Adaptivelocalizationforsatelliteradianceobservationsinanensemble
Kalman filter
LiliLei1 ,JeffWhitaker2,andJeffAnderson31NanjingUniversity2NOAA/ESRL/PSD
3NCAR/CISL/IMAGe
NANJING UNIVERSITY
The8th EnKF Workshop
Motivation(1)
• Assimilationofsatelliteradianceshasbeenproventohavepositiveimpactsontheforecastskill,especiallyforregionswithsparseconventionalobservations.
• LocalizationisanessentialcomponenttoeffectivelyassimilatesatelliteradiancesinensembleKalmanfilterswithaffordableensemblesizes.
• Butlocalizingtheimpactofradianceobservationsisnotstraightforward,sincesatelliteradiancesareintegralobservationswhoselocationanddistancearenotwelldefinedinthevertical.
Motivation(2)
• Anadaptiveglobalgroupfilter(GGF)wasproposedbyuseofclimatologicalensemblestoprovidetheoreticalestimateofverticallocalizationfunctionsfortheAMSU-Aradianceobservations(Leietal.2016).
• Twoquestionsremain:– Canthelocalizationfunctionbeestimatedadaptivelyalongwiththeassimilation?
– Cantheadaptivelocalizationbeappliedtoeveryobservationtypethatareassimilated?
GlobalGroupFilter(GGF)
4
Collectingensemblepriorsofobservationsandstatevariablesinanassimilationcycle
- DefineYo asthesetofallensemblepriorestimatesforonetypeofobservations(e.g.,NOAA-15AMSU-Achannel6).
- DefineXv asthesetofonekindofstatevariables(e.g.,temperature)thatareinterpolatedtothehorizontallocationsofobservations.
∈Yo ={yl,n} l {1,…,L},n {1,…,N}∈
L isthetotalnumberofobservationsofthisgiventype,andN istheensemblesize
Xv ={ } k {1,…,K}∈ K isthenumberofmodelverticallevelsxl,nk
GlobalGroupFilter(GGF)
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- Ateachverticallevelk,thesamplecorrelationsbetweentheobservationsandstatevariablescanbecomputed by
- RandomlysubsetthesamplecorrelationstoG groups,andtherearrangedsamplecorrelationsby ,g {1,…,G} and m {1,…,M},whereM issamplesize
theoverbardenotestheensemblemean
rlk =
xl ,nk − xl
k( ) yl ,n − yl( )n=1
N
∑
xl ,nk − xl
k( )2n=1
N
∑ yl ,n − yl( )2n=1
N
∑
rlk
rm,gk ∈
∈
GlobalGroupFilter(GGF)
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- Thelocalizationvaluek formodellevelk isdefinedtominimizethesamplingerrorofthesamplecorrelations,whichgives
- Aftercomputingk foreachmodelverticallevelk,anadaptiveverticallocalizationfunction(GGF)foragivenobservationtypeandstatevariablekindisobtained.
α
α k =
rm,gk
g=1
G
∑⎛
⎝⎜⎞
⎠⎟
2
m=1
M
∑ rm,gk( )2
g=1
G
∑m=1
M
∑ −1
G−1
α
GGFofNOAA-18AMSU-Achannel7withtemperature
GGFofNOAA-18AMSU-Achannel7withtemperature
,observationverticallocation,wheremaximummeancorrelationoccurs
pvo
,localizationwidth ofthefittedGCfunctiontotheGGFcvo
,GGFlocalizationvalueat,whichgivesthemaximumofGCfunction
lmaxvo
pvo
GGFsofNOAA-18AMSU-Achannel7
Thethreelocalizationparametersthatgivesthelargestmeansamplecorrelationareused.
GGFsofMetOp-BMHSchannel4
ThethreelocalizationparametersfromtheGGFwithstatevariablehumidityareused.
ExperimentalDesign• Ensembleassimilationexperimentswith80ensemble
membersareconductedusingtheNCEPGlobalForecastSystem(GFS)modelwitharesolutionT254L64.
• AllradianceobservationsthatareusedintheNCEPGlobalDataAssimilationSystem(GDAS)areassimilatedevery6h.
