microwave radiometer retrievals

COSTES1303TrainingSchool3September2017,Dublin

Ground-basedprofilingnetworksforimprovingweatherforecasts:Microwaveradiometerretrievals

MicrowaveRadiometerRetrievals

Ulrich Löhnert (University of Cologne)

with contributions from Nico Cimini, Susanne Crewell, Harald

Czekala, Thomas Rose,..

Ground-basedprofilingnetworksforimprovingweatherforecasts(COSTES1303TrainingSchool)

EMSWorkshop,3September2017,Dublin



What“products”canweexpectfromMWR?

conHnuousdatainall-skycondiHons:resoluHonofsecondstominutes

path-integratedcloudliquidwater

(mostreliablemethodoverall)

lowresoluHonwatervapor(H)profile,but

excellentpath-integratedvalues

temperature(T)profileofthePBL,lowresoluHonprofile

above

rel.humidity

Measurementfocus:PBL



Microwaveregion:ExHncHon=AbsorpHon

3

InformaFonfromatmosphericthermalemission

Kirchhoff‘slaw:absorpHonisdirectly

proporHonaltoemission(LTE)

àBrightnesstemperaturespectrum



MicrowaveTBspectrumstandardatmosphere

oxygen

watervapor



TB@51–

58GHz

MWRMeasurementsatJOYCE11June2013

TB@22–

31GHz

cloudliquidsignalincreasesstronglywithfrequency

watervaporsignalisstrongestat22GHzlinecenter

stronglytemperaturedependent



ForwardproblemDescribedragon‘strack

Butnow:whataboutthedragonwhenyouonlyknowthetrack?

BernhardMayer,LMUMünchen

Ambiguouscorrectanswers:A,B,CorD??

InverseProblemI

X



Track=Brightnesstemperatures

€

y = F(x,b)+εInverseProblemII

Forwardproblem=RadiaHvetransfer Dragon=

Atmosphere Uncertaintyoftrack

measurementandFSo:whattodoiftheanswerstoour

measurementsareambiguous?



RetrieveonlyalimitednumberofparametersIntegratedWaterVapour(IWV)LiquidWaterPath(LWP)

10kgm-2correspondtoaliquidcolumnof1cm

àbothintegratedcolumnamounts

IWV = ρWV dzz=0

z=TOA

∫

LWP = ρliquid dzz=0

z=TOA

∫



RetrievalofIWVandLWP

IWV=a1+b1*TB24–c1*TB31LWP=a2–b2*TB24+c2*TB31

standardatmosphere

LWP=250gm-2

TBAmplitudeofH2OlineisproporHonaltoIWV

CloudsleadtoaTBincrease,mainlyinwindowchannels

WatervaporleadstoaTBincreasemainlyatH2Oline



StaFsFcalcorrelaFonsTBvs.IWV/LWP

IWV

LWP

clearsky

cloudy

IWV

IWV

IWV LWP

IWV=a1+b1*TB24–c1*TB31LWP=a2–b2*TB24+c2*TB31



IWV&LWPRetrieval



TBHmeseriesofmulHplefrequencychannelsonthe

rightsideofthe22GHzline

Whatabouthumidityprofiles?

Frequency / GHz

TB /

K

more WV contribution from higher levels at line center

relatively higher WV contribution from lower levels at line shoulder

However: contributions in different channels highly correlated



Typical:TBHmeseriesof7frequencychannelsontherightsideofthe22GHzline

WaterVaporWeighHngFuncHons

2-3degreesoffreedomforsignal

Whatabouthumidityprofiles?



