Adaptive localization for satellite radiance observations in an ... · •Assimilation of satellite radiances has been proven to have positive impacts on the forecast skill, especially

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)

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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