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  Modeling of Atmospheric Chemistry

  Mathematical modeling of atmospheric composition is a formidable scientific and computational challenge. This comprehensive presentation of the modeling methods used in atmospheric chemistry focuses on both theory and practice, from the fundamental principles behind models, through to their applications in interpreting observations. An encyclopedic coverage of methods used in atmospheric modeling, including their advantages and disadvantages, makes this a one-stop resource with a large scope. Particular emphasis is given to the mathematical formulation of chemical, radiative, and aerosol processes; advection and turbulent transport; emission and deposition processes; as well as major chapters on model evaluation and inverse modeling. The modeling of atmospheric chemistry is an intrinsically interdisciplinary endeavor, bringing together meteorology, radiative transfer, physical chemistry, and biogeochemistry. This book is therefore of value to a broad readership. Introductory chapters and a review of the relevant mathematics make the book instantly accessible to graduate students and researchers in the atmospheric sciences.

  Guy P. Brasseur is a Senior Scientist and former Director at the Max Planck Institute for Meteorology in Hamburg, Germany, and a Distinguished Scholar at the National Center for Atmospheric Research in Boulder, USA. He received his doctor’s degree at the University of Brussels and has conducted research in Belgium, the USA, and Germany. He was Professor at the Universities of Brussels and Hamburg. His scientific interests include questions related to atmospheric chemistry and air pollution, biogeochemical cycles, climate change, and upper atmosphere chemistry and dynamics. He has chaired several international research programs, and is associated with national academies in Hamburg, Germany, Brussels, Belgium, and Oslo, Norway.

  Daniel J. Jacob is the Vasco McCoy Family Professor of Atmospheric Chemistry and Environmental Engineering at Harvard University. He received his PhD from Caltech in 1985 and joined the Harvard faculty in 1987. His research covers a wide range of topics in atmospheric composition, with focus on model development and applications to interpretation of observations. Among his professional honors are the NASA Distinguished Public Service Medal (2003), the AGU Macelwane Medal (1994), and the Packard Fellowship for Science and Engineering (1989). Jacob has published over 350 research papers and trained over 80 PhD students and postdocs in atmospheric chemistry modeling over the course of his career.

  “This exceptional volume by two pioneers in the field covers every essential aspect of atmospheric modeling.”

  - John Seinfeld, California Institute of Technology

  “An impressive and comprehensive description of the theoretical underpinning and practical application of atmospheric chemistry modeling. Soon to be a classic reference for graduate students and researchers in the field.”

  - Colette L. Heald, Massachusetts Institute of Technology

  “Brasseur and Jacob, both world leaders in modeling atmospheric chemistry, have written a thoroughly engaging textbook. The breadth and depth of the material covered in the book is impressive, but a major strength of the book is the ability of the authors to present often complex information in an accessible way. I have no doubt that this book will help educate future generations of scientists and be a reference point for researchers worldwide. It will certainly become a well-thumbed volume on my bookshelf.

  - Paul Palmer, University of Edinburgh

  “This excellent book provides a comprehensive introduction and reference to modeling of atmospheric chemistry from two of the pioneering authorities in the field. From the historical motivations through to modern-day approaches, the atmospheric physical, chemical and radiative components of the model framework are described. What makes this book particularly relevant and timely is the discussion of the methods for integrating observations and models that are at the forefront of current scientific advancement.”

  - David P. Edwards, National Center for Atmospheric Research

  Modeling of Atmospheric Chemistry

  Guy P. Brasseur

  Max Planck Institute for Meteorology and National Center for Atmospheric Research

  Daniel J. Jacob

  Harvard University

  University Printing House, Cambridge CB2 8BS, United Kingdom

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  www.cambridge.org

  Information on this title: www.cambridge.org/9781107146969

  © Guy P. Brasseur and Daniel J. Jacob 2017

  This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press.

  First published 2017

  Printed in the United States of America by Sheridan Books, Inc.

