Fundamentals of boundary-layer meteorology

260 Pages·2018·4.51 MB·English

by  Lee

Springer Atmospheric Sciences
Xuhui Lee
Fundamentals
of Boundary-
Layer
Meteorology
Springer Atmospheric Sciences
Moreinformationaboutthisseriesathttp://www.springer.com/series/10176
Xuhui Lee
Fundamentals of
Boundary-Layer
Meteorology
123
XuhuiLee
SchoolofForestryandEnvironmentalStudies
YaleUniversity
NewHaven,Connecticut,USA
ISSN2194-5217 ISSN2194-5225 (electronic)
SpringerAtmosphericSciences
ISBN978-3-319-60851-8 ISBN978-3-319-60853-2 (eBook)
DOI10.1007/978-3-319-60853-2
LibraryofCongressControlNumber:2017948647
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Acknowledgments
I wish to thank the following colleagues for their review of the manuscript: Brian
Amiro (Chap.4), Don Aylor (Chap.5), Dennis Baldocchi (Chap.8), Rob Clement
(Chap.3), Tim Griffis (Chaps.1, 2, 10 and 11), Bill Massman (Chaps.2 and 9),
HaPeSchmid(Chap.7),NatalieSchultz(Chaps.1,7and10),JielunSun(Chap.6),
andLeiZhao(Chap.10).ThanksalsogotoChangCao,ChengHu,ChengLiu,and
ZhenZhangfortheirbeta-testingoftheproblemsets.
YaleUniversity XuhuiLee
December2016
v
Contents
1 Introduction................................................................. 1
1.1 Boundary-LayerMeteorology....................................... 1
1.2 ApplicationTopics ................................................... 4
1.3 StructureofThisBook............................................... 8
1.4 HowtoUseThisBook............................................... 9
2 FundamentalEquations ................................................... 11
2.1 CoordinateSystems.................................................. 11
2.2 PrincipleofMomentumConservation .............................. 12
2.3 ConservationofMass................................................ 15
2.4 ConservationofEnergy.............................................. 18
2.5 TheIdealGasLaw ................................................... 20
2.6 TheSurfaceEnergyBalance......................................... 22
2.7 Problems.............................................................. 25
References.................................................................... 27
3 GoverningEquationsforMeanQuantities.............................. 29
3.1 ReynoldsDecomposition ............................................ 29
3.2 FlowIncompressibility............................................... 33
3.3 The Mean Equations for Velocity, Mixing Ratio,
andPotentialTemperature........................................... 35
3.4 SimplifiedOne-DimensionalEquations............................. 37
3.5 TheClosureProblem................................................. 40
3.6 QuantifyingEddyFluxes ............................................ 45
3.7 Problems.............................................................. 51
References.................................................................... 56
4 GenerationandMaintenanceofAtmosphericTurbulence ............ 57
4.1 EnergyPoolsandEnergyTransfers................................. 57
4.2 BudgetoftheMeanFlowKineticEnergy .......................... 60
4.3 BudgetoftheTurbulentKineticEnergy ............................ 64
vii
viii Contents
4.4 AirStability........................................................... 68
4.5 Problems.............................................................. 75
References.................................................................... 79
5 FlowinPlantCanopies..................................................... 81
5.1 CanopyMorphology ................................................. 81
5.2 CanopyVolumeAveraging .......................................... 82
5.3 TheMeanMomentumEquations.................................... 85
5.4 AnalyticalWindProfilesintheCanopy............................. 87
5.5 BudgetsofMeanFlowandTurbulentKineticEnergy ............. 89
5.6 ShearInstabilityandTransitiontoTurbulence ..................... 91
5.7 Problems.............................................................. 97
References.................................................................... 100
6 BalanceofForcesintheAtmosphericBoundaryLayer................ 101
6.1 AtmosphericLayers.................................................. 101
6.2 BalanceofForcesinNeutralandConvectiveConditions.......... 107
6.3 BalanceofForcesinStableConditions............................. 110
6.4 Problems.............................................................. 116
References.................................................................... 119
7 TracerDiffusionintheLowerBoundaryLayer ........................ 121
7.1 BasicConstraints..................................................... 121
7.2 Point-SourceDiffusioninHomogeneousTurbulence.............. 124
7.3 Gaussian Plume Model for Elevated Sources
intheBoundaryLayer ............................................... 129
7.4 DiffusionfromGround-LevelSources.............................. 132
7.5 DiffusioninPlantCanopies.......................................... 136
7.6 FootprintTheory ..................................................... 138
7.7 Problems.............................................................. 145
References.................................................................... 148
