This book gives a comprehensive and lucid account of the science of the atmospheric boundary layer (ABL). Its purpose is to provide a moderately advanced text aimed at the experienced researcher or teacher working in the atmospheric and related sciences. Its importance lies in the breadth of the material covered, with a careful balance between mathematical description and physical interpretation.

Cambridge atmospheric and space science series

The atmospheric boundary layer

Cambridge atmospheric and space science series

Editors John T. Houghton Michael J . Rycroft Alexander J. Dessler

Titles in print in this series M. H. Rees, Physics and chemistry of the upper atmosphere Roger Daley, Atmospheric data analysis Ya. L. AI'pert, Space plasma, Volumes 1 and 2 J. R. Garratt, The atmospheric boundary layer J. K. Hargreaves, The solar-terrestrial environment Sergei Sahzin, Whistler-mode waves in a hot plasma

The atmospheric boundary layer J. R. Garratt Division of Atmospheric Research, CSIRO, Melbourne, Australia

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CAMBRIDGE UNIVERSITY PRESS

cambridge university press

Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo, Delhi, Tokyo, Mexico City Cambridge University Press The Edinburgh Building, Cambridge cb2 8ru, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521467452 © Cambridge University Press 1992 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 1992 First paperback edition (with corrections) 1994 A catalogue record for this publication is available from the British Library Library of Congress Cataloguing in Publication Data Garratt, J. R. The atmospheric boundary layer / J. R. Garratt. p. cm. – (Cambridge atmospheric and space science series) Includes bibliographical references and index. ISBN 0 521 38052 9 1. Planetary boundary layer. 2. Atmospheric physics. I. Title. II. Series. QC880.4.B65G37 1992 551.5-dc20 91-34340 CIP isbn 978-0-521-38052-2 Hardback isbn 978-0-521-46745-2 Paperback Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate. Information regarding prices, travel timetables, and other factual information given in this work is correct at the time of first printing but Cambridge University Press does not guarantee the accuracy of such information thereafter.

Contents

Preface Symbols Abbreviations 1 The atmospheric boundary layer 1.1 Introduction 1.2 History 1.3 Observing the ABL 1.4 ABL modelling 1.5 Applications 1.6 Scope of the book 1. 7 Nomenclature and some definitions Notes and bibliography

ix xi

xvii 1 1 3 5 5 6 7 8 12

2 Basic equations for mean and fluctuating quantities 2.1 Turbulence and flow description 2.2 Governing equations for mean and fluctuating quantities 2.3 The simplified mean equations 2.4 The turbulence closure problem 2.5 The second-moment equations 2.6 Turbulent kinetic energy and stability parameters Notes and bibliography

15 15 20 25 26 29 32 38

3 Scaling laws for mean and turbulent quantities 3.1 The wind profile: simple considerations 3.2 Wind profile laws: the neutral case 3.3 Monin-Obukhov similarity theory: the non-neutral surface layer 3.4 Generalized ABL similarity theory 3.5 Similarity theory and turbulence statistics Notes and bibliography

40 40 42 49 60 70 82

4 Surface roughness and local advection 4.1 Aerodynamic characteristics of the land

85 85 vii

Contents

viii 4.2 4.3 4.4 4.5

Scalar roughness lengths The vegetation canopy Flow over the sea Local advection and the internal boundary layer Notes and bibliography

89 93 97 104 113

5 Energy fluxes at the land surface 5.1 Surface energy balance and soil heat flux 5.2 Radiation fluxes 5.3 Evaporation 5.4 Condensation Notes and bibliography

115 115 120 125 139 143

6 The thermally stratified atmospheric boundary layer 6.1 The convective boundary layer 6.2 The stable (nocturnal) boundary layer 6.3 The marine atmospheric boundary layer 6.4 Mesoscale flow and IBL growth Notes and bibliography

145 145 164 182 186 191

7 The cloud-topped boundary layer 7.1 General properties of the CTBL 7.2 Observations 7.3 Radiation fluxes and cloud-top radiative cooling 7.4 Entrainment and entrainment instability 7.5 Numerical modelling of the CTBL Notes and bibliography

