« 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

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.

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 B B ii is calculated: B ii = a A ii (t-dt) + M A ii B ij is estimated from diagonal elements using f function  Inversion of HBH T + O + R is possible  Estimate of B is straightforward To simplify Observation operators  Observation errors spatially and temporally uncorrelated.

Growth of the Model error and representativeness B Diagonal elements : Observation errors covariance matrix  diagonal: r 0 and t 0 parameters to fit (representativeness defined by Lorenc et al., 1994)

Correlation Function B: Non diagonal elements Choice of f formulation: - Distance, PV, Equivalent Latitude, PV gradient - Exponential or gaussian F = correlation function Other 2 parameters to fit: d 0 and PV 0 (or Phi 0, DPV 0 )

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(x b )  2 = OmF 2 / (B ii 2 + r ii 2 + 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 are used to tune offline the correlation lengths and  2 the error parameters - Minimisation of (  2 –n) + OmF / H(x) on-line using the Powell method

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

MIMOSA Test Run: MIPAS, 2000 February 550 K isentropic level, 2.5 days of data The model is initialised with a Climatology (the worst !) The CTM model Mission Scenario Data Assimilation x a = x b +K(y - H(x b ))

MIPAS vs. GOMOS GOMOS MIPAS

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

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

Comparison with airborne O3 in-situ measurements

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GOMOS 2002 Antarctic Vortex Split

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

Assimilation of MLS ozone, Fierli et al., 2002 Assimilation of GOMOS Assimilation of MIPAS data  in progress Extend to other chemical species  in progress H 2 O

Method (a lexical question) The so-called Kalman Filter x a = x b +K(y - H(x b )) K = BH T (HBH T + O + R) -1 Where: X a is the analysis (n-vector) X b 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)

A = B – KHB B = Q + MAM T 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  HBH T + O + R should be inversed The dimensions of the system are too big