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Kazumasa Aonashi ([email protected]) Kozo Okamoto, Munehiko Yamaguchi and Seiji Origuchi (JMA/MRI) 7 th IPWG workshop Dual Scale Neighboring Ensemble Approach for the Cloud-Resolving Model Ensemble Variational Assimilation 1

7 IPWG workshop - ISAC - CNRipwg/meetings/tsukuba-2014/pres/19-5...using neighboring members of the target points (5 x 5 grids). Cxx Cx sx sLsds sl sl (1, 2) (1 , 2 ) () 10 Separation

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Kazumasa Aonashi ([email protected])Kozo Okamoto, Munehiko Yamaguchi and Seiji Origuchi (JMA/MRI)

7th IPWG workshop

Dual Scale Neighboring Ensemble Approach for the Cloud-Resolving Model

Ensemble Variational Assimilation

1

2014/1/15 GPM PI WS

GOAL: Ensemble-based Variational Assimilation System to incorporate MWR TBs into CRMs

SST, Winds

Cloud Particles

Frozen Precip.

Snow Aggregates

Melting Layer

Rain Drops

Scattering

Radiation0℃

MWR TBsMWR TBs are functionsof various atmospheric and surface variables

3 mm-3cm

Water Vapor

JMANHM(Saito et al,2001)• Resolution: 5 km• Grids: 400 x 400 x 38

Ensemble-based Variational Assim

System

Ensemble-based Variational AssimilationObs.

T=t0 T=t1 T=t2

Ensemble forecasts

Mean of Ensemble forecasts

1 1( )1

f f Tf t t

e N

X XP

RCalculation of analysis of Ensemble mean

3

Calculation of analysis of error cov. and Ensemble member.

))(())((21)()(21 11 XHYRXHYXXPXXJ fffx

Problem in EnVA: Sampling errorForecast error corr. of W (04/6/9/15z 7h fcst)

Heavy rain(170,195)

Weak rain(260,210)

Rain-free(220,150)

200 km200 km

Severe sampling error for precip-related variables

4

OUTLINE• Estimation of CRM forecast error covariance

– Ensemble forecast error analysis– Dual-scale neighboring ensemble method

• Introduction to ensemble-based variational assimilation

• Experiment results using simulated data• Summary

5

Ensemble forecastsExtra-tropical Low(Jan. 27, 2003)

Typhoon CONSON(June. 9, 2004)

C

Baiu case(June 1, 2004)

JMANHM (res. 5km, 400x400x38)100 members started with

perturbed initial dataGeostrophically-balanced perturbation plus HumidityRandom perturbation with various

horizontal and vertical scales(Mitchell et al. 2002)

6

7

Forecast error noises of precip-related variablesdue to sampling error (Typhoon case)

Vertical cross-corr. @(260,190)

V

W

Precip

RHW2

PT

U

Precip W RHW2 PT U V

Horizontal corr. of Precip@(260,190) (Z=3km)

500km

Areas with large Sampling errorTyphoon case, H~3 km

8

Averaged distance of area with horizontal correlation of precipitation over 0.5

horizontal correlation of precipitationH~3km

500 km

X

X

Horizontal correlation of ensemble forecast error (H~ 5 km)Ave over whole domain (black: U, green:RHW2, red:W)

km

9

km

Rain-free area Weak PrecipPR 1-3 mm/hr

Heavy PrecipPR >10mm/hr

TyphoonTyphoonTyphoon

LowLowLow

Dual-scale Neighboring Ensemble Method(1) Dual Scale Separation

(2) Neighboring Ensemble (NE) methodSpectrally localized forecast error correlation (Buehner 2010) :

we approximated the forecast error correlation for deviation using neighboring members of the target points (5 x 5 grids).

( 1, 2) ( 1 , 2 ) ( )sl slC x x C x s x s L s ds

10

Separation of ensemble forecast error into large-scale modes ( 65 km ave.) and local modes (deviation).

Assume that precip-related variables only have local modes.

