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ISBN: 978-3-031-40094-0

Series Statement: Mathematics of planet earth volume 11

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Additional Edition: Erscheint auch als Druck-Ausgabe, Paperback ISBN 978-3-031-40096-4

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DOI: 10.1007/978-3-031-40094-0

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UID:

Format: 1 Online-Ressource.

ISBN: 978-3-031-40094-0

Series Statement: Mathematics of planet earth volume 11

Additional Edition: Erscheint auch als Druck-Ausgabe, Hardcover ISBN 978-3-031-40093-3

Additional Edition: Erscheint auch als Druck-Ausgabe, Paperback ISBN 978-3-031-40096-4

Language: English

Keywords: Konferenzschrift

DOI: 10.1007/978-3-031-40094-0

URL: Volltext  (kostenfrei)

URL: Volltext  (kostenfrei)

UID:

Format: 1 Online-Ressource.

ISBN: 978-3-031-40094-0

Series Statement: Mathematics of planet earth volume 11

Additional Edition: Erscheint auch als Druck-Ausgabe, Hardcover ISBN 978-3-031-40093-3

Additional Edition: Erscheint auch als Druck-Ausgabe, Paperback ISBN 978-3-031-40096-4

Language: English

Keywords: Konferenzschrift

DOI: 10.1007/978-3-031-40094-0

URL: Volltext  (kostenfrei)

URL: Volltext  (kostenfrei)

UID:

Format: 1 Online-Ressource

ISBN: 9783031400940

Series Statement: Mathematics of planet earth volume 11

Additional Edition: Erscheint auch als Druck-Ausgabe, Hardcover ISBN 978-3-031-40093-3

Additional Edition: Erscheint auch als Druck-Ausgabe, Paperback ISBN 978-3-031-40096-4

Language: English

Keywords: Konferenzschrift

DOI: 10.1007/978-3-031-40094-0

URL: Volltext  (kostenfrei)

URL: Volltext  (kostenfrei)

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Format: 1 online resource (XIV, 338 p. 65 illus., 60 illus. in color.)

Edition: 1st ed. 2024.

ISBN: 3-031-40094-1

Series Statement: Mathematics of Planet Earth, 11

Content: This open access proceedings volume brings selected, peer-reviewed contributions presented at the Third Stochastic Transport in Upper Ocean Dynamics (STUOD) 2022 Workshop, held virtually and in person at the Imperial College London, UK, September 26–29, 2022. The STUOD project is supported by an ERC Synergy Grant, and led by Imperial College London, the National Institute for Research in Computer Science and Automatic Control (INRIA) and the French Research Institute for Exploitation of the Sea (IFREMER). The project aims to deliver new capabilities for assessing variability and uncertainty in upper ocean dynamics. It will provide decision makers a means of quantifying the effects of local patterns of sea level rise, heat uptake, carbon storage and change of oxygen content and pH in the ocean. Its multimodal monitoring will enhance the scientific understanding of marine debris transport, tracking of oil spills and accumulation of plastic in the sea. All topics of these proceedings are essential to the scientific foundations of oceanography which has a vital role in climate science. Studies convened in this volume focus on a range of fundamental areas, including: Observations at a high resolution of upper ocean properties such as temperature, salinity, topography, wind, waves and velocity; Large scale numerical simulations; Data-based stochastic equations for upper ocean dynamics that quantify simulation error; Stochastic data assimilation to reduce uncertainty. These fundamental subjects in modern science and technology are urgently required in order to meet the challenges of climate change faced today by human society. This proceedings volume represents a lasting legacy of crucial scientific expertise to help meet this ongoing challenge, for the benefit of academics and professionals in pure and applied mathematics, computational science, data analysis, data assimilation and oceanography.

