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« 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
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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.
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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.
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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)
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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)
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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
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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
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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))
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MIPAS vs. GOMOS
GOMOS
MIPAS
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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 ?
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Antarctic ozone collar
How well dynamical barriers are reproduced ?
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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
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Comparison with airborne O3 in-situ measurements
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94-08-06 Flight
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94-08-08 Flight
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GOMOS 2002 Antarctic Vortex Split
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* SMR-ODIN--- Free Model GOMOS Assimilation
Diagnostic:RMS(Obs – Forecast) / Forecast
No bias
Comparison with independant Data
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• 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
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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)
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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