ALBERT

Note: Contents: Abbreviations. - Partial List of Symbols. - 1 THE GOVERNING EQUATIONS. - 1-1 Introduction. - 1-2 Equation of Motion. - 1-3 Continuity Equation. - 1-4. - Equation of State. - 1-5 First Law of Thermodynamics. - 1-6 The Complete System of Equations. - 1-7 Coordinate Systems. - 1-8 Map Projections. - 1-8-1 Polar Stereographic Projection. - 1-8-2 Mercator Projection. - 1-8-3 Lambert Conformal Projection. - 1-8-4 Additional Remarks. - 1-9 Alternate Vertical Coordinates. - 1-9-1 Pressure Vertical Coordinate. - 1-9-2 Isentropic Vertical Coordinate Θ. - 1-10 Some Energy Relations. - 1-10-1 Kinetic Energy. - 1-10-2 Potential Energy. - 1-11 Available Potential Energy. - 1-12 Vorticity and Divergence Equations. - 1-12-1 Divergence Equations. - 2 WAVE MOTION IN THE ATMOSPHERE: PART 1. - 2-1 Introduction. - 2-2 Linearized Equations. - 2-3 Pure Sound Waves. - 2-4 Sound Waves and Internal Gravity Waves. - 2-5 Surface Gravity Waves. - 2-6 Inertial Gravity Waves and Rossby Waves. - 2-7 Response to Initial Conditions. - 2-8 Geostrophic Adiustment. - 3 SCALE ANALYSIS. - 3-1 Introduction. - 3-2 Shallow-Water Equations. - 3-3 Baroclinic Equations. - 3-4 Midlatitude Analysis. - 3-5 Tropics. - 3-6 Planetary Scale. - 3-7 Balance System. - 4 ATMOSPHERIC WAVES: PART. - 4-1 Introduction. - 4-2 Rossby Waves. - 4-3 Conditions for Barotropic Instability. - 4-4 Some Unstable Profiles. - 4-5 Linear Shear. - 4-6 Barotropic Effects in the Atmosphere. - 4-7 Baroclinic Instability. - 4-8 Baroclinic Instability with Linear Shear. - 4-9 Two-Level Model. - 4-10 Wave Structure. - 4-11 Vertical Energy Propagation. - 4-12 Barotropic Equatorial Waves. - 4-13 Vertical Structure of Equatorial Waves. - 5 NUMERICAL METHODS. - 5-1 Introduction. - 5-2 Finite Difference Methods. - 5-3 The Advection Equation. - 5-4 Some Basic Concepts. - 5-5 Stability Analysis. - 5-5-1 The Matrix Method. - 5-5-2 Von Neumann Method. - 5-5-3 The Energy Method. - 5-6 Examples of the Von Neumann Method. - 5-6-1 Euler Scheme. - 5-6-2 Uncentered Differencing, Von Neumann Method. - 5-6-3 Trapezoidal Implicit Scheme. - 5-6-4 Euler Backward Scheme. - 5-6-5 Fourth-Order Space Differencing. - 5-6-6 Oscillation Equation. - 5-6-7 Two-Dimensional Advection Equation. - 5-6-8 External Gravity Waves, Leapfrog Scheme. - 5-6-9 Staggered Grid. - 5-7 Forward-Backward Scheme, Pressure Averaging, and Semi-Implicit Methods. - 5-7-1 Forward-Backward Scheme. - 5-7-2 Pressure Averaging. - 5-7-3 Time Averaging. - 5-7-4 Semi-Implicit Method. - 5-7-5 Lax Wendroff Scheme. - 5-8 A Summary of Some Difference Schemes. - 5-9 Parabolic Equations. - 5-10 Elliptic Equations. - 5-10-1 Relaxation Method. - 5-10-2 Direct Methods. - 5-10-3 Gaussian Elimination. - 5-10-4 Buneman Variant. - 5-10-5 Helmholtz Equation on a Sphere. - 5-10-6 Reduction of a Three-Dimensional Elliptic Equation to Two-Dimensional Equations. - 5-11 Nonlinear Instability and Aliasing. - 5-11-1 Discrete Mesh. - 5-11-2 Primitive Equations Considerations. - 6 GALERKIN METHODS. - 6-1 Introduction. - 6-2 Example with Spectral and Finite Element Methods. - 6-3 Time Dependence. - 6-4 Barotropic Vorticity Equation with Fourier Basis Functions. - 6-5 Transform Method. - 6-6 Spectral Model of Shallow-Water Equations. - 6-7 Advection Equation with Finite Elements. - 6-8 Barotropic Vorticity Equation with Finite Elements. - 7 NUMERICAL PREDICTION MODELS. - 7-1 Filtered Models. - 7-1-1 Quasi-Geostrophic Equivalent Barotropic Model. - 7-1-1-1 Energetics of the Barotropic Model. - 7-1-2 Quasi-Geostrophic Multilevel Baroclinic Model. - 7-1-3 Linear Balanced Model. - 7-1-4 Nonlinear Balanced Model. - 7-2 Primitive Equation Models. - 7-2-1 