Hydrologie continentale ressources eau Tworequirements...
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Bloc 1. Hydrologie quantitative 1. Introduction: water cycles on Earth 2. Water in the atmosphere 3. Evapotranspiration 3.1 Introduction 3.2 Turbulent fluxes in the ABL 3.3 From turbulence to aerodynamic resistance 3.4 Aerodynamic methods 3.5 The Earth’s energy balance 3.6 Formulations related to the energy budget M1 SDE ‐ MEC558 Hydrologie continentale et ressources en eau Continental Hydrology and Water Resources 2 Two requirements for evaporation from natural surfaces 3.1 Introduction Figure 3.1 Brutsaert, p118 1. Energy supply 2. Escape mecanism = turbulence 3 3.2 Turbulent fluxes in the ABL Fluid mechanics In a fluid in motion along a surface, a boundary layer is the layer of fluid in the immediate vicinity of the surface where the effects of friction are significant. In particular, velocity is zero at the surface. A boundary layer can be either laminar or turbulent (cf Reynolds number) Garratt (1992). The atmospheric boundary layer. In the atmospheric context, it has never been easy to define precisely what the boundary layer is. Nevertheless a useful working definition identifies the boundary layer as the layer of air directly above the Earth’s surface in which the effects of the surface (friction, heating and cooling) are felt directly on time scales less than a day, and in which significant fluxes of momentum, heat or matter are carried by turbulent motion on a scale of the order of the depth of the boundary layer or less. The atmospheric boundary layer 4 Outer layer / couche d’Ekman : vent en spirale par équilibre entre gradient de pression, force de Coriolis et friction Couche de surface : direction du vent constante + profils logarithmiques de vitesse Couche “rugueuse” : où la vitesse tend vers 0 : u(z 0 )=0 Si H 1.5 km ( 850 mb) : 0.1H 150 m 0.01H ‐ 0.001H 15 ‐ 1.5 m 0,01H 0,001H 3.2 Turbulent fluxes in the ABL Vertical structure of the ABL 5
Transcript of Hydrologie continentale ressources eau Tworequirements...
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Bloc1.Hydrologiequantitative
1. Introduction:watercyclesonEarth2. Waterintheatmosphere3. Evapotranspiration
3.1 Introduction3.2 TurbulentfluxesintheABL3.3 Fromturbulencetoaerodynamicresistance3.4 Aerodynamicmethods3.5 TheEarthsenergybalance3.6 Formulationsrelatedtotheenergybudget
M1SDEMEC558Hydrologiecontinentaleetressourceseneau
ContinentalHydrology andWaterResources
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Two requirements forevaporation from natural surfaces
3.1 Introduction Figure3.1
Brutsaert,p118
1.Energy supply
2.Escapemecanism =turbulence
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3.2 TurbulentfluxesintheABL
Fluidmechanics
Inafluidinmotionalongasurface,aboundarylayeristhelayeroffluidintheimmediatevicinityofthesurfacewheretheeffectsoffrictionaresignificant.Inparticular,velocityiszeroatthesurface.
Aboundarylayercanbeeitherlaminarorturbulent(cf Reynoldsnumber)
Garratt(1992).Theatmosphericboundarylayer.
Intheatmosphericcontext,ithasneverbeeneasytodefinepreciselywhattheboundarylayeris.
NeverthelessausefulworkingdefinitionidentifiestheboundarylayerasthelayerofairdirectlyabovetheEarthssurfaceinwhichtheeffectsofthesurface(friction,heatingandcooling)arefeltdirectlyontimescaleslessthanaday,andinwhichsignificantfluxesofmomentum,heatormatterarecarriedbyturbulentmotiononascaleoftheorderofthedepthoftheboundarylayerorless.
