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F. FIERLI (1,2), A. HAUCHECORNE (2), S. RHARMILI (2), S. BEKKI (2), F. LEFEVRE (2), M. SNELS (1)

« Data assimilation in isentropic coordinates » Which Accuracy can be achieved using an high resolution transport model ?. F. FIERLI (1,2), A. HAUCHECORNE (2), S. RHARMILI (2), S. BEKKI (2), F. LEFEVRE (2), M. SNELS (1) ISAC-CNR, Italy Service d’Aéronomie du CNRS, IPSL, France Methodology

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F. FIERLI (1,2), A. HAUCHECORNE (2), S. RHARMILI (2), S. BEKKI (2), F. LEFEVRE (2), M. SNELS (1)

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  1. « Data assimilation in isentropic coordinates »Which Accuracy can be achieved using an high resolution transport model ? F. FIERLI (1,2), A. HAUCHECORNE (2), S. RHARMILI (2), S. BEKKI (2), F. LEFEVRE (2), M. SNELS (1) ISAC-CNR, Italy Service d’Aéronomie du CNRS, IPSL, France Methodology Assessment of the method on ENVISAT simulated data Dynamical barriers GOMOS data assimilation

  2. Introduction Method for assimilating sequentially tracer measurements in isentropic chemistry-transport models MIMOSA High resolution isentropic advection model (Hauchecorne et al., 2001, Fierli et al. 2002) Additional information originating from the correlation between tracer and potential vorticity to be exploited in the assimilation algorithm  Use of isentropic coordinates The relatively low computational cost of the model makes it possible to run it at high resolutions and describe in details the distribution of long-lived chemical species.

  3. Simplified Kalman Filter Sequential assimilation: whenever an observation becomes available , it is used to update the predicted value by the model which is run simultaneously Optimal interpolation is used to combine observations and outputs of the model; To reduce the Covariance Matrix (Menard, Khattatov, 2000): • Horizontal and vertical forecast error covariances are independent • The time evolution of diagonal elements of BBii is calculated: Bii = a Aii (t-dt) + MAii • Bij is estimated from diagonal elements using ffunction  Inversion of HBHT + O + R is possible • Estimate of B is straightforward To simplify Observation operators  Observation errors spatially and temporally uncorrelated.

  4. Growth of the Model error and representativeness B Diagonal elements : Observation errors covariance matrix  diagonal: r0 and t0 parameters to fit (representativeness defined by Lorenc et al., 1994)

  5. Correlation Function B: Non diagonal elements F = correlation function Choice of f formulation: - Distance, PV, Equivalent Latitude, PV gradient - Exponential or gaussian Other 2 parameters to fit: d0 and PV0 (or Phi0, DPV0)

  6. Estimate of the assimilation parameters 2 criterion and Observation minus Forecast OmF RMS minimization used to determine assimilation parameters (as in Menard et al., 2000, Khattatov et al, 2001) OmF or innovation vector = y - H(xb) 2 = OmF 2 / (Bii2 + rii2 + e)  e = Obs. error Blending of a priori information and the OmF estimate Conditions: - 2 n and does not show any time trend - OmF Minimum - Conditions areused to tune offline the correlation lengths and 2 the error parameters - Minimisation of (2 –n) + OmF / H(x) on-line using the Powell method

  7. Test Run: The quality of DAThe impact of different data True Atmosphere (CTM Model) Mission Scenario of MIPAS and GOMOS data Simulated data Assimilation Assessment MIMOSA Model

  8. Test Run: MIPAS, 2000 February550 K isentropic level, 2.5 days of data The CTM model Mission Scenario xa = xb+K(y - H(xb)) Data Assimilation The model is initialised with a Climatology (the worst !) MIMOSA

  9. MIPAS vs. GOMOS GOMOS MIPAS

  10. Antarctic ozone collarHow well dynamical barriers are reproduced ? • MLS data • 05/08/94 to 15/08/94, 550 K to 435 K level, MLS error < 10 % • 2 estimate • Ozone « collar » analysis

  11. Antarctic ozone collarHow well dynamical barriers are reproduced ?

  12. Estimate of the assimilation parameters 2 evolution Climatology from Fortuin-Kelder Initial error: 5 and 30 % • Test using: • Different formulations of correlation function • Different Meteorological winds • Best if using PV and distance formulation  Slight difference using NCEP or ECMWF winds

  13. Comparison with airborne O3 in-situ measurements

  14. 94-08-06 Flight

  15. 94-08-08 Flight

  16. GOMOS 2002 Antarctic Vortex Split

  17. Comparison with independant Data * SMR-ODIN --- Free Model GOMOS Assimilation • Diagnostic: • RMS(Obs – Forecast) / Forecast • No bias

  18. Assimilation of MLS ozone, Fierli et al., 2002 • Assimilation of GOMOS • Assimilation of MIPAS data  in progress • Extend to other chemical species  in progress H2O

  19. Method (a lexical question)The so-called Kalman Filter xa = xb+K(y - H(xb)) K = BHT (HBHT + O + R)-1 Where: Xa is the analysis (n-vector) Xb is the background (forecast, first guess) B is the covariance matrix (n*n) H is the observational operator (n*m) y are the observations (m-vector) O is the observation operator(m*m) R is the significativity operator(m*m)

  20. A = B – KHB B = Q + MAMT Where: A is the analysed covariance matrix B is the forecast Covariance matrix M is the Model operator Q is the Model error • Model should be re-run n*n times • HBHT + O + R should be inversed The dimensions of the system are too big

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