• Thegridpoint statisticalinterpolation(GSI)isusedtocomputetheobservationpriorsfortheensemblemeanandeachensemblemember.Thebiascorrectionisadaptedfromanexperimentassimilatingbothconventionalandradianceobservations.
• TheobservationerrorvarianceR usesthesamevaluesasintheNCEPGDAS.
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ExperimentalDesign• Theensemblesquarerootfilter(EnSRF)intheNOAA
operationalEnKF isusedtoassimilatetheobservations.• Multiplicativecovarianceinflationthatrelaxesposterior
ensemblespreadbacktopriorensemblespreadisusedwithrelaxationcoefficient0.85.
• Duringmodelintegration,stochasticphysicsareusedtorepresentthemodeluncertainty.Noadditiveinflationisapplied.
• HorizontallocalizationusestheGClocalizationfunctionthattaperstheobservationimpactto0at1250km.
• VerticallocalizationusestheGClocalizationfunctionwithagivenlocalizationwidth(defaultvalueis1.5(ln(hPa))oradaptivelyestimatedlocalizationparameters.
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Channels0 2 4 6 8 10 12 14 16
p vo
0
500
1000
1500
Channels0 2 4 6 8 10 12 14 16
c vo
0
2
4
6
Channels0 2 4 6 8 10 12 14 16
lmax
vo
0.2
0.4
0.6
0.8
1
Adaptivelyestimatedlocalizationparams.forAMSU-A
Theestimatedlocalizationparametersvaryamongthechannels.
Theygenerallyagreewitheachotheramongdifferentsatelliteplatforms.
Channels0 1 2 3 4 5 6
p vo
200
400
600
800
1000
Channels0 1 2 3 4 5 6
c vo
0.6
0.8
1
1.2
1.4
1.6
Channels0 1 2 3 4 5 6
lmax
vo
0.3
0.4
0.5
0.6
0.7
0.8
Adaptivelyestimatedlocalizationparams.forMHS
TheestimatedlocalizationwidthandmaximumlocalizationvalueforMHSradianceobservationsaregenerallysmallerthanthoseforAMSU-Aradianceobservations.
cvo
lmaxvo
Channels0 2 4 6 8 10 12 14 16
p vo
0
200
400
600
800
1000
Channels0 2 4 6 8 10 12 14 16
c vo
0
2
4
6
Channels0 2 4 6 8 10 12 14 16
lmax
vo
0.4
0.6
0.8
1
Adaptivelyestimatedlocalizationparams.forHIRS/4
TheresultsfromtheinfraredsounderHIRS/4onboardMetOp-AareconsistentwiththosefrommicrowavesoundersAMSU-AandMHS.
Therefore,thethreelocalizationparameterscanbeadaptivelyestimatedforeachchannelofbothmicrowaveandinfraredsounders.
6-hpriorsverifiedrelativetoconventionalobservations
EnKF-GGFa:usestheestimatedlocalizationwidthEnKF-GGFb:usesandtheestimatedobs.verticallocationEnKF-GGFc:uses,,andthemaximumGCvalue
cvo
pvo
cvo
cvo
pvo
lmaxvo
6-hpriorsverifiedrelativetoconventionalobservations
ExperimentGGFb producesverysimilarresultstoexperimentEnKF-GC3.0thatistheoptimalGCwidth.ExperimentGGFb doesnotrequireadditionalcomputationalcosttotunethebestGCwidth.
Conclusions• Aglobalgroupfilter(GGF)isusedtoadaptivelyestimatethe
verticallocalizationfunctionforradianceobservations.UsingaGCfunctiontfittheGGF,threelocalizationparameters,observationverticallocation,localizationwidth ,andmaximumlocalizationvalue,areobtained.
• Theselocalizationparameterscanbeadaptivelyestimatedforeachchannelofbothmicrowaveandinfraredsoundersfromanysatelliteplatform.
• VerificationsrelativetotheconventionalobservationsshowthattheestimatedlocalizationwidthreduceserrorsthanthedefaultGCwidth,andtheestimatedobservationverticallocationfurtherincreasestheadvantages,butthemaximumlocalizationvaluedecreasestheadvantages.
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pvo
cvo
lmaxvo
