Mesoscale Meteorological Modeling

The second edition of Mesoscale Meteorological Modeling is a fully revised resource for researchers and practitioners in the growing field of meteorological modeling at the mesoscale. Pielke has enhanced the new edition by quantifying model capability (uncertainty) by a detailed evaluation of the assumptions of parameterization and error propagation. Mesoscale models are applied in a wide variety of studies, including weather prediction, regional and local climate assessments, and air pollution investigations.

Preface

ix

Preface to Second Edition

xiii

Foreword

xv

Introduction

1

(2)

Basic Set of Equations

3

(19)

Conservation of Mass

3

(2)

Conservation of Heat

5

(8)

Conservation of Motion

13

(4)

Conservation of Water

17

(1)

Conservation of Other Gaseous and Aerosol Materials

18

(1)

Summary

18

(4)

Simplification of the Basic Equations

22

(19)

Conservation of Mass

22

(7)

Conservation of Motion

29

(1)

Conservation of Motion

29

(10)

Conservation of Water and Other Gaseous and Aerosol Contaminants

39

(2)

Averaging the Conservation Relations

41

(17)

Definition of Averages

41

(8)

Vorticity Equation

49

(2)

Diagnostic Equation for Nonhydrostatic Pressure

51

(2)

Scaled Pressure Form

53

(2)

Summary

55

(3)

Physical and Analytic Modeling

58

(64)

Physical Models

59

(6)

Linear Models

65

(47)

Long's Analytic Solution to Nonlinear Momentum Flow

112

(10)

Coordinate Transformations

122

(42)

Tensor Analysis

122

(8)

Generalized Vertical Coordinate

130

(8)

The Sigma-z Coordinate System

138

(15)

Derivation of Drainage Flow Equations Using Two Different Coordinate Representations

153

(5)

Summary

158

(2)

Application of Terrain---Following Coordinate Systems

160

(4)

Parameterization---Averaged Subgrid-Scale Fluxes

164

(46)

Basic Terms

166

(6)

Surface--Layer Parameterization

172

(13)

Planetary Boundary---Layer Parameterization

185

(17)

Heterogenous Boundary Layers

202

(8)

Averaged Radiation Flux Divergence

210

(41)

Introduction

210

(1)

Basic Concepts

210

(4)

Longwave Radiative Flux

214

(19)

Shortwave Radiative Flux

233

(14)

Examples of Parameterizations and Level of Complexity

247

(4)

Parameterization of Moist Thermodynamic Processes

251

(30)

Introduction

251

(2)

Parameterization of the Influences of Phase Changes of Water in a Convectively Stable Atmosphere (∂&thetas;E/∂z > 0)

253

(8)

Parameterization of the Influences of Phase Changes of Water in a Convectively Unstable Atmosphere (∂&thetas;E/∂z ≤ 0)

261

(12)

Examples of Parameterizations and Level of Complexity

273

(8)

Methods of Solution

281

(66)

Finite Difference Schemes---An Introduction

282

(34)

Upstream Interpolation Schemes---An Introduction

316

(10)

Diagnostic Equations

326

(3)

Time Splitting

329

(1)

Nonlinear Effects

330

(12)

Summary

342

(5)

Boundary and Initial Conditions

347

(95)

Grid and Domain Structure

347

(17)

Initialization

364

(15)

Spatial Boundary Conditions

379

(63)

Model Evaluation

442

(30)

Evaluation Criteria

442

(1)

Comparison with Analytic Theory

443

(2)

Comparison with Other Numerical Models

445

(1)

Comparison Against Different Model Formulations

446

(8)

Calculation of Model Budgets

454

(8)

Comparison with Observations

462

(7)

Model Sensitivity Analyses

469

(3)

Examples of Mesoscale Models

472

(59)

Terrain---Induced Mesoscale Systems

473

(41)

Synoptically---Induced Mesoscale Systems

514

(17)

Appendix A: The Solution of Eqs. (10--28) and (10--47)

531

(3)

Appendix B: Model Summaries

534

(16)

Appendix C: Summary of Several Cumulus Cloud Parameterization Schemes

550

(6)

Appendix D: BATS, LAPS, and LEAF Comparison Tables

556

(14)

Appendix E: Summary of Datasets (2000)

570

(1)

References

571

(90)

Index

661

(12)

List of Volumes in the Series

673

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Mesoscale Meteorological Modeling

Summary

Table of Contents

Supplemental Materials