6 th th WM WMO O Sym ymposium osium on Dat ata a Assi As simil milation ation Dual Scale Neighboring Ensemble Approach for the Cloud-Resolving Model Ensemble Variational Assimilation Kazumasa Aonashi (aonashi@mri-jma.go.jp) Kozo Okamoto, Munehiko Yamaguchi and Seiji Origuchi (JMA/MRI) 1
Goal: Data assimilation of MWI TBs into CRMs JMANHM （ Saito et Ensemble-based al,2001) Variational Assim • Resolution: 5 km System • Grids: 400 x 400 x 38 MWI TBs (PR) forecast error covariance of Precip-related variables Precip. 2
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 3
Ensemble forecasts JMANHM (res. 5km, 400x400x38) Extra-tropical Low 100 members started with (Jan. 27, 2003) perturbed initial data Geostrophically-balanced perturbation plus Humidity Random perturbation with various horizontal and vertical scales (Mitchell et al. 2002) Baiu case Typhoon CONSON (June 1, 2004) (June. 9, 2004) C 4
Forecast error noises of precip-related variables due to sampling error (Typhoon case) Horizontal corr. of Precip Vertical cross-corr. @(260,190) (Z=3km) @(260,190) Precip W RHW2 PT U V V U PT 500km RHW2 W Pre cip 5
Areas with large Sampling error Typhoon case, H~3 km horizontal correlation of precipitation H~3km X Averaged distance of area 500 X with horizontal correlation km of precipitation over 0.5 6
Horizontal correlation of ensemble forecast error (H~ 5 km) Ave over whole domain （ black: U, green:RHW2, red ： W ） Weak Precip Heavy Precip Rain-free area PR 1-3 mm/hr PR >10mm/hr Typhoon Typhoon Typhoon km km Low Low Low 7
Cross correlation of CRM variables in the vertical Ave. whole Domain (Typhoon) Rain-free areas 1)Cross correlation between precipitation-related variables and other variables increases with precipitation rate. 2) Variables can be classified in terms of precipitation rate. Weak rain areas Heavy rain areas 8
Neighboring ensemble • Hypothesis of Buehner and Charron (2007) Correlations in spectral space decreases as the difference in wave number increases. • Spectral Localization Power spectral of horizontal ensemble ˆ ˆ ˆ C ( 1, 2) k k C k k ( 1, 2) L ( 1, 2) k k forecast error (H~5000m) : Typhoon sl sl • When transformed into spatial domain W U C ( 1, 2) x x C x ( 1 s x , 2 s L ) ( ) s ds sl sl 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). 9
Comparison of forecast error corr. between conventional and NE methods Averaged distance of area with Vertical cross-correlation at horizontal corr. of precip. > 0.5 (260,190) Typhoon case Conventional NE Method Conventional NE Method Precip W RHW2 PT U V V U PT RHW2 W Pre cip 10
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). Horizontal correlation cal. from the SVD modes No separation Separation Precip 500 500 km km U 500 500 km km 11
En EnVA VA: : mi min. n. cos ost t fu func nctio tion n in in th the e En Ensem embl ble e fo forec ecast ast er error or sub ubspa pace ce • Minimize the cost function with non-linear Obs. term. 1 1 J 1 2 ( X X ) P ( X X ) 1 2 ( Y H ( X )) R ( Y H ( X )) x f f f • Assume the analysis error belongs to the space spanned by dual-scale NE vertical SVD mode: U ＝ G G f f a X X U NE U g g t ( U U ) S G G G f f P = P S U NE , t ( U U ) S g g g • Horizontal pattern of S is adaptively determined. 12
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) 13
Assimilation of Sim. Precip. Retrieval (Typhoon: 04/6/9/22 UTC) TRUTH 600 km FG ANAL 600 600 km km 14
Increment profiles of hydrometers (Typhoon: 04/6/9/22 UTC) （ green:rain, Black:snow, Yellow ： graupel ） 15
Analysis increments of hydrometers (Typhoon: 04/6/9/22 UTC) Precip. Rain water @1460m 600 600 km km Graupel Snow @5910m @5910m 600 600 km km 16
Assimilation of Sim. Precip.Retrieval (Low: 03/1/27/04 UTC) TRUTH 800 km FG ANAL 800 800 km km 17
Analysis increments of hydrometers (Low: 03/1/27/04 UTC) Precip. Rain water @930m 800 800 km km Graupel Snow @3770m @3770m 800 800 km km 18
Assimilation: Simulated sonde data (U@850hPa) Analysis Increment U@1460m Wk Pr. 1000 km H W N Hv Pr. No Pr. 1000 1000 km km 19
Assimilation: Simulated sonde data (U@850hPa) Analysis Increment profiles （ black: U, green:V, Yellow: PT, red:RHW2 ） Wk Pr. H W N Hv Pr. No Pr. 20
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
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