This book sets forth the physical, mathematical, and numerical foundations of computer models used to understand and predict the global ocean climate system. Aimed at students and researchers of ocean and climate science who seek to understand the physical content of ocean model equations and numerical methods for their solution, it is largely general in formulation and employs modern mathematical techniques. It also highlights certain areas of cutting-edge research. Stephen Griffies presents material that spans a broad spectrum of issues critical for modern ocean climate models. Topics are organized into parts consisting of related chapters, with each part largely self-contained. Early chapters focus on the basic equations arising from classical mechanics and thermodynamics used to rationalize ocean fluid dynamics. These equations are then cast into a form appropriate for numerical models of finite grid resolution. Basic discretization methods are described for commonly used classes of ocean climate models. The book proceeds to focus on the parameterization of phenomena occurring at scales unresolved by the ocean model, which represents a large part of modern oceanographic research. The final part provides a tutorial on the tensor methods that are used throughout the book, in a general and elegant fashion, to formulate the equations.

The National Academies' Board on Atmospheric Sciences and Climate (BASC) held a workshop to explore and evaluate current efforts to model physical processes of coupled atmosphere-land-ocean (A-L-O) models. Numerical models of the atmosphere and ocean are central to weather prediction, research, and education. Although great strides have been made over the past few decades in understanding the atmosphere and ocean, modeling capabilities, and numerical A-L-O simulations, some unresolved processes in the models do not adequately represent knowledge of the underlying physics. Moreover, there is evidence that further progress in numerical simulations is being impeded by the slow pace of improvement in the representation of key physical processes in the models and the fact that geophysical flow models are not receiving the attention needed to make these tools more useful and accurate. These models often are used to predict future events, so it is imperative that their underlying physical processes be represented as robustly as possible. During the workshop, the parameterization of physical processes in A-L-O models was addressed, including associated errors, testing, and efforts to improve the use of parameterizations. Participants also examined intellectual and scientific challenges in modeling and highlighted the idea that some of the key impediments to progress in representing physical processes are primarily cultural in nature.

Coupled atmosphere-ocean models are at the core of numerical climate models. There is an extraordinarily broad class of coupled atmosphere-ocean models ranging from sets of equations that can be solved analytically to highly detailed representations of Nature requiring the most advanced computers for execution. The models are applied to subjects including the conceptual understanding of Earth's climate, predictions that support human activities in a variable climate, and projections aimed to prepare society for climate change. The present book fills a void in the current literature by presenting a basic and yet rigorous treatment of how the models of the atmosphere and the ocean are put together into a coupled system. The text of the book is divided into chapters organized according to complexity of the components that are coupled. Two full chapters are dedicated to current efforts on the development of generalist couplers and coupling methodologies all over the world.