On the use of the saddle formulation in weakly-constrained 4D-VAR data assimilation

Serge Gratton; Selime Gürol; Ehouarn Simon; Philippe Toint

On the use of the saddle formulation in weakly-constrained 4D-VAR data assimilation

Serge Gratton, Selime Gürol, Ehouarn Simon, Philippe Toint

Namur Institute for Complex Systems

Research output: Working paper

35 Downloads (Pure)

Abstract

This paper discusses the practical use of the saddle variational formulation
for the weakly-constrained 4D-VAR method in data assimilation. 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 whose practical performance is compared to that of other
formulations. This comparison is conducted on two data assimilation instances
(Burgers equation and the Quasi-Geostrophic model), using two different
assumptions on parallel computing environment. Because these
variants essentially retain the parallelization advantages of the original
proposal, they often --- but not always --- perform best, even for moderate
numbers of computing processes.

Original language	English
Publisher	Arxiv
Volume	1709.06383
Publication status	Submitted - 20 Sept 2017

Keywords

data assimilation
weather forecasting
Numerical optimization
Least-squares problems

Access to Document

Using the saddle formulation in data assimilationSubmitted manuscript, 1.19 MB

6 Article

A data assimilation algorithm for predicting rain
Janjić, T., Ruckstuhl, Y. & Toint, P. L., Apr 2021, In: Quarterly Journal of the Royal Meteorological Society. 147, 736, p. 1949-1963 15 p.
Research output: Contribution to journal › Article › peer-review

Open Access
A note on preconditioning weighted linear least-squares with consequences for weakly constrained variational data assimilation
Gratton, S., Selime, G., Simon, E. & Toint, P., Apr 2018, In: Quarterly Journal of the Royal Meteorological Society. 144, 712, p. 934-940 7 p.
Research output: Contribution to journal › Article › peer-review

File
31 Downloads (Pure)
BFO, a trainable derivative-free Brute Force Optimizer for nonlinear bound-constrained optimization and equilibrium computations with continuous and discrete variables
Porcelli, M. & Toint, P., 30 Jun 2017, In: Transactions of the American Methematical Society on Mathematical Software. 44, 1, 28 p., 6.
Research output: Contribution to journal › Article › peer-review

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54 Downloads (Pure)

1 Active

ADALGOPT: ADALGOPT - Advanced algorithms in nonlinear optimization
Sartenaer, A. (CoI) & Toint, P. (CoI)
1/01/87 → …
Project: Research Axis

1 Invited talk

A primal-dual approach of weak-constrained variational data assimilation: (Iterate) History matters
Toint, P. (Speaker)
13 Oct 2017
Activity: Talk or presentation types › Invited talk

Cite this

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title = "On the use of the saddle formulation in weakly-constrained 4D-VAR data assimilation",

abstract = "This paper discusses the practical use of the saddle variational formulationfor the weakly-constrained 4D-VAR method in data assimilation. It is shownthat the method, in its original form, may produce erratic results or divergebecause of the inherent lack of monotonicity of the produced objectivefunction values. Convergent, variationaly coherent variants of the algorithmare then proposed whose practical performance is compared to that of otherformulations. This comparison is conducted on two data assimilation instances(Burgers equation and the Quasi-Geostrophic model), using two differentassumptions on parallel computing environment. Because thesevariants essentially retain the parallelization advantages of the originalproposal, they often --- but not always --- perform best, even for moderatenumbers of computing processes.",

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AU - Simon, Ehouarn

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N2 - This paper discusses the practical use of the saddle variational formulationfor the weakly-constrained 4D-VAR method in data assimilation. It is shownthat the method, in its original form, may produce erratic results or divergebecause of the inherent lack of monotonicity of the produced objectivefunction values. Convergent, variationaly coherent variants of the algorithmare then proposed whose practical performance is compared to that of otherformulations. This comparison is conducted on two data assimilation instances(Burgers equation and the Quasi-Geostrophic model), using two differentassumptions on parallel computing environment. Because thesevariants essentially retain the parallelization advantages of the originalproposal, they often --- but not always --- perform best, even for moderatenumbers of computing processes.

AB - This paper discusses the practical use of the saddle variational formulationfor the weakly-constrained 4D-VAR method in data assimilation. It is shownthat the method, in its original form, may produce erratic results or divergebecause of the inherent lack of monotonicity of the produced objectivefunction values. Convergent, variationaly coherent variants of the algorithmare then proposed whose practical performance is compared to that of otherformulations. This comparison is conducted on two data assimilation instances(Burgers equation and the Quasi-Geostrophic model), using two differentassumptions on parallel computing environment. Because thesevariants essentially retain the parallelization advantages of the originalproposal, they often --- but not always --- perform best, even for moderatenumbers of computing processes.

KW - data assimilation

KW - weather forecasting

KW - Numerical optimization

KW - Least-squares problems

M3 - Working paper

VL - 1709.06383

BT - On the use of the saddle formulation in weakly-constrained 4D-VAR data assimilation

PB - Arxiv

ER -

On the use of the saddle formulation in weakly-constrained 4D-VAR data assimilation

Abstract

Keywords

Access to Document

Fingerprint

Research output

A data assimilation algorithm for predicting rain

A note on preconditioning weighted linear least-squares with consequences for weakly constrained variational data assimilation

BFO, a trainable derivative-free Brute Force Optimizer for nonlinear bound-constrained optimization and equilibrium computations with continuous and discrete variables

Projects

ADALGOPT: ADALGOPT - Advanced algorithms in nonlinear optimization

Activities

A primal-dual approach of weak-constrained variational data assimilation: (Iterate) History matters

Cite this