A multivariate balance operator for variational ocean data assimilation

Weaver, Anthony; Deltel, Charles; Machu, Éric; Ricci, Sophie; Daget, Nicolas

doi:10.1256/qj.05.119

Cited by 158 publications

(136 citation statements)

References 36 publications

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“…Others scenarios, as the Dual formalism which takes into account the possible error of model M , lead to others and sometime more sophisticated computations( [14,15]). The goal of this paper is not to present all the possible scenarios but to focus on the complexity of the algorithm needed for their implementation.…”

Section: Introductionmentioning

confidence: 99%

YAO: A Software for Variational Data Assimilation Using Numerical Models

Nardi¹,

Sorror²,

Badran³

et al. 2009

Computational Science and Its Applications – ICCSA 2009

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Abstract. Variational data assimilation consists in estimating control parameters of a numerical model in order to minimize the misfit between the forecast values and some actual observations. The gradient based minimization methods require the multiplication of the transpose jacobian matrix (adjoint model), which is of huge dimension, with the derivative vector of the cost function at the observation points. We present a method based on a modular graph concept and two algorithms to avoid these expensive multiplications. The first step of the method is a propagation algorithm on the graph that allows computing the output of the numerical model and its linear tangent, the second is a backpropagation on the graph that allows the computation of the adjoint model. The YAO software implements these two steps using appropriate algorithms. We present a brief description of YAO functionalities.

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Section: Introductionmentioning

confidence: 99%

YAO: A Software for Variational Data Assimilation Using Numerical Models

Nardi¹,

Sorror²,

Badran³

et al. 2009

Computational Science and Its Applications – ICCSA 2009

View full text Add to dashboard Cite

show abstract

“…The data assimilation method is a variant of the multivariate incremental 3D-Var FGAT (First-Guess at Appropriate Time) method described in Weaver et al (2003Weaver et al ( , 2005 and Ricci et al (2005). A short description is given below to highlight those features of the method that are important in this study.…”

Section: Data Assimilation Methodsmentioning

confidence: 99%

“…The operators K ηT and K ηS in Equation (13) (Lagerloef et al, 1999). A detailed description of the multivariate balance operator can be found in Weaver et al (2005). The increment δw and background-error covariance matrix B (w) are formally defined with respect to w b .…”

Section: Data Assimilation Methodsmentioning

confidence: 99%

“…In this study, as in Weaver et al (2005), σ max T = 1.5 • C, δz = 10 m, σ ml T = 0.5 • C, and σ do T = 0.07 • C. Finally, the σ b T were smoothed in each model level using a diffusion (Gaussian) filter with geographically dependent length-scales identical to those specified in the horizontal correlation operator.…”

Section: Parametrized Error Variance Matrix: D (1) ( W)mentioning

confidence: 99%

“…The procedure involves using the square root of the (localized) ensemble covariance matrix to transform the control vector into a vector of background-state increments. The basic transformation is designed to precondition the minimization problem and is standard in variational assimilation systems that employ more conventional background-error covariance formulations based on covariance models (Derber and Bouttier, 1999;Lorenc, 2003a;Weaver et al, 2005). Methods to define the background-error covariance matrix as a linear combination of an ensemble-estimated matrix and a covariance model matrix have also been proposed (Hamill and Synder, 2000;Lorenc, 2003b;Buehner, 2005).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Ensemble estimation of background‐error variances in a three‐dimensional variational data assimilation system for the global ocean

Daget

Weaver

Balmaseda

2009

Quart J Royal Meteoro Soc

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This paper studies the sensitivity of global ocean analyses to two flow-dependent formulations of the background-error standard deviations (σ b ) for temperature and salinity in a three-dimensional variational data assimilation (3D-Var) system. The first formulation is based on an empirical parameterization of σ b in terms of the vertical gradients of the background temperature and salinity fields, while the second formulation involves a more sophisticated approach that derives σ b from the spread of an ensemble of background states. The ensembles are created by explicitly perturbing both the surface fluxes (wind stress, fresh water and heat) used to force the model and the observations (temperature and salinity profiles) used in the assimilation process. The two formulations are compared in two cycled 3D-Var experiments for the period 1993-2000. In both experiments, the observation-error standard deviations (σ o ) are geographically dependent and estimated from a model-data comparison prior to assimilation. An additional 3D-Var experiment that employs the parametrized σ b but a simpler σ o formulation, and a control experiment involving no data assimilation, were also conducted and used for comparison.All 3D-Var experiments produce a significant reduction in the mean and standard deviation of the temperature and salinity innovations compared to those of the control experiment. The largest differences between the two σ b formulations occur in the upper 150 m, where the parametrized σ b are notably larger than the ensemble σ b . In this region, the innovation statistics are slightly better for the parametrized σ b . Statistical consistency checks indicate that both schemes underestimate σ b , the underestimation being stronger with the ensemble formulation. The error growth between cycles, however, is much reduced with the ensemble σ b , suggesting that the analyses produced with the ensemble σ b are in better balance than those produced with the parametrized σ b . This claim is supported by independent data comparisons involving model fields not directly constrained by the assimilated temperature and salinity profiles. In particular, sea-surface height (SSH) anomalies in the northwest Atlantic and zonal velocities in the equatorial Pacific are clearly better with the ensemble σ b than with the parametrized σ b . Results also show that while some aspects of those variables are improved with data assimilation (SSH anomalies and currents in the central and eastern Pacific), other aspects are degraded (SSH anomalies in the northwest Atlantic, currents in the western Pacific). Areas for improving the ensemble method and for making better use of the ensemble information are discussed.

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4D variational data assimilation for locally nested models: Complementary theoretical aspects and application to a 2D shallow water model

Simon¹,

Debreu

Blayo

2011

Numerical Methods in Fluids

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SUMMARYWe consider the application of a four-dimensional variational data assimilation method to a numerical model, which employs local mesh refinement to improve its solution. We focus on structured meshes where a high-resolution grid is embedded in a coarser resolution one, which covers the entire domain. The formulation of the nested variational data assimilation algorithm was derived in a preliminary work (Int. J. Numer. Meth. Fluids 2008; under review). We are interested here in complementary theoretical aspects. We present first a model for the multi-grid background error covariance matrix. Then, we propose a variant of our algorithms based on the addition of control variables in the inter-grid transfers in order to allow for a reduction of the errors linked to the interactions between the grids. These formulations are illustrated and discussed in the test case experiment of a 2D shallow water model.

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A multivariate balance operator for variational ocean data assimilation

Cited by 158 publications

References 36 publications

YAO: A Software for Variational Data Assimilation Using Numerical Models

YAO: A Software for Variational Data Assimilation Using Numerical Models

Ensemble estimation of background‐error variances in a three‐dimensional variational data assimilation system for the global ocean

4D variational data assimilation for locally nested models: Complementary theoretical aspects and application to a 2D shallow water model

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