This book which is the outcome of a NATO-Advanced Study Institute on Mod­ elling the Ocean Circulation and Geochemical Tracer Transport is concerned with using models to infer the ocean circulation. Understanding our climate is one of the major problems of the late twentieth century. The possible climatic changes resulting from the rise in atmospheric carbon dioxide and other trace gases are of primary interest and the ocean pla. ys a ma. jor role in determining the magnitude, temporal evolution and regional distribution of those changes. Because of the poor observational basis the ocean general circulation is not well understood. The World Ocean Circulation Experiment (WOCE) which is now underway is an attempt to improve our knowledge of ocean dynamics and thermodynamics on global scales relevant to climate change. Despite those efforts, the oceanic data base is likely to remain scarce and it is crucial to use appropriate methods in order to extract the maximum amount of information from observations. The book contains a thorough analysis of methods to combine data of val'ious types with dynamical concepts, and to assimilate data directly into ocean models. The properties of geocl;temical tracers such as HC, He, Tritium and Freons and how they may be used to impose integral constraints on the ocean circulation are discussed.

Tracer Inverse Problems.- 1. Introduction.- 2. Interpolation and Map Making.- 3. Simple Estimation.- 4. Using Steady Tracers.- 5. Time Dependent Problems.- Appendix. Some Notes on the History of Inverse Methods in Ocean Circulation Problems.- A Geometrical Interpretation of Inverse Problems.- 1. The Overdetermined Case.- 2. The Underdetermined Case.- 3. The Singular Value Decomposition (SVD).- Determining Diffusivities from Hydrographic Data by Inverse Methods with Applications to the Circumpolar Current.- 1. Introduction to Ill-posed and Noisy Problems.- 2. The Physical Model.- 3. The Inverse Model.- 4. Examples: Circulation and mixing in the Southern Ocean.- Ocean Acoustic Tomography: a Primer.- 1. Introduction.- 2. Elementary Hydrodynamics and Acoustics.- 3. Ocean Sound Speed Distribution.- 4. Rays and Modes.- 5. Capsule Description of the Tomographic Method.- 6. A Simple Ray Example.- 7. Notes on Hardware Limitations and Observational Errors.- 8. Inversions.- 9. Some Results and Future Plans.- 10. Conclusions.- 11. Literature.- The Circulation in the Western North Atlantic Determined by a Nonlinear Inverse Method..- 1. Introduction.- 2. A Nonlinear Inverse Formalism.- 3. The Circulation in the Western North Atlantic.- Altimeter Data Assimilation into Ocean Circulation Models - Some Preliminary Results.- 1. Introduction.- 2. A Dynamic Initialization Scheme.- 3. Time and Space Dependence of the Observations.- 4. Geosat Assimilation in the Agulhas Retroflection Region.- 5. Discussion.- Assimilation of Data into Ocean Models.- 1. Introduction.- 2. Theory.- 3. Applications.- 4. Conclusions.- Driving of Non-linear Time-dependent Ocean Models by Observation of Transient Tracers - a Problem of Constrained Optimisation.- 1. Introduction.- 2. A Control Problem.- 3. AnElegant and Efficient Way to Calculate the Gradient of the Cost Function.- 4. The Ocean Model and its Adjoint.- 5. Results.- 6. Model Parameters as Control Variables.- 7. Sensitivity.- 8. Conclusions.- Assimilation of XBT Data Using a Variational Technique.- 1. Introduction.- 2. Implementation of Variational Assimilation Using Lagrange Multipliers.- 3. Results.- The Role of Real-Time Four-Dimensional Data Assimilation in the Quality Control, Interpretation, and Synthesis of Climate Data.- 1. Introduction.- 2. The Importance of Accurate Data Assimilation for NWP.- 3. The Analysis Module.- 4. Non-linear Normal Mode Initialization.- 5. The Forecast Model.- 6. Quality Control and Data Monitoring.- 7. The Value and Limitations of Global NWP Datasets for Climate Studies.- 8. Inversion and Quality Control of Remotely Sensed Data.- 9. Real-Time Integration and Synthesis of WCRP Observations.- to Chemical Tracers of the Ocean Circulation.- 1. Dimensional Analysis of a Tracer Conservation Equation.- 2. General Information on Tracers of Ocean Circulation.- 3. Surface Boundary Conditions.- 4. Mixing in the Deep Ocean.- 5. Conclusion.- On Oceanic Boundary Conditions for Tritium, on Tritiugenic 3He, and on the Tritium-3He Age Concept.- 1. Introduction.- 2. Tritium Ocean Surface Boundary Condition.- 3. Separation of Tritiugenic 3He.- 4. The Tritium-3He Age Concept.- 5. Tritium-3He Age Distributions on Isopycnal Surfaces in the Lower Northeast Atlantic Main Thermocline.- 6. Conclusions.- Ocean Carbon Models and Inverse Methods.- 1. Introduction.- 2. Diagnostic Equations.- 3. Parameterization of the Model: Methodological Issues for Inverse Methods.- 4. Some Preliminary Experiments.- Model of the Nutrient and Carbon Cycles in the North Atlantic. An Application of Linear Programming Methods.- 1. Introduction.- 2. The Model.- 3. Results for the 'Inorganic' Case.- 4. Results for the 'Inorganic and Organic' Case.- 5. Summary.- The Design of Numerical Models of the Ocean Circulation.- 1. Fundamentals of Model Design.- 2. Stability.- 3. Stability of Advective Schemes and Vertical Coordinates.- 4. The Application of Ocean General Circulation Models.- Instabilities and Multiple Steady States of the Thermohaline Circulation.- 1. Introduction.- 2. Box Models.- 3. 2-D Model.- 4. GFDL Model.- 5. Conclusions.- Subgridscale Representation.- 1. Introduction.- 2. Organization.- 3. Quasi-horizontal Stirring.- 4. Quasi-vertical Mixing.- 5. Benthic Boundary Processes.- Appendix A.- Appendix B.