As an independent comparison, a semi-empirical sea level model calibrated to temperature and GMSL over the past two millennia estimates median GMSL rise within 7-8 cm of these projections. By 2150, relative to the 2.0• C scenario and based on median sea level projections, GMST stabilization of 1.5• C spares the inundation of lands currently home to about 5 million people, including 60 000 individuals currently residing in Small Island Developing States. We quantify projected changes to the expected frequency of historical 10-, 100-, and 500-year ESL events using frequency amplification factors that incorporate uncertainty in both local SLR and historical return periods of ESLs. By 2150, relative to a 2.0• C scenario, the reduction in the frequency amplification of the historical 100 year ESL event arising from a 1.5• C GMST stabilization is greatest in the eastern United States, with ESL event frequency amplification being reduced by about half at most tide gauges. In general, smaller reductions are projected for Small Island Developing States.