Horizontal correlation URHW2W

Comparison of forecast error corr. between conventional and NE methods

11

ConventionalNE Method

Averaged distance of area with horizontal corr. of precip. > 0.5

Precip W RHW2 PT U V

V

W

Precip

RHW2

PT

U

Vertical cross-correlation at (260,190) Typhoon case

ConventionalNE Method

EnVA: min. cost function in the Ensemble forecast error subspace

• Minimize the cost function with non-linear Obs. term.

• Assume the analysis error belongs to the space spanned by the dual-scale NE modes:

• Horizontal pattern of S is adaptively determined.

G Gf f aNE

g g

UX X U

U

))(())((21)()(21 11 XHYRXHYXXPXXJ fffx

f,

( )P =

( )

tG G Gf

U NE tg g g

U U SP S

U U S

12

EnVA(OSSE)

Typhoon Conson(04/6/9/22 UTC)

JMANHM(Saito et al, 2005) 5 km res.

First guess: Ensemble forecast (04/6/9/15 ) :100 members started with perturbed initial dataObservation: Conventional + TMI TB

13

Surface Precipitation (mm/h) and TB19v (K)for 04/6/9/22 UTC

14

First guess(Mean of Ens. FCST)

Truth TBo

Analysis ofEns. mean

TB19vRainyareas

SurfPrecip>0.1 mm/h

OSSE: Hourly PrecipitationTruth(Init: 04/6/9/22 UTC) FT=1-6h

15

FT=1 FT=2 FT=3

FT=4 FT=5 FT=6

Ensemble Forecast for Hourly PrecipitationNoDA (Init: 04/6/9/22 UTC, 100 member)

started with the first guess

16

FT=1 FT=2 FT=3

FT=4 FT=5 FT=6

Ensemble Forecast for Hourly PrecipitationDA(Init: 04/6/9/22 UTC, 100 member)

started with the EnVA analyses

17

FT=1 FT=2 FT=3

FT=4 FT=5 FT=6

Areas Classified with Precip(1mm/hr)Green (Forecast O, Truth O); Blue (Forecast X, Truth O);

Orange (Forecast O, Truth X)NoDA (Init: 04/6/9/22 UTC) FT=1-6h

18

FT=1 FT=2 FT=3

FT=4 FT=5 FT=6

Areas Classified with Precip(1mm/hr)Green (Forecast O, Truth O); Blue (Forecast X, Truth O);

Orange (Forecast O, Truth X)DA (Init: 04/6/9/22 UTC) FT=1-6h

19

FT=1 FT=2 FT=3

FT=4 FT=5 FT=6

POD for NoDA(dash) and DA(solid)(Init: 04/6/9/22 UTC) FT=1-6h

Blue: Th=1 mm/hrRed: Th=3 mm/hr

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1 2 3 4 5 6

POD

POD1ENS

POD1ETKF

POD3ENS

POD3ETKF

Summary

• Estimation of CRM forecast error covariance– Ensemble forecast error analysis– Dual-scale neighboring ensemble method

• Introduction to ensemble-based variational assimilation

• Experiment results using simulated data• Future directions (real data, FA cycle)

21

Backup

• backup slides

22

Sample error-damping methods of previous studies

• Spatial Localization (Lorenc, 2003)

• Spectral Localization (Buehner and Charron, 2007)

– When transformed into spatial domain

• Variable Localization (Kang, 2011)

ˆ ˆ ˆ( 1, 2) ( 1, 2) ( 1, 2)sl ENS slC k k C k k L k k

( 1, 2) ( 1 , 2 ) ( )sl ENS slC x x C x s x s L s ds

1,2( 1, 2) ( 1, 2) ( )sp ENSC x x C x x S

( 1, 2) ( 1, 2) ( 1, 2)v ENSC v v C v v v v

23

Power spectral of horizontal ensemble forecast error (H~5000m) : Typhoon

W U

1) Precip and W are diagonal, other had significant amplitudesfor low-frequency, off-diagonal modes.2) The presumption of the spectral localization “Correlations in spectral space decreases as the difference in wave number increases” is valid.

24

1)Cross correlation between precipitation-related variables and other variables increases with precipitation rate.2) Variables can be classified in terms of precipitation rate.

