Modeling in general, and for climate in particular, involves an understanding of the physical phenomena at several stages, which are nicely and concisely developed in this work: conceptual, mathematical, numerical, and computational.

At the conceptual level, Drake describes how weather is observed and recorded, and the most important climate phenomena, like El Niño and the Gulf Stream, or physical phenomena, like the Coriolis force, vorticity, thermodynamics, geophysical turbulence, and even some theories like the butterfly effect and the Gaia hypothesis.

At the mathematical level, the necessary momentum equations for fluid flow and the transport equations are thoroughly described.

Regarding numerical aspects, the discretization of partial differential equations using the control volume method, or Galerkin spectral methods, is described. Time integration is explained, as well as the solution of the resulting linear system of equations with Cholesky factorization and conjugate gradient methods, among other numerical methods. Some numerical analysis is explained, in particular about consistency, stability, and convergence.

Computational implementation of the models is made in MATLAB. This, together with some extra material, which includes several lectures about climate change and stochastic differential equations, can be downloaded online (http://www.siam.org/books/mm19/).

This powerful overview concerning climate modeling is extremely useful for both specialists and modelers in general, as it covers all of the steps in the modeling process. I totally recommend this lecture to a large audience, from mature undergraduates to specialists in mathematics, physics, and engineering who are concerned with climate description, prediction, and the evaluation of its consequences.