Note: Internal tides energy transfers and interactions with the mesoscale circulation in two contrasted areas of the North Atlantic -- Sparse-stochastic model reduction for 2D Euler equations -- Effect of Transport Noise on Kelvin–Helmholtz instability -- On the 3D Navier-Stokes Equations with Stochastic Lie Transport -- On the interactions between mean flows and inertial gravity waves in the WKB approximation -- Toward a stochastic parameterization for oceanic deep convection -- Comparison of Stochastic Parametrization Schemes using Data Assimilation on Triad Models -- An explicit method to determine Casimirs in 2D geophysical flows -- Correlated structures in a balanced motion interacting with an internal wave -- Linear wave solutions of a stochastic shallow water model -- Analysis of Sea Surface Temperature variability using machine learning -- Data assimilation: A dynamic homotopy-based coupling approach -- Constrained random diffeomorphisms for data assimilation -- Stochastic compressible Navier–Stokes equations under location uncertainty -- Data driven stochastic primitive equations with dynamic modes decomposition.

Additional Edition: ISBN 3-031-40093-3

Language: English

DOI: 10.1007/978-3-031-40094-0

UID:

Format: 1 online resource (347 pages)

Edition: 1st ed.

ISBN: 9783031400940

Series Statement: Mathematics of Planet Earth Series v.11

Content: Intro -- Preface -- Contents -- Internal Tides Energy Transfers and Interactions with the Mesoscale Circulation in Two Contrasted Areas of the North Atlantic -- 1 Introduction -- 2 Governing Equations and Energy Budget -- 3 Data and Method -- 3.1 eNATL60 Simulation -- 3.2 Filtering and Computing Methods -- 4 Results -- 4.1 Life Cycle of the Internal Tide -- 4.2 Importance of the Different Contributions in the Energy Transfers -- 4.2.1 Detailed View of Coupling Terms -- 4.2.2 Modal Energy Budget -- 5 Conclusion -- References -- Sparse-Stochastic Model Reduction for 2D Euler Equations -- 1 Introduction -- 2 Sparse-Stochastic Model Reduction -- 3 Numerical Simulations -- 4 Conclusions and Outlook -- References -- Effect of Transport Noise on Kelvin-Helmholtz Instability -- 1 Introduction -- 2 Model Formulation -- 2.1 Point Vortex Method for Inviscid Flows -- 2.2 Point Vortex Method for Viscous Flows -- 3 Point Vortex Method with Environmental Noise -- 3.1 Transport Noise and Deterministic Scaling Limit -- 3.2 A Digression on the Theoretical Selection of the Noise -- 4 Numerical Results -- 4.1 Setting: Kelvin-Helmholtz Instability -- 4.1.1 The Role of Intrinsic Instability -- 4.1.2 The Role of Viscosity and Stability Restoration -- 4.2 Numerical Results on Environmental Noise -- 4.2.1 Selection of Divergence Free Field -- 4.2.2 Positions and Intensities of Fixed Vortices -- 4.2.3 Effect of Small Scale Common Noise -- 4.3 Diagnostics -- 5 Concluding Remarks -- References -- On the 3D Navier-Stokes Equations with Stochastic Lie Transport -- Introduction -- 1 Introduction -- 2 Preliminaries -- 2.1 Elementary Notation -- 2.2 Functional Framework -- 2.3 The SALT Operator -- 3 The Velocity Equation on the Torus -- 3.1 Definitions and Results -- 3.2 Operator Bounds -- 3.3 Proof of Proposition 3.2 -- 3.4 Proofs of Theorems 3.1 and 3.6.

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Additional Edition: ISBN 9783031400933

Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 9783031400933

Language: English

Keywords: Electronic books.

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UID:

Format: 1 Online-Ressource (XIV, 338 p. 65 illus., 60 illus. in color.)

ISBN: 9783031400940

Series Statement: Mathematics of Planet Earth 11

Content: Internal tides energy transfers and interactions with the mesoscale circulation in two contrasted areas of the North Atlantic -- Sparse-stochastic model reduction for 2D Euler equations -- Effect of Transport Noise on Kelvin–Helmholtz instability -- On the 3D Navier-Stokes Equations with Stochastic Lie Transport -- On the interactions between mean flows and inertial gravity waves in the WKB approximation -- Toward a stochastic parameterization for oceanic deep convection -- Comparison of Stochastic Parametrization Schemes using Data Assimilation on Triad Models -- An explicit method to determine Casimirs in 2D geophysical flows -- Correlated structures in a balanced motion interacting with an internal wave -- Linear wave solutions of a stochastic shallow water model -- Analysis of Sea Surface Temperature variability using machine learning -- Data assimilation: A dynamic homotopy-based coupling approach -- Constrained random diffeomorphisms for data assimilation -- Stochastic compressible Navier–Stokes equations under location uncertainty -- Data driven stochastic primitive equations with dynamic modes decomposition.