Constraints from Continuous Equations. - 7-2-2 Vertical Differencing. - 7-3 Staggered Grid Systems. - 7-4 Example of a Staggered Primitive Equation Model. - 7-4-1 Equations in Curvilinear Coordinates. - 7-4-2 Horizontal Differencing. - 7-4-3 Energy Conservation. - 7-5 Potential Enstrophy Conserving Scheme. - 7-5-1 Continuous Integral Constraints. - 7-5-2 Difference Equations. - 7-5-3 Constraints Enforced. - 7-6 Spherical Grids. - 7-7 Fine Mesh Modeling. - 7-7-1 One-Way Influence. - 7-7-2 Boundary Conditions. - 7-7-3 Two-Way Interaction. - 7-7-4 Initialization on a Bounded Region. - 7-8 Baroclinic Spectral Models. - 7-9 Isentropic Coordinate Models. - 7-10 Upper Boundary Conditions. - 7-11 Mountain Effects. - 8 BOUNDARY LAYER REPRESENTATIONS. - 8-1 Introduction. - 8-2 Reynolds Equations. - 8-3 Bulk Formulas. - 8-4 Eddy Viscosity, K-Theory. - 8-5 Combined Prandtl and Ekman Layers. - 8-5-1 Prandtl Layer (Neutral Stratification). - 8-5-2 Ekman Layer. - 8-6 Nonneutral Surface Layer. - 8-6-1 Matching Ekman Spiral. - 8-7 Similarity Solutions for the Entire PBL. - 8-7-1 Deardorff Mixed Layer Model. - 8-7-2 Surface Layer. - 8-7-3 Matching Solutions for the Surface and Mixed Layers. - 8-7-4 Surface Wind Direction. - 8-7-5 Modified Transfer Coefficients. - 8-8 A Prediction Equation for h. - 8-8-1 Further Comments on PBL Parameterization. - 8-9 High-Resolution Model. - 8-9-1 The Coefficient of Eddy Viscosity. - 8-9-2 Surface Temperature. - 8-9-3 Some Prediction Model Details. - 8-10 Mean Turbulent Field Closure Models (Second-Order Closure). - 9 INCLUSION OF MOISTURE. - 9-1 Moisture Conservation Equation. - 9-1-1 Modified Thermodynamic Equation. - 9-1-2 Equivalent Potential Temperature and Static Energy. - 9-2 Convective Adjustment. - 9-2-1 Case A. Dry Convection, q 〈 qs. - 9-2-2 Case B. Moist Adjustment q ≥ qs. - 9-3 Modeling Cloud Processes. - 9-3-1 Nonconvective Condensation. - 9-4 Cumulus Parameterization. - 9-4-1 Introduction. - 9-4-2 Kuo Method. - 9-5 Parameterizations Involving Cloud Models. - 9-6 Arakawa and Schubert Model. - 9-6-1 Large-Scale Budget Equations. - 9-6-2 Cloud Budget Equations. - 10 RADIATION PARAMETERIZATION. - 10-1 Terrestrial Radiation. - 10-2 Absorbing Substances. - 10-3 Simplified Transmission Functions. - 10-4 Discretization, Long-Wave Radiation. - 10-4-1 Clear Sky. - 10-4-2 Cloudy Sky. - 10-5 Solar Radiation. - 10-5-1 Clear Sky. - 10-5-2 Cloudy Sky, One Cloud Layer. - 10-5-3 Two Contiguous Cloud Layers. - 10-5-4 Two Separated Cloud Layers. - 10-6 Miscellany. - 11 OBJECTIVE ANALYSIS AND INITIALIZATION. - 11-1 Introduction. - 11-2 A Three-Dimensional Analysis. - 11-3 Statistical Methods, Multivariate Analysis. - 11-4 Initialization. - 11-4-1 Introduction. - 11-4-2 Damping Techniques. - 11-4-3 Static Initialization. - 11-4-4 Variational Method. - 11-4-5 Normal Mode Expansions. - 11-4-6 Variational Normal Mode Initialization. - 11-5 Dynamic Balancing. - 11-6 Four-Dimensional Data Assimilation. - 11-7 Newtonian Relaxation or "Nudging". - 11-8 Smoothing and Filtering. - 11-8-1 Two-Dimensional Smoothers. - 11-8-2 Bandpass Filters. - 11-8-3 Boundary Effects. - 12 OCEAN DYNAMICS AND MODELING. - 12-1 Introduction. - 12-2 Wind-Driven Barotropic Models. - 12-3 Nonlinear Effects. - 12-4 Barotropic Numerical Models. - 12-5 Simple Thermohaline Models. - 12-6 Baroclinic Numerical Models. - 12-7 Bottom Topography Effects. - 12-8 Synoptic Scale Eddies. - 12-9 Mixed Layer Models. - 12-10 Problems in Ocean Modeling. - 13 WEATHER AND CLIMATE PREDICTION. - 13-1 Introduction. - 13-2 Current Forecasting Skill. - 13-2-1 Short Range. - 13-2-2 Medium and Longer Ranges. - 13-2-3 Additional Comments on Forecasting. - 13-3 Predictability of the Atmosphere. - 13-4 Statistical-Dynamical Prediction. - 13-4-1 Simple Empirical Corrections. - 13-4-2 Stochastic-Dynamical Prediction. - 13-5 Climate and Climate Prediction. - Appendix Mathematical Relations. - References. - Index.

