Mathematics and Climate

Mathematics and Climate, Second Edition reflects progress made in the discipline since the first edition—a winner of the Atmospheric Science Librarians International Choice Award in 2013—published that year. The book emphasizes conceptual models that capture critical components of Earth's climate system and answers how and why certain phenomena occur. These models describe, among others, energy balance and temperature distributions, ocean circulation patterns, and ice caps and glaciation cycles. They are used to introduce methods from applied mathematics, with a focus on dynamical systems, bifurcation and stability theory, Fourier analysis, and statistics, including regression analysis and extreme value theory. Mathematics and Climate, Second Edition contains a layered atmosphere model for the greenhouse effect, a new chapter on a model for glacial cycles, updated sections on paleoclimate reconstruction, and exercises at the end of each chapter to stimulate critical thinking and communication skills. Additionally, it provides suggestions for further study and more advanced projects, an extensive list of references, and a glossary of terms for the nontechnical reader. Introduction to Nonsmooth Analysis and Optimization offers a thorough examination of analysis and algorithms—first- and second-order methods—in infinite dimensions, as well as a self-contained and accessible introduction to set-valued and variational analysis for optimization problems (including novel calculus results for relevant situations). It is accompanied by Julia code to replicate the numerical results.

Hans Kaper is affiliated with Georgetown University and serves as the editor-in-chief of SIAM News and the SIAM book series on Mathematical Modeling and Computation. He spent most of his professional career at Argonne National Laboratory and served as Program Director for Applied Mathematics at the National Science Foundation. He is a Corresponding Member of the Royal Netherlands Academy of Sciences, a 2009 SIAM Fellow, and a 2023 AAAS Fellow. He is the (co)author of four books and more than 100 articles in refereed journals. He served on the SIAM Committee on Science Policy and was Chair of the SIAM Activity Group on Dynamical Systems and founding Chair of the SIAM Activity Group on Mathematics of Planet Earth. Hans Engler is Professor Emeritus of Mathematics at Georgetown University and former Department Chair. He served as Program Director for Applied Mathematics at the National Science Foundation and as Chair of the SIAM Activity Group on Mathematics of Planet Earth. He has also done mathematical and statistical consulting work with government agencies and private companies.