Content: This open access proceedings volume brings selected, peer-reviewed contributions presented at the Third Stochastic Transport in Upper Ocean Dynamics (STUOD) 2022 Workshop, held virtually and in person at the Imperial College London, UK, September 26–29, 2022. The STUOD project is supported by an ERC Synergy Grant, and led by Imperial College London, the National Institute for Research in Computer Science and Automatic Control (INRIA) and the French Research Institute for Exploitation of the Sea (IFREMER). The project aims to deliver new capabilities for assessing variability and uncertainty in upper ocean dynamics. It will provide decision makers a means of quantifying the effects of local patterns of sea level rise, heat uptake, carbon storage and change of oxygen content and pH in the ocean. Its multimodal monitoring will enhance the scientific understanding of marine debris transport, tracking of oil spills and accumulation of plastic in the sea. All topics of these proceedings are essential to the scientific foundations of oceanography which has a vital role in climate science. Studies convened in this volume focus on a range of fundamental areas, including: Observations at a high resolution of upper ocean properties such as temperature, salinity, topography, wind, waves and velocity; Large scale numerical simulations; Data-based stochastic equations for upper ocean dynamics that quantify simulation error; Stochastic data assimilation to reduce uncertainty. These fundamental subjects in modern science and technology are urgently required in order to meet the challenges of climate change faced today by human society. This proceedings volume represents a lasting legacy of crucial scientific expertise to help meet this ongoing challenge, for the benefit of academics and professionals in pure and applied mathematics, computational science, data analysis, data assimilation and oceanography.

Note: Open Access

Additional Edition: ISBN 9783031400933

Additional Edition: ISBN 9783031400957

Additional Edition: ISBN 9783031400964

Additional Edition: Erscheint auch als Druck-Ausgabe Stochastic transport in upper ocean dynamics II Cham : Springer, 2024 ISBN 9783031400933

Language: English

DOI: 10.1007/978-3-031-40094-0

URL: kostenfrei

UID:

Format: XIV, 338 p. 65 illus., 60 illus. in color. , online resource.

Edition: 1st ed. 2024.

ISBN: 9783031400940

Series Statement: Mathematics of Planet Earth, 11

Content: This open access proceedings volume brings selected, peer-reviewed contributions presented at the Third Stochastic Transport in Upper Ocean Dynamics (STUOD) 2022 Workshop, held virtually and in person at the Imperial College London, UK, September 26-29, 2022. The STUOD project is supported by an ERC Synergy Grant, and led by Imperial College London, the National Institute for Research in Computer Science and Automatic Control (INRIA) and the French Research Institute for Exploitation of the Sea (IFREMER). The project aims to deliver new capabilities for assessing variability and uncertainty in upper ocean dynamics. It will provide decision makers a means of quantifying the effects of local patterns of sea level rise, heat uptake, carbon storage and change of oxygen content and pH in the ocean. Its multimodal monitoring will enhance the scientific understanding of marine debris transport, tracking of oil spills and accumulation of plastic in the sea. All topics of these proceedings are essential to the scientific foundations of oceanography which has a vital role in climate science. Studies convened in this volume focus on a range of fundamental areas, including: Observations at a high resolution of upper ocean properties such as temperature, salinity, topography, wind, waves and velocity; Large scale numerical simulations; Data-based stochastic equations for upper ocean dynamics that quantify simulation error; Stochastic data assimilation to reduce uncertainty. These fundamental subjects in modern science and technology are urgently required in order to meet the challenges of climate change faced today by human society. This proceedings volume represents a lasting legacy of crucial scientific expertise to help meet this ongoing challenge, for the benefit of academics and professionals in pure and applied mathematics, computational science, data analysis, data assimilation and oceanography.

