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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.
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
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.
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.
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.
We interviewed Toby Tyrrell about his new book “On Gaia” last week. This week, we’re proud to link to this article in which he details some of the research that led him to view the Gaia Hypothesis with a critical eye:
Q: Why did you write this book
A: My aim was to determine whether the Gaia hypothesis is a credible explanation of how life and environment interact on Earth.
Q: What is the Gaia hypothesis?
A: James Lovelock’s Gaia hypothesis, first put forward in the 1970’s, proposes that life has played a critical role in shaping the planetary environment and climate over ~3 billion years, in order to keep it habitable or even optimal for life down through the geological ages. Life has not been merely a passive passenger on a fortuitously habitable Earth, it is claimed, but rather has shaped the environment and helped to keep it comfortable.
Q: Why has there been so much interest in the Gaia hypothesis?
A: In part because it suggests answers to some fundamental questions of widespread interest, such as how it is that Earth remained continuously habitable for so long, how did our planet and the life upon it end up the way they are, and how does the Earth system work?
Q: Lots of scientists have considered Gaia before – what is different about this book?
A: Previous books have been mostly reviews of the scientific debates over Gaia, collections of scientific papers, or congratulatory restatements of Gaia by supporters. This book is the first to submit the Gaia hypothesis to detailed sceptical scrutiny, subjecting each of three main arguments put forward in support of Gaia to close analysis, and comparing them to modern evidence collected in the more than 30 years since the Gaia hypothesis was first proposed. It is the first book containing a hard-nosed and thorough examination of the Gaia hypothesis.
Q: What are the three main arguments that have been advanced in support of Gaia?
A: Firstly, that the Earth is very comfortable for life. Secondly, that the presence of life on Earth has profoundly altered the nature of the planetary environment. And thirdly, that the environment has remained fairly stable over geological time.
Q: What is the main conclusion of the book?
A: That the Gaia hypothesis does not “hold up in court”: it is not consistent with modern scientific evidence and understanding and should therefore be rejected.
Q: What are the reasons given for rejecting the Gaia hypothesis?
A: Firstly because there are no facts or phenomena that can be explained only by Gaia (no ‘smoking gun’). Secondly because there is no proven mechanism for Gaia (no accepted reason for why it should emerge out of natural selection). And thirdly because the key lines of argument that Lovelock and others advanced in support of Gaia either give equally strong support to alternative hypotheses or else are mistaken. For instance the planet is not excessively favourable for life: it has been colder than optimal during the ice ages that have occupied the majority of the last few million years, and unnecessary nitrogen starvation is ubiquitous. Its environmental history has not been all that stable: we now have abundant evidence of past environmental instability, from ice age cycles to seawater Mg/Ca variation to Snowball/Slushball Earths.
Q: If life and its environment do not interact in the way suggested by Gaia (life moulding the environment towards its own convenience) then how do they interact?
A: Through ‘coevolution’. Stephen Schneider and Randi Londer put forward the idea of a coevolution between life and its environment: biological processes such as oxygen production by photosynthesis shape the environment, and, clearly, the environment also strongly influences life through evolution of organisms to fit their environments. Coevolution recognises that both affect the other. Unlike Gaia, however, coevolution does not claim any emergent property out of the two-way interaction between life and environment. It is neutral with regards to predictions about the resulting effect on the environment. It does not suggest that the interaction tends to improve living conditions on Earth.
Q: If the Gaia hypothesis is not the reason, then why did the Earth remain habitable for such an enormously long interval of time?
A: This may relate partly to the weak Anthropic Principle, whereby we logically cannot observe any facts that preclude our own existence. So however infrequent it may be in the universe for a planet to remain continuously habitable over billions of years, we happen to be on just such a planet. According to this way of thinking, Earth may just have been lucky, with no sentient observers having evolved on other planets which were not so lucky, i.e. where conditions became sterile at some point. Another possible explanation for extended habitability in the absence of Gaia is a predominantly inorganic thermostat, such as has been suggested for silicate weathering.
Q: Why would people be interested in this book?
