Applicable Atmospheric Dynamics

The following sections are included:

• Dedication
• Preface
• Contents

The following sections are included:

• Introduction
• Primitive Equations
  • The Equations
  • Eulerian Form of the Equations
  • Scale Analysis of the Momentum Equation
  • Diabatic Heating
  • Atmospheric Constituents
  • Boundary and Initial Conditions
• Representation of the Location with Coordinates
  • Spherical Coordinates
  • Map Projections
  • Cartesian Coordinates
• Alternate Vertical Coordinates
  • General Formulation
  • Pressure Vertical Coordinate
  • Sigma Vertical Coordinate
  • Isentropic Vertical Coordinate
  • Hybrid Vertical Coordinates
  • Pseudo-Height and Log-Pressure Vertical Coordinates
• Vorticity and Divergence Equations
  • Vorticity, Absolute Vorticity and Divergence
  • Vorticity Equations
  • The Vorticity and the Divergence as Prognostic State Variables
  • The Vorticity and the Divergence Equation in Pressure Coordinate System
  • Reduced Forms of the Vorticity and the Divergence Equations
• Potential Vorticity (PV)
  • General Case
  • Hydrostatic Case
  • Computation of the Potential Vorticity
  • Vertical Structure of the Potential Vorticity Field
  • Potential Vorticity Inversion and “PV-thinking”
• Integral Invariants
  • Hamiltonian Form of the Governing Equations
  • Energy, Momentum, and Angular Momentum
  • Integrals of the Potential Vorticity
  • Integral Invariants of the Simplified Equations

The following sections are included:

• Introduction
• Zonal-Mean Structure of the Atmosphere
  • Zonal-Mean Temperature Field
  • Zonal-Mean Potential Temperature Field
  • Zonal-Mean Wind Field
  • Available Potential Energy
• Quasi-Geostrophic Baroclinic Equations
  • General Assumptions
  • Quasi-Geostrophic Potential Vorticity
  • Quasi-Geostrophic ω-Equation
  • Quasi-Geostrophic Baroclinic Model Equations
• Atmospheric Waves
  • General Formulation
  • Large and Synoptic Scale Waves: Rossby Waves and Unstable Baroclinic Waves
  • Techniques to Detect Synoptic-Scale Wave Packets
  • Eddy Kinetic Energy Equation
  • Shallow-Water Waves with Constant Amplitude
  • Convectively Coupled Equatorial Waves: Shallow-Water Waves with Latitude Dependent Amplitude

The following sections are included:

• Introduction
• Dynamical Cores
• Spatial Discretization
  • Nonlinear Interactions in the Horizontally Discretized Equations
  • Three- and Two-Dimensional Turbulence
  • Spectral Transform Method
  • Finite-Difference Methods
  • Finite-Volume and Spectral-Element Schemes
• Temporal Discretization
  • Explicit and Implicit Schemes
  • Semi-Implicit Schemes
  • Semi-Lagrangian Schemes
• Parameterization Schemes
  • Radiative Processes
  • Boundary Layer Turbulence and Ocean-Land-Atmosphere Interactions
  • Convective Processes
  • Microphysics
  • Orographic Drag
• State-of-the-Art Numerical Models
  • Global Models
  • Limited Area Models
• Simplified and Idealized Numerical Models
  • Simplified Models
  • Idealized Models
• Measures of Forecast Error
  • Root-Mean-Square Error
  • Anomaly Correlation
• Models as Dynamical Systems
  • Finite-Dimensional State Vector
  • Nonlinear Models
  • Linearized Models
  • Lyapunov Exponents and Vectors
  • Transient Perturbation Growth
  • Forecast Ensembles

The following sections are included:

• Introduction
• General Formulation for Normally Distributed Observation Errors
  • The Cost Function
  • Behavior of the Cost Function
  • Sequential Formulation for the Linear Case: Kalman Filter
  • Computation of the Kalman Gain Matrix
  • Sequential Formulation for the Nonlinear Case: Extended Kalman Filter
  • Serial Processing of the Observations
  • Sensitivity to Nonlinearities: Simulated Observations Experiments
  • Robust Statistics
  • The Sequential Cost Function and Bayes' Rule
• 3-Dimensional Schemes
  • General Formulation
  • Optimal Interpolation
  • 3-Dimensional Variational Schemes
  • Proxies for the Background Error
  • Balance Constraints
• 4-Dimensional Algorithms
  • 4-Dimensional Variational Schemes
  • Ensemble-based Kalman Filtering (EnKF)
  • Hybrid Schemes
• Accounting for Model Errors and Observation Bias
  • Model Errors
  • Modifying the Observation Function
  • Modifying the Model Dynamics
  • Modifying the Observation Error Statistics
  • Sequential Schemes
  • Weak Constraint 4D-Var
• Assimilating Satellite-based Observations
  • Radiative Transfer in the Infrared and Microwave Ranges
  • Assimilating Radiance Observations
  • Assimilating Retrievals
• Frequently Assimilated Observation Types
  • In Situ Observations
  • Satellite-based Observations
  • Diagnosing and Predicting the Forecast Effect of Observations
• Reanalysis Data Sets
  • First Generation Data Sets
  • Second Generation Data Sets
  • Third Generation Data Sets

The following sections are included:

• Bibliography
• Index