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Fast Implementation of Localization for Ensemble DA

Fast Implementation of Localization for Ensemble DA. B. Wang 1,2 and J.-J. Liu 1 1 LASG/IAP, Chinese Academy of Sciences 2 CESS, Tsinghua University. DAOS -2012 ， Sep 20 , 2012. EnKF. The formula of EnKF without localization. Localization:. where.

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Fast Implementation of Localization for Ensemble DA

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  1. Fast Implementation of Localization for Ensemble DA B. Wang1,2 and J.-J. Liu1 1LASG/IAP, Chinese Academy of Sciences 2CESS, Tsinghua University DAOS-2012，Sep 20, 2012

  2. EnKF The formula of EnKF without localization Localization: where ρxy, ρyy: Filtering matrices; : Schür product operator

  3. andrespectively represent the horizontal and vertical distances between the i-thand j-th row vectors; and are the horizontal and vertical Schür radius. The elements of filter matrix ρxy (similar for ρyy): where the filtering function C0is defined as(Gaspari and Cohn, 1999)

  4. Issues caused by Localization Before localization, it is easy to get the solution: After localization, huge computing time is required for the solution: diagonal

  5. The extra multiplications due to localization • Available solution to the issue • To split the observation vector into a combination of low-dimension sub-vectors • To sequentially assimilate the low-dimension observation sub-vectors

  6. Our new method is tosplitfilter matrix in localization mx-dimension filter eigenvector my-dimension filter eigenvector Filter matrices N is the number of the major modes of the filter matrix

  7. Expansion of filter function in localization Filter function: Base function Orthogonal Weighting function

  8. One-Dimension Filter N=10 Green: Black: where N=15 N=20 C x

  9. Two-Dimension Filter N=10 N=15 N=20 True: y x

  10. EnKF with extended samples where

  11. Experiment with simple model Lorenz-96 model: • Spatial coordinate: • Forcing parameter: • Solution scheme:4th -order Runge-Kutta scheme • Time stepsize: 0.05 time unit • Periodic boundary conditions: • Note: 0.05 time unit ~6h(Lorenz and Emanuel, 1998)

  12. Red：EnKF with 10 sample (with localization) Blue:EnKF with 500 sample (without localization) RMSE Step of assimilation cycle

  13. Experiment based on an operational prediction model: AREM RMSEs averaged from 850hPa to 100hPa H CTRL: No assimilation with prediction as IC ERA：Using ERA40 as IC, no assimilation AIRS：Assimilating T & Q of AIRS only TEMP: Assimilating Radiosondes only AIRS+TEMP: With random perturbation AIRS+TEMP—2: No random perturbation

  14. Q T U V

  15. Summary • Localization for EnKF can be economically implemented using an orthogonal expansion of filter function; • The new implementation can be applied to other ensemble-based DA, e.g., En-3DVar and En-4DVar.

  16. Comments, please. Thank you!

  17. “True” states: simulations during a period of time unit after a long-term integration (e.g., 105 model time steps) of the model from an arbitrary IC . • Observations of all model variables: “true” states plus uncorrelated random noise with standard Gaussian distribution (with zero mean and variance of 0.16) • Assimilation experiments: assimilation cycles over a period of 200 days using the EnKF with 18-hr assimilation window and, respectively. 500 samples are used for the experiments so that they have good representativeness.

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