Four-dimensional data assimilation with a wide range of scales

Tanguay, Monique; Bartello, Peter; Gauthier, Pierre

doi:10.3402/tellusa.v47i5.11625

Cited by 15 publications

(19 citation statements)

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“…Problems in the conditioning could also explain a case of poor convergence in a 4D-Var experiment reported by Andersson et al (2000). Convergence of the minimization is therefore still an issue and given the nonlinear nature of the model, so is the existence of multiple minima (Tanguay et al, 1995).…”

Section: Resultsmentioning

confidence: 99%

“…In Thépaut and Courtier (1991) and later on in Tanguay et al (1995) and Laroche and Gauthier (1999), it is shown that for the largescale dynamics, 4D-Var adjusts the more energetic large-scale components first. To determine the analysis increments of 4D-Var within the inner loop, Courtier et al (1994) then proposed to use the tangent linear model (TLM) and its adjoint (Adj) at a coarser resolution with simplified physical parameterizations.…”

Section: The Incremental Form Of 4d-varmentioning

confidence: 99%

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Operational Implementation of Variational Data Assimilation

Gauthier¹

2003

Data Assimilation for the Earth System

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Section: Resultsmentioning

confidence: 99%

Section: The Incremental Form Of 4d-varmentioning

confidence: 99%

Operational Implementation of Variational Data Assimilation

Gauthier¹

2003

Data Assimilation for the Earth System

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“…The vorticity is the Laplacian of the stream function, ζ = ∇ 2 ψ, and the horizontal wind components are u = −∂ψ/∂y, and v = ∂ψ/∂x, J being the Jacobian, f a forcing term, and D a linear dissipation operator. A detailed description of this model can be found in Tanguay et al (1995) and Laroche and Gauthier (1998).…”

Section: Experimental Settingmentioning

confidence: 99%

“…The model that will be used is the same two-dimensional barotropic non-divergent model used by Tanguay et al (1995) and Laroche and Gauthier (1998) to solve the barotropic vorticity equation on the β-plane:…”

Section: Experimental Settingmentioning

confidence: 99%

“…A background state is built from a previous run of the model for which the initial state has been slightly perturbed, and the background-error covariance matrix is constructed such that B = C , where is the diagonal matrix of the standard deviation and C represents homogeneous isotropic correlations (Appendix B in Gauthier et al, 1993). The correlation length is set to three grid points, which corresponds to approximately 300 km since our domain size corresponds roughly to 7000 km (Tanguay et al, 1995). 3D/4D-var and 3D/4D-PSAS assimilation experiments were conducted with minimizations performed with both MINRES and CG for comparison and stopped using the termination criterion R 1 , for = 10 −4 .…”

Section: Experimental Settingmentioning

confidence: 99%

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Convergence properties of the primal and dual forms of variational data assimilation

Akkraoui

Gauthier

2010

Quart J Royal Meteoro Soc

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The variational data assimilation problem can be solved in either its primal (3D/4D-Var) or dual (3D/4D-PSAS) form. The methods are equivalent at convergence but the dual method exhibits a spurious behaviour at the beginning of the minimization which leads to less probable states than the background state. This is a serious concern when using the dual method in operational implementations when only a finite number of iterations can be afforded. Two classes of minimization algorithms are examined in this article: the conjugate gradient (CG) and the minimum residual (MINRES) methods. While the CG algorithms ensure a monotonic reduction of the cost function, those based on the MINRES enforce instead a monotonic decrease of the norm of the gradient. In this article, it is shown that when applied to the minimization of the dual problem, the MINRES algorithms also lead to iterates for which their 'image' in physical space leads to a monotonic decrease of the primal cost function. A relationship is established showing that the primal objective function is related to the value of the dual cost function and the norm of its gradient. This holds for the incremental forms of both the three-and four-dimensional cases. A new convergence criterion is introduced based on the error norm in model space to make sure that, for the dual problem, the same accuracy is obtained in the analysis when only a finite number of iterations is completed.

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On the role of statistics in climate research

Zwiers¹,

Storch²

2004

Intl Journal of Climatology

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We review the role of statistical analysis in the climate sciences. Special emphasis is given to attempts to construct dynamical knowledge from limited observational evidence, and to the ongoing task of drawing detailed and reliable information on the state, and change, of climate that is needed, for example, for short-term and seasonal forecasting. We conclude with recommendations of how to improve the practice of statistical analysis in the climate sciences by drawing more efficiently on relevant developments in statistical mathematics.

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Four-dimensional data assimilation with a wide range of scales

Cited by 15 publications

References 0 publications

Operational Implementation of Variational Data Assimilation

Operational Implementation of Variational Data Assimilation

Convergence properties of the primal and dual forms of variational data assimilation

On the role of statistics in climate research

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