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Applicable Atmospheric Dynamics : Techniques for the Exploration of Atmospheric Dynamics

作者: Istvan Szunyogh 出版社: World Scientific Publishing Co Pte Ltd
ISBN: 9789814335690分类号: P433 /S998
出版时间: 2014-11-05有354人浏览

Applicable Atmospheric Dynamics : Techniques for the Exploration of Atmospheric Dynamics

[Book Description]

This book offers an overview of advanced techniques to study atmospheric dynamics by numerical experimentation. It is primarily intended for scientists and graduate students working on interdisciplinary research problems at the intersection of the atmospheric sciences, applied mathematics, statistics and physics. Scientists interested in adopting techniques from the atmospheric sciences to study other complex systems may also find most of the topics covered in the book interesting. The specific techniques covered in the book have either proven or potential value in solving practical problems of atmospheric dynamics.

[Table of Contents]
Preface                                            vii
1 Governing Equations                              1  (188)
  1.1 Introduction                                 1  (1)
  1.2 Primitive Equations                          2  (44)
    1.2.1 The Equations                            3  (11)
    1.2.2 Eulerian Form of the Equations           14 (4)
    1.2.3 Scale Analysis of the Momentum           18 (10)
    Equation
    1.2.4 Diabatic Heating                         28 (7)
    1.2.5 Atmospheric Constituents                 35 (4)
    1.2.6 Boundary and Initial Conditions          39 (7)
  1.3 Representation of the Location with          46 (27)
  Coordinates
    1.3.1 Spherical Coordinates                    46 (14)
    1.3.2 Map Projections                          60 (10)
    1.3.3 Cartesian Coordinates                    70 (3)
  1.4 Alternate Vertical Coordinates               73 (44)
    1.4.1 General Formulation                      74 (6)
    1.4.2 Pressure Vertical Coordinate             80 (19)
    1.4.3 Sigma Vertical Coordinate                99 (2)
    1.4.4 Isentropic Vertical Coordinate           101(9)
    1.4.5 Hybrid Vertical Coordinates              110(2)
    1.4.6 Pseudo-Height and Log-Pressure           112(5)
    Vertical Coordinates
  1.5 Vorticity and Divergence Equations           117(34)
    1.5.1 Vorticity, Absolute Vorticity and        118(1)
    Divergence
    1.5.2 Vorticity Equations                      119(7)
    1.5.3 The Vorticity and the Divergence as      126(1)
    Prognostic State Variables
    1.5.4 The Vorticity and the Divergence         127(8)
    Equation in Pressure Coordinate System
    1.5.5 Reduced Forms of the Vorticity and       135(16)
    the Divergence Equations
  1.6 Potential Vorticity (PV)                     151(26)
    1.6.1 General Case                             151(4)
    1.6.2 Hydrostatic Case                         155(9)
    1.6.3 Computation of the Potential Vorticity   164(3)
    1.6.4 Vertical Structure of the Potential      167(7)
    Vorticity Field
    1.6.5 Potential Vorticity Inversion and        174(3)
    "PV-thinking"
  1.7 Integral Invariants                          177(12)
    1.7.1 Hamiltonian Form of the Governing        177(6)
    Equations
    1.7.2 Energy, Momentum, and Angular Momentum   183(1)
    1.7.3 Integrals of the Potential Vorticity     183(1)
    1.7.4 Integral Invariants of the Simplified    184(5)
    Equations
2 Perturbation Dynamics                            189(98)
  2.1 Introduction                                 189(2)
  2.2 Zonal-Mean Structure of the Atmosphere       191(8)
    2.2.1 Zonal-Mean Temperature Field             192(1)
    2.2.2 Zonal-Mean Potential Temperature Field   193(2)
    2.2.3 Zonal-Mean Wind Field                    195(3)
    2.2.4 Available Potential Energy               198(1)
  2.3 Quasi-Geostrophic Baroclinic Equations       199(14)
    2.3.1 General Assumptions                      200(4)
    2.3.2 Quasi-Geostrophic Potential Vorticity    204(2)
    2.3.3 Quasi-Geostrophic w-Equation             206(1)
    2.3.4 Quasi-Geostrophic Baroclinic Model       206(7)
    Equations
  2.4 Atmospheric Waves                            213(74)
    2.4.1 General Formulation                      214(18)
    2.4.2 Large and Synoptic Scale Waves:          232(24)
    Rossby Waves and Unstable Baroclinic Waves
    2.4.3 Techniques to Detect Synoptic-Scale      256(7)
    Wave Packets
    2.4.4 Eddy Kinetic Energy Equation             263(13)
    2.4.5 Shallow-Water Waves with Constant        276(3)
    Amplitude
    2.4.6 Convectively Coupled Equatorial          279(8)
    Waves: Shallow-Water Waves with Latitude
    Dependent Amplitude
3 Numerical Models                                 287(118)
  3.1 Introduction                                 287(2)
