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.