In October it was 10 years since Sandy. In almost every retelling the flood in Manhattan came from 2 things meeting: a huge storm surge and a high tide under a full moon. I repeated this story myself. I never asked how often the high tide part is really there, in Sandy or in other floods.
So I took 2 tide gauges with a century of data, The Battery in New York and Boston. Then I stitched them with the Atlantic hurricane catalog.
What a storm adds to the tide
The tide is known years ahead. NOAA publishes the predicted time and height of every high water and the gauge records what really came. The highest observed level around a predicted high water minus the prediction is called the skew surge, the part the weather added.
From the NOAA CO-OPS API I downloaded hourly heights from 1921 to December 20, 2022 and the predicted high and low waters. That is about 70,000 high waters per station. For hurricanes I took HURDAT2 from the National Hurricane Center, the October version that ends with 2021. The analysis is about 300 lines of Python 3.10 with only the standard library.
The predictions are fixed to the sea level of 1983 to 2001, so the sea level rise sits inside the skew surge. At The Battery its median goes from −0.21 m in 1921 to +0.11 m in 2022. For the statistics I subtract the median of each year. The water levels I leave as they were, because that is the water people really had in the streets.
Before counting I wrote down 4 expectations. The biggest surges would not care about the tide height. In Boston the tide range is 3.1 m and I expected most of the 20 highest waters on a high tide from the top quarter. At The Battery the range is 1.5 m and I expected less than half. The other 2 come below.
Where I almost published the wrong list
My first top 20 for The Battery had no Donna from 1960 and no Irene from 2011. Donna was the record before Sandy, but the rest of the list looked fine and I almost moved on.
My script had used only 34,514 high waters out of about 70,000. The window around each predicted high water starts halfway to the previous low water. When the gap is an odd number of minutes, that point has 30 seconds. I rounded it to the full hour by setting the minutes to zero and forgot the seconds. So the keys did not match the hourly data and the window looked like it had a gap. Windows with gaps I skipped without a message. After the fix 66,689 high waters at The Battery have a complete window and Donna is second with 3.05 m.
The storm does not choose the tide
I took the top 1% of skew surges at each station. At The Battery that is 669 high waters with a surge of 0.485 m or more, at Boston 714 with 0.41 m or more. Kendall’s tau between the predicted high water and the surge is +0.007 at The Battery and −0.007 at Boston, with p 0.80 and 0.77.
My first expectation also had a number: 20 to 30% of extreme surges would come on a high water from the top quarter. At The Battery it is 14.9%, at Boston 19.5%, both below my range. It took me a moment to see why. Of the 669 extremes at The Battery 144 came in December and 121 in January, none in July. The mean predicted high water in January is 1.34 m and in September 1.55 m, so most storms come when the tides are lower. Counted month by month, the expected share is 17.4% and 22.0% and the difference is not significant.
Williams and Horsburgh with colleagues showed this in 2016 on 77 gauges, New York among them, including the seasonal effect. I only repeated it with public NOAA data up to 2022.
Sandy and Boston
Sandy’s peak at The Battery was 4.28 m above mean lower low water in the 6 minute data, at 01:12 UTC on October 30. In the hourly data, which I use for everything here, it is 4.26 m. The high water predicted for 00:48 was 1.48 m. It was the full moon, but this was the lower of the 2 high waters of that day. Among all high waters since 1921 it is at the 56th percentile. Almost all of Sandy was the surge, 2.79 m, the biggest in the record by far. With the highest predicted tide within 15 days, 1.93 m, the same surge would have given 4.71 m.
Boston is a different place. Of its 20 highest waters 16 came on a high tide from the top quarter. The record is the storm of January 4, 2018. NOAA put it 2 cm above the Blizzard of 1978, in my hourly data both are 4.58 m. In 2018 the tide was at the 98.5th percentile and the surge was 0.97 m. After the sea level correction that is not even in Boston’s top 20 surges. At The Battery 10 of the 20 highest waters came on the top quarter, so exactly half and not less than half as I expected.
The coincidences that did not happen interest me more. On December 7, 2003 Boston had a surge of 1.04 m on a tide at the 13th percentile. The water stopped at 3.73 m, below the minor flood level. With the highest tide within 15 days it would have been 4.76 m, above the record.
I expected at least 3 of the 20 biggest surges at The Battery to cross the major flood level on such a tide. Of the 15 that stayed below it, 12 would have crossed. At Boston only 1 of the 20 reached the major level of 4.43 m, the threshold of NOAA’s National Ocean Service. 13 more would have reached it, 2 of them by less than 2 cm. This is a simple sum that assumes the surge does not change with the tide. The independence above makes it reasonable, but it does not prove that one storm would bring the same surge on another tide.
Hurricanes
I joined every event with HURDAT2: a cyclone track point within 500 km of the gauge and within 24 hours of the peak. At The Battery 4 of the 20 biggest surges have one, at Boston 3.
Then I read the tracks. 2 of these storms, October 1991 and Wanda in 2021, start in the catalog as extratropical lows, so here the catalog lists the nor’easter itself. Donna in 1960 and Irene were tropical near New York. Carol in 1954 turned extratropical a few hours before Boston’s peak and Sandy shortly before landfall. So tropical cyclones are 2 or 3 of the 20 at The Battery and at most 1 at Boston, less than half as I expected. Everything else is ordinary storms, mostly from October to March.
What I did not check
Both stations are on the same coast with the same type of tide. Compared with NOAA’s 6 minute high waters, hourly data misses the peak by up to 3.6 cm at The Battery in 99% of cases. At Boston it is 7 cm. The 3 day window that separates events and the 500 km radius are my choices and I did not try other values. The scenario with a higher tide ignores how surge and tide interact in shallow water, which Horsburgh and Wilson described for the North Sea in 2007. Waves and rain are not in the gauge at all. I did not look at damage data, so flood level here is only the NOAA threshold.