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 ® +Â¥ ) 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)