I was interviewed the other day for a 5-minute radio news clip and written article by Matthew Schuerman of WNYC, on the Corps of Engineers plans for protecting Staten Island’s low-lying southeastern neighborhoods from flooding. A big question was whether the Corps’ planning for sea level rise and use of a 50-year planning period for cost-benefit analysis looked long enough into the future.

Here, I am posting a summary of how I came to the conclusion that the chances of storm surge flooding going over the levees and filling the neighborhoods in the coming 50 years are 4%. Another statistic I compute, which isn’t in Schuerman’s story, is that the chances of less severe flooding, due to overtopping by waves only, are 24%. These are approximate percentages, with some simplifications that could be improved upon fairly easily, but the computations were done quickly last Thursday for his story airing tomorrow.

There are two types of flooding that might occur — wave overtopping and still-water level overtopping. Wave overtopping would periodically send water over the levee, when waves strike. Still-water overtopping is what occurred during Sandy, when the average water level at the worst of the storm was about 3 feet above Father Capodanno Boulevard, so the water was rushing in continuously, and rapidly filled the neighborhoods with water.

A 4% chance over 50 years is fairly low odds, but important because it is important that people not consider these levees as ‘protection’ so much as ‘risk reduction’, following the wording changes preferred by the Corps and NYC.

Quoting the Corps Interim Feasibility Report:

In the very rare occurrence that coastal stillwater levels exceed the 15.6 feet NGVD 1929 design level of the project (approximately a 0.3% annual-chance-event or about the 300 year storm), the ocean surge could breach the line of protection inundating the study area to the level of surge. Therefore it is extremely important that residents follow New York City evacuation orders and protocol to help decrease risks to life safety in the event of a severe coastal storm event.

Now, onto the technical details — The Corps of Engineers designed the elevation of the levees based on the benefits vs costs for the next 50 years, and came up with an optimal height of 19.8 feet above mean sea level (20.5 ft NGVD29). Based on my quick reading of their report and some quick Q&A with someone from the Corps, this appears to include a flood level of 14.9 ft above mean sea level, plus 0.7 ft for continuation of the past sea level rise rate, over the next 50 years, plus (I assume, from subtraction) 4.2 ft to account for wave crest heights and possible overtopping of the levee due to waves.

According the the Corps, with today’s sea level, the return period of a flood that would cause waves to overtop this is 300-years; that means in 2015 there is only a 0.3% chance of waves overtopping it this year (if the system were built today). The return period of a flood that would cause still-water overtopping of the levees is about 2000 years, or a 0.05% chance per year. I am estimating these from FEMA’s data, which I used in our New York City Panel on Climate Change (NPCC) report chapter on how sea level rise would impact flooding around NYC. The Corps used their own data, which I do not have access to, so they might get slightly different results.

The president’s recent directive on planning infrastructure have suggested one should use a conservative high-end approach to accounting for sea level rise when planning infrastructure, aiming for 500-year flood, 100-year plus 3 feet, or best available information, which we actually have in this case from the latest 2015 report from the NPCC.

The Corps apparently isn’t yet instructed to think in this way, and this is often the case with federal government, given the hot button issue of (whisper) climate change. And thus, they are using the 0.7 ft based on the historical, linear sea level rise rate instead of these other choices.

First, looking at the probability of the less likely (but more severe) case of still-water overtopping, illustrated with the figure below — If I take a mid-range (50th-percentile) estimate of 20 inches of sea level rise by 2065 from the NPCC (doing some simple linear interpolations from numbers in their report), the return period of the flood that would overtop the structure reduces from ~2000 years to ~1000 years by 2065, meaning about the chance each year goes from 0.05% per year to a 0.1% chance per year.

Flood exceedance curves, showing return period (10, 100, 1000 years) versus still-water elevation. (black solid line) FEMA’s flood return period curve for Midland Beach, Staten Island, offset by +0.6 feet to match the Corps’ numbers. (blue solid line) the same curve, offset by 20 inches of sea level rise, showing a reduction in return period for the 20.5 foot flood from ~2000 years (dashed lines) to ~1000 years.

These are low odds, but a roughly 0.1% chance per year over 50 years adds up, though probabilities don’t exactly add/sum (see footnote below on how I make this computation). The probability of still-water overtopping the levee at any time over this 50-year period is 4%. Again, this accounts for a mid-range estimate of sea level rise. Performing the same computation with a high-end 90th-percentile sea level rise of 39 inches by 2065, this rises to 6%.

Lastly, looking at the probability of the more likely case of wave overtopping of the levee — using the mid-range NPCC sea level rise estimate and also accounting for higher wave crests hitting the shoreline (deeper water means less breaking, higher wave crests by a factor of 1.55 times sea level rise), the return period of the flood that would overtop the structure reduces to 130 years in 2065, meaning about the chance each year goes from 0.3% per year to a ~0.8% chance per year. (If one assumes high-end sea level rise occurs, the result is a 45-year return period in 2065). The cumulative probability of wave overtopping over 50 years is about 24%. (Or 44% using the high-end estimate of sea level rise).

Footnote on accumulated probability of flooding, over time — I actually compute this as the chances of NOT flooding, by multiplying each year’s chances of not flooding, then subtract the result from 100%. This is like flipping a coin twice — each time, the probability of getting heads is 50%, but you don’t simply sum them to know the probability of heads after two flips (100% is not correct). The probability of getting heads after two tries is actually aggregated using the multiples of each flip’s probability of not succeeding (1/2 times 1/2 equals 1/4), then taking 1.0 minus this value, giving 0.75 or a 75% chance. In Matlab, I am linearly interpolating the (growing) annual flood probability for each year between 2015 and 2065, and then I compute the cumulative product over a string of 50 years.

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