دانلود کتاب Stochastic Transport in Upper Ocean Dynamics: STUOD 2021 Workshop, London, UK, September 20–23

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Preface Organization Contents Blow-Up of Strong Solutions of the Thermal Quasi-GeostrophicEquation 1 Introduction 1.1 Notations 1.2 Main Result 2 Blow-Up 2.1 Estimate for the 2D Modified Helmholtz Equation or the Screened Poisson Equation 2.2 Log-Sobolev Estimate for Velocity Gradient 2.3 A Priori Estimate References Modeling Under Location Uncertainty: A Convergent Large-Scale Representation of the Navier-Stokes Equations 1 Introduction 2 Modelling Under Location Uncertainty 3 Notations and Main Result 4 Proofs of the Main Result References A Stochastic Benjamin-Bona-Mahony Type Equation 1 Introduction 2 Truncation 3 Proof of the Main Result References Observation-Based Noise Calibration: An Efficient Dynamics for the Ensemble Kalman Filter 1 Introduction 2 The Stochastic SQG Model Under Location Uncertainty (LU) 3 Girsanov Theorem and Noise Calibration 3.1 Change of Measure 3.2 Computation of the Girsanov Drift 4 Experiments 5 Conclusion References A Two-Step Numerical Scheme in Time for Surface Quasi Geostrophic Equations Under Location Uncertainty 1 Introduction 2 Numerical Schemes 2.1 Derivation of a Milstein Scheme 2.1.1 Lévy Area Simulation 2.2 Multi-Step Schemes 3 Numerical Results 4 Conclusion and Perspectives Appendix: Convergence of Euler-Maruyama Scheme Under Moderate Noise References The Dissipation Properties of Transport Noise 1 Introduction 2 Well-Posedness and Motivations 2.1 Notations and Definitions 2.2 Motivations 3 Main Results 4 Explicit Computations 4.1 Explicit Construction 4.2 Numerical Simulation References Existence and Uniqueness of Maximal Solutions to a 3D Navier-Stokes Equation with Stochastic Lie Transport 1 Introduction 2 SALT Navier-Stokes and Results 2.1 Preliminaries from Stochastic Analysis 2.2 SALT Navier-Stokes Equation 2.3 Notions of Solution and Results 3 Abstract Framework and Results 3.1 Assumption Set 1 3.2 Assumption Set 2 3.3 Notions of Solution and Results 4 Abstract Solution Method and Application 4.1 Abstract Solution Method 4.2 SALT Navier-Stokes in the Abstract Framework Appendix References Coupling of Waves to Sea Surface Currents Via Horizontal Density Gradients 1 Introduction 1.1 Submesoscale Sea Surface Dynamics 2 Submesoscale Thermal Wave-Current Dynamics on a Free Surface 2.1 Surface Waves as Symmetry-Breaking Features of Local Force Imbalances 2.2 A Tale of Two Maps: Currents and Waves 2.3 Thermal Potential Vorticity (TPV) Dynamics on a Free Surface 2.4 CM Equations in the Slowly Varying Envelope (SVE) Approximation 2.5 Thermal Potential Vorticity Dynamics with SVE on a Free Surface 3 Numerical Implementation 4 Conclusion and Outlook References Variational Stochastic Parameterisations and Their Applications to Primitive Equation Models 1 Introduction 2 Stochastic Primitive Equations 2.1 Variational Principles for Stochastic Primitive Equations 2.2 Conservation Laws 3 Calibration of the Stochastic Parameters 3.1 Lagrangian Paths 3.2 Eulerian Differences 4 Results 5 Summary and Discussion Appendix: Numerical Implementation Bibliography A Pathwise Parameterisation for Stochastic Transport 1 Introduction 2 Problem Formulation 3 Methodology 4 Robustness 5 Numerical Results Appendix References Stochastic Parameterization with Dynamic Mode Decomposition 1 Introduction 2 Modelling Under Location Uncertainty 2.1 Stochastic Flow 2.2 Stochastic QG Model 3 Numerical Parameterization of Unresolved Flow 3.1 EOF-Based Method 3.2 DMD-Based Method 4 Numerical Experiments 4.1 Configurations 4.2 Diagnostics 4.3 Discussion 5 Conclusions References Deep Learning for the Benes Filter 1 Introduction 1.1 Nonlinear Stochastic Filtering Problem 1.2 Filtering Equation and General Splitting Method 2 Derivation and Outline of the Deep Learning Algorithm 2.1 Feynman–Kac Representation 2.2 The Benes Filtering Model 2.3 Neural Network Model for the Prediction Step 2.4 Monte-Carlo Normalisation Step 3 Numerical Results for the Benes Filter 3.1 No Domain Adaptation 3.2 With Domain Adaptation 4 Conclusion and Outlook References End-to-End Kalman Filter in a High Dimensional Linear Embedding of the Observations 1 Introduction 2 Method 3 Numerical Experiments 3.1 Preliminary Analysis on SST Anomaly Data 3.2 Shallow Water Equation (SWE) Case-Study 4 Conclusion References Dynamical Properties of Weather Regime Transitions 1 Introduction 2 European-Atlantic Weather Regime Transitions 3 Dimensionality Around Transitions 4 Persistence Around Transitions 5 Conclusion and Perspectives Appendix 1: Data Description: Twentieth Century Reanalysis Appendix 2: Statistical Descriptors Empirical Orthogonal Functions Gaussian Mixture Model Appendix 3: Dynamical Indicators Local Dimensions Inverse Persistence θ References Frequentist Perspective on Robust Parameter Estimation Using the Ensemble Kalman Filter 1 Introduction 2 Ensemble Kalman Parameter Estimation 3 Frequentist Analysis 4 Multi-Scale Data 5 Numerical Example 6 Conclusions References Random Ocean Swell-Rays: A Stochastic Framework 1 Introduction 2 Wave-Current Interaction in the Literature 3 The Time-Decorrelation Assumption 3.1 The Ray Lagrangian Correlation Time 3.2 Ray Absolute Diffusivity 3.3 A Practical Estimation 4 Numerical Simulations 5 Conclusion References Modified (Hyper-)Viscosity for Coarse-Resolution Ocean Models 1 Introduction 2 Double Gyre Quasi-Geostrophic Model 2.1 Governing Equations 2.2 Pytorch Implementation 2.3 Eddy-Resolving and Eddy-Permitting Regimes 3 Proposed Modified Viscosity 3.1 Motivation 3.2 Modified Viscosity 3.3 Modified Viscosity Regularization 3.4 Iterative Procedure 4 Results and Discussion 4.1 Statistics 4.2 Iterative Procedure 5 Conclusion Appendix Downsampling Procedure Parameter Tables References Primitive Equations Under Location Uncertainty: Analytical Description and Model Development 1 Introduction 2 Location Uncertainty (LU) 3 Stochastic Transport Theorem 4 Boussinesq Equations 5 Methods 6 Results 7 Conclusions References Bridging Koopman Operator and Time-Series Auto-Correlation Based Hilbert–Schmidt Operator 1 Introduction 2 Preliminaries and the Main Result 3 Proof of the Main Result References Index