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# How Math Helped Forecast Hurricane Sandy

The mathematics of predicting a hurricane's path

Ensemble of forecasts shows Sandy's predicted swerve and the likely regions where landfall would occur; the dotted line is the actual track of the storm.

Image: COURTESY OF EUROPEAN CENTER FOR MEDIUM-RANGE WEATHER FORECASTS

Many early forecasts for Hurricane Sandy last year predicted that the system would fizzle over the Atlantic. Yet a model developed by researchers at the European Center for Medium-Range Forecasts showed a more alarming scenario: the storm would instead turn west to threaten the Eastern Seaboard. The model's refined predictions pinpointed the hurricane's landfall around the New Jersey area in time to allow residents to seek higher ground. The key to the more accurate forecast involved mathematical mastery of the storm's chaotic behavior.

Weather forecasts are calculated with computers that solve equations involving variables such as wind speed, pressure, temperature, air density and humidity. If the earth somehow possessed just one weather system, our fist shaking at forecasts could end. Instead, of course, the planet harbors many systems that intermix across boundaries and scales, making forecasting a tangled problem.

In the case of Sandy, forecasters monitored a higher-order variable called potential vorticity, a measure of a weather system's swirl, to help predict the storm's future development. A crucial ingredient for Sandy's devastating landfall proved to be an enhancement of this swirl measure caused by a trough of low-pressure air that was thousands of miles away in the northeastern Pacific when the tropical depression first formed. As Sandy moved north from the Caribbean, the distant trough traveled east across the U.S. on what turned out to be a collision course. On October 29 Sandy's warm, moist air began to rise as it approached the trough's cooler air, whipping up stronger winds. As the two weather systems coiled around each other, Sandy surged in strength and curved toward the nation's northeastern shoreline, just as the European researchers had foreseen. The ultimate accuracy of the group's forecasts about a week before Sandy's landfall can be attributed to the success of its model in predicting and capturing the interaction between these weather systems.

The step-by-step quantification of this stormy choreography was accomplished solely through the careful application of mathematics. By predicting Sandy's landfall, in a very real sense, the European team's math helped to save American lives.

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Roulstone and Norbury are authors of Invisible in the Storm: The Role of Mathematics in Understanding Weather (Princeton University Press).
Roulstone and Norbury are authors of Invisible in the Storm: The Role of Mathematics in Understanding Weather (Princeton University Press).

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1. 1. oldmanbim 06:35 PM 7/23/13

A homerun is great, a grand slam is stupendous. But, even Casey struck out. What is ECMRF's batting average?

2. 2. Dave X 11:03 AM 7/25/13

ECMWF's batting average is pretty good. Part of the reason is that their maths allow them to incorporate polar satellite measurements in their models: http://www.noaanews.noaa.gov/stories2012/20121211_poesandsandy.html and http://www.wunderground.com/blog/JeffMasters/superstorm-sandy-and-the-importance-of-polar-orbiting-satellites-in-fo

3. 3. oldmanbim 08:22 PM 7/25/13

Thanks, Dave X. I found Masters' blog the most useful. Especially, "While the ECMWF model was the best performing model for tracking Atlantic hurricanes in both 2010 and 2011, and had done very well again so far in 2012, the American GFS model had outperformed the ECMWF model several times during the 2012 season."

4. 4. Ian Roulstone 03:51 AM 7/26/13

One of the remarkable features of the ECMWF forecast was the prediction, the day before Sandy formed, of a "substantial cyclonic windstorm" in the NJ area on 30th October. That is, the ECMWF ensemble system had flagged Sandy even before the storm developed. More information is available in the ECMWF newsletter (article by Hewson on page 9):
Naturally, an in-depth analysis of the performance of the model is on-going.

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