Note: TABLE OF CONTENTS: ACKNOWLEDGEMENTS. - PREFACE. - INTRODUCTION. - SYMBOLS AND NOTATION. - PART I. FUNDAMENTAL PHYSICS AND MATERIALS TECHNOLOGY OF ICE. - 1.General Concepts. - 1. Introduction. - 2. Equations of Balance. - 3. Material Response. - (a) General constitutive relations, simple materials. - (b) The rule of material objectivity. - (c) Material symmetry. - (d) Constitutive response for isotropie bodies. - (e) Materials with bounded memory-some constitutive representations. - (f) Incompressibility. - (g) Some representations of isotropic functions. - 4. The Entropy Principle. - (a) The viscous heat-conducting compressible fluid. - (b) The viscous heat-conducting incompressible fluid. - (c) Pressure and extra stress as independent variables. - (d) Thermoelastic solid. - (e) Final remarks. - 5. Phase Changes. - (a) Phase changes for a viscous compressible heat-conducting fluid. - (b) Phase changes for a viscous incompressible heat-conducting fluid. - References. - 2. A Brief Summary of Constitutive Relations for Ice. - 1. Preliminary Remarks. - 2. The Mechanical Properties of Hexagonal Ice. - (a) The crystal structure of ordinary ice. - (b) The elastic behavior of hexagonal ice. - (c) The inelastic behavior of single-crystal ice. - 3. The Mechanical Properties of Polycrystalline Ice. - (a) The elastic behavior of polycrystalline ice. - (b) Linear viscoelastic properties of polycrystalline ice. - (α) General theory. - (β) Experimental results. - (c) Non-linear viscous deformation and creep. - (α) Results of creep tests. - (β) Generalization to a three-dimensional flow law. - (γ) Other flow laws. - 4. The Mechanical Properties of Sea Ice. - (a) The phase diagram of standard sea ice and its brine conten. - (b) Elastic properties. - (c) Other material properties. - References. - PART II. THE DEFORMATION OF AN ICE MASS UNDER ITS OWN WEIGHT. - 3. A Mathematical Ice-flow Model and its Application to Parallel-sided Ice Slabs. - 1. Motivation and Physical Description. - 2. The Basic Model - Its Field Equations and Boundary Conditions. - (a) The field equations. - (α) Cold ice region. - (β) Temperate ice region. - (b) Boundary conditions. - (α) At the free surface. - (β) Along the ice-water interface. - (γ) Along the bedrock surface. - (δ) Along the melting surface. - 3. The Response of a Parallel-sided Ice Slab to Steady Conditions. - (a) Dimensionless forms of the field equations. - (b) Parallel-sided ice slab, a first approximation to glacier and ice-shelf flow dynamics. - (α) Velocity and temperature fields x-independent. - (β) Extending and compressing flow. - (γ) Floating ice shelves 4. Concluding Remark. - References. - 4. Thermo-mechanical Response of Nearly Parallel-sided Ice Slabs Sliding over their Bed. - 1. Motivation. - 2. The Basic Boundary-value Problem and its Reduction to Linear Form. - 3. The Solution of the Boundary-value Problems. - (a) Zeroth-order problem. - (b) First-order problem. - (α) Harmonic perturbation from uniform flow for a zero accumulation rate. - (β) Analytic solution for a Newtonian fluid. - (γ) Numerical solution for non-linear rheology. - (δ) Effect of a steady accumulation rate. - (ε) A historical note on a previous approach. - (η) The first-order temperature problem. - (c) Numerical results for steady state. - (α) Transfer of bottom protuberances to the surface. - (β) Basal stresses. - (γ) Surface velocities. - (δ) Effect