Theatmospheric boundary layer
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Outerlayer/couche dEkman :ventenspirale parquilibre entregradientdepression,forcedeCoriolis etfriction
Couche desurface:directionduventconstante +profils logarithmiques devitesse
Couche rugueuse:o lavitesse tendvers 0:u(z0)=0
SiH 1.5km( 850mb):0.1H 150m0.01H 0.001H 15 1.5m
0,01H0,001H
3.2 TurbulentfluxesintheABL
VerticalstructureoftheABL
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3.2 TurbulentfluxesintheABL
Surfacelayer thehorizontalscales ofairflowarelarger thantheverticalones
Roughnesslayer
Brutsaert p38
Figure3.2
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3.2 TurbulentfluxesintheABL Figure3.3
Reynoldsdecomposition
Mean over15minto1h,fluctuationat much higher frequency
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Convectivetransportofwatervapor is :
Reynoldsdecomposition applies toqandthewind speedcomponents.After timeaveraging (inthesense ofReynolds):
ABL:scales ofatmospheric flowandmean velocities arelarger along thehorizontal
Assuming uniform source/sink at thesurface,concentrationsmostly changealongtheverticalandcan be assumed constantinthehorizontaldirection
3.2 TurbulentfluxesintheABL
Interesting consequences from turbulence
transportbymean flow transportbyturbulence
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3.2 TurbulentfluxesintheABL
Surfaceturbulentfluxes
Onaccount ofcontinuity overauniform surface,theverticalfluxesmustbe constantwith z
Surface=source
Surface=sink
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3.2 TurbulentfluxesintheABL
Thelandsurfaceis asink forhorizontalmomentum (mu)
0 :shear stressat thesurface[kgm1 s2]
u* :frictionvelocity[ms1]
u*depends on fluidviscosity surfaceroughness meanhorizontalvelocity
Figure3.4
Dingman p59310
Horizontalmomentum inneutral conditions
3.3 From turbulencetoaerodynamic resistance
Figure3.5
Guyotp83z0=roughness length =valeurdezou(z)=0(parextrapolation)
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Turbulenceclosure anddimensional analysis
3.3 From turbulencetoaerodynamic resistance Figure3.5
Stull,1988.AnIntroductiontoBoundaryLayerMeteorology
When theempirical dataareplotted ongraphsofonedimensionless groupversusanother,often datafrom many disparatemeteorological conditionswill result inonecommon curve,yielding asimilarity relationship that maybe universal.
Dimensional analysis hasbeenused extensively andsuccessfully instudiesoftheatmospheric boundary layer,where turbulenceprecludes othermoreprecise descriptionsoftheflowbecause exactsolutionsoftheequations ofmotionareimpossibletofind duetotheclosure problem.
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Horizontalmomentum inneutral conditions
Lesdiffrentescourbescorrespondentdesvitessesmoyennesdiffrentespourunealtitudedonne,i.e.desu*diffrentes
Elmentsdesimilarit: relationssemilog pente=k/u* z0(liausite)
3.3 From turbulencetoaerodynamic resistance Figure3.6
Guyotp8413
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Roughness length z0
3.3 From turbulencetoaerodynamic resistance Figure3.7
Brutsaert p4514
Mean qprofileinneutral conditions
3.3 From turbulencetoaerodynamic resistance
Dimensional analysis
Brutsaert p45
WARNING:z0v
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Eddycovariance
3.4 Aerodynamic methods
wandqaremeasured at thesame place,at very highfrequency >510Hz
Sonic anemometers Infrared hygrometers
Figure3.11
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Eddycovariance
3.4 Aerodynamic methods
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Toursdeflux
3.4 Aerodynamic methods
Bulk method
Cd,Ce,Ch pourleshauteursdemesurez1etz2(sachantz0,z0v,z0h,oupas)
Mesures:u(z1),q(z2)etT(z2)+T0andq0 Surtoututilissurlesocansetlacryosphre
Mesuresatmosphriques1niveauviades dragcoefficients constants:
=
Figure3.12
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Thegoalis toestimate E
We start from theaerodynamic equation
We assumewe knowra andq(z) theunknown is q0
Theprinciple is torelateq0 toqs(T0)