8 PrincipleofEddyCovariance............................................. 149
8.1 Introduction........................................................... 149
8.2 TheCanopySourceTerm............................................ 150
8.3 TheConceptofNetEcosystemExchange.......................... 153
8.4 TheChamberMethod................................................ 154
8.5 TheEddyCovarianceControlVolume.............................. 156
8.6 EddyCovarianceinAdvection-FreeConditions.................... 160
8.7 VerticalAdvection.................................................... 161
8.8 HorizontalAdvection ................................................ 166
8.9 PracticalConsiderations ............................................. 168
8.10 Problems.............................................................. 169
References.................................................................... 173
Contents ix
9 DensityEffectsonFluxMeasurements .................................. 175
9.1 DensityEffects ....................................................... 175
9.2 DensityCorrectionstoEddyCovarianceFluxes.................... 176
9.3 DensityEffectsonFlux-GradientRelation ......................... 181
9.4 DensityCorrectionstoChamberFluxes ............................ 184
9.5 Problems.............................................................. 186
References.................................................................... 189
10 EnergyBalance,Evaporation,andSurfaceTemperature ............. 191
10.1 ResistanceAnalogyforLeaf-ScaleFluxes.......................... 191
10.2 CanopyEnergyBalanceandtheBig-LeafModel.................. 195
10.3 One-SourceModelinRemoteSensingApplications............... 198
10.4 Two-SourceModelofEvaporation.................................. 200
10.5 ImprovedRepresentationsofSurface-AirExchange............... 203
10.6 One-SourceModelofSurfaceTemperature ........................ 205
10.7 Problems.............................................................. 210
References.................................................................... 213
11 Budgets of Heat, Water Vapor, and Trace Gases
intheAtmosphericBoundaryLayer..................................... 215
11.1 Introduction........................................................... 215
11.2 TheSlabApproximationoftheConvectiveBoundaryLayer...... 216
11.3 Boundary-LayerGrowthandEntrainment.......................... 219
11.4 HeatBudgetintheConvectiveBoundaryLayer.................... 227
11.5 CarbonDioxideBudgetintheConvectiveBoundaryLayer....... 229
11.6 WaterVaporBudgetintheConvectiveBoundaryLayer........... 232
11.7 TraceGasesintheNighttimeStableBoundaryLayer.............. 233
11.8 TheEquilibriumBoundaryLayer ................................... 235
11.9 Problems.............................................................. 238
References.................................................................... 242
SymbolsandConstants.......................................................... 243
Index............................................................................... 251
Chapter 1
Introduction
1.1 Boundary-LayerMeteorology
Boundary-layermeteorology,asubdisciplineofmeteorology,isconcernedwiththe
stateofandprocessesintheairlayerinimmediatecontactwiththeEarth’ssurface.
Thisairlayer,about1kminthicknessandtermedtheatmosphericboundarylayer
(Fig.1.1), is the interface between the free atmosphere and the Earth’s surface,
whichcanbelandecosystems,lakes,icefields,ortheoceans.Fromtheatmospheric
perspective, the boundary layer is the lower boundary of large-scale atmospheric
flows.From thebiospheric perspective, conditions intheboundary layer imposea
top-downinfluenceonecosystemfunctions.
The boundary layer’s physical state is described with variables such as tem-
perature, humidity, pressure, and wind, and its chemical state with variables that
measure the abundance of trace gases such as carbon dioxide and air pollutants.
The physical state variables are tightly related to the dynamic aspects (level of
turbulence, diffusion efficiency, and air stability) of the boundary layer, whereas
the chemical state variables, except aerosols, are passive scalars that have no
direct dynamic consequences. Changes in boundary-layer state are controlled by
processesthattransfermomentum,energy,andmaterialswithintheboundarylayer
andbetweentheboundarylayerandthesurfacebeloworthefreeatmospherealoft.
Fluxvariablesareusedtoquantifytherateofthesetransferprocesses.Animportant
goalofboundary-layermeteorologyistostudytherelationshipsbetweenthestate
andtheprocessvariables.
Radiation energy exchange with the surface is a key process that regulates the
physical and chemical state of the boundary layer. In cloud-free conditions, the
boundary layer is basically transparent to solar radiation. Absorption, reflection,
andemissionoftheradiationenergyoccuronlyatthesurface.Absorptionofsolar
radiation by the Earth’s surface in daylight hours warms the boundary layer, and
loss of longwave radiation at night cools it. Solar radiation supplies energy for
evapotranspiration, the process in which liquid water is lost to the atmosphere
©SpringerInternationalPublishingAG2018 1
X.Lee,FundamentalsofBoundary-LayerMeteorology,
SpringerAtmosphericSciences,DOI10.1007/978-3-319-60853-2_1