Hurricane Sandy and Global Warnings, an original article by Ian Roulstone and John Norbury

Hurricane Sandy and Global Warnings

Ian Roulstone and John Norbury

There are many heroes in the story of Hurricane Sandy, but we arguably owe the greatest debt of gratitude to mathematicians who wrangle massive amounts of data to improve the accuracy of our weather predictions. Two devastating storms, decades apart, provide a fantastic snapshot of how weather prediction has improved thanks to the introduction of computational mathematics over the last century.

Just over 75 years ago, on September 9th 1938 above the warm tropical waters near the Cape Verde islands, a storm gathered. As the weather system intensified, it was ushered westward by the prevailing larger-scale ridge of high pressure over the Atlantic. By the 16th the storm had become a hurricane, and the captain of a Brazilian freighter caught sight of the tempest northeast of Puerto Rico. He radioed the U.S. Weather Bureau to warn them of the impending danger – no satellites or sophisticated computer models to help the forecasters in those days.

A deep trough of low pressure over Appalachia forced the storm northward, avoiding the Bahamas and Florida, and towards the north-eastern seaboard of the United States. The forecasters were relying on real-time reports of the storm’s progress, but it advanced at an incredible pace, moving northward at nearly 70mph. By the time the Weather Bureau realised it was on a collision course with Long Island it was too late. The death toll from the Great New England Hurricane approached 600, with over 700 injured, and the damage was estimated at $308 million – or around $4.8 billion at today’s prices.

History very nearly repeated itself on October 29 and 30th last year, when Hurricane Sandy slammed into New Jersey. Meteorologists referred to Superstorm Sandy as a “multi-hazard event”, with major damage resulting from wind gusts, from high seas, from a tidal surge, from heavy rain, and even from driving snow. The number of fatalities in the U.S., attributed either directly or indirectly to Hurricane Sandy, were around 160: a tragedy, but mercifully fewer than the number killed by the Great Hurricane of 1938.

It is almost certain that timely warnings averted greater catastrophe last year. Unlike the storm of 1938, which caught forecasters by surprise, one of the most remarkable features of the forecast of Hurricane Sandy from the European Centre for Medium-Range Weather Forecasts (ECMWF) was the prediction made on October 21st, 36 hours before Sandy even formed, of a one-in-four chance of a severe storm, centred on New York, on October 30th.

ECMWF routinely produce two types of forecast for 10 days ahead. As they state in a recent newsletter “The ECMWF global medium-range forecast comprises a high-resolution forecast (HRES) and an ensemble of lower-resolution forecasts (ENS)”, and it was the ENS that helped forewarn of Sandy.

To calculate a forecast we use supercomputers to solve seven equations for the seven basic variables that describe weather: wind speed and direction (3 variables), pressure, temperature, air density, and humidity. The equations governing weather are highly nonlinear. This means that the ‘cause and effect’ relationships between the basic variables can become ferociously complex. To deal with the potential loss of predictability, forecasters study not one, but many forecasts, called an ensemble. Each member of the ensemble is started from a slightly different initial state. These different initial states reflect our ignorance of exactly how weather systems form. If the forecasts predict similar outcomes, we can be reasonably confident, but if they produce very different scenarios, then the situation is more problematic.

In the figure below the ensemble of forecasts for Sandy, starting at midday on October 23rd indicates the high probability of the ‘left turn’ and the most probable landfall – information that helped save lives. The inset at top right shows the strike probability chart that highlights the region around New York within which there is 25% chance of a severe storm by midnight on October 30th. This forecast was computed from an earlier ensemble starting at midday on October 21st and gave forecasters the vital “heads-up” of severe weather striking a highly populated area.

Forecasting Superstorm Sandy: The ensemble of forecasts covering the 10 days from the formation of the cyclone on October 23; the dotted black line is the actual track of the storm. Top right inset shows the storm strike probability from midday October 21. Bottom right inset shows the ensemble predictions of Sandy’s central pressure. © ECMWF

Forecasting Superstorm Sandy: The ensemble of forecasts covering the 10 days from the formation of the cyclone on October 23; the dotted black line is the actual track of the storm. Top right inset shows the storm strike probability from midday October 21. Bottom right inset shows the ensemble predictions of Sandy’s central pressure. © ECMWF

The science of weather and climate prediction was utterly transformed in the second half of the 20th Century by high-performance computing. But in order to fully exploit the computational power, and the information gathered by weather satellites and weather radar, we need mathematics.  As we explained in our article in Scientific American [hyperlink] math quantified the choreography of Hurricane Sandy. And to account for the ever-present uncertainties in the science of weather forecasting, math delivers the tools to analyse the predictions and to highlight the dangers.

Lives were saved because of the quality of our weather forecasts, which are made possible by an international group of mathematicians and weather prediction centers. The math that helps us quantify uncertainty in weather forecasting is being used to quantify uncertainty in climate prediction. It is easy to underestimate the value of this research, but investing in this science is vital if we are to stave off future billions in damages.

