EGS2003 Migliorini

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Assimilation of the information content of Envisat MIPAS data Stefano Migliorini Data Assimilation Research Centre, University of Reading Thanks to: R. Bannister, R. Brugge, A. Geer, W. Lahoz, A. O’Neill, C. Piccolo, C. Rodgers : 

Assimilation of the information content of Envisat MIPAS data Stefano Migliorini Data Assimilation Research Centre, University of Reading Thanks to: R. Bannister, R. Brugge, A. Geer, W. Lahoz, A. O’Neill, C. Piccolo, C. Rodgers

Outline: 

Outline Discussion of the C. Rodgers’ theoretical framework on how to assimilate the information content of retrievals without any a priori contamination Our work in DARC for its application to the assimilation of MIPAS ozone data Conclusions

3DVar cost function: observation term: 

3DVar cost function: observation term Assimilation of radiances: Y is a vector of radiances, H is the jacobian of the forward model Problems with hyperspectral sensors: too much information Assimilation of retrievals: y is a vector of e.g. mass mixing ratios, H is an interpolation or a layer averaging operator The a priori information used in the retrieval process can lead to correlation with background errors covariances are generally neglected

Characterisation of retrievals: 

When the forward model is linear within one standard deviation from the solution, the retrieval can be expressed as zr is the retrieved atmospheric profile zr0 is the simulated retrieval from a simulated noise-free measurement using the forward model A is the averaging kernel matrix x0 is the a priori information used in the retrieval Ge is the retrieval error Characterisation of retrievals

Example: MIPAS ozone retrieval: 

zr [ppmv] zr0 [ppmv] x0 [ppmv] Ax0 [ppmv] y [ppmv] A * 10 Example: MIPAS ozone retrieval Pressure [hPa] 1000 10 0.1 1000 10 0.1 0 10 0 10 0 10

Assimilation of retrievals (removing the a priori!): 

Assimilation of retrievals (removing the a priori!) Expressing the retrieval as The relationship between the measurement and the state vector is now and the observation term can be written as

‘Optimal’ assimilation of retrievals: 

‘Optimal’ assimilation of retrievals Errors on y are uncorrelated with background (a-priori) errors used in the retrieval As a consequence, errors on y are uncorrelated with background errors in the background term of the cost function Assimilation of y instead of zr leads to a more consistent estimate of the real atmospheric state.

The model grid: 

The model grid The full state vector grid must be defined on a grid fine enough to capture the internal variability of the atmosphere The model grid used in data assimilation is generally on a coarser grid To minimise the cost function we need to interpolate the model fields to the state vector (“fine”) grid The true state will in general be different from the result of an interpolation from the model grid to the state vector grid:

Fine grid vs. coarse grid: 

Fine grid vs. coarse grid xm x xw = W xm fine grid coarse grid

Contribution of different grids: 

Contribution of different grids We can express the retrieval as true state on the model grid ‘residual’ due to the interpolation on the fine grid where

Representation error: 

Representation error Defining we can write

How do we estimate Sb ?: 

How do we estimate Sb ? To calculate the state vector covariance matrix Sb it is possible to use a lower-dimensional covariance matrix, B We can choose B as the background error covariance matrix estimated via the NMC method Then But Sb is now singular: we need to make it meaningful by e.g. extrapolating from its non-zero eigenvalues

Ozone state vector covariance matrix : 

Ozone state vector covariance matrix ECMWF ozone background error covariance matrix covariance matrix on the forward model grid

Ozone state vector covariance matrix : 

Ozone state vector covariance matrix ECMWF ozone background error covariance matrix covariance matrix on the forward model grid

Ozone state vector covariance matrix : 

Ozone state vector covariance matrix

Systematic errors: 

Systematic errors Forward model errors Spectroscopic database errors Horizontal homogeneity error Non-LTE errors Instrumental errors Spectral calibration errors Radiometric calibration errors Instrument line shape and field of view errors If each retrieval is considered on its own, systematic errors can be treated as random errors

MIPAS ozone error budget: 

MIPAS ozone error budget random, p and T propagation on ozone, systematic and total errors

Pre-whitening: 

Pre-whitening Adding each error contribution and setting The 3DVar cost function for satellite retrievals is where the noise in the observation term is now “white” (observation error covariance is a unit matrix)

Summary: 

Summary To perform an “optimal” assimilation (e.g. in a minimum variance sense) of satellite retrievals IS POSSIBLE. The information needed is The a priori on the state vector grid The averaging kernel matrix The covariance matrix of the retrieval noise, both random and systematic The covariance matrix of an ensemble of state vectors, interpolated from the vertical background error covariance matrix on the model grid

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