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Kazumasa Aonashi* and Hisaki Eito Meteorological Research Institute, Tsukuba, Japan

Kazumasa Aonashi* and Hisaki Eito Meteorological Research Institute, Tsukuba, Japan aonashi@mri-jma.go.jp. July 27, 2011 IGARSS2011. Displaced Ensemble variational assimilation method to incorporate microwave imager TBs into a cloud-resolving model. Satellite Observation (TRMM).

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Kazumasa Aonashi* and Hisaki Eito Meteorological Research Institute, Tsukuba, Japan

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  1. Kazumasa Aonashi* and Hisaki Eito Meteorological Research Institute, Tsukuba, Japan aonashi@mri-jma.go.jp July 27, 2011 IGARSS2011 Displaced Ensemble variational assimilation method toincorporate microwave imager TBs into a cloud-resolving model

  2. Satellite Observation (TRMM) 3 mm-3cm (100-10GHz) Microwave Imager 10μm Infrared Imager Radiation from Rain Scattering by Frozen Particles Cloud Top Temp. Scattering Cloud Particles Frozen Precip. Snow Aggregates 85GHz 19GHz Radar 2cm 0℃ Melting Layer Back scattering from Precip. Radiation Rain Drops SST, Winds

  3. Cloud-Resolving Model used • JMANHM(Saito et al,2001) • Resolution: 5 km • Grids: 400 x 400 x 38 • Time interval: 15 s Explicitly forecasts 6 species of water substances

  4. Goal: Data assimilation of MWI TBs into CRMs Cloud Reslv. Model + Data Assim System Hydrological Model MWI TBs (PR) Precip.

  5. OUTLINE Introduction Methodology Ensemble-based Variational Assimilation (EnVA) Displacement error correction (DEC) Application results Case (2004/6/9) Typhoon CONSON(0404) Assimilation Results Impact on precipitation forecasts Summary & future directions

  6. TMI 040609.OP37437

  7. OUTLINE Introduction Methodology Ensemble-based Variational Assimilation (EnVA) Displacement error correction (DEC) Application results Case (2004/6/9) Typhoon200404 Assimilation Results Impact on precipitation forecasts Summary & future directions

  8. Methodology Ensemble-based Variational Assimilation (EnVA) (Lorenc 2003, Zupanski 2005) Displacement error correction (DEC) Data assimilation schemes

  9. To estimate the flow-dependency of the error covariance Why Ensemble-based method?: Heavy Rain Area Rain-free Area 200km 10km Ensemble forecast error corr. of PT (04/6/9/22 UTC)

  10. To address the non-linearity of TBs Why Variational Method? MWI TBs are non-linear function of various CRM variables. • TB becomes saturatedas optical thickness increases: • TB depression mainly due to frozen precipitation becomes dominant after saturation.

  11. Obs. Presupposition of Ensemble-based assimilation Ensemble forecasts have enough spread to include (Obs. – Ens. Mean) Analysis ensemble mean Analysis w/ errors FCST ensemble mean T=t0 T=t1 T=t2

  12. Displacement error betw. Observation &Ensemble forecast AMSRE TB19v (2003/1/27/04z) • Large scale displacement errors of rainy areas between the MWI observation and Ensemble forecasts • Presupposition of Ensemble assimilation is not satisfied in observed rain areas without forecasted rain. Mean of Ensemble Forecast (2003/1/26/21 UTC FT=7h)

  13. Obs. Assimilation can give erroneous analysis when the presupposition is not satisfied. Ensemble-based assimilation for observed rain areas without forecasted rain Analysis ensemble mean Signals from rain can be misinterpreted as those from other variables Analysis w/ errors FCST ensemble mean T=t0 T=t1 T=t2 Displacement error correction is needed!

  14. Displaced Ensemble variational assimilation method In addition to , we introduced to assimilation. The optimal analysis value maximizes : Assimilation results in the following 2 steps: 1) DEC scheme to derive from 2)EnVA scheme using the DEC Ensembles to derive from

  15. Assimilation method Fig. 1: CRM Ensemble Forecasts MWI TBs Displacement Error Correction Ensemble-based Variational Assimilation

  16. DEC scheme: min. cost function for d Bayes’ Theorem can be expressed as the cond. Prob. of Y given  : We assume Gaussian dist. of :   whereis the empirically determined scale of the displacement error. We derived the large-scale pattern of by minimizing (Hoffman and Grassotti ,1996) :

  17. Detection of the large-scale pattern of optimum displacement We derived the large-scale pattern of from , following Hoffman and Grassotti (1996) : We transformed into the control variable in wave space, using the double Fourier expansion. We used the quasi-Newton scheme (Press et al. 1996) to minimize the cost function in wave space. we transformed the optimum into the large-scale pattern of by the double Fourier inversion.

