ASSIMILATION OF SATELLITE TRACER DATA AND OPTIMISATION USING SELF-CONSISTENCY DIAGNOSTICS Saad Rharmili, Slimane Bekki, SA-IPSL, CNRS/UPMC

Assimilation of MLS O3 data in MIMOSA  High resolution isentropic transport model (there is another version of the model with chemistry) .  Forced with meteorological analysis (ECMWF, NCEP)  Sequential assimilation of tracer observations (MLS O3)  Assimilation window (6h): observations advected forward and backward to the assimilation time.

Frequency of MLS observations 1 day (about 1000 profiles) 10 days

Initial stateAnalysis model Observations model MIMOSA Sequential assimilation scheme

Kalman Filter M : Model operator Q : covariance matrix of model errors (adjust model error growth) Analysis: Analysis Error : Time evolution of state vector and background errors: Innovation Forecast H : interpolation operator K : gain matrix B t : covariance matrix of background errors (adjust correlation lengths) O : covariance matrix of observation errors (adjust representativeness errors)

Parameterisation of the model error growth and of the representativeness error b ii : diagonal elements of B Covariance matrix of observation errors (assumed diagonal) Time evolution of background error: Gain matrix: Parameter 1 : t 0 (model error growth) Parameter 2 : r 0 (representativeness error)

Parameterisation of correlation function Non-diagonal elements of B: Correlation function = f(distance) f ij correlation function between points i and j Parameter 3 : D 0, (distance correlation length)

RESIDU D’ASSIMILATION: VECTEUR INNOVATION ~ 0 (si coherent) Covariance du vecteur innovation: si coherent

COHERENCE INTERNE: TEST DE X 2 Erreurs a posteriori Erreurs a priori si coherent

AUTRES RESIDUS D’ASSIMILATION

Diagnostique d’erreur de prévision Diagnostique d’erreur d’observation AUTRES TESTS DE COHERENCE INTERNE

Optimisation of the assimilation system according to two diagnostics RMS(OmF) Self-consistency test: OmF versus a-priori errors O and B Assimilation of MLS data (about 1000 profiles/day) into MIMOSA for several isentropic levels between 400 and 900K from 15 to 25/08/93 -> Recherche des paramètres optimums to, ro and Do par minimisation RMS( OmF) et/ou (X 2 /p -1).

QUELQUES RESULTATS DE MINIMISATION RMS(OmF) minimum et/ou (X 2 /p – 1) minimum -> to, ro et Do varient

MINIMISATION GLOBALE SOUS CONTRAINTE RMS(OmF) minimum avec X 2 /p=1 -> to, ro et Do varient

2 GROS PROBLEMES 1/ X 2 < 1 2/ Do = f(frequence des obs.) determiner Do (indépendant de to et ro)

RMS(OmF) minimum avec X 2 /p=1 -> to, ro et Do varient Erreurs de mesure expérimentale et de représentativité sont modélisées même paramètre:

2 GROS PROBLEMES 1/ X 2 < 1 2/ Do (correlation) = f(frequence des obs.) determiner Do (indépendant de to et ro)

METHODE NMC: LONGUEUR DE CORRELATION

MINIMISATION GLOBALE SOUS CONTRAINTE RMS(OmF) minimum avec Xo 2 /p et Xf 2 /p =1 -> to et ro (Do fixe)

CONCLUSIONS