193 194 200 207 212 216 222

8 Atmospheric boundary-layer modelling and parameterization schemes 8.1 Introduction 8.2 Surface temperature 8.3 Surface humidity (soil moisture) 8.4 Canopy parameterization 8.5 Surface fluxes 8.6 Rate equation for ABL depth 8.7 Turbulence closure schemes 8.8 ABL cloud parameterization Notes and bibliography

224 224 226 229 235 243 244 245 256 257

9 The atmospheric boundary layer, climate and climate modelling 9.1 Introduction 9.2 Sensitivity of climate to the ABL and to land surface 9.3 Research priorities Notes and bibliography Appendices References Index

258 258 262 267 277 279 294 311

Preface

In the last few years there have appeared several books on the atmospheric boundary layer (ABL) and related topics that have helped fill a void existing for some time. These recent books have provided a more general introduction to the subject not found in the numerous advanced and specialist texts and research monographs that became available through the 1970s and 1980s. Plans for the present work were well under way when the books by Stull and by Sorbjan appeared. However, the subject of the ABL covers so many areas (turbulence, dynamics, cloud physics, radiation, the physics of heat and mass transfer, soil physics, surface vegetation, numerical modelling) that no one book covers quite the right material with the necessary emphasis and attention to detail. It is hoped that the present book fills in some gaps in our knowledge, and brings to the subject an emphasis that many readers will find useful. It is aimed especially at the many researchers in the atmospheric and associated sciences who require a moderately advanced text on the ABL in which the many links between turbulence, air-surface transfer, boundary-layer structure and dynamics, and numerical modelling are discussed and elaborated upon. Within the book, I have attempted to emphasize the application of ABL ideas to numerical modelling of the climate, and it should be possible for any experienced research worker to trace the origins of specific ABL parameterization schemes, and to relate these to the fundamental principles and detailed physics of the process of interest. The book should be useful to postgraduate students and university teachers in the atmospheric (and related) sciences who require a treatment beyond the introductory level. Finally, it seemed natural that the Atmospheric and Space Science series planned by Cambridge University Press should contain one text on the ABL. It is hoped that this text will nicely complement the other contributions. The book comprises nine chapters, four appendices (data tables, information sources, physical constants) and an extensive reference list. It is inevitably a compromise between a fundamental treatise on the one hand and a specialist research monograph on the other. Considerable effort has been made to provide a balance between mathematical description and physical interpretation, beix

x

Preface

tween observed behaviour and model simulation. Chapter 1 serves as an introduction, with Chapters 2 and 3 dealing with the development of mean and turbulence equations, and the many scaling laws and theories that are the cornerstone of any serious ABL treatment. Modelling of the ABL is crucially dependent for its realism on the surface boundary conditions, and Chapters 4 and 5 deal with aerodynamic and energy considerations, with attention to both dry and wet land surfaces and the sea. The structure of the clear-sky, thermally stratified ABL is treated in Chapter 6, including the convective and stable cases over homogeneous land, the marine ABL and the internal boundary layer at the coastline. Chapter 7 then extends the discussion to the cloudy ABL. This is seen as particularly relevant since the extensive stratocumulus regions over the sub-tropical oceans and stratus regions over the Arctic are now identified as key players in the climate system. Finally, Chapters 8 and 9 bring much of the book's material together in a discussion of appropriate ABL and surface parameterization schemes for the general circulation models of the atmosphere that are being used for climate simulation. I have taken note of the many comments made by reviewers at various stages in the book's production, in particular regarding the question of references. Most books, depending upon their style, contain either few, if any, references (e.g. Rees' book on the physics and chemistry of the upper atmosphere) or references are almost too plentiful (e.g. Brutsaert's book on evaporation into the atmosphere). My choice was to list at the end of the book references to specialist material not discussed at length in the text, and to supplement this reference list with a set of brief notes and recommended further reading at the end of each chapter. It is hoped that any unnecessary duplication has been minimized. Several colleagues read selected chapters of the manuscript, made corrections and suggested improvements in the presentation. I wish to thank Drs T. Beer, R. R. Brook, J. J. Finnigan, R. L. Hughes, D. H. Lenschow, J. L. Mcgregor, F. T. M. Nieuwstadt and M. R. Raupach and, in particular, Drs P. C. Manins and K. R. McNaughton. I am especially indebted to Dr B. L. Sawford for carefully and critically reading the greater part of the manuscript. I gratefully acknowledge Ms Louise Carr for her enthusiastic approach to the drafting of the original artwork. I wish to thank publishers and individual scientists who kindly gave their permission to reproduce figures from the published literature. Susan Parkinson, copy editor at CUP, provided the final polish to the manuscript, as well as ensuring consistency, continuity and correct grammar. This undertaking began during a sabbatical leave as Assistant Professor at the Department of Atmospheric Science, Colorado State University in 1987-8. An early draft of the book served as the basis of a lecture course given in the Department during the period January to May 1988. Part of the material contained in the final draft is used in a lecture course given to honours and postgraduate students in the Department of Mathematics, Monash University. The writing of the book depended ultimately on the enviable working environment provided in the Commonwealth Scientific and Industrial Research Organisation and on the patience and understanding of my wife Dianne.