Note: Internal tides energy transfers and interactions with the mesoscale circulation in two contrasted areas of the North Atlantic -- Sparse-stochastic model reduction for 2D Euler equations -- Effect of Transport Noise on Kelvin-Helmholtz instability -- On the 3D Navier-Stokes Equations with Stochastic Lie Transport -- On the interactions between mean flows and inertial gravity waves in the WKB approximation -- Toward a stochastic parameterization for oceanic deep convection -- Comparison of Stochastic Parametrization Schemes using Data Assimilation on Triad Models -- An explicit method to determine Casimirs in 2D geophysical flows -- Correlated structures in a balanced motion interacting with an internal wave -- Linear wave solutions of a stochastic shallow water model -- Analysis of Sea Surface Temperature variability using machine learning -- Data assimilation: A dynamic homotopy-based coupling approach -- Constrained random diffeomorphisms for data assimilation -- Stochastic compressible Navier-Stokes equations under location uncertainty -- Data driven stochastic primitive equations with dynamic modes decomposition.

In: Springer Nature eBook

Additional Edition: Printed edition: ISBN 9783031400933

Additional Edition: Printed edition: ISBN 9783031400957

Additional Edition: Printed edition: ISBN 9783031400964

Language: English

DOI: 10.1007/978-3-031-40094-0

URL: https://doi.org/10.1007/978-3-031-40094-0

UID:

Format: 1 online resource (347 pages)

Edition: 1st ed.

