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

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

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