  3.2 Dynamical Cores                              289(1)
  3.3 Spatial Discretization                       290(33)
    3.3.1 Nonlinear Interactions in the            291(10)
    Horizontally Discretized Equations
    3.3.2 Three- and Two-Dimensional Turbulence    301(7)
    3.3.3 Spectral Transform Method                308(10)
    3.3.4 Finite-Difference Methods                318(4)
    3.3.5 Finite-Volume and Spectral-Element       322(1)
    Schemes
  3.4 Temporal Discretization                      323(8)
    3.4.1 Explicit and Implicit Schemes            323(3)
    3.4.2 Semi-Implicit Schemes                    326(1)
    3.4.3 Semi-Lagrangian Schemes                  327(4)
  3.5 Parameterization Schemes                     331(4)
    3.5.1 Radiative Processes                      332(1)
    3.5.2 Boundary Layer Turbulence and            333(1)
    Ocean-Land-Atmosphere Interactions
    3.5.3 Convective Processes                     333(1)
    3.5.4 Microphysics                             334(1)
    3.5.5 Orographic Drag                          334(1)
  3.6 State-of-the-Art Numerical Models            335(3)
    3.6.1 Global Models                            335(1)
    3.6.2 Limited Area Models                      336(2)
  3.7 Simplified and Idealized Numerical Models    338(10)
    3.7.1 Simplified Models                        339(4)
    3.7.2 Idealized Models                         343(5)
  3.8 Measures of Forecast Error                   348(14)
    3.8.1 Root-Mean-Square Error                   350(7)
    3.8.2 Anomaly Correlation                      357(5)
  3.9 Models as Dynamical Systems                  362(43)
    3.9.1 Finite-Dimensional State Vector          362(1)
    3.9.2 Nonlinear Models                         363(5)
    3.9.3 Linearized Models                        368(10)
    3.9.4 Lyapunov Exponents and Vectors           378(12)
    3.9.5 Transient Perturbation Growth            390(4)
    3.9.6 Forecast Ensembles                       394(11)
4 Data Assimilation                                405(132)
  4.1 Introduction                                 405(1)
  4.2 General Formulation for Normally             405(40)
  Distributed Observation Errors
    4.2.1 The Cost Function                        405(4)
    4.2.2 Behavior of the Cost Function            409(5)
    4.2.3 Sequential Formulation for the Linear    414(7)
    Case: Kalman Filter
    4.2.4 Computation of the Kalman Gain Matrix    421(3)
    4.2.5 Sequential Formulation for the           424(3)
    Nonlinear Case: Extended Kalman Filter
    4.2.6 Serial Processing of the Observations    427(3)
    4.2.7 Sensitivity to Nonlinearities:           430(10)
    Simulated Observa- tions Experiments
    4.2.8 Robust Statistics                        440(2)
    4.2.9 The Sequential Cost Function and         442(3)
    Bayes' Rule
  4.3 3-Dimensional Schemes                        445(16)
    4.3.1 General Formulation                      445(2)
    4.3.2 Optimal Interpolation                    447(3)
    4.3.3 3-Dimensional Variational Schemes        450(8)
    4.3.4 Proxies for the Background Error         458(2)
    4.3.5 Balance Constraints                      460(1)
  4.4 4-Dimensional Algorithms                     461(23)
    4.4.1 4-Dimensional Variational Schemes        462(2)
    4.4.2 Ensemble-based Kalman Filtering (EnKF)   464(19)
    4.4.3 Hybrid Schemes                           483(1)
  4.5 Accounting for Model Errors and              484(18)
  Observation Bias
    4.5.1 Model Errors                             485(1)
    4.5.2 Modifying the Observation Function       486(2)
    4.5.3 Modifying the Model Dynamics             488(1)
    4.5.4 Modifying the Observation Error          489(1)
    Statistics
    4.5.5 Sequential Schemes                       490(11)
    4.5.6 Weak Constraint 4D-Var                   501(1)
  4.6 Assimilating Satellite-based Observations    502(16)
    4.6.1 Radiative Transfer in the Infrared       504(3)
    and Microwave Ranges
    4.6.2 Assimilating Radiance Observations       507(4)
    4.6.3 Assimilating Retrievals                  511(7)
    4.7 Frequently Assimilated Observation Types   518(1)
  4.7.1 In Situ Observations                       518(13)
    4.7.2 Satellite-based Observations             520(7)
    4.7.3 Diagnosing and Predicting the            527(4)
    Forecast Effect of Observations
  4.8 Reanalysis Data Sets                         531(6)
    4.8.1 First Generation Data Sets               532(2)
    4.8.2 Second Generation Data Sets              534(1)
    4.8.3 Third Generation Data Sets               535(2)
Bibliography                                       537(20)
Index                                              557
 

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