of a steady accumulation rate. - 4. Remarks on Response to a Time-dependent Accumulation Rate. - 5. Surface-wave Stability Analysis. - (a) The eigenvalue problem. - (b) Discussion of results. - 6. Final Remarks. - References. - 5. The Application of the Shallow-ice Approximation. - 1. Background and Previous Work. - 2. Derivation of the Basal Shear-stress Formula by Integrating the Momentum Equations over Ice Thickness. - (a) Derivation. - (b) The use of the basal shear-stress formula in applied glaciology. - 3. Solution of the Ice-flow Problem using the Shallow-ice Approximation. - (a) Governing equations. - (b) Shallow-ice approximation. - (c) Construction of the perturbation solution. - (d) Results. - (e) Temperature field. - 4. Theoretical Steady-state Profiles. - (a) Earlier theories and their limitations. - (b) Surface profiles determined by using the shallow-ice approximation. - 5. An Alternative Scaling - a Proper Analysis of Dynamics of Ice Sheets with Ice Divides. - (a) Finite-bed inclination. - (b) Small-bed inclination. - (c) Illustrations. - References. - 6. The Response of a Glacier or an Ice Sheet to Seasonal and Climatic Changes. - 1. Statement of the Problem. - 2. Development of the Kinematic Wave Theory. - (a) Full non-linear theory. - (b) Perturbation expansion-linear theory. - (c) An estimate for the coefficients C and D. - (d) Boundary and initial conditions. - 3. Theoretical Solutions for a Model Glacier. - (a) Solutions neglecting diffusion. - (b) Theoretical solutions for a diffusive model. - (α) Coefficient functions for the special model. - (β) Solution for a step function. - (γ) General solution for uniform accumulation rate. - (δ) The inverse problem - calculation of climate from variations of the snout. - 4. General Treatment for an Arbitrary Valley Glacier. - (a) Fourier analysis in time. - (α) Low-frequency response. - (β) High-frequency response. - (γ) Use of the results. - (b) Direct integration methods. - 5. Derivation of the Surface-wave Equation from First Principles Non-linear Theory. - (a) Surface waves in the shallow-ice approximation. - (α) Integration by the methods of characteristics. - (β) An illustrative example. - (γ) A remark on linearization. - (δ) Effects of diffusion. - (b) Remarks regarding time-dependent surface profiles in ice sheets. - (c) Long waves in an infinite ice slab - Is accounting for diffusion enough?. - (α) Basic equations. - (β) Construction of perturbation solutions. - (γ) Numerical results. - 6. Concluding Remarks. - References. - 7. Three-dimensional and Local Flow Effects in Glaciers and Ice Sheets. - 1. Introduction. - 2. Effect of Valley Sides on the Motion of a Glacier. - (a) Solutions in special cases. - (α) Exact solutions for the limiting cases. - (β) Solution for a slightly off-circular channel. - (γ) A note on very deep and wide channels. - (b) A useful result for symmetrical channels with no boundary slip. - (c) Numerical solution - discussion of results. - 3. Three-dimensional Flow Effects in Ice Sheets. - (a) Basic equations. - (b) Decoupling of the stress-velocity problem from the problem of surface profile. - (c) The equation describing the surface geometry. - (d) The margin conditions. - 4. Variational Principles. - (a) Fundamental variational theorem. - (b) Variational principle for velocities. - (c) Reciprocal variational theorem. - (d) Maximum and minimum principles. - (e) Adoption of the variational principles to ice problems. - 5. Discussion of Some Finite-element Solutions. - References. - Appendix: Detailed Calculations Pertaining to Higher-order Stresses in the Shallow-ice Approximation. - AUTHOR INDEX. - SUBJECT INDEX.