« 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, ItalyService 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 Bii is calculated: Bii = a Aii (t-dt) + M Aii

• Bij is estimated from diagonal elements using f function

Inversion of HBHT + 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

t] Δt)(t i

x [t(t)ii

q avec

(t)ii

q(t)ii

b Mt)(t ii

b

20

QM B MB Tatdtt

B Diagonal elements :

1T

t

T

t O)H B (HH BK

Observation errors covariance matrix diagonal:

nobservatio:iy 2

02 )

iy r ()

i(yerr

iiO

r0 and t0 parameters to fit (representativeness defined by Lorenc et al., 1994)

Correlation Function

B: Non diagonal elements

ijf jj

bii

bijb

Choice of f formulation: - Distance, PV, Equivalent Latitude, PV gradient- Exponential or gaussian

jet i entre distanceet PV de différence : ij

det ij

pv

expexp )PV,(d ff PV

ijΔPV

d

ijΔd

00ijijij

F = correlation function

Other 2 parameters to fit: d0 and PV0 (or Phi0, DPV0)

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 + rii

2 + e) e = Obs. errorBlending 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 DAThe impact of different data

True Atmosphere (CTM Model)

Mission Scenario of MIPAS and GOMOS data

Simulated data

MIMOSA Model

AssimilationAssessment

MIMOSA

Test Run: MIPAS, 2000 February550 K isentropic level, 2.5 days of data

The model is initialised with a Climatology (the worst !)

The CTM model

Mission Scenario

Data Assimilation

xa = xb+K(y - H(xb))

MIPAS vs. GOMOS

GOMOS

MIPAS

MLS data05/08/94 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 ?

Antarctic ozone collar

How well dynamical barriers are reproduced ?

Estimate of the assimilation parameters

2 evolutionClimatology from Fortuin-KelderInitial 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

94-08-06 Flight

94-08-08 Flight

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 H2O

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)

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