 


For further insights into the math behind weather and climate prediction, see Roulstone and Norbury’s new book Invisible in the Storm: The Role of Mathematics in Understanding Weather.

 

Climate Change: a Movie and the Math by Ian Roulstone and John Norbury

Climate Change: a Movie and the Math

By Ian Roulstone and John Norbury

Next week the Intergovernmental Panel on Climate Change (IPCC) will release the first of three reports that constitute their Fifth Assessment Report on climate change. This first report, The Physical Science Basis, will cover a huge range of topics from the carbon cycle to extreme weather. But climate prediction also relies heavily on mathematics, which is used to quantify uncertainties and improve the models.

The role of math is illustrated by a remarkable video of our ever-changing weather. Last month the National Oceanic and Atmospheric Administration (NOAA) decommissioned Geostationary Operational Environmental Satellite 12 (GOES-12), which monitored our weather for the past 10 years from its isolated vantage point 36,000 kilometers above America and the Atlantic Ocean.

GOES-12 had seen it all – from wildfires, volcanic ash, and landscape parched by drought, to Hurricanes Ike, Katrina and Sandy, and the blizzards that gripped the central United States in the winter of 2009-10. NOAA created a video – 187 seconds and 3641 images – one snapshot from each day of its operational life, which amounts to 10 years’ weather flashing before our eyes in just over 3 minutes. It’s dramatic and amazing:

In Scientific American, Evelyn Lamb commented on how this video highlights “a tension between the unpredictability of the weather and its repetitiveness”. Even after a few seconds it becomes clear that the patterns revealed by clouds differ from one part of the globe to another. Great towering cumulonimbus bubble up and unleash thunderstorms in tropical regions every day, while in more temperate mid-latitudes, the ubiquitous low pressure systems whirl across the Atlantic carrying their warm and cold fronts to Europe. The occasional hurricane, spawned in the tropics, careers towards the United States (Hurricane Sandy can be seen at about 2’50’’). But the mayhem is orchestrated: the cyclones almost seem like a train of ripples or waves, following preferred tracks, and the towering storms are confined largely to the tropics.

CaptureThis image of water vapour in the atmosphere (taken by GOES-13) reveals the swirling cyclones and the tropical storms. While the detail varies from hour to hour and from day to day, there are recurring patterns. Image courtesy of NEODAAS/University of Dundee.

In fact, this movie is affording us a glimpse of a remarkable world – it is a roller-coaster ride on the ‘weather attractor’.

An ‘attractor’ is a mathematician’s way of representing recurring behavior in complex systems, such as our atmosphere. A familiar illustration of an attractor can be seen in the figure below, and it is named after one of the fathers of chaos, Edward Lorenz.

Capture
The Lorenz attractor: every point within the space delineated by the coordinate axes represents a possible state of a circulating fluid, such as the ascent of warm air and the temperature difference of the warmer rising air to the cooler descending air. The points on the ‘butterfly wings’ are the attractor: they represent the set of states through (or around) which such a system will evolve. Even if the system begins from a state that does not lie on the attractor, it tends towards the states that do. The transition from one wing of the attractor to the other (which might represent a change in the ‘weather’) can be difficult to predict, due to inherent chaos in the system. But the overall pattern captures the repetitiveness.

It is impossible to illustrate the weather attractor for the atmosphere in terms of a simple three-dimensional image: Lorenz’s very simple model of a circulating cell had only three variables. Our modern computer models used in climate prediction have around 100 million variables, so the attractor resides in a space we cannot even begin to visualise. And this is why the movie created by NOAA is so valuable: it gives us a vivid impression of the repetitiveness emerging from otherwise complex, chaotic behaviour.

Weather forecasters try to predict how our atmosphere evolves and how it moves around the attractor – a hugely difficult task that requires us to explore many possible outcomes (called an ensemble of forecasts) when trying to estimate the weather several days ahead. But climate scientists are faced with a very different problem: instead of trying to figure out which point on the 100 million-dimensional attractor represents the weather 100 years from now, they are trying to figure out whether the shape of the attractor is changing. In other words, are the butterfly wings ‘folding’ as the average weather changes? This is a mathematician’s way of quantifying climate change.

If 100 years from now, when a distant successor of GOES-12 is retired, our descendants create a movie of this future weather, will they see the same patterns of recurring behaviour, or will there be more hurricanes? Will the waves of cyclones follow different tracks? And will tropical storms be more intense? Math enables us to “capture the pattern” even though chaos stops us from saying exactly what will happen, and to calculate answers to these questions we have to calculate how the weather attractor is changing.

 


This article is cross-posted with the Huffington Post: http://www.huffingtonpost.com/ian-roulstone/climate-prediction-mathematics_b_3961853.html

For further insights into the math behind weather and climate prediction, see Roulstone and Norbury’s new book Invisible in the Storm: The Role of Mathematics in Understanding Weather.