Symbols

Vector quantities are bold A circumflex denotes a vertical average The subscript m denotes a mixed-layer value The subscript 0 denotes a surface or surface-layer value in most cases The superscript * denotes a saturation value in most cases A

ao

ABL similarity constant/function (velocity); IBL growth constant drag-law constant (analytical form) inverse scale height; cloud-top entrainment instability parameter; soil-moisture parameter free convection constants; turbulence-closure constants

B B- 1

Bowen ratio; ABL similarity constant/function (velocity) interfacial sublayer parameter

b

soil index parameter

bM , bH , bt.,bfI bo

drag-law constants (analytical form)

a

C CD, C DO CE CH

Cg

C gH

Ci

Cs Cv c

soil-moisture parameter ABL similarity constant/function (temperature) surface-layer, interfacial drag coefficient water vapour transfer coefficient heat transfer coefficient geostrophic drag coefficient; soil heat capacity per unit area large-scale heat-transfer coefficient transfer coefficient for surface i volumetric heat capacity for soil canopy heat capacity per unit area scalar concentration; drag-law constant (analytical form); ABL depth parameter soil-moisture parameter specific heat at constant pressure for air Xl

xii

Symbols

specific heats for soil and canopy turbulence-closure constants D Da DIJ

damping depth Dalton number soil-moisture diffusivity zero-plane displacement soil-layer thicknesses

E,E p EL

evaporation, potential evaporation evaporation quantity combining energy and aerodynamic terms turbulent kinetic energy; vapour pressure the vector (1, 1, 1) with components, ei' unity saturation vapour pressure

d do, db d 2 , d3

e

e e*

stability functions vertical flux of soil water Coriolis parameter; normalized frequency (nz/u) normalized frequency (nh/u); fractional area G

g H h, hb he

hd he hi

hr hs hss

magnitude of the geostrophic wind; soil heat flux; stability function acceleration due to gravity sensible heat flux boundary-layer depth, internal boundary-layer depth height of canopy; depth of elevated cloudy mixed layer depth of interfacial sublayer depth of equilibrium NBL depth of nocturnal (surface) inversion sand diameter or height of roughness elements depth of surface layer equilibrium or inner layer depth square root of minus one eddy diffusivity bottom-up, top-down diffusivities soil-hydraulic conductivity von Karman constant soil thermal conductivity; friction coefficient molecular thermal conductivity of dry air Monin-Obukhov length; averaging length leaf area index (LAI) horizontal length scale mixing length

