AMeteorologicalDistribu1onSystemforHigh‐Resolu1on

TerrestrialModeling

(MicroMet)

AgeelIbrahimBushara

Introduc1on•  Quasi‐physicallybasedmeteorologicalmodelforhighresolu1on

(e.g.,30m‐1‐km)

•  FivevariabletouseMicroMet:Precipita1on,RH,airTemperature,WindSpeedandwinddirec1onateach1mestep,inornearthebasin

•  Forincomingsolarandlongwaveradia1ons,andsurfacepressure:MicroMetusesitssubmodelstogeneratedistribu1ons,orcreatedistribu1onsfromobserva1onsaspartofdataassimila1on

•  MicroMetpreprocessor:iden1fiesandcorrectspoten1aldeficienciesandfillsmissingdata;autorregressivemovingaverage

•  Spa1alinterpola1onusingBarnesschemeandsubsequentcorrec1onsforinterpolatedfieldsusingTemperature‐eleva1on,wind‐topography,humidity‐cloudinessandradia1on‐cloud‐topographyrela1onships.

Preprocessor

•  Meteorologicalvariablesconvertedtoacommonheight

•  Fillsvariablesofmissingdateswithundefinevalues(‐999)•  SeriesofQualityAssurance(QA):

 Checkforvaluesoutsideacceptablerange Seeksconsecu1vevaluesthatexceedsacceptableincrement

 Findconstantconsecu1vevalueswithnoobservechangewithin1melimit

•  Fillsmissing1meseriesdatawithcalculatedvalues

A)Spa1alInterpola1on(Barnes,1964)•  BarnesappliedGaussiandistance‐dependentweighingfunc1on

(1)

r,distancebetweenobserva1onandgridpoint,f(dn),filterparametersmoothinginterpolatedfield

•  Bernesappliestwosuccessivecorrec1ons:•  1)usingEq.1,assignvaluesforallgrids•  2)Decreasinginfluenceradius,residuals,differencecorrec1on

addedtofirst‐passfield

•  MicroMetcanextrapolatedatatovalleysormountainousregions

MicroMetModel

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w = exp[− r2

f (dn)]

B)MeteorologicalVariables

•  Todistributeairtemperatureassumingneutralatmosphericstabilityanddefiningvaryingairtemperaturelapserate(oruserdefined)

•  Sta1ontemperatureadjustedtoacommonlevel:

(2)•  Referencesta1onsusedtointerpolategridsusingBarnesscheme

•  Griddedtopographydatausedtoadjustreferencelevelgriddedtemperaturetotopographiceleva1ondatausing:

(3)

MicroMetModel

1)AirTemperature

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T0 = Tstn −Γ(z0 − zstn )

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T = T0 −Γ(z − z0)

B)MeteorologicalVariables

•  RHisnonlinearofeleva1on,rela1velylineardewpoint(Td)temperatureusedforeleva1onadjustment

•  Convertsta1onRHtoTd(0C)usingairtemperatureT(0C):

(4)

(5)•  Fromequa1on5,weget(e),thenTd(0C)canbecalculated:

(6)

MicroMetModel

2)Rela1veHumidity

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es = aexp( bTc + T

)

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RH =ees

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Td =c ln(e /a)b − ln(e /a)

•  Tdforallsta1onsadjustedtocommonlevelusingEq.2;temperatureisTdtemperatureanddewpointtemperturelapserate,lambda(m‐1)isvaporpressurecoefficient(Table1)

(7)

•  UsingBarnesscheme,referenceleveldewpointtemperaturesinterpolatedtomodelgrid

•  Eq.3isusedtoobtainTdforeacheleva1on•  GriddedTdconvertedtoRHusingEqs.(4)and(5)

2)Rela1veHumiditycont’

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Γd = λ cb

WindSpeedandDirec1on•  Windspeed(W)convertedtozonal,u,andmeridional,v:

(8) (9)

•  uandvinterpolatedformodelgridusingBarnesscheme•  Resul1ngvaluesconvertedbacktowindspeedanddirec1on (10)

(11)•  Griddedwindspeed&direc1onmodifiedtoaccounttopography

(12)

(13)

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u = −W sinθ

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u = −W cosθ

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W = u2 + v 2

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θ =3π2− tan−1(v

u)

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β = tan−1 ∂z∂x

2

+∂z∂y

2

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ξ =3π2− tan−1

∂z∂y

∂z∂x

WindSpeedandDirec1on•  Curvaturecomputedforeachgriddefiningcurvatureradiusη(m):

