Atlantic Ocean

How Math Helped Forecast Hurricane Sandy.

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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 depressionfirst 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.

Source: http://www.scientificamerican.com

The Maths Behind the Heat Wave.

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A heat wave in the UK is usually measured by temperatures reaching in excess of 30 degrees Celsius for more than a week. The current heat wave – the longest spell of hot weather in seven years – is welcomed by most after one of the most prolonged winters on record; but if temperatures remain high, health risks and environmental hazards, such as crop failure, wildfires, and water shortages, become a real concern. So how good are we at predicting heat waves? Are they related to global warming? And do we know when it will rain again?

US-WEATHER-HEATWAVE

Maths helps us to answer these questions. Forecasting a heat wave relies on an accurate prediction of the jet stream, and the attendant troughs of low pressure and ridges of high pressure. The present spell of hot weather in the UK is related to the dramatic shift of the jet stream in early July to a northerly position relative to the British Isles.

Jet streams were among the first meteorological phenomena to be understood and quantified by mathematics. The breakthrough was made by a Swedish meteorologist who moved to the United States in 1925 and subsequently changed the face of meteorology, in both the US and worldwide. His name was Carl-Gustaf Rossby, and his name is immortalized in the Rossby wave – a key mechanism in controlling extreme weather such as heat waves.

Rossby waves are similar to water waves, but instead of water moving up and down, the air stream undulates northwards and southwards. Rossby waves are revealed by distinctive patterns of the troughs and ridges. These mostly westward propagating waves are quirkily associated with eastward-moving weather. However, from time-to-time the waves come to a halt – remaining stationary over a particular region.

Forecasters call this “blocking”, which is when a weather event such as a heat wave persists in an area for a long period of time. One undulation of a Rossby wave generally has an east-west extent of about five thousand kilometres (roughly across the northern Atlantic Ocean). By studying how the actual spacing of the troughs and ridges compares to an undulation calculated for the average winds, we estimate their subsequent motion.

Understanding how patterns in the jet streams change with the climate is critical. One of the major factors that influence the dynamics of a jet stream is the thermal wind equation. This equation states that the vertical rate of change of the horizontal wind is proportional to the horizontal rate of change of temperature. This means that the decrease in temperature towards the North Pole causes winds to develop a larger eastward component with altitude. The strong eastward moving jet streams are in part a consequence of the simple fact that the equator is warmer than the north and south poles. So, if the equator to pole temperature differences were to be modified as a consequence of climate change, this would most likely have a major impact on the behaviour of the jet streams.

Because jet streams are large-scale features of weather, forecasters can be reasonably confident in their ability to predict how the jets will change from day to day. The computer models used in forecasting divide the entire atmosphere into millions of ‘weather pixels’. Each pixel covers a horizontal area roughly 15km by 15km, and there are about 70 vertical layers of these pixels throughout the depth of the atmosphere. One of the crucial factors in determining whether or not a weather system can be forecast on the computer accurately is the ratio of the size of the system to the size of a typical pixel: weather phenomenon that are many more times larger than a weather pixel, and will therefore be represented by perhaps many thousands of pixels, are likely to be forecast well. This is the case for the jet streams.

On the other hand we know that prolonged periods of hot weather invariably give rise to severe thunderstorms. Thunderstorms are usually very local phenomenon, and they are not well resolved by the current computer models. For this reason, the periods of hot weather can be forecast with considerable accuracy, while forecasters may only be able to indicate the likelihood of isolated, but often damaging, thunderstorms.

 


Source: http://www.huffingtonpost.co.uk

Earth’s plates move slower than thought.

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The mystery of erratic changes in the history of Earth’s past and current plate motions has been cracked by academics from The Australian National University.

Dr Giampiero Iaffaldano, from the Research School of Earth Sciences in the ANU College of Physical and Mathematical Sciences, led a team that found true changes in plate motions occur on timescales no shorter than a few million years.

“The scenario arising from recent data was puzzling because plates appeared to move erratically and significantly over geologically-short periods of less than one million years,” said Dr Iaffaldano.

“This posed a conundrum, as the forces that would be required to explain their sudden motions far exceed the most optimistic estimates we could make.”

Dr Iaffaldano’s research focused on the detailed records of plate motions across the mid-oceanic ridges in the South Pacific, Indian and Atlantic Oceans. After accounting for data noise – the portion of data that was unrelated to Earth’s plate motions – he found that true changes in plate motions occur on timescales no shorter than five million years.

“A major discovery of the study is that, upon noise reduction, true changes in plate motions occur on timescales no shorter than a few million years. This yields simpler movement patterns and more plausible dynamics,” he said.

“We showed that noise is in fact a significant bias to our understanding of the forces shaping Earth’s surface, particularly as more and more measurements of plate motions are made available.

“This does not mean that these measurements are wrong, but we need to reduce noise as much as possible before making any geophysical conclusions. In our study we provide for the first time a method to do so in a simple and efficient way, by statistically determining the likelihood of a certain plate-motion change at a given time in the geologic past.”

Source: Science Alert