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DATA ASSIMILATION
IFS documentation Front Page
Table of contents
CHAPTER 1 Incremental
formulation of 3D/4D variational assimilation-an overview
CHAPTER 2 3D variational assimilation
CHAPTER 3 4D variational assimilation
CHAPTER 4 Background term
CHAPTER 5 Conventional observational
constraints
CHAPTER 6 Satellite observational
constraints
CHAPTER 7 Background, analysis
and forecast errors
CHAPTER 8 Gravity-wave control
CHAPTER 9 Data partitioning (OBSORT)
CHAPTER 10 Observation screening
CHAPTER 11 Analysis of snow
CHAPTER 12 Land surface analysis
CHAPTER 13 SST and sea-ice analysis
CHAPTER 14 Reduced-rank Kalman filter
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8.7 Implementation of DFI as a weak constraint in 4D-Var
In the context of variational data assimilation, the digital filter is used as a weak constraint. A penalty term is added to the cost function and replaces the NMI based penalty term.
During each integration of the tangent linear model in the inner loop of the 4D-Var, the digital filter is applied to the increments. This gives a filtered increment valid at the mid-point of the assimilation window (array RACCSPA). The value of the non-filtered increment valid at the same time is also stored (array RSTOSPA).
The weak constraint term which is added to the cost function is the moist energy norm of the departure between those two states times a weight factor. All these computations are conducted in spectral space and applied to the spectral fields. The norm of the departure is computed in two steps. In EVJCDFI, the difference between RACCSPA and RSTOSPA is computed and summed in array RSUMJCDFI for each wavenumber. Then, in EVCOST, the contributions from each wavenumbers and variables are added to obtain the final value of the penalty term.
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20.03.2002 |
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