A: It considers some of the great questions about the nature of our planet, its history, and how it came to give rise to us. Many fascinating topics are covered, often from little-known corners of the natural world. Examples include: hummingbirds in the High Andes and the similarity of their beaks to the flowers they extract nectar from, the wonderfully-named Walsby’s square archaeon in the Dead Sea, the ever-lasting durability of the waste that coral reefs generate (not everything in nature is recycled), changes in the nature of the saltiness of seawater over geological time, and differences in the way Australian snakes bear young depending on climate (they don’t always lay eggs).
Q: Are there any implications for the current era of global change?
A: Yes, it is suggested that belief in the Gaia hypothesis can lead to excessive complacency about the robustness and resilience of the natural system. Gaia emphasizes stabilising feedbacks and protective mechanisms that keep the environment in check. If Gaia is rejected, however, we are left with a less comforting view of the natural system. Without Gaia it is easier to appreciate that the natural system contains lines of weakness and other susceptibilities. One such line of weakness that has already been demonstrated is the ozone layer depletion by CFC’s. I have argued in the book that there is no over-riding Gaia to protect our planet’s life support system. Maintaining the Earth’s environment is up to us.
Each year, World Water Day is held on the 22nd of March as an international means of emphasizing the importance of freshwater and advocating for the sustainable management of Earth’s water resources. According to UN Water, this year’s theme is International Year of Water Cooperation. Celebrations all over the globe are in full swing today. Check out the World Map of Events to get involved!
Want to broaden your understanding of water systems and sustainability? Our Princeton Primers in Climate series are the ideal first place to turn to get the essential facts and to begin further investigation–whether in the classroom or in one’s own reading chair.
The Cryosphere by Shawn J. Marshall
Introduction to the cryosphere and the broader role it plays in our global climate system. Looks at each component of the cryosphere and how it works–seasonal snow, permafrost, river and lake ice, sea ice, glaciers, ice sheets, and ice shelves. Marshall describes how snow and ice interact with our atmosphere and oceans and how they influence climate, sea level, and ocean circulation.
Atmosphere, Clouds, and Climate by David Randall
David Randall looks at how the atmosphere regulates radiative energy flows and transports energy through weather systems such as thunderstorms, monsoons, hurricanes, and winter storms. Randall explains how these processes work, and also how precipitation, cloud formation, and other phase changes of water strongly influence weather and climate.
Climate and the Oceans by Geoffrey K. Vallis
Offers a short, self-contained introduction to the subject. This illustrated primer begins by briefly describing the world’s climate system and ocean circulation and goes on to explain the important ways that the oceans influence climate. Topics covered include the oceans’ effects on the seasons, heat transport between equator and pole, climate variability, and global warming.
Celebrate World Water Day! Today, enlighten yourself and inform others about the sustainable management of the world’s water supply.
We are publishing Invisible in the Storm by Ian Roulstone and John Norbury next month. The book explains how mathematics and meteorology come together to predict the weekly weather, prepare us for incredible weather events like Hurricane Sandy, and contribute to our understanding of climate change. They kindly answered a few of my questions for the Princeton University Press Blog:
1. I’ll start with the thing everyone is talking about. It seems like extreme weather more prevalent in recent years. With Hurricane Sandy and the recent unprecedented Nor’Easter behind us (ed. note: I’m writing from NJ), it bears asking whether the future holds more extreme weather? Can mathematics help answer this question?
Mathematicians think about weather and climate in an unusual way. Our ever-changing weather can be visualized as a curve meandering through an abstract mathematical space of logically possible weather. Any one point of the curve corresponds to a particular state of the weather. The surprise is that the curve does not wander around randomly–patterns emerge. One part of the pattern may correspond to ‘warm and dry’ and another part to ‘cold and wet’. Predicting changes in the weather for the week ahead involves working out if the curve will drift from one part of the pattern to another. Understanding climate involves working out how the pattern itself will change.
2. So, is the pattern changing toward more extreme weather or can we not answer this question yet?
If we compare the results from different climate models (from different research institutions and weather bureaus around the world), then they show an increase in global average temperature over the next century. However, this could lead to quite different conditions in different parts of the world. For example, if the Gulf Stream was weakened, Europe could experience colder weather. However, we know our models are not perfect, and mathematics is helping us to understand the errors that are inherent in the compuer-generated simulations. This work is important as it will help us to estimate the likely extremes in weather and climate with greater confidence.
