Quick Questions for Ian Roulstone and John Norbury, co-authors of Invisible in the Storm

Ian Roulstone (top) and John Norbury (bottom) are authors of Invisible in the Storm: The Role of Mathematics in Understanding Weather and experts on the application of mathematics in meteorology and weather prediction. As we head into hurricane season along the Eastern coast of the United States, we are still not fully recovered from Hurricane Sandy, empty lots still dot the stretch between Seaside and Point Pleasant and in countless other beach communities. But it could have been worse without the advance warning of meteorologists, so we had a few questions about the accuracy of weather prediction and how it can be further refined in the future.

Now, on to the questions!

Ian RoulstoneNorbury


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?

“We can use mathematics to warn us of the potential for chaotic behaviour, and this enables us to assess the risks of extreme events.”

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.


bookjacket Invisible in the Storm
The Role of Mathematics in Understanding Weather
Ian Roulstone & John Norbury



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.

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.