DIGITAL FILTERING AND DATA ASSIMILATION
A. INTRODUCTION
A.1. Sources of noise in assimilation
A.2. Filtering or initialization methods
A review of the various filtering schemes
Incremental approach
A short historical account
A.3. Principles of digital filtering using non-recursive filters
Theorical application
Practical application
Use for NWP
B. INITIALIZATION USING NON-RECURSIVE DIGITAL FILTERS
B.1. Choice of the initial trajectory and related problems
The problem of initialization
The DFI bias
B.2. Comparaison of available schemes
Old scheme
New scheme
Formulation of the filtered state
Advantages of the new scheme
Incremental initialization
B.3. Interaction with coupling
Constraints
Standard coupling along DFI in ALADIN
Main alternative
C. SOME OTHER APPLICATIONS OF NON-RECURSIVE DIGITAL FILTERING
C.1. Launching or finalization
C.2. Jc-dfi (as a weak constraint in 4d-var assimilation)
Framework of 4d-var assimilation
Principle
Formulation of the cost function
But ...
C.3. Semi-internal initialization in 4d-var assimilation
C.4. Blending of spectral fields
An application of digital filter initialization
Principles
Basic formulation
D. CHOICE OF A DIGITAL FILTER
D.1. Available non-recursive digital filters in ALADIN
Definition of non-recursive filters
The "Ideal low-pass" filter
The "Ideal low-pass" filter with a "Lanczos" window
The "Optimal" filter
The "Dolph-Chebyshev" filter
Some more details about the "Dolph-Chebyshev" filter ...
The "Ideal low-pass" filter with a "Dolph" window
D.2. Available recursive digital filters in ALADIN
Discrete formulations of the filtered state for a recursive filter of order K
Ideal (as N ® +¥ ) response function
Effective response
Examples
Principle
Computation of weights, using simple polynomial functions
Computation of weights, using a more complicated scheme (spline-type functions)
Example of effective responses (polynomial fit)
Example of effective responses (splin fit)
General features
Initialization and derived applications
Use in 4d-var assimilation
Digital filters for variational assimilation and blending
E. BIBLIOGRAPHY