ExampleHumidityProfile



TemperatureProfileRetrieval

O2absorpHoncomplex

O2hasaconstantmixingraHowithheightàTBonlyafuncHonoftemperatureand

pressure

Atmospheresaturated(~blackbody)àTemperature

informaHonfromlowerlevels

ThefurtherawayfromtheabsorpHoncomplex

center,themoreinformaHonoriginatesfromhigherlevelsintheatmosphere

cloudy

clear



TemperatureRetrieval

surfacetemperature

Typical:TBHmeseriesof7frequencychannelsontheleb

handsideofthe60GHzabsorpHoncomplex

TB@51–

58GHz



TB@57GHz≈Temp.in100m

Physicaltemperature–TBat57.3GHzcorrelaFon

BrightnessTemperature/K BrightnessTemperature/K

Tempe

rature@

100m

/K

Tempe

rature@

2km/K



TB@55GHz≈Temp.in2km

Physicaltemperature–TBat55GHzcorrelaFon

BrightnessTemperature/K BrightnessTemperature/K

Tempe

rature@

100m

/K

Tempe

rature@

2km/K



19

WhichChannelContributesfromwhichHeights?•  Strongredundancyinallchannels•  HowcantheheightinformaHonbemadevisible?

àWeighHngFuncHons

~3degreesoffreedomforsignal



addiHonaltemperatureprofileinformaHoninopHcallythickcase

MicrowaveradiometerelevaFonscanning

Bri

ghtn

ess

Tem

pera

ture

[K

]

Bri

ghtn

ess

Tem

pera

ture

[K

]

Alt

itud

e [m

]

Alt

itud

e [m

]

Elevation Angle [DEG] Elevation Angle [DEG]

Temperature [K] Temperature [K]

needtoassumehorizontalhomogeneity



ABLDevelopment

20 21 22 23

3 2 1

13

0

6 7

9 11 12

9 8

21



PotenFaltemperatureretrievalPotenHaltemperature

worksalsoincloudycondiHons



RepresentaFvedataset(radiosonde)

ClouddiagnosHcmodel

Atmosphericprofilesp(z),T(z),q(z),LWC(z)

RT-Model

TB(ν)

Inversemodel:e.g.mulHvariateregression,NN

RT-Model

TB(ν)

Algorithm

Training Test

EvaluaHon

RetrievalDesign

T(e.g.@z=1km) T(e.g.@z=1km)

T(z=1km)=a(z)+b(z)·TB1+c(z)·TB12+d(z)·TB2+e(z)·TB22+..



ObservaHons:Brightnesstemperature

TBfromHATPRO

“OpFmalEsFmaFon”

aprioriatmosphericprofile:climatologyormodel

forecast

OpHmizedatmosphericprofile

Isatmosphericprofileconsistentwiththe

observaHons?

+

Needtobegiven:Correlated(!)uncertainHesofTBandaprioriprofile

RepeatiteraFvelyunHlconvergencecriterionismet

AdvancedVariaFonalApproaches



ProfileofthepreviousiteraHon

SoluHonincrement,ifà0convergenceisreached

„Pulls“soluHontowardsaprioriprofile;howstronglyisdeterminedthroughweighHngwithSa-1

MakessoluHonphysicallyconsistentwithobservaHon;howstronglyisdeterminedthroughweighHngwithSe-1,KTtransformsfromytoxspace

WeighHngofthewholesoluHonupdatebyweighHngwiththesumofobservaHonandaprioriuncertainty

IftheerrorsofobservaHonandaprioriareesHmatedcorrectly,thediagonalcomponentsofSwillgivetheexpectedrandomerrorateachheight

( ) ( )11 1 1 1

1 ( ) ( )T Ti i a i i i a i aFε ε

−− − − −+

⎡ ⎤= + + − − −⎣ ⎦ix x S K S K K S y x S x x

18.Juni201225

OpFmalEsFmaFonEquaFons

y:ObservaHonvector(TB)F:Forwardmodel(radiaHvetransferoperator)K:Jacobian(∂F/∂x)xa:aprioriprofileSε:ErrorcovariancematrixSa:aprioricovariancematrixS:ErrorcovariancesoluHon

Updatedprofile

S−1 = Sa−1 +K i

TSε−1K i( )



TowhatwouldyouinvertthisK-bandsignal?

Thank’sforyouakenFon!

microwave radiometer retrievals

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