  A catalogue record for this publication is available from the British Library.

  Library of Congress Cataloging-in-Publication Data

  Names: Brasseur, Guy. | Jacob, Daniel J., 1958–

  Title: Modeling of atmospheric chemistry / Guy P. Brasseur, Max Planck Institute for Meteorology, Hamburg, Daniel J. Jacob, Harvard University.

  Description: Cambridge : Cambridge University Press, 2017. | Includes bibliographical references and index.

  Identifiers: LCCN 2016040128 | ISBN 9781107146969 (Hardback : alk. paper)

  Subjects: LCSH: Atmospheric chemistry–Mathematical models. | Atmospheric diffusion–Mathematical models.

  Classification: LCC QC879 .B6974 2017 | DDC 551.51/1–dc23 LC record available at https://lccn.loc.gov/2016040128

  ISBN 978-1-107-14696-9 Hardback

  Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party Internet Web sites referred to in this publication and does not guarantee that any content on such Web sites is, or will remain, accurate or appropriate.

  Contents

  Preface

  List of Symbols

  1The Concept of Model1.1Introduction

  1.2What is a Model?

  1.3Mathematical Models

  1.4Meteorological Models

  1.5Climate Models

  1.6Atmospheric Chemistry Models

  1.7Types of Atmospheric Chemistry Models

  1.8Models as Components of Observing Systems

  1.9High-Performance Computing

  2Atmospheric Structure and Dynamics2.1Introduction

  2.2Global Energy Budget

  2.3Vertical Structure of the Atmosphere

  2.4Temperature, Pressure, and Density: The Equation of State

  2.5Atmospheric Humidity

  2.6Atmospheric Stability2.6.1The Hydrostatic Approximation

  2.6.2Adiabatic Lapse Rate and Stability

  2.7Geostrophic Balance

  2.8Barotropic and Baroclinic Atmospheres

  2.9General Circulation of the Troposphere

  2.10Planetary Boundary Layer

  2.11Middle Atmosphere Dynamics

  3Chemical Processes in the Atmosphere3.1Introduction

  3.2Oxygen Species and Stratospheric Ozone

  3.3Hydrogen Oxide Radicals

  3.4Nitrogen Oxide Radicals

  3.5Volatile Organic Compoun
ds and Carbon Monoxide

  3.6Tropospheric Ozone

  3.7Halogen Radicals

  3.8Sulfur Species

  3.9Aerosol Particles3.9.1Size Distribution

  3.9.2Chemical Composition

  3.9.3Mixing State, Hygroscopicity, and Activation

  3.9.4Optical Properties

  4Model Equations and Numerical Approaches4.1Introduction

  4.2Continuity Equation for Chemical Species4.2.1Eulerian and Lagrangian Formulations

  4.2.2Advection

  4.2.3Turbulent Mixing

  4.2.4Convection

  4.2.5Wet Scavenging

  4.2.6Chemistry

  4.2.7Surface Exchange

  4.2.8Green Function for Lagrangian Transport

  4.2.9Initial and Boundary Conditions

  4.3Continuity Equation for Aerosols

  4.4Atmospheric Lifetime and Characteristic Timescales4.4.1Atmospheric Lifetime

  4.4.2Relaxation Timescales in Response to a Perturbation

  4.5Conservation Equations for Atmospheric Dynamics4.5.1Mass

  4.5.2Momentum

  4.5.3Energy

  4.5.4Primitive and Non-Hydrostatic Equations

  4.6Vertical Coordinates4.6.1Pressure Coordinate System

  4.6.2Log-Pressure Altitude Coordinate System

  4.6.3Terrain-Following Coordinate Systems

  4.6.4Isentropic Coordinate System

  4.7Lower-Dimensional Models4.7.1Two-Dimensional Models

  4.7.2One-Dimensional Models

  4.7.3Zero-Dimensional Models

  4.8Numerical Frameworks for Eulerian Models4.8.1Finite Difference (Grid Point) Methods

