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The Actuary The magazine of the Institute & Faculty of Actuaries
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Invisible in the storm: the role of mathematics in understanding weather by Ian Roulstone and John Norbury

05 SEPTEMBER 2013 | BY COLIN J W CZAPIEWSKI
Invisible in the storm: Book cover

Publisher: Princeton University Press
ISBN: 10 0691152721 ISBN-13 978-0691152721
RRP: £24.95


“Like meteorologists, actuaries use past experience with justified theoretical detail”

We are all used to seeing weather forecasters attempt, and sometimes fail, to indicate what we might expect for tomorrow, and perhaps even for next week and further. Sometimes, as Michael Fish found to his cost in 1987, it can go terribly wrong.

This very readable book provides an excellent insight into the history of forecasting the weather, with a considerable, but not too challenging, mathematical bent.

The book uses ‘tech boxes’ for those who wish to follow the more scientific reasoning, while enabling the more casual reader to enjoy the subject in an easy fashion. Simple examples are introduced and then just enough is added to illustrate how predicting can quickly become complicated. For example, imagine a second arm is attached to the end of a single pendulum. Without it, the linear motion is very easy to ascertain, but the second arm makes the motion non-linear and exceedingly difficult to assess.

The history of forecasting weather is dealt with in detail. The origins go hand in hand with developments in mathematics and physics. Many pioneers who had a part to play in weather forecasting are familiar names in other fields as well, including Euler (fluids) and Lorenz (chaos), but some are associated just with weather forecasting such as Bjerknes, Rossby and Charney. The laws of physics we all learned at school are closely connected with justifying weather forecasting theoretically.

The many similarities to actuarial work include the importance of knowing and understanding the theoretical background to the methods used. Like meteorologists, actuaries use the combination of past experience with justified theoretical detail to predict future events. We also sometimes get the answers wrong, but the process of understanding why is useful in improving techniques. We both use models, and judge the ‘method skill’, or appropriateness and accuracy, of the model. As we all know, “all models are wrong, but some are useful”. The authors conclude that it is necessary to get the most out of mathematics to improve models of future weather.

There was an early recognition of the impossibility of accurate predictions in every circumstance, but also a realisation that very useful forecasting could be performed, and so significant efforts were made to ensure that there were intensive theoretical and practical advancements. The utter complexity of the Earth’s atmosphere, the plethora of physical laws that impinge upon the science and the problem of interaction, or feedback, all combine to make this a challenging subject.

Weather forecasting is compared with other historical interests such as astronomy, which seem to have had relatively more practical success. Owing to the massive bodies involved in the main astronomical calculations, as compared to their environment, this greater success was inevitable.

The different characteristics and approaches are clearly explained in the book. It is to the credit of such pioneers in centuries past that they were able to use the science of theoretical mathematics that was still developing to answer some of the practical issues related to weather forecasting.

Clearly, the advent and development of computers widened the scope of weather forecasters to produce more accurate forecasts, although by this stage their approach had changed and rather than attempting to predict the actual weather, they acknowledged that a more useful contribution was to state the likelihood of the weather being as they predicted, and to highlight the scope for uncertainty.

Climate change is discussed in the book, albeit more briefly than desired. The authors stress just how uncertain the effects of such changes would be on the Earth’s weather patterns.

The future of weather forecasting indicates that the current improvements of models, computer power, mathematical techniques and a better understanding of the forces that affect the weather will contribute to make forecasting more reliable. Over the past 25 years, forecasts of the actual air pressure at sea level, which is an appropriate measurement of the reliability of weather forecasts, have improved significantly. But it seems that the sheer quantum of variables that affect the weather and the unpredictability of their interaction, or feedback, means this improvement will become less pronounced over time.

There will never be truly accurate local forecasts, or forecasts well into the future, but there will be much better, and more reliable, general forecasts.


Colin J W Czapiewski is an actuary, consultant and non-executive director