Cross correlation of CRM variables in the vertical Ave. whole Domain (Typhoon)

Weak rain areas

Rain-free areas

Heavy rain areas

25

Neighboring ensemble• Hypothesis of Buehner and Charron (2007)

Correlations in spectral space decreases as the difference in wave number increases.

• Spectral Localization

• When transformed into spatial domain

Spectral-Localized correlation is a weighted, spatially-shifted average of correlation over the neighboring points.

• we approximated the forecast error correlation using neighboring ensemble (NE) members of the target points (5 x 5 grids).

ˆ ˆ ˆ( 1, 2) ( 1, 2) ( 1, 2)sl slC k k C k k L k k

( 1, 2) ( 1 , 2 ) ( )sl slC x x C x s x s L s ds

Power spectral of horizontal ensemble forecast error (H~5000m) : Typhoon

W U

26

Horizontal correlation cal. from the SVD modes

27

Precip

U

No separation Separation

To reduce degree of freedom, we use SVD modes of vertical cross correlation of NE forecast error

Separation of NE into large-scale modes ( 65 km ave.) and local modes (derivation).

500km

500km

500km

500km

Averaged distance of area with horizontal correlation of precipitation over 0.5

(Typhoon case, H~3 km)

28

Conventional NE Method

29

Vertical cross-correlation at a large sampling error point (260,190 Typhoon)

Conventional NE MethodPrecip W RHW2 PT U

V

W

Precip

RHW2

PT

U

V Precip W RHW2 PT U V

Space spanned by NE vertical SVD modes

• NE member (~2500) =Ensemble (100 mem.) x Grid box (5x5)

• To reduce degree of freedom, we use SVD modes of vertical cross correlation of NE forecast error

• Space spanned by the NE vertical SVD modes:

30

1

1

1

1

(1) (1)( ) ( )

(1) (1)( ) ( )

G G N

G h G N hfNE

g g N

g h g N h

u uu K M u K M

Uu u

u K M u K M

EnVADetermination of cost function• Cost function in the NE vertical SVD space

31

11 1( ) ( ) { ( ) } { ( ) }2 2

a f t f a f a t aU UJ U U P U U H U Y R H U Y

,

( )( )

G Ga f aNE

g g

tG G Gf f

U U NE tg g g

UU U

U

U U SP P S

U U S

1 1

1 1 1

: 1 2 { } 1 2{ ( ) } { ( ) }

1 2 { } 1 2 { } 1 2{ ( , ) } { ( , ) }

at a a t a

t t tG G G g g g G g G g

J trace S H Y R H Y

trace S trace S H Y R H Y

EnVADetermination of cost function• Since vertical SVD modes are independent ,

cost function results in that of horizontal components:

32

1 1

1

1

: 1 2 { } 1 2{ ( ) } { ( ) }

1 2 { } 1 2{ }

1 2{ ( , ) } { ( , ) }

h

at a a t ah h h h h

t tGh Gh Gh g g

tGh g Gh g

J J

trace S H Y R H Y

trace S

H Y R H Y

EnVADiagonalization of background

term• Block-Diagonalize

• Approximation of (Adaptive Localization)

33

GhS1

1

: 1 2 { } 1 2{ }

1 2{ ( , ) } { ( , ) }kb

at a tkb kb kb g g

a t akb g kb g

J trace S

H Y R H Y

1/ 2kbS

2 2 1/ 2 1/ 2| | , fkb center center kb kbS Corr S C

1 2 akb kb kbS

Adaptive Localization:

200km

10km

Heavy Rain Area Rain-free AreaTo estimate the flow-dependency

of the error correlation

Ensemble forecast error corr. of PT (04/6/9/22 UTC) 34

EnVAMinimization of cost function

• Minimize the cost function

• To solve the non-linear min. problem, we follow Aonashi and Eito (2011).

• Approximate the gradient of the observation with the finite differences about the forecast error.

35

10 0

1 11 2{ } [ ( , ) ] [ ( , ) ]2 2

t t tkb kb g g kb g kb g

kbJ H d R H d

Increment @ Okinawa for Sonde.OkiBlack (Truth-1st guess), Green (Anal-1st guess)

36

U

PT

V

RHW2

Increment @ 1460mfor Sonde.Okinawa

37

U V

PT RHW2