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Digital Filtering and data assimilation (presentation, 2000)

June 2001

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)

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