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What inspired you to get into this field?
Every day millions of clouds form, grow, and move above us, blown by the restless winds of our ever-changing atmosphere. Sometimes they bring rain and sometimes they bring snow – nearly always in an erratic, non-recurring way. Why should we ever be able to forecast weather three days or a week ahead? How can we possibly forecast climate ten years or more in the future? The secret behind successful forecasting involves a judicious mix of big weather-satellite data, information technology, and meteorology. What inspired us was that mathematics turns out to be crucial to bringing it all together.
Why did you write this book?
Many books describe various types of weather for a general audience. Other books describe the physical science of forecasting for more specialist audiences. But no-one has explained, for a general readership, the ideas behind the successful algorithms of the latest weather and climate apps running on today’s supercomputers. Our book describes the achievements and the challenges of modern weather and climate prediction.
There’s quite a lot about the history and personalities involved in the development of weather forecasting in your book; why did you consider this aspect important?
When reviewing the historical development of weather science over the past three centuries, we found the role of individuals ploughing their own furrow to be at least as important as that of big government organisations. And those pioneers ranged from essentially self-taught, and often very lonely individuals, to charming and successful prodigies. Is there a lesson here for future research organisation?
Weather forecasts are pretty good for the next day or two, but not infallible: can we hope for significant improvements in forecasting over the next few years?
The successful forecasts of weather events such as the landfall of Hurricane Sandy in New Jersey in October 2012, and the St Jude Day storm over southern England in October 2013, both giving nearly a week’s warning of the oncoming disaster, give a taste of what is possible. Bigger computers, more satellites and radar observations, and even cleverer algorithms will separate the predictable weather from the unpredictable gust or individual thunderstorm. Further improvements will rely not only on advanced technology, but also, as we explain in our book, on capturing the natural variability of weather using mathematics.
But isn’t weather chaotic?
Wind, warmth and rain are all part of weather. But the very winds are themselves tumbling weather about. This feedback of cause and effect, where the “effects help cause the causes”, has its origins in both the winds and the rain. Clouds are carried by the wind, and rainfall condensing in clouds releases further heat, which changes the wind. So chaotic feedback can result in unexpected consequences, such as the ice-storm or cloudburst that wasn’t mentioned in the forecast. But we can use mathematics to warn us of the potential for chaotic behaviour, and this enables us to assess the risks of extreme events.
Are weather and climate predictions essentially “big data” problems?
We argue no. Weather agencies will continually upgrade their supercomputers, and have a never-ending thirst for weather data, mostly from satellites observing the land and sea. But if all we do is train computer programs by using data, then our forecasting will remain primitive. Scientific ideas formulated with mathematical insight give the edge to intelligent forecasting apps.
So computer prediction relies in various ways on clever mathematics: it gives a language to describe the problem on a machine; it extracts the predictable essence from the weather data; and it selects the predictable future from the surrounding cloud of random uncertainty. This latter point will come to dominate climate prediction, as we untangle the complex interactions of the atmosphere, oceans, ice-caps and life in its many varied forms.
Can climate models produce reliable scenarios for decision-makers?
The models currently used to predict climate change have proved invaluable in attributing trends in global warming to human activity. The physical principles that govern average global temperatures involve the conservation of energy, and these over-arching principles are represented very accurately by the numerical models. But we have to be sure how to validate the predictions: running a model does not, in itself, equate to understanding.
As we explain, although climate prediction is hugely complicated, mathematics helps us separate the predictable phenomena from the unpredictable. Discriminating between the two is important, and it is frequently overlooked when debating the reliability of climate models. Only when we take such factors into account can we – and that includes elected officials – gauge the risks we face from climate change.
What do you hope people will take away from this book?
From government policy and corporate strategy to personal lifestyle choices, we all need to understand the rational basis of weather and climate prediction. Answers to many urgent and pressing environmental questions are far from clear-cut. Predicting the future of our environment is a hugely challenging problem that will not be solved by number-crunching alone. Chaos and the butterfly effect were the buzzwords of the closing decades of the 20th Century. But incomplete and inaccurate data need not be insurmountable obstacles to scientific progress, and mathematics shows us the way forward.
What is UnShark Week, you ask?
A birthday held six months away from the real one, is an UnBirthday. So, for the thousands of ocean species that are just as interesting and sometimes more extreme than sharks, we propose the week of Feb 3-8, 2014 as UnSharkWeek.
UnSharkWeek will introduce fans of Shark Week to other extreme forms of life in the sea. There are all sorts of really cool things happening in the harshest environments on Earth, so join Steve Palumbi, one of the world’s leading marine biologists, as he celebrates some of the deepest, fastest, oldest, and just plain strangest creatures found in the ocean.
Follow along here: http://unsharkweek.tumblr.com/
For more information about The Extreme Life of the Sea by Steve and Anthony Palumbi or to read an excerpt from the book, please visit this web site: http://press.princeton.edu/titles/10178.html
This book officially publishes in March 2014 and will be available in three formats: Print, standard eBook, and enhanced eBook (featuring a dozen exclusive videos that are beautifully produced and informative).
For more about the book, please visit our web site: http://press.princeton.edu/titles/10178.html
“The oceans are our most precious treasure, full of creatures and stories more fantastic than any science fiction. The Extreme Life of the Sea is a fascinating exploration of this vast mysterious universe. Wonderfully written, it will grab you from page one and carry you all the way through. A must-read for everyone.”–Philippe Cousteau
“This book brims with fascinating tales of life in the sea, told with freshness, wit, and verve. Simply wonderful.”–Callum Roberts, author of The Ocean of Life: The Fate of Man and the Sea
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.
Today, all across the globe, we’re celebrating Earth Day. This year, Earth Day Network has declared its focus The Face of Climate Change. Each year on April 22, we acknowledge our appreciation for the amazing planet we call home and the take steps to protect it. What will you do today to celebrate Mother Earth? Here are some books to get you started. Get reading!
The Long Thaw: How Humans Are Changing the Next 100,000 Years of Earth’s Climate
Hubbert’s Peak: The Impending World Oil Shortage (New Edition)
The World’s Rarest Birds
The White Planet: The Evolution and Future of Our Frozen World
Eco-Republic: What the Ancients Can Teach Us about Ethics, Virtue, and Sustainable Living
How to Build a Habitable Planet: The Story of Earth from the Big Bang to Humankind (Revised and Expanded Edition)
Also, be sure to check out our Princeton Primers in Climate series. These primers reveal the physical workings of the global climate system with unmatched accessibility and detail. Princeton Primers in Climate is the ideal first place to turn to get the essential facts, presented with uncompromising clarity, and to begin further investigation–whether in the classroom or in one’s own reading chair.
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.