ISBN: 9783031400940

Series Statement: Mathematics of Planet Earth Series ; v.11

Note: Intro -- Preface -- Contents -- Internal Tides Energy Transfers and Interactions with the Mesoscale Circulation in Two Contrasted Areas of the North Atlantic -- 1 Introduction -- 2 Governing Equations and Energy Budget -- 3 Data and Method -- 3.1 eNATL60 Simulation -- 3.2 Filtering and Computing Methods -- 4 Results -- 4.1 Life Cycle of the Internal Tide -- 4.2 Importance of the Different Contributions in the Energy Transfers -- 4.2.1 Detailed View of Coupling Terms -- 4.2.2 Modal Energy Budget -- 5 Conclusion -- References -- Sparse-Stochastic Model Reduction for 2D Euler Equations -- 1 Introduction -- 2 Sparse-Stochastic Model Reduction -- 3 Numerical Simulations -- 4 Conclusions and Outlook -- References -- Effect of Transport Noise on Kelvin-Helmholtz Instability -- 1 Introduction -- 2 Model Formulation -- 2.1 Point Vortex Method for Inviscid Flows -- 2.2 Point Vortex Method for Viscous Flows -- 3 Point Vortex Method with Environmental Noise -- 3.1 Transport Noise and Deterministic Scaling Limit -- 3.2 A Digression on the Theoretical Selection of the Noise -- 4 Numerical Results -- 4.1 Setting: Kelvin-Helmholtz Instability -- 4.1.1 The Role of Intrinsic Instability -- 4.1.2 The Role of Viscosity and Stability Restoration -- 4.2 Numerical Results on Environmental Noise -- 4.2.1 Selection of Divergence Free Field -- 4.2.2 Positions and Intensities of Fixed Vortices -- 4.2.3 Effect of Small Scale Common Noise -- 4.3 Diagnostics -- 5 Concluding Remarks -- References -- On the 3D Navier-Stokes Equations with Stochastic Lie Transport -- Introduction -- 1 Introduction -- 2 Preliminaries -- 2.1 Elementary Notation -- 2.2 Functional Framework -- 2.3 The SALT Operator -- 3 The Velocity Equation on the Torus -- 3.1 Definitions and Results -- 3.2 Operator Bounds -- 3.3 Proof of Proposition 3.2 -- 3.4 Proofs of Theorems 3.1 and 3.6. , 4 The Vorticity Equation on a Bounded Main -- 4.1 Deriving the Equation -- 4.2 Definitions and Results -- 4.3 Operator Bounds -- 4.4 Proof of Theorem 4.3 -- 5 Appendices -- 5.1 Proofs from Sects.2.3, 3.2, and 4.3 -- 5.2 A Conversion from Stratonovich to Itô -- 5.3 Abstract Solution Criterion I -- 5.4 Abstract Solution Criterion II -- References -- On the Interactions Between Mean Flows and Inertial Gravity Waves in the WKB Approximation -- 1 Introduction -- 2 Deterministic 3D Euler-Boussinesq (EB) Internal Gravity Waves -- 2.1 Lagrangian Formulation of the WMFI Equations at Leading Order -- 2.2 Hamiltonian Structure for the WMFI Equations at Leading Order -- 3 Stochastic WMFI -- 4 Conclusion -- Appendix: Asymptotic Expansion -- References -- Toward a Stochastic Parameterization for Oceanic Deep Convection -- 1 Introduction -- 2 Stochastic Formulation of Direct Non-hydrostatic Pressure Correction -- 3 Numerical Implementation and Simulations -- 3.1 Stochastic, Non-hydrostatic Pressure Correction -- 3.2 Numerical Experiments -- 4 Results -- 5 Conclusion and Perspectives -- References -- Comparison of Stochastic Parametrization Schemes Using Data Assimilation on Triad Models -- 1 Introduction -- 2 Reduced Order Models for Incompressible Fluids -- 2.1 Reduced Order Models for the 3D Euler Equation -- 2.2 Stochastic Parametrizations for the 3D Euler Equation -- 2.2.1 Modelling Under the Stochastic Advection by Lie Transport Principle -- 2.2.2 Modeling Under the Location Uncertainty Principle -- 2.3 Triad Model Comparison -- 3 Data Assimilation Comparison -- 3.1 Numerical Studies -- 3.1.1 Numerical Implementation -- 3.1.2 Data Assimilation for the Deterministic Model -- 3.1.3 Reduced Order Model Realisations -- 3.1.4 Model Statistics -- 3.1.5 Data Assimilation -- 4 Conclusions -- Appendix 1: Notation and Basic Identities -- Notation -- Vector Identities. , Appendix 2: Derivation of Triad Models -- Deterministic Euler -- SALT Euler -- LU Euler -- Appendix 3: Supplementary Numerics -- Calibration of the Noise Amplitude -- Data Assimilation Verification -- References -- An Explicit Method to Determine Casimirs in 2D Geophysical Flows -- 1 Introduction -- 2 Geophysical Flows -- 3 Explicitly Determining the Casimirs -- 4 Conclusion -- References -- Correlated Structures in a Balanced Motion Interacting with an Internal Wave -- 1 Introduction -- 2 Model -- 3 Methods -- 3.1 Spectral Proper Orthogonal Decomposition -- 3.2 Broadband Proper Orthogonal Decomposition -- 3.2.1 Complex Demodulation of the Wave Field -- 3.2.2 Link with SPOD -- 3.2.3 Extended Broadband Proper Orthogonal Decomposition -- 4 Results -- 5 Summary and Perspectives -- References -- Linear Wave Solutions of a Stochastic Shallow Water Model -- 1 Introduction -- 2 Review of RSW-LU -- 3 Stationary Solution -- 4 Stochastic Rotating Shallow Water Waves -- 4.1 Ensemble-Mean Waves Under Homogeneous Noise -- 4.1.1 Mean Poincaré Waves -- 4.1.2 Mean Geostrophic Mode -- 4.2 Path-Wise Waves Under Constant Noise -- 4.2.1 Stochastic Poincaré Waves -- 4.2.2 Stochastic Geostrophic Mode -- 4.3 Approximation of Path-Wise Waves Under Homogeneous Noise -- 4.3.1 Stochastic Poincaré Waves -- 4.3.2 Stochastic Geostrophic Mode -- 4.4 Numerical Illustrations -- 5 Shallow Water PV Dynamics and Geostrophic Adjustment -- 6 Conclusions -- References -- Analysis of Sea Surface Temperature Variability Using Machine Learning -- 1 Introduction -- 2 Method -- 2.1 Deterministic Model Hypothesis -- 2.2 Stochastic Model Hypothesis: The Stochastic NbedDyn -- 3 Numerical Experiments -- 3.1 Data -- 3.2 Analysis of the Deterministic Model -- 3.3 Analysis of the Stochastic Model -- 4 Conclusion -- Appendix 1: Training -- Appendix 2: Parameterization of the Diffusion Function. , References -- Data Assimilation: A Dynamic Homotopy-Based Coupling Approach -- 1 Introduction -- 2 Problem Formulation and Background -- 3 Schrödinger Bridge Approach -- 4 Homotopy Induced Dynamic Coupling -- 5 Numerical Implementation -- 5.1 Ensemble Kalman Mean Field Approximation -- 5.2 Particle Approximation and Time-Stepping -- 6 Examples -- 6.1 Pure Diffusion Processes -- 6.2 Purely Deterministic Processes -- 6.3 Linear Gaussian Case -- 6.4 Nonlinear Diffusion Example -- 6.5 Lorenz-63 Example -- 7 Conclusions -- Appendix 1: Derivation of Control Term Equation -- Appendix 2: Ensemble Kalman Filter Approximations -- References -- Constrained Random Diffeomorphisms for Data Assimilation -- 1 Introduction -- 2 Induced Stochastic PDE -- 3 Comparison with Other Perturbation Schemes -- 3.1 Comparison with the LU Equations -- 3.1.1 0-Forms in the LU Framework -- 3.1.2 n-Forms in the LU Framework -- 3.2 The SALT Perturbation Scheme -- 4 Conclusion -- Appendix: Expression of Tt*θ -- References -- Stochastic Compressible Navier-Stokes Equations Under Location Uncertainty -- 1 Introduction -- 2 Stochastic Reynolds Transport Theorem -- 3 Stochastic Compressible Navier-Stokes Equations -- 3.1 Non-dimensioning -- 3.2 Continuity -- 3.3 Momentum -- 3.4 Energy -- 3.5 Equation of State -- 4 Low Mach Approximation -- 5 Boussinesq-Hydrostatic Approximation -- 6 Extension to Non-Boussinesq -- 7 Conclusion -- Appendix A: Stochastic Reynolds Transport Theorem from Stratonovich to Itō -- Appendix B: Calculation Rules -- Distributivity of the Stochastic Transport Operator -- Work of Random Forces -- Appendix C: Displacement of a Transported Control Surface -- References -- Data Driven Stochastic Primitive Equations with Dynamic Modes Decomposition -- 1 Introduction -- 2 Location Uncertainty (LU) -- 3 Stochastic Boussinesq Equations -- 4 Methods. , 4.1 High Resolution Data Filtering -- 4.2 Off-Line Noise Modelling Through DMD -- 4.3 On-Line Noise Reconstruction -- 5 Results -- 6 Conclusions -- References -- Index.