  4.8.2Finite Volume (Grid Cell) Methods

  4.8.3Model Grids

  4.9Spectral Methods

  4.10Finite Element Method

  4.11Lagrangian Approaches4.11.1Models for Single Trajectories

  4.11.2Stochastic Models

  4.11.3Global and Regional Three-Dimensional Lagrangian Models

  4.11.4Semi-Lagrangian Models

  4.12Atmospheric Plume Models4.12.1Gaussian Plume Models

  4.12.2Puff Models

  4.13Statistical Models4.13.1Multiple Linear Regression Models

  4.13.2Artificial Neural Networks

  4.14Operator Splitting

  4.15Filtering4.15.1Diffusive Filters

  4.15.2Digital Spatial Filters

  4.15.3Spectral Filters

  4.15.4Time-Smoothing Filters

  4.16Interpolation and Remapping4.16.1Global Polynomial Interpolation

  4.16.2Piecewise Interpolation

  4.16.3Distance-Weighted Interpolation

  4.16.4Kriging

  4.16.5Correction for Local Effects

  4.16.6Conservative Remapping

  5Formulations of Radiative, Chemical, and Aerosol Rates5.1Introduction

  5.2Radiative Transfer5.2.1Definitions

  5.2.2Blackbody Radiation

  5.2.3Extra-Terrestrial Solar Spectrum

  5.2.4Penetration of Solar Radiation in the Atmosphere

  5.2.5Emission and Absorption of Terrestrial Radiation

  5.3Gas Phase Chemistry5.3.1Photolysis

  5.3.2Elementary Chemical Kinetics

  5.4Chemical Mechanisms

  5.5Multiphase and Heterogeneous Chemistry5.5.1Gas–Particle Equilibrium

  5.5.2Mass Transfer Limitations

  5.5.3Reactive Uptake Probability

  5.6Aerosol Microphysics5.6.1Formulation of Aerosol Processes

  5.6.2Representation of the Size Distribution

  6Numerical Methods for Chemical Systems6.1Introduction

  6.2General Considerations6.2.1Fully Explicit Equation

  6.2.2Fully Implicit Equation

  6.2.3Improving Accuracy

  6.2.4Explicit Versus Implicit Solvers

  6.3Explicit Solvers6.3.1Exponential Approximation

  6.3.2Quasi Steady-State Approximation

  6.3.3Extrapolation Technique (ET)

  6.3.4CHEMEQ Solver

  6.3.5TWOSTEP method

  6.4Implicit Solvers6.4.1Backward Euler

  6.4.2Rosenbrock Solvers

  6.4.3Gear Solver

  7Numerical Methods for Advection7.1Introduction

  7.2The Advection Equation

  7.3Elementary Finite Difference Methods7.3.1Methods Using Centered Space Differences

  7.3.2Methods Using Space-Uncentered Differences

  7.3.3Multilevel Algorithms

  7.3.4Performance of Elementary Finite Difference Algorithms

  7.3.5Generalization to Variable Wind Speed and Grid Size

  7.3.6Mass Conservation

  7.3.7Multidimensional Cases

  7.3.8Boundary Conditions

  7.4Elementary Finite Volume Methods7.4.1One-Dimensional Formulation

  7.4.2Two-Dimensional Formulation

  7.5Preserving Monotonicity: Flux-Corrected Transport

  7.6Advanced Eulerian Methods

  7.7Lagrangian Methods

  7.8Semi-Lagrangian Methods7.8.1Grid Point Based SLT Schemes

  7.8.2Finite Volume Based SLT Schemes

  7.9Spectral, Finite Element, and Spectral Element Methods

  7.10Numerical Fixers and Filters

  7.11Concluding Remarks

  8Parameterization of Subgrid-Scale Processes8.1Introduction

  8.2Reynolds Decomposition: Mean and Eddy Components

  8.3Chemical Covariance

  8.4Closure Relations8.4.1First-Order Closure

  8.4.2Higher-Order Closures

  8.5Stochastic Representation of Turbulent Reacting Flows

  8.6Numerical Solution of the Diffusion Equation8.6.1Explicit Schemes for the 1-D Diffusion Equation

