This book provides a survey of the frontiers of research in the numerical modeling and mathematical analysis used in the study of the atmosphere and oceans. The details of the current practices in global atmospheric and ocean models, the assimilation of observational data into such models and the numerical techniques used in theoretical analysis of the atmosphere and ocean are among the topics covered.* Truly interdisciplinary: scientific interactions between specialties of atmospheric and ocean sciences and applied and computational mathematics * Uses the approach of computational mathematicians, applied and numerical analysts and the tools appropriate for unsolved problems in the atmospheric and oceanic sciences* Contributions uniquely address central problems and provide a survey of the frontier of research