1. Thisis trivialforsaturated surface!
Inthis case,we speak ofevaporation at potential rate
2.Evaporationfrom soils
Introductionofasoil resistance,which depends onsoil moisture
3.4 Aerodynamic methods
Resistance models fordifferent surfaceconditions
(
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Transpirationfrom leaves andstomatal resistance
Evaporationoffreewater
Transpirationfrom oneleaf
Structureofonestomata
3.4 Aerodynamic methods Figure3.13
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Stomatal conductance asafunction ofenvironmental conditions
3.4 Aerodynamic methods Figure3.14
Guyotp127VPD=es(Ta)ea23
3.4 Aerodynamic methods
Complex canopy
LAI=Leaf AreaIndex=If=Ratiooftotalprojectedleafarea(onesideonly)perunitgroundarea
Transpirationinparallelfromdifferentleaflayers Solarradiationisattenuatedbythecanopy
Figure3.15
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SVAT(SoilVegetationAtmosphere Transfers)models
3.4 Aerodynamic methods Figure3.16
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BilandnergiemoyendusystmeTerre
Mars 2000 Mars 2004, valeurs en W/m (Trenberth et al., 2009)
3.5TheEarths energy balance Figure3.17
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Solar andterrestrial radiation
Wiendisplacement law :thewavelength ofradiationemitted byablackbodyis inversely proportional toits absolute temperature
3.5TheEarths energy balance
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3.5TheEarths energy balance
Bilanradiatifensurface
Albdo(sansunit)
Limonsilteux sec 0,23Limonargileuxsec 0,18Limonargileuxhumide 0,11
Herbe/Gazon/Crops 0,150,25Fort 0,050,20
Eau 0,030,1Neige 0,70,95
MoraineduglacierZongoBolivie,Andes,Alti=5200m
(Gascoin etal.,2009)VWC=volumetric watercontent
Figure3.18
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Annualmeannetsurfaceradiation calculatedfromtheECMWF40yearreanalysis.UnitsareW/m2.
FromKallberg etal2005.ERA40Atlas,ECMWF.
3.5TheEarths energy balance
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Enrgimestationnaire(quilibre)ousiestassezpetit:
Gpeutsouventtrengligdevantlesautrestermes:
Bilandnergiedunecouchedesurface
Bilanradiatifdelasurface:
Tempraturedunecouchedesurfacedpaisseur
3.5TheEarths energy balance
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Rledel'eaudanslebilandnergiemoyendusystmeTerre
LEdissipates50%ofabsorbedsolarradiation,and80%ofnetradiationatthesurface(usingvaluesfromFigure3.2)
LEH
3.5TheEarths energy balance
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Saturated surfaces
3.6 Formulationsrelated totheenergy budget
Radiativecontrol
Aerodynamiccontrol
ThePenman equation hasbeencalibrated forboth: freewater saturated vegetation covers :MtoFrancehaslongused the
Penman equation tocalculate thereference ET,ET032
Importantdfinitions
3.6 Formulationsrelated totheenergy budget
PotentialevaporationEvaporationfromalargeuniformsurfacethatissufficientlywetsothattheairissaturatedatthesurface(ex:freewater,soilorvegetationcoverafterarainshower).Thisquantitydoesnotdependonthesoil/vegetationcharacteristics,apartfromtheirroughnessandalbedo,thuscorrespondstotheconceptofclimaticevaporationdemand.
PotentialET(Thornthwaite,1948)MaximumETfromalargeareacoveredcompletelyanduniformlybyanactivelygrowingvegetationwithanonlimitingsoilmoisturesupply
ReferenceET=ET0Idem,butforareferencegrass,withspecificproperties:height=0.12m,albedo=0.23,rc =70s/m(=rcmin asthereisnostress)
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ReferenceET
ThePenmanMonteith equation can be used for: unstressed reference grass (r0 =70s/m)=>ET0(FAOrecommendation) unstressed vegetation stressed vegetation using theadequate setofresistances
3.6 Formulationsrelated totheenergy budget
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From theunstressed reference grass togeneric vegetation covers
3.6 Formulationsrelated totheenergy budget Figure3.19
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Actual ET
3.4 Formulationsrelated totheenergy budget
Figure3.20
Stressfactorasafunction ofasoil moisture index
TheeffectofKc andtheenvironmentalstressesonETc canalsobedescribedbyappropriateresistanceformulationswithinthePenmanMonteith equation.
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Actual ET
3.4 Formulationsrelated totheenergy budget Figure3.20
TheeffectofKc andtheenvironmentalstressesonETc canalsobedescribedbyappropriateresistanceformulationswithinthePenmanMonteith equation. 37
Stressfactorasafunction ofsoil moisture
with < 1
Stressed ET
Unstressed ET