  8.6.2Implicit Schemes for the 1-D Diffusion Equation

  8.6.3Numerical Algorithms for the Multidimensional Diffusion Equation

  8.7Planetary Boundary Layer Processes8.7.1Mean Atmospheric Wind Velocity and Temperature

  8.7.2Boundary Layer Turbulence Closure

  8.7.3Surface Layer

  8.8Deep Convection

  8.9Wet Deposition8.9.1Scavenging in Convective Updrafts

  8.9.2Rainout and Washout

  8.10Lightning and NOx Production

  8.11Gravity Waves

  8.12Dynamical Barriers

  8.13Free Tropospheric Plumes

  9Surface Fluxes9.1Introduction

  9.2Emission9.2.1Terrestrial Biogenic Emissions

  9.2.2Open Fires

  9.2.3Volcanoes

  9.2.4Anthropogenic Emissions

  9.2.5Mechanical Emissions: Sea Salt and Dust

  9.3One-Way Dry Deposition9.3.1Dry Deposition Velocity

  9.3.2Momentum Deposition to a Flat Rough Surface

  9.3.3Big-Leaf Model for Dry Deposition

  9.3.4Aerodynamic Resistance

  9.3.5Quasi-Laminar Boundary Layer Resistance

  9.3.6Surface Resistance

  9.3.7Factors Controlling the Dry Deposition Velocity

  9.3.8Gravitational Settling

  9.4Two-Way Surface Flux

  10Atmospheric Observations and Model Evaluation10.1Introduction

  10.2Atmospheric Observations10.2.1In-Situ Observations of Gases

  10.2.2In-Situ Observations of Aerosols

  10.2.3Remote Sensing

  10.2.4Measurement of Surface Fluxes

  10.2.5Observation Platforms

  10.3Characterization of Errors10.3.1Errors in Observations

  10.3.2Errors in Models

  10.4General Considerations for Model Evaluation10.4.1Selection of Observations

  10.4.2Use of Satellite Observations

  10.4.3Preliminary Evaluation and Temporal Scales

  10.4.4Aerosol Metrics

  10.4.5Scatterplots

  10.5Measures of Model Skill10.5.1Basic Metrics

  10.5.2The Taylor Diagram

  10.5.3The Target Diagram

  10.6Significance in the Difference Between Two Data Sets

  10.7Using Models to Interpret Observations

  11Inverse
Modeling for Atmospheric Chemistry11.1Introduction

  11.2Bayes’ Theorem

  11.3A Simple Scalar Example

  11.4Vector-Matrix Tools11.4.1Error Covariance Matrix

  11.4.2Gaussian Probability Density Function for Vectors

  11.4.3Jacobian Matrix

  11.4.4Adjoint

  11.5Analytical Inversion11.5.1Optimal Estimate

  11.5.2Averaging Kernel Matrix

  11.5.3Degrees of Freedom for Signal

  11.5.4Evaluation of the Inverse Solution

  11.5.5Limitations on State Vector Dimension: Aggregation Error

  11.6Adjoint-Based Inversion

  11.7Markov Chain Monte Carlo (MCMC) Methods

  11.8Other Optimization Methods

  11.9Positivity of the Solution

  11.10Data Assimilation11.10.13DVAR Data Assimilation and the Kalman Filter

  11.10.24DVAR Data Assimilation

  11.11Observing System Simulation Experiments

  Appendix APhysical Constants and Other DataA.1General and Universal Constants

  A.2Earth

  A.3Dry Air

  A.4Water

  Appendix BUnits, Multiplying Prefixes, and Conversion FactorsB.1International System of Units

  B.2Multiplying Prefixes

  B.3Conversion Factors

  B.4Commonly Used Units for Atmospheric Concentrations