We are in the midst of a huge uncontrolled experiment with the earth’s climate. Whatever view one might take on the question of global climate change, it is hard to imagine not being interested in the outcome. Since controlled experiments are not possible, mathematical modeling offers one avenue toward understanding what factors have the biggest influence on climate. The current book is an introduction to the mathematical study of climate by two authors who have been closely involved with the Mathematics and Climate Research Network, a virtual organization of researchers and students located at many different universities and other institutions. This book had its origin in a Masters level course on mathematics and climate at Georgetown University.

One of the challenges in this area is that the study of climate includes aspects of so many different sciences. Just to name a few, there are: physics, chemistry, biology, geology, geochemistry, geophysics, biogeochemistry and oceanography. It is both frustrating and fascinating — there is always something new to learn.

This poses quite a challenge to authors of an introductory book for mathematics students. They carry it off pretty well. The mathematical and statistical content is mostly what a student might see in applied mathematics and multivariate statistics courses. The material on climate science often comes from original research papers that have appeared over the past couple of decades. It is a good mix that offers students an excellent sense of what actual working applied mathematics can be.

Where the book has weaknesses it is because it tries too much. There are probably too many topics and the treatment of some of them is just too cursory. Yet, as an introduction, the authors do a quite creditable job at exposing students very effectively to some very complex questions. The book’s overall theme is to use the techniques of dynamical systems in conjunction with statistical analysis of historical data to develop relatively simple conceptual models that can reproduce observed climactic phenomena.

Things that work especially well in the book are the presentation of the general setting (the earth’s energy budget and the role of the oceans and the atmosphere), the development of the dynamical systems approach, and the integration of data analysis and statistics into the mix. The most disappointing part is the treatment of data assimilation. Although it is an intriguing subject the treatment is so brief that a student might be completely bewildered by the bare sketch of it here.

This is a textbook that is mostly accessible to advanced undergraduates. It has lots of good exercises and would be highly suitable for a topics course. It is also an excellent introduction for anyone with even a modest interest in the subject.

Bill Satzer (wjsatzer@mmm.com) is a senior intellectual property scientist at 3M Company, having previously been a lab manager at 3M for composites and electromagnetic materials. His training is in dynamical systems and particularly celestial mechanics; his current interests are broadly in applied mathematics and the teaching of mathematics.