A reduced-order strategy for 4D-Var data assimilation

Robert, Christian; Durbiano, Sophie; Blayo, Éric; Verron, Jacques; Blum, Jacques; Dimet, F.‐X. Le

doi:10.1016/j.jmarsys.2005.04.003

Cited by 48 publications

(53 citation statements)

References 35 publications

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“…We address these issues in the next section. Robert et al (2005) (see also Robert et al, 2006) make use of the EOFs to define an appropriate reduced control space and estimation of the background-error covariance matrix. In their approach, an optimal solution is sought in the full space but the problem of computational cost is addressed by considering a reduced 4D-Var to provide a relevant initial guess for the full-space minimization.…”

Section: Enhanced Gauss-newton Methods For 4d-varmentioning

confidence: 99%

A reduced and limited‐memory preconditioned approach for the 4D‐Var data‐assimilation problem

Gratton

Laloyaux

Sartenaer

et al. 2011

Quart J Royal Meteoro Soc

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We recall a theoretical analysis of the equivalence between the Kalman filter and the four-dimensional variational (4D-Var) approach to solve data-assimilation problems. This result is then extended to cover the comparison of the singular evolutive extended Kalman (SEEK) filter with a reduced variant of the 4D-Var algorithm. We next concentrate on the solution of the 4D-Var, which is usually computed with a (truncated) Gauss-Newton algorithm using a preconditioned conjugate-gradient-like (CG) method. Motivated by the equivalence of the abovementioned algorithms, we explore techniques used in the SEEK filter and based on empirical orthogonal functions (EOFs) as an attempt to accelerate the Gauss-Newton method further. This leads to the development of an appropriate starting point for the CG method, together with that of a powerful limited-memory preconditioner (LMP), as shown by preliminary numerical experiments performed on a shallowwater model.

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Section: Enhanced Gauss-newton Methods For 4d-varmentioning

confidence: 99%

A reduced and limited‐memory preconditioned approach for the 4D‐Var data‐assimilation problem

Gratton

Laloyaux

Sartenaer

et al. 2011

Quart J Royal Meteoro Soc

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“…Note that the formulation of Trj4DVar is similar to model-order reduced 4D-Var (MOR-4D-Var) methods (Robert et al 2005), or the family of four-dimensional (4D) ensemble-variational data assimilation (4DEnVar) methods (Lorenc et al 2015). The objective of the MOR-4D-Var approach is to seek a low-rank approximation of the model to reduce the computational effort of 4D-Var, and that of 4DEnVar is to obtain a low-rank and flow-dependent representation of the background error statistics.…”

Section: Example: Trajectory-based 4d-var Approachmentioning

confidence: 99%

Evaluation Criteria on the Design for Assimilating Remote Sensing Data Using Variational Approaches

Sha

Heemink

Lin

et al. 2017

Monthly Weather Review

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Remote sensing, as a powerful tool for monitoring atmospheric phenomena, has been playing an increasingly important role in inverse modeling. Remote sensing instruments measure quantities that often combine several state variables as one. This creates very strong correlations between the state variables that share the same observation variable. This may cause numerical problems resulting in a low convergence rate or inaccurate estimates in gradient-based variational assimilation if improper error statistics are used. In this paper, two criteria or scoring rules are proposed to quantify the numerical robustness of assimilating a specific set of remote sensing observations and to quantify the reliability of the estimates of the parameters. The criteria are derived by analyzing how the correlations are created via shared observation data and how they may influence the process of variational data assimilation. Experimental tests are conducted and show a good level of agreement with theory. The results illustrate the capability of the criteria to indicate the reliability of the assimilation process. Both criteria can be used with observing system simulation experiments (OSSEs) and in combination with other verification scores.

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“…The implementation of this method additionally results in a drastic reduction of the dimension of the control space and thus the minimisation process [24,25]. Reduced order 4D-Var can also be used to precondition 4D-Var, and reduce computational cost [26].…”

Section: Introductionmentioning

confidence: 99%

“…The dual-weighted POD approach provides an 'enriched' set of basis functions combining information from both model dynamics and the data assimilation system. The practical utility of this approach has been extended to include ocean and climate modelling and the solution of inverse problems ( [24], [25], [37] and [29]). The POD-based 4D VAR not only reduces the dimension of control space, but also reduces the size of dynamical model, both in dramatic ways ( [37,38]).…”

Section: Introductionmentioning

confidence: 99%

A POD reduced‐order 4D‐Var adaptive mesh ocean modelling approach

Fang

Pain

Navon

et al. 2008

Numerical Methods in Fluids

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A novel Proper Orthogonal Decomposition (POD) inverse model developed for a mesh adaptive ocean model, the Imperial College Ocean Model(ICOM) is herein presented. The new POD model is validated by application to a gyre flow test case where it invertis for initial conditions. ( **** Say something quantitative about how well the model performed here, one short sentence will do). Error estimation (including the error in POD reduced modelling and the interpolation error in adaptive meshes) was used to show that quality of reduced adaptive mesh models was (**** say something quantitative about the results of this estimation).New criteria are applied for POD adaptivity in this approach. When the optimization loses control ( i.e., when in the process of optimisation of the new control variables depart significantly from the ones on which the POD reduced model is based upon) the set of POD snapshots are refreshed. when the optimization loses its control, i.e., when in the process of optimisation the new control variables depart significantly from the ones on which the POD reduced model is based upon. Previously developed numerical approaches (Fang et al. (2007)) are employed to accurately represent the geostrophic balance and improve the efficiency of the POD simulation;The feasibility of the proposed methodology as well as and it's ability to assessing the error in POD results are demonstrated in a range of numerical experiments including:-

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A reduced-order strategy for 4D-Var data assimilation

Cited by 48 publications

References 35 publications

A reduced and limited‐memory preconditioned approach for the 4D‐Var data‐assimilation problem

A reduced and limited‐memory preconditioned approach for the 4D‐Var data‐assimilation problem

Evaluation Criteria on the Design for Assimilating Remote Sensing Data Using Variational Approaches

A POD reduced‐order 4D‐Var adaptive mesh ocean modelling approach

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