# Guaranteeing the convergence of the saddle formulation in weakly-constrained 4D-VAR data assimilation

Serge Gratton, Selime Gürol, Ehouarn Simon, Philippe Toint

Research output: Contribution to journalArticle

### Abstract

This paper discusses convergence issues for the saddle variational formulation
of the weakly-constrained 4D-VAR method in data assimilation, a method whose main interests are its parallelizable nature and its limited use of the inverse of the correlation matrices. It is shown that the method, in its original form, may produce erratic results or diverge because of the inherent lack of monotonicity of the produced objective function values. Convergent, variationaly coherent variants of the algorithm are then proposed which largely retain the desirable features of the original proposal, and the circumstances in which these variants may be preferable to other approaches is briefly discussed.
Language English Quarterly Journal of the Royal Meteorological Society Accepted/In press - 2018

### Fingerprint

Data Assimilation
data assimilation
Formulation
Correlation Matrix
erratic
Variational Formulation
Diverge
Monotonicity
Objective function
matrix
method

### Keywords

• weather forecasting
• numerical algorithms
• Convergence theory

### Cite this

title = "Guaranteeing the convergence of the saddle formulation in weakly-constrained 4D-VAR data assimilation",
abstract = "This paper discusses convergence issues for the saddle variational formulationof the weakly-constrained 4D-VAR method in data assimilation, a method whose main interests are its parallelizable nature and its limited use of the inverse of the correlation matrices. It is shown that the method, in its original form, may produce erratic results or diverge because of the inherent lack of monotonicity of the produced objective function values. Convergent, variationaly coherent variants of the algorithm are then proposed which largely retain the desirable features of the original proposal, and the circumstances in which these variants may be preferable to other approaches is briefly discussed.",
keywords = "weather forecasting, numerical algorithms, Convergence theory",
author = "Serge Gratton and Selime G{\"u}rol and Ehouarn Simon and Philippe Toint",
year = "2018",
language = "English",
journal = "Quarterly Journal of the Royal Meteorological Society",
issn = "0035-9009",
publisher = "John Wiley and Sons Ltd",

}

In: Quarterly Journal of the Royal Meteorological Society, 2018.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Guaranteeing the convergence of the saddle formulation in weakly-constrained 4D-VAR data assimilation

AU - Gratton,Serge

AU - Gürol,Selime

AU - Simon,Ehouarn

AU - Toint,Philippe

PY - 2018

Y1 - 2018

N2 - This paper discusses convergence issues for the saddle variational formulationof the weakly-constrained 4D-VAR method in data assimilation, a method whose main interests are its parallelizable nature and its limited use of the inverse of the correlation matrices. It is shown that the method, in its original form, may produce erratic results or diverge because of the inherent lack of monotonicity of the produced objective function values. Convergent, variationaly coherent variants of the algorithm are then proposed which largely retain the desirable features of the original proposal, and the circumstances in which these variants may be preferable to other approaches is briefly discussed.

AB - This paper discusses convergence issues for the saddle variational formulationof the weakly-constrained 4D-VAR method in data assimilation, a method whose main interests are its parallelizable nature and its limited use of the inverse of the correlation matrices. It is shown that the method, in its original form, may produce erratic results or diverge because of the inherent lack of monotonicity of the produced objective function values. Convergent, variationaly coherent variants of the algorithm are then proposed which largely retain the desirable features of the original proposal, and the circumstances in which these variants may be preferable to other approaches is briefly discussed.

KW - weather forecasting

KW - numerical algorithms

KW - Convergence theory

M3 - Article

JO - Quarterly Journal of the Royal Meteorological Society

T2 - Quarterly Journal of the Royal Meteorological Society

JF - Quarterly Journal of the Royal Meteorological Society

SN - 0035-9009

ER -