This book addresses the problem of inferring the state of the ocean circulation, from a mathematical perspective.

Addressing the problems of making inferences from noisy observations and imperfect theories, this 2006 book introduces many inference tools and practical applications. Starting with fundamental algebraic and statistical ideas, it is ideal for graduate students and researchers in oceanography, climate science, and geophysical fluid dynamics.

Inverse Modeling of the Ocean and Atmosphere is a graduate-level book for students of oceanography and meteorology, and anyone interested in combining computer models and observations of the hydrosphere or solid earth. A step-by-step development of maximally efficient inversion algorithms, using ideal models, is complemented by computer codes and comprehensive details for realistic models. Variational tools and statistical concepts are concisely introduced, and applications to contemporary research models, together with elaborate observing systems, are examined in detail. The book offers a review of the various alternative approaches, and further advanced research topics are discussed. Derived from the author's lecture notes, this book constitutes an ideal course companion for graduate students, as well as being a valuable reference source for researchers and managers in theoretical earth science, civil engineering and applied mathematics.

The ability to ascertain the implications of a changing climate are based first and foremost on our understanding the fundamental balances comprising earth’s climate. The global energy budget is integral to this understanding, and the poleward transport of heat by the oceans is an intrinsic component of the energy balance. In this chapter, we look to describe what is presently known about ocean heat transport and its role in the climate system. At the end of the last century, as part of the World Ocean Circulation Experiment (WOCE) and the Joint Global Ocean Flux Study (JGOFS), the ocean-going research community completed a decade-long international effort to explore the ocean through the acquisition of a single consistent and comparable set of high-quality, full-depth observations. This global-scale field campaign was designed to determine the mean steady-state basin-scale circulation and meridional ocean heat transport. At the time, it was recognized that this mean was unlikely to be stationary. It was also understood that patterns of variability that had yet to be measured would influence our eventual understanding of these one-time “synoptic” observations. A decade later, time series of ocean heat transport (from moorings, repeat XBT and CTD lines and profiling floats), although still quite short and either spatially and/or temporally sparse, are now becoming available. The WOCE/JGOFS programs of the 1990s have been extended through large international efforts first by the Climate Variability and Predictability program and now by the Global Ocean Ship-based Hydrographic Investigations Program. Through these newly acquired time series, improvements in analysis techniques, and recent modeling advances, we are beginning to describe ocean heat transport variability and to understand its possible response to and role in climate change. In this chapter, we focus on what has been learnt about ocean heat transport through in situ observations. We include some history, a detailed description of ocean heat transport computation and decomposition, and a discussion of the present state of the science, seeking to measure ocean heat transport variability.

Published by the American Geophysical Union as part of the Geophysical Monograph Series, Volume 173. The ocean's meridional overturning circulation (MOC) is a key factor in climate change. The Atlantic MOC, in particular, is believed to play an active role in the regional and global climate variability. It is associated with the recent debate on rapid climate change, the Atlantic Multi-Decadal Oscillation (AMO), global warming, and Atlantic hurricanes. This is the first book to deal with all aspects of the ocean's large-scale meridional overturning circulation, and is a coherent presentation, from a mechanistic point of view, of our current understanding of paleo, present-day, and future variability and change. It presents the current state of the science by bringing together the world's leading experts in physical, chemical, and biological oceanography, marine geology, geochemistry, paleoceanography, and climate modeling. A mix of overview and research papers makes this volume suitable not only for experts in the field, but also for students and anyone interested in climate change and the oceans.

This book describes mathematical techniques for interpreting measurements of greenhouse gases in order to learn about their sources and sinks. It is aimed at researchers and graduate students embarking upon studies in this area. Established researchers will also find its extensive referencing invaluable.

The book represents all the knowledge we currently have on ocean circulation. It presents an up-to-date summary of the state of the science relating to the role of the oceans in the physical climate system.The book is structured to guide the reader through the wide range of World Ocean Circulation Experiment (WOCE) science in a consistent way. Cross-references between contributors have been added, and the book has a comprehensive index and unified reference list.The book is simple to read, at the undergraduate level. It was written by the best scientists in the world who have collaborated to carry out years of experiments to better understand ocean circulation.

Mounting evidence that human activities are substantially modifying the Earth's climate brings a new imperative to the study of the ocean's large-scale circulation. This textbook provides a concise but comprehensive introduction to the theory of large-scale ocean circulation, as it is currently understood and established. Students and instructors will benefit from the carefully chosen chapter-by-chapter exercises. This advanced textbook is invaluable for graduate students and researchers in the fields of oceanic, atmospheric and climate sciences, and other geophysical scientists, as well as physicists and mathematicians with a quantitative interest in the planetary fluid environment.

The past 20 years have provided us with an unprecedented ability to observe, monitor, and forecast the oceans. In situ and remotely sensed ocean observations in combination with ocean general circulation models using data assimilation and state estimation methods underpin climate applications. State estimation aims to provide a dynamically consistent estimation of ocean fields, of errors of these fields, and of certain model parameters such as mixing coefficients. Conversely, data assimilation tools have been developed predominantly for ocean prediction applications and ocean reanalyses. This chapter describes approaches used by state estimation and data assimilation systems in synthesizing observations and model dynamics. We highlight some applications, including their limitations for climate research, and address the challenges ahead in relation to the ocean observing system.

Conceptual models are a vital tool for understanding the processes that maintain the global ocean circulation, both in nature and in complex numerical ocean models. In this chapter we provide a broad overview of our conceptual understanding of the wind-driven circulation, the thermohaline circulation, and their transient behavior. While our conceptual understanding of the time-mean wind-driven circulation is now fairly mature, basic questions remain regarding the thermohaline circulation, for example, surrounding its overall strength and stability. Similarly, basic questions remain regarding the transient adjustment and internal variability of the ocean circulation.