  18. Fig. 1: Assimilation method CRM Ensemble Forecasts MWI TBs Displacement Error Correction Ensemble-based Variational Assimilation

  19. EnVA: min. cost function in the Ensemble forecast error subspace Minimize the cost function Assume the analysis error belongs to the Ensemble forecast error subspace (Lorenc, 2003): Forecast error covariance is determined by localization Cost function in the Ensemble forecast error subspace:

  20. Calculation of the optimum analysis Detection of the optimum by minimizing Transform of using eigenvectors of S: Minimize the diagonalized cost function Approximate the gradient of the observation with the finite differences about the forecast error: Following Zupanski (2005), we calculated the analysis of each Ensemble members, from the Ensemble analysis error covariance.

  21. Applicationresults Case (2004/6/9) Typhoon CONSON (0404) Assimilation Results Impact on precipitation forecasts

  22. Case (2004/6/9/22 UTC) TY CONSON 1) Assimilate TMI TBs (10v, 19v, 21v) 2) 100 member Ensemble (init. 04/6/9/15 UTC:FG) TMI TB19v RAM (mm/hr)

  23. TB19v from TMI and CRM outputs DE: After DEC FG: First guess TMI CN: DE+ EnVA ND: NoDE+ EnVA

  24. RAM and Rain mix. ratio analysis (z=930m) FG DE RAM ND CN

  25. RH(contours) and W(shades) along N-S FG DE N M S ND CN N S S N

  26. CRM Variables vs. TBc at Point M FG DE Qr(930m) vs.TB19v FG DE RTW (3880m) vs.TB21v

  27. Hourly Precip. forecasts(FT=0-1 h) 22-23Z 9th FG DE RAM ND CN

  28. Hourly Precip. Forecasts (FT=3-4 h) 01-02Z 10th FG DE RAM ND CN

  29. Summary Ensemble-based data assimilation can give erroneous analysis, particularly for observed rain areas without forecasted rain.  In order to solve this problem, we developed the Ensemble-based assimilation methodthat uses Ensemble forecast error covariance with displacement error correction. This method consisted of a displacement error correction scheme and an Ensemble-based variational assimilation scheme.

  30. Summary • We applied this method to assimilate TMI TBs (10, 19, and 21 GHz with vertical polarization) for a Typhoon case (9th June 2004). • The results showed that the assimilation of TMI TBs alleviated the large-scale displacement errors and improved precip forecasts. • The DEC scheme also avoided misinterpretation of TB increments due to precip displacements as those from other variables.

  31. Forecast error corr. of W (04/6/9/15z 7h fcst) 200 km 200 km Heavy rain (170,195) Severe sampling error for precip-related variables Weak rain (260,210) Rain-free (220,150)

  32. Thank you for your attention. End

  33. Ensemble-based Variational Assimilation Method Why Ensemble-based Assimilation method?: To address the flow-dependency of the error covariance Why Variational Assimilation Method?: To address the non-linearity of TBs

  34. Why Ensemble-based method?:Ensemble forecast corr. of PT (04/6/9/22 UTC) Heavy Rain Area Rain-free Area 1000 km 200km 10km To address the flow-dependency of the error covariance

  35. Cloud-Resolving Model used • JMANHM(Saito et al,2001) • Resolution: 5 km • Grids: 400 x 400 x 38 • Time interval: 15 s • Initial and boundary data • JMA’s operational regional model • Basic equations : Hydrostatic primitive • Precipitation scheme: • Moist convective adjustment • + Arakawa-Schubert • + Large scale condensation • Resolution: 20 km • Grids: 257 x 217 x 36

  36. Cloud Microphysical Scheme • Explicit cloud microphysics scheme based on bulk method (Lin et al.,1983; Murakami, 1990; Ikawa and Saito, 1991) • The water substances are categorized into 6 water species (water vapor, cloud water, rain, cloud ice, snow and graupel) • Explicitly predicting the mixing ratios and the number concentrations of frozen particles

  37. Why EnVA?Emission & Scattering signals vs. hydrometers Convective rain (Jan. 27, 2003) Emission Singals At 18 GHz τ ∝ LN(Ts-TB) Ts-TB= Ts(1-εs)exp(-2τ) Scattering Singals At 89 GHz τ ∝ LN(TB/TBflh) TB=TBflh Exp(-τ)

  38. Fig. 1: Assimilation method CRM Ensemble Forecasts MWI TBs Displacement Error Correction Ensemble-based Variational Assimilation

  39. Post-fit residuals Jx=24316.6 Jb=0 Jo=24316.6 DE: FG: Jx= 9435.2 Jb=0 Jo= 9435.2 LN: DE+ EnVA. 1st Jx= 6883.0 Jb= 14.5 Jo= 6868.4 CN: ND: Jx= 4105.4 Jb= 834.5 Jo= 3270.9 Jx= 2431.9 Jb= 290.9 Jo= 2141.0

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