3. To return to the end of your first answer, how can mathematics detect climate change?
Climate depends on many factors: the atmosphere, the oceans, the icecaps, land usage, and life in all its forms. Not only are there many interconnections between these systems, the timescales over which changes occur vary enormously: trees can be felled in a few hours or days–changing the character of the local landscape quickly–but carbon stocks in soil vary much more slowly, perhaps over several millennia. To predict future climate we have to account for the short- and long-timescale effects, and this can pose subtle problems. Mathematics helps us to quantify how the different timescales of the changes in the components of the Earth system impact on predictions of climate change. Using mathematics, we calculate how cloud patterns change over the next five days, and how the Arctic ice-sheet changes over the next five years.
4. How does mathematics help forecasters predict the weather for the week ahead?
One of the main sources of information for a new forecast is yesterday’s forecast. New generations of satellites gather more, and more accurate, readings, ranging from the sea surface temperature to the state of the stratosphere. Data is exchanged freely around the world among weather bureaus; global weather prediction relies upon this protocol. However, we will never have perfect, complete weather data, and this is why we need mathematical techniques to combine the new information with the old.
5. Years ago, it seems like weather was much simpler — will it rain, snow, sleet, or be sunny? These days, mathematics enables weather forecasters to forecast more than rain or shine: the computer simulations are useful for predicting everything from pollen levels and pollution to flood risk and forest fires. Can you explain how mathematics is part of this?
Mathematics is the language we use to describe the world around us in a way that facilitates predictions of the future. Even though hay fever and floods are very different natural phenomena, predictions of their occurrence can be made using mathematical models. Weather forecasters are actively engaged in combining their predictions with models that help us forecast weather-related phenomena.
6. It sounds like a one-way street — mathematics helps us understand meteorology — but you note in the book that the relationship is more reciprocal. Can you elaborate?
To most of us, meteorology and mathematics are a world apart: why should calculus tell us anything about the formation of snowflakes? But mathematics has played an ever-growing and crucial role in the development of meteorology and weather forecasting over the past two centuries. Our story explains how mathematics that was originally developed for very different purposes, such as studying the ether or the dynamics of the solar system, is now helping us to understand the dynamics of the atmosphere and oceans, and the changes in our climate. And it is a two-way process: the diversity of phenomena we seek to quantify means we have to describe them using new mathematical ideas that capture the rapid changes, the slow changes, the randomness, and the order, we observe.
7. Is there a current area of mathematical/meteorological research that you are particularly excited about? Ie – what’s next?
There’s one particular subject that’s attracting a lot of attention right now: it is called data assimilation. This is the part of the forecasting process where new observational information about the state of the atmosphere is combined with the previous forecast, to give us the starting conditions for the next forecast. Improvements to this part of the forecasting process nearly always lead to better forecasts. And the technology applies to modelling the climate too. In this case, we’re not so much interested in whether we have the correct starting conditions, but whether we have used the correct values of the parameters that define the processes and physical phenomena which affect climate–for example, the carbon cycle, from leaves to biomass and carbon dioxide. One of the reasons this is a really exciting area for mathematicians is that we need some new mathematical ideas to analyse these problem. At the moment we rely heavily on math that was developed over 50 years ago–and it works very well–but as we strive to increase the detail we want to represent in our weather and climate models, we have to unravel the Gordian knot that ties together the many different parts of the Earth system we have to represent.
Our video series on the HOW CLIMATE WORKS symposium held at Princeton University this past fall concludes with the Q&A session following the final talk of the day. We hope you have enjoyed your symposium vidoes. For furthur reading, check out our Princeton Primers in Climate series.
Part 8 from the How Climate Works symposium brings us Andrew Ingersoll of the California Institute of Technology on planetary climates. This fall we will be publishing his book of the same toipc PLANETARY CLIMATES.
Part 7 from the How Climate Works symposium features Shawn Marshall of the University of Calgary on the cryosphere. We published his excellent book on the subject in the Fall or 2011 called THE CRYOSPHERE.
Continuing with our series on talks from Princeton’s HOW CLIMATE WORKS symposium, here we see Princeton University geoscience professor Michael Bender discussing Paleoclimate. His new book PALEOCLIMATE will be availble July 2013.