# Estimating Chances and Timing of Flood Levels

To project the probabilities of coastal floods reaching different heights in the future (through a combination of storms, tides, and sea level rise), we used a statistical approach based on patterns of historical extreme water levels superimposed with projected sea level rise. We used complete available hourly local historical records of sea surface heights to estimate water height “exceedance probabilities” at NOAA water level stations, selecting only stations with a minimum 30 years of hourly records. Exceedance probabilities relate water heights to their annual probability: for example, water heights with a 1% chance of being reached in any given year (“100-year” or “century” floods) are higher than those with a 10% chance (“decade floods”), and so forth. Above a certain water height threshold (unique to each water level station, depending on its distribution of past storm events), we use specialized extreme value statistical methods (employing Generalized Pareto Distributions) to estimate these exceedance probabilities. Below the water height threshold, we use the average frequencies of storm events from the historical record to compute probabilities (employing Poisson Distributions). In computing the baseline exceedance probabilities, we filter out the effects of ongoing, historical sea level rise, so that they are influenced only by tides, storms, and seasonal shifts in water level.

Once established, exceedance probabilities are simple to adjust to account for the future impacts of sea level rise. For example, an event reaching 5 feet, after one foot of sea level rise, has the same probability as an event reaching 4 feet of elevation in the baseline case.

To estimate the multi-year risk that a particular height, H, will be reached or exceeded by (as opposed to within) some future year – for example, 2040 – we first compute the annual probability of at least one flood exceeding H in each intermediate year, e.g. 2016, 2017,..., 2040, incorporating local projections of annual sea level rise. We then combine these annual probabilities to find the overall chances of such a flood occurring in this time period. As with our projections of sea level rise, and for similar reasons, we limit our presentation to likelihoods of reaching different flood levels at decade resolution.

Our calculations only consider flood levels reaching elevations relative to the local average high tide line, rather than pure storm surge, which is calculated as the extra water height above the predicted tidal water level at that moment in time. Our focus is not on storm surge alone, but rather how high water actually gets, due to storm surge, plus tide, plus sea level rise. This analysis assumes that historic storm patterns will not change; in other words, it does not address the possibility that storms might change in frequency or severity due to climate change. (Research suggests that in many areas storms will become more intense; there is less consensus around changes in frequency, but overall flooding is expected to worsen, making our approach likely to understate risk.)

This analysis was based on data taken at water level stations. Tides, storm surge, and the resulting statistics vary from place to place, sometimes over short distances, due to factors including land and ocean geometry and storm directions. Therefore, results from stations may be taken as rough indicators, but not precise estimates, for their neighborhoods and regions, and the quality and coverage of indication will vary.

These methods we use to project coastal flood height probabilities, together with our methods of projecting sea level rise and estimating exposure risk, underlie the statistics presented in Surging Seas Risk Finder and its associated state fact sheets, reports, and data downloads. For additional description and explanation, see this peer-reviewed paper. (The sub-threshold exceedance probabilities and multi-year approach described here extend this paper slightly)