Additional Edition: Print version: Chapron, Bertrand Stochastic Transport in Upper Ocean Dynamics II Cham : Springer,c2023 ISBN 9783031400933

Language: English

Keywords: Electronic books.

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UID:

Format: 1 Online-Ressource (338 p.)

ISBN: 9783031400940 , 9783031400933

Series Statement: Mathematics of Planet Earth

Content: This open access proceedings volume brings selected, peer-reviewed contributions presented at the Third Stochastic Transport in Upper Ocean Dynamics (STUOD) 2022 Workshop, held virtually and in person at the Imperial College London, UK, September 26–29, 2022. The STUOD project is supported by an ERC Synergy Grant, and led by Imperial College London, the National Institute for Research in Computer Science and Automatic Control (INRIA) and the French Research Institute for Exploitation of the Sea (IFREMER). The project aims to deliver new capabilities for assessing variability and uncertainty in upper ocean dynamics. It will provide decision makers a means of quantifying the effects of local patterns of sea level rise, heat uptake, carbon storage and change of oxygen content and pH in the ocean. Its multimodal monitoring will enhance the scientific understanding of marine debris transport, tracking of oil spills and accumulation of plastic in the sea. All topics of these proceedings are essential to the scientific foundations of oceanography which has a vital role in climate science. Studies convened in this volume focus on a range of fundamental areas, including: Observations at a high resolution of upper ocean properties such as temperature, salinity, topography, wind, waves and velocity; Large scale numerical simulations; Data-based stochastic equations for upper ocean dynamics that quantify simulation error; Stochastic data assimilation to reduce uncertainty. These fundamental subjects in modern science and technology are urgently required in order to meet the challenges of climate change faced today by human society. This proceedings volume represents a lasting legacy of crucial scientific expertise to help meet this ongoing challenge, for the benefit of academics and professionals in pure and applied mathematics, computational science, data analysis, data assimilation and oceanography

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