They explore how weather forecasters today formulate their ideas through state-of-the-art mathematics, taking into account limitations to predictability.

The history of the growth and professionalization of American meteorology and its transformation into a physics- and mathematics-based scientific discipline. For much of the first half of the twentieth century, meteorology was more art than science, dependent on an individual forecaster's lifetime of local experience. In Weather by the Numbers, Kristine Harper tells the story of the transformation of meteorology from a “guessing science” into a sophisticated scientific discipline based on physics and mathematics. What made this possible was the development of the electronic digital computer; earlier attempts at numerical weather prediction had foundered on the human inability to solve nonlinear equations quickly enough for timely forecasting. After World War II, the combination of an expanded observation network developed for military purposes, newly trained meteorologists, savvy about math and physics, and the nascent digital computer created a new way of approaching atmospheric theory and weather forecasting. This transformation of a discipline, Harper writes, was the most important intellectual achievement of twentieth-century meteorology, and paved the way for the growth of computer-assisted modeling in all the sciences.

Mathematics and Climate is a timely textbook aimed at students and researchers in mathematics and statistics who are interested in current issues of climate science, as well as at climate scientists who wish to become familiar with qualitative and quantitative methods of mathematics and statistics. The authors emphasize conceptual models that capture important aspects of Earth's climate system and present the mathematical and statistical techniques that can be applied to their analysis. Topics from climate science include the Earth?s energy balance, temperature distribution, ocean circulation patterns such as El Ni?o?Southern Oscillation, ice caps and glaciation periods, the carbon cycle, and the biological pump. Among the mathematical and statistical techniques presented in the text are dynamical systems and bifurcation theory, Fourier analysis, conservation laws, regression analysis, and extreme value theory. The following features make Mathematics and Climate a valuable teaching resource: issues of current interest in climate science and sustainability are used to introduce the student to the methods of mathematics and statistics; the mathematical sophistication increases as the book progresses and topics can thus be selected according to interest and level of knowledge; each chapter ends with a set of exercises that reinforce or enhance the material presented in the chapter and stimulate critical thinking and communication skills; and the book contains an extensive list of references to the literature, a glossary of terms for the nontechnical reader, and a detailed index.

Numerical models have become essential tools in environmental science, particularly in weather forecasting and climate prediction. This book provides a comprehensive overview of the techniques used in these fields, with emphasis on the design of the most recent numerical models of the atmosphere. It presents a short history of numerical weather prediction and its evolution, before describing the various model equations and how to solve them numerically. It outlines the main elements of a meteorological forecast suite, and the theory is illustrated throughout with practical examples of operational models and parameterizations of physical processes. This book is founded on the author's many years of experience, as a scientist at Météo-France and teaching university-level courses. It is a practical and accessible textbook for graduate courses and a handy resource for researchers and professionals in atmospheric physics, meteorology and climatology, as well as the related disciplines of fluid dynamics, hydrology and oceanography.

Lesson ideas in this thematic unit are based on the whole language approach which encourages cooperative learning.

The material provides an historical background to forecasting developments as well as introducing recent advances. The book will be of interest to both mathematicians and physicians, the topics covered include equations of dynamical meteorology, first integrals, non-linear stability, well-posedness of boundary problems, non-smooth solutions, parame