## Roots of Unity

Mathematics: learning it, doing it, celebrating it.

# The Most Breathtaking Video of the Weather You’ll Watch This Week

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Last Monday, the National Oceanic and Atmospheric Administration (NOAA) released a video of the past 10 years of weather in the Americas. The Geostationary Operational Environmental Satellite GOES-12, which had monitored the weather in North and South America since April 2003, was retired on August 16. This video shows one photo a day from the time the satellite was operating.

187 seconds. 3641 images.

The hurricanes stood out to me the most. Hurricane Katrina at the 0:45 mark looks no different from several storms before and after it. Hurricane Ike, which knocked out my power for five days and caused \$30 billion of damage in the US and \$7 billion in Cuba, is almost undetectable. It must be around the 1:40 mark, but the storm that covered the Gulf of Mexico in pictures on the Weather Channel comes and goes too quickly for me to pinpoint it for sure. Hurricane Sandy is fresh in our minds, and you can see it pretty clearly at the 2:50 mark in the video, but it too forms and dissipates in the blink of an eye.

The NOAA video seems to highlight a tension between the unpredictability of the weather and its repetitiveness. Every summer, the west coast of Africa seems to "pitch" hurricanes to the Caribbean. Sometimes the Yucatan or Caribbean islands bat them into the north Atlantic, and sometimes they come right over the plate to the shores of the Gulf States. (OK, the baseball metaphor is a little strained at this point, and it's definitely Gulf state-o-centric because my main experience with hurricanes was in Houston.) On a day-to-day basis, we are limited in how well we can predict the weather because it's such a chaotic system, but we can also assume that we'll see certain weather patterns in certain places at certain times of the year.

Although I am a theoretical mathematician, I've been seeing a lot about the applied mathematical field of weather prediction lately. I've attended several talks this year about mathematics and weather prediction, and I've been reading the Mathematics of Planet Earth blog, which often has posts about how to model the weather.

Due to the unpredictability of the weather, meteorologists use ensemble forecasting to make predictions. Small changes in conditions can eventually build up to very large differences, so in ensemble forecasting, several models are used and their results aggregated. Each model has slightly different assumptions and random variations in initial data built in, and the group of predictions taken as a whole helps give people an idea of how likely different possibilities are.

As an article from the August 2013 issue of Scientific American points out, the ensemble forecasting used by the European Centre for Medium-Range Weather Forecasts (ECMWF) did a remarkable job of predicting Sandy. Seven days before the storm made landfall, most of the models used by the ECMWF showed a cyclone hitting New Jersey around October 30. Although the devastation and loss of life were high, the accuracy of the ECMWF prediction saved lives. The success of the ECMWF Sandy forecasts garnered a great deal of media attention. A post on Dr. Jeff Masters' WunderBlog discusses what made the ECMWF predictions so much better than those used by the National Hurricane Center, and he links to a Houston Chronicle interview and article on the subject. You can also read an article about it on page 9 of the ECMWF Autumn 2012 newsletter (pdf).

Ensemble forecasts are used on the larger climate scale as well. In March I went to a talk by Berkeley professor of atmospheric sciences Inez Fung in which she discussed some of the history of weather and climate predictions and the challenges ahead. You can watch a video of a similar lecture she gave later that month here. I don't want to spoil anything, but at one point the word "computer" is used to mean "person who does computations." We have certainly come a long way since people tried to calculate the weather by hand!

Most recently, I attended Christopher Danforth's lecture at MathFest in Hartford, CT. Danforth is an applied mathematician at the University of Vermont, and his blog post about chaos in weather predictions is great reading. He wrote it to celebrate the 50th anniversary of the famed paper by Ed Lorenz that gives us the idea of the "butterfly effect" and arrives at fourteen days as an upper limit to how far in advance we can predict the weather. During Danforth's talk, a room full of mathematicians was absolutely mesmerized by a video of simulated gas swirling in a ring, which also appears on that blog post.

The weather is supposed to be a dull topic, but I can't stop watching that NOAA video and thinking about the chaos within its repetitive yearly pattern.

The views expressed are those of the author and are not necessarily those of Scientific American.