News Release

How to predict the weather -- with maths

New book shows how rigorous mathematical analysis can be exploited to explain real-world weather

Book Announcement

World Scientific

The Mathematics of Large-Scale Atmosphere and Ocean

image: Cover of "The Mathematics of Large-Scale Atmosphere and Ocean" view more 

Credit: World Scientific

We can now forecast the weather for a week ahead with giant computer models, but this gives no idea why it behaves as it does. Meteorologist Mike Cullen explains this in The Mathematics of Large-Scale Atmosphere and Ocean.

Nearly all published work on understanding the way that the weather behaves is either based on linear theory or is purely descriptive. This book describes a nonlinear theory that is based on the same physical understanding that has always been exploited in the descriptive explanations. Comparisons with the computer models used in forecast production demonstrates the validity of the nonlinear theory. This understanding is very important in interpreting weather forecasts as well as in considering the likely effects of climate change.

This book assumes a basic knowledge of the linear theory which can be found in many textbooks, and advances it into the nonlinear regime. In particular, it identifies separate regimes which require different treatment, which is often obscured in current textbooks. While the underpinning mathematics is highly technical, the book describes the methods in more physical terms and refers the reader to the mathematical analysis literature for the detailed proofs.

Mike starts by reminding us how predictable the weather is, and how it is amazing that such a complicated system can be predicted a week in advance. He then notes that many commentators seem to expect that the weather is infinitely predictable, and draw on chaos theory to say why it isn’t. So the real challenge is to explain why weather forecasts as so good, and Mike reviews much of the traditional background developed in the 1940s and 1950s, before going on to describe the huge advances in the nonlinear theory of weather made in the last 35 years. He describes how variational techniques developed for game theory and economics can be applied to large-scale weather. These show that extreme behaviour locally is to be expected, and may be highly predictable. So the popular concept that extreme weather must have a logical explanation can be satisfied.

The Mathematics of Large-Scale Atmosphere and Ocean retails for US$138 / £120 (hardcover) and is also available in electronic formats. To order or know more about the book, visit


About the Author

Mike Cullen has worked at the UK Met Office for many years, mostly on the development of the computer models used for weather forecasting. His desire to understand the behaviour of the models led him to establish links with a wide variety of academics both in the UK and elsewhere. A particular highlight was a research programme at the Isaac Newton Institute in Cambridge in 1996, which led to the development of much of the rigorous mathematics described in the book.

About World Scientific Publishing Co.

World Scientific Publishing is a leading international independent publisher of books and journals for the scholarly, research and professional communities. World Scientific collaborates with prestigious organisations like the Nobel Foundation and US National Academies Press to bring high quality academic and professional content to researchers and academics worldwide. The company publishes about 600 books and over 140 journals in various fields annually. To find out more about World Scientific, please visit

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