Digital Filtering and data assimilation (presentation, 2000)
Article published on June 2001
last modification on 21 June 2007
DIGITAL FILTERING AND DATA ASSIMILATION, presentation of Dominique Giard during the ALATNET seminar on Data Assimilation, June 11-22, 2001.
- 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
-
-
- D.3. Boundary filters
-
-
- 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)
-
-
- D.4. Criteria of choice
-
-
- General features
-
-
-
- Initialization and derived applications
-
-
-
- Use in 4d-var assimilation
-
-
-
- Digital filters for variational assimilation and blending
-
- E. BIBLIOGRAPHY
-
- E.1. Introduction
-
- E.2. Digital filtering in NWP
-
- E.3. "Normal mode" initialization (some examples)
-
- E.4. Other filtering methods (some examples)