Symbols

xiii

characteristic length scale; canopy length scale blending height characteristic length scale of the mean flow integral length scale water mass baroclinity parameter (components Mx and My) mean molecular weight of dry air, water vapour corrected absorber mass of gas; profile curvature index; depth of intercepted canopy water N

n P, P g Pr

Pt

P,PR

Brunt-Vaisala frequency natural frequency; profile curvature index precipitation rate, precipitation rate under a canopy Prandtl number turbulent Prandtl number atmospheric pressure, reference pressure specific humidity (surface value qo) saturation specific humidity liquid water content, total water specific humidity

universal gas constant; scale-height ratio; ratio of entrainment and surface scalar fluxes; runoff bulk ABL Richardson number Rb Reynolds number, roughness Reynolds number Re, Re* Rf, Rf flux Richardson number, layer-averaged flux Richardson number gradient Richardson number, critical value of Ri Ri, Ric bulk Richardson number RiB Ro surface Rossby number R d , R v , Rw gas constants for dry air, water vapour and moist air radius of the Earth RE Rradiative heat flux component ] I net radiation, net longwave radiation R N , RN shortwave flux, longwave flux of radiation R s , RL r radiative flux fraction at cloud top; mixing ratio r vector space variable aerodynamic resistance ra excess resistance to transfer rb internal canopy aerodynamic resistances rb, r d soil-surface relative humidity rh surface resistance, unconstrained surface resistance rs , ri bulk stomatal resistance, leaf stomatal resistance rst, r sti

R

S Sc St

stability function Schmidt number Stant0n number

xiv Se S Sm Sv

So

T Te T f, TOf Tv T s, Te T*, T v * t

Symbols the solar irradiance (solar constant) general property (wind component, temperature, mass concentration); 8q*/8T vertically averaged value of s in the mixed layer nondimensional shear vector nondimensional temperature gradient absolute temperature (surface value To); averaging period; NBL time scale; day length effective temperature of Earth's system foliage temperature virtual temperature soil and canopy temperatures convective temperature scale, cloudy convective temperature scale time

Uf Ug Ugi Ui U*

large-scale wind wind component (Ul) in the x-direction ageostrophic wind component in the x-direction local free convection velocity scale geostrophic wind component in the x-direction geostrophic wind component wind component friction velocity (surface-value u*o)

V Vg V Vag Ve Vg Vs V1]

velocity vector geostrophic velocity vector wind component (uz) in the y-direction ageostrophic wind component in the y-direction characteristic velocity scale geostrophic wind component in the y-direction characteristic velocity scale of the mean flow Kolmogorov velocity scale

W S , We W* W Wh W*

energy storage terms cloudy convective velocity scale vertical wind component (U3) vertical velocity at the ABL top convective velocity scale

X

space variable; fetch; evaporation fraction

Y Y

non dimensional heat flux space variable

Z

vertical distance above the surface space variable; height above the zero-plane displacement vertical space coordinate in the soil; vertical distance measured

U U U ag

z z'

Symbols

xv

downwards from the cloud top aerodynamic roughness length roughness scaling lengths for temperature and humidity depth of the roughness sublayer cross-isobar flow angle; slope angle; general albedo Charnock's constant albedo of foliage, ground surface albedo high-frequency water-wave spectrum constant free convection constant; stable IBL parameter ratio of entrainment and surface heat fluxes Monin-Obukhov profile constant spectral inertial sub range constants Y Yc Yl, Y2 Yo

yo'

!1 C s 151 bu , b T , Dq Dij

psychrometric constant (c p/A) Zilitinkevich constant of the NBL Monin-Obukhov profile constants; roughness constant (Yl) potential temperature gradient above h lapse-rate correction layer thicknesses in the atmosphere layer thickness in the soil change in property concentration across the nocturnal (surface) inversion change in property concentration across the NBL or stable IBL difference in property concentration between that at h + E and the mixed-layer value change in property concentration across the cloud top depth of viscous sublayer depths of interfacial sublayer Kronecker delta tensor rate of viscous dissipation of TKE; emissivity; height increment emissivity of foliage, ground alternating unit tensor surface emissivity stability parameter,

"

11k 11, 11s 11w

z/ L

unit vector (components 11) Kolmogorov length scale soil volumetric moisture content, saturation value wilting value of soil moisture content potential temperature, virtual potential temperature equivalent potential temperature