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

This research explores a novel method to assimilate microwave imager data into cloud-resolving models for improved precipitation forecasts. The study focuses on the impact of displacement error correction on data assimilation and its application in typhoon forecasting. By employing an ensemble-based variational assimilation approach, the research aims to enhance the accuracy of precipitation predictions using satellite observations and hydrological models.

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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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