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.

86400Nlon 1lat1 x

Frequency of MLS observations

1 day (about 1000 profiles) 10 days

Initial state Analysis Analysismodel

Observations Observations

model

0x fx

fx

ax

ax

0t 1t 2t

MIMOSA

Sequential assimilation scheme

Kalman Filter

)x(yxx bt

bt

at HK

O)H B (HH BK 1Tt

Tt

M : Model operator

Q : covariance matrix of model errors (adjust model error growth)

at

bdtt xMx

Analysis:

Btdt M Bta MT Q

Analysis Error: tat B )(B HK I

Time evolution of state vector and background errors:

InnovationForecast

H : interpolation operator K : gain matrixBt : 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

bii

(t t) M bii

(t) qii

(t) i : grid point

with qii

(t) [t 0 xi (t) t]2

QM B MB Tattt

bii: diagonal elements of B

1T

t

T

t O)H B (HH BK

Covariance matrix of observation errors (assumed diagonal)

oii

err (yi)2 ( r0 yi

)2 i : observation

Time evolution of background error:

Gain matrix:

Parameter 1 : t0 (model error growth)

Parameter 2 : r0 (representativeness error)

Parameterisation of correlation function

Non-diagonal elements of B:

ijf jj

bii

bijb

Correlation function = f(distance)

fij exp dij

D0

fij correlation function between points i and j

Parameter 3 : D0, (distance correlation length)

jet i pointsbetween distance : ij

d

RESIDU D’ASSIMILATION: VECTEUR INNOVATION

~ 0 (si coherent)

Covariance du vecteur innovation:

si coherent

COHERENCE INTERNE: TEST DE X2

Erreurs a posterioriErreurs 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) mean arithmetic: H(x))-(y (OmF) RMS 2

ns)observatio of(number H(x)yOH B HH(x)y1TT2 p

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 (X2/p -1).

QUELQUES RESULTATS DE MINIMISATION

RMS(OmF) minimum et/ou (X2/p – 1) minimum-> to, ro et Do varient

MINIMISATION GLOBALE SOUS CONTRAINTE

RMS(OmF) minimum avec X2/p=1-> to, ro et Do varient

2 GROS PROBLEMES

1/ X2 < 1

2/ Do = f(frequence des obs.)

determiner Do (indépendant de to et ro)

RMS(OmF) minimum avec X2/p=1-> to, ro et Do varient

Erreurs de mesure expérimentale et de représentativité sont modélisées même paramètre:

2 GROS PROBLEMES

1/ X2 < 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 Xo2/p et Xf2/p =1-> to et ro (Do fixe)

CONCLUSIONS