(14)

•  Slopeindirec1onofwindΩs: (15)

•  ΩcandΩsarescaledto(‐0.5and0.5)•  WindweighingfactorWwusedtomodifywindspeed

(16)

•  Ωc+Ωs=1,Wwtobebetween0.5and1.5

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Ωc =14

z − 12 (zW + zE )2η

+z − 12 (zS + zN )

2η+

z − 12 (zSW + zZE )2 2η

+z − 12 (zNW + zSE )

2 2η

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Ωs = β cos(θ −ξ)

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Ww =1+ γ sΩs + γ cΩc

WindSpeedandDirec1on

•  Terrainmodifiedwindspeedin(m/s):

(17)

•  Winddirec1onsmodifiedbydiver1ngfactorθd:

(18)

•  Terrainmodifiedwinddirec1on:

(16)

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Wt =WwW

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θt = θ + θd€

θd = −0.5Ωs sin 2 ξ −θ( )[ ]

4)Solarradia1on•  RH700calculatedusingEqs.1,2,4and5.Tocalculatecloudcover:

(20)

•  Solarradia1onstrikingearth’ssurface:

(21)

(22)

•  Φla1tude,ζhouranglefromlocalsolarnoon,Zsolarzenithangle

(23)hhouroftheday,δsolardeclina1onanglegivenby:

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σ c = 0.832exp RH700 −10041.6

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Qsi = S ψdir cosi +ψdif cosZ[ ]

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cosZ = sinδ sinφ + cosδcosφ sinτ

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τ = πh −1212

4)Solarradia1on (24)

•  ΦTSolarla1tudeoftropicCancer,ddayoftheyear,drdayofthesummersols1ce,dynumberofdaysinayear

(25)

•  Solarazimuthwithsouthhavingzeroazimuth:

(26)

•  Toaccountforscapering,absorp1onandreflec1onofsolarbycloud,solarradia1onisscaledby:

(27)

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δ = φT cos 2πd − drdy

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cosi = cosβ cosZ + sinβ sinZ cos(µ −ξ s)

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µ = sin cosδ sinτsinZ

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ψdir = (0.6 − 0.2cosZ)(1−σ c )

4)Solarradia1oncont

(28)•  Ifobserva1onsavailable,thedifferencebetweenmodeland

observa1oniscomputed,andspa1allydistributedusingBarnesscheme

•  Abovedifferenceaddedtomodelhavingfinalspa1allydistributedsolarradia1ons(dataassimila1on)

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ψdif = (0.3− 0.1cosZ)σ c

5)Longwaveradia1on•  Incominglongwaveradia1oncalculatedconsideringcloudand

eleva1onrelatedvaria1ons:

(29)•  Atmosphereemissivity,ε,isgivenby:

(30)

z<200

200≤z≤3000

3000<z

(31)•  Itusesdataassimila1ontechniqueasforsolarradia1on

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Qli = εσT 4

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ε = k 1+ Zsσ c2( ) 1− Xs exp(−Yse /T)[ ]

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Cs = C1

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Cs = C2

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Cs = C1 + (z − z1)(C2 −C1z2 − z1

)

6)Surfacepressure•  Inabsenceofobserva1ons,pressureisgivenby:

(32)

•  P0sealevelpressure(101.3KPa),Hisscaleheightofatmosphere(about8000m)

•  Ifobserva1onsavailabletheycanbecombinedwithsurfacepressuremodelaspartofdataassimila1on

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p = p0 exp(−zH)

7)Precipita1on•  Observedprecipita1ondistributedinthedomainusingBarnes

scheme

•  Togeneratetopographicreferencesurface,sta1onseleva1onsalsointerpolatedtomodelgrid

•  Precipita1onadjustmentfunc1onisnonlinearfunc1onofeleva1ondifference

•  Modelledliquidwaterprecipita1onratecomputedusing:

(33)

•  P0interpolatedsta1onprecipita1on,z0isinterpolatedsta1oneleva1onsurface,✗(Km‐1)isafactorisdefinedtovaryseasonally(Table1)

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p = p01+ χ(z − z0)1− χ(z − z0)

ShortcomingsNofeedbacksbetweenthelandandatmosphereforcalcula1onof

nearsurfaceatmosphericcondi1ons

•  Nosurfaceenergybalance

شكرا

Annex