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Assimilation Techniques: 4dVar
April 2001
By Mike Fisher
European Centre for Medium-Range Weather
Forecasts.
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2 . Comparison between the ECMWF 3dVar and 4dVar systems
The ECMWF 4dVar system is, from the technical point of view, very similar to the 3dVar system. Both systems use the same unix scripts, and share much of the Fortran code. The same background error covariance matrix and observation operators are used, and most of the peripheral tasks such as fetching and archiving of fields and observations are the same for the two analysis systems.
The main differences between the ECMWF 3dVar and 4dVar analyses (apart from the obvious difference that 4dVar includes integrations of the tangent linear and adjoint models during the minimization) are as follows:
| • In 4dVar we perform two incremental updates. The tangent linear and adjoint models used during the first update include only very simple parameterizations of physical processes (Buizza 1994). A more complete package of physical parameterizations (Mahfouf and Rabier, 2000) is included for the second update. However, the parameterizations are computationally expensive. To reduce computational expense, the second update carries out fewer iterations of minimization than the first. |
| • For historical reasons, 3dVar approximates the tangent linear observation operators using a finite difference: |
|
(1) |
| whereas 4dVar uses the true tangent linear operators. |
| • In 3dVar, all observations for the 6-hour window centred on the analysis time are collected together and are compared with the high-resolution trajectory at the nominal analysis time. The incremental cost function is: |
|
(2) |
| In 4dVar, the observations are divided into 1-hour timeslots and compared with the trajectory at the appropriate time: |
|
(3) |
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06.06.2002 |
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