Efficiency of a POD‐based reduced second‐order adjoint model in 4D‐Var data assimilation

Daescu, Dacian N.; Navon, I. M.

doi:10.1002/fld.1316

Cited by 78 publications

(64 citation statements)

References 45 publications

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“…The simplicity of the SW model allowed us to implement an SOA model with the aid of automatic differentiation software (Giering and Kaminski 1998). The verification of the SOA model included a Taylor series test (Daescu and Navon 2007) and a Hessian symmetry test using pairs of random vectors. An approximate solution to the linear system at stage S3 was computed by imposing the con-…”

Section: B Forecast Error Sensitivity Analysismentioning

confidence: 99%

On the Sensitivity Equations of Four-Dimensional Variational (4D-Var) Data Assimilation

Daescu

2008

Monthly Weather Review

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The equations of the forecast sensitivity to observations and to the background estimate in a fourdimensional variational data assimilation system (4D-Var DAS) are derived from the first-order optimality condition in unconstrained minimization. Estimation of the impact of uncertainties in the specification of the error statistics is considered by evaluating the sensitivity to the observation and background error covariance matrices. The information provided by the error covariance sensitivity analysis is used to identify the input components for which improved estimates of the statistical properties of the errors are of most benefit to the analysis and forecast. A close relationship is established between the sensitivities within each input pair data/error covariance such that once the observation and background sensitivities are available the evaluation of the sensitivity to the specification of the corresponding error statistics requires little additional computational effort. The relevance of the 4D-Var sensitivity equations to assess the data impact in practical applications is discussed. Computational issues are addressed and idealized 4D-Var experiments are set up with a finite-volume shallow-water model to illustrate the theoretical concepts. Time-dependent observation sensitivity and potential applications to improve the model forecast are presented. Guidance provided by the sensitivity fields is used to adjust a 4D-Var DAS to achieve forecast error reduction through assimilation of supplementary data and through an accurate specification of a few of the background error variances.

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Section: B Forecast Error Sensitivity Analysismentioning

confidence: 99%

On the Sensitivity Equations of Four-Dimensional Variational (4D-Var) Data Assimilation

Daescu

2008

Monthly Weather Review

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“…Second-order derivatives in the reduced space may be computed if a full second-order adjoint model is available (Daescu and Navon 2007). Consequently, computational savings may be achieved only by a drastic reduction in the number of iterations because of the low dimension of the optimization problem (13).…”

Section: A the Reduced-order 4dvarmentioning

confidence: 99%

A Dual-Weighted Approach to Order Reduction in 4DVAR Data Assimilation

Daescu

Navon

2008

Monthly Weather Review

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Strategies to achieve order reduction in four-dimensional variational data assimilation (4DVAR) search for an optimal low-rank state subspace for the analysis update. A common feature of the reduction methods proposed in atmospheric and oceanographic studies is that the identification of the basis functions relies on the model dynamics only, without properly accounting for the specific details of the data assimilation system (DAS). In this