Assi As simil milation ation Dual Scale Neighboring Ensemble - - PowerPoint PPT Presentation

Kazumasa Aonashi (aonashi@mri-jma.go.jp) Kozo Okamoto, Munehiko Yamaguchi and Seiji Origuchi (JMA/MRI)

6th

th WM

WMO O Sym ymposium

• sium on Dat

ata a As Assi simil milation ation Dual Scale Neighboring Ensemble Approach for the Cloud-Resolving Model Ensemble Variational Assimilation

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Goal: Data assimilation of MWI TBs into CRMs

Ensemble-based Variational Assim System

MWI TBs (PR) Precip.

JMANHM（Saito et al,2001)

• Resolution: 5 km
• Grids: 400 x 400 x 38

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forecast error covariance of Precip-related variables

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

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Ensemble forecasts

Extra-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 data Geostrophically-balanced perturbation plus Humidity Random perturbation with various horizontal and vertical scales (Mitchell et al. 2002)

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

Vertical cross-corr. @(260,190)

V W Pre cip RHW2 PT U Precip W RHW2 PT U V

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

500km

Areas with large Sampling error Typhoon case, H~3 km

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Averaged distance of area with horizontal correlation

• f precipitation over 0.5

horizontal correlation of precipitation H~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

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km

Rain-free area Weak Precip

PR 1-3 mm/hr

Heavy Precip

PR >10mm/hr

Typhoon Typhoon Typhoon Low Low Low

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

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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 sl

C k k C k k L k k

( 1, 2) ( 1 , 2 ) ( )

sl sl

C x x C x s x s L s ds

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

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Comparison of forecast error corr. between conventional and NE methods

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Conventional NE Method

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

Precip W RHW2 PT U V V W Pre cip RHW2 PT U

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

Conventional NE Method

Horizontal correlation cal. from the SVD modes

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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).

500 km 500 km 500 km 500 km

En EnVA VA: : mi min.

• n. cos
• st

t fu func nctio tion n in in th the e En Ensem embl ble e fo forec ecast ast er error

• r sub

ubspa pace ce

• Minimize the cost function with non-linear Obs. term.
• Assume the analysis error belongs to the space

spanned by dual-scale NE vertical SVD mode:

• Horizontal pattern of S is adaptively determined.

G G f f a NE g g

U X X U U ＝

)) ( ( )) ( ( 2 1 ) ( ) ( 2 1

1 1

X H Y R X H Y X X P X X J

f f f x

   

f ,

( ) P = ( )

t G G G f U NE t g g g

U U S P S U U S

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Experiment results using simulated data

(1) Check neighboring ensemble method on precip-related variables > Assimilate simulated precip. retrieval data (2) NE scale separation & adaptive localization > Assimilate simulated sonde data (U@850hPa)

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Assimilation of Sim. Precip. Retrieval (Typhoon: 04/6/9/22 UTC)

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TRUTH ANAL FG

600 km 600 km 600 km

Increment profiles of hydrometers (Typhoon: 04/6/9/22 UTC)

（green:rain, Black:snow, Yellow： graupel）

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Analysis increments of hydrometers (Typhoon: 04/6/9/22 UTC)

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Rain water @1460m Snow @5910m Graupel @5910m Precip.

600 km 600 km 600 km 600 km

Assimilation of Sim. Precip.Retrieval (Low: 03/1/27/04 UTC)

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TRUTH FG ANAL

800 km 800 km 800 km

Analysis increments of hydrometers (Low: 03/1/27/04 UTC)

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Precip. Rain water @930m Graupel @3770m Snow @3770m

800 km 800 km 800 km 800 km

Assimilation: Simulated sonde data (U@850hPa) Analysis Increment U@1460m

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Wk Pr. No Pr. Hv Pr.

H W N

1000 km 1000 km 1000 km

Assimilation: Simulated sonde data (U@850hPa) Analysis Increment profiles （black: U, green:V, Yellow: PT, red:RHW2）

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Wk Pr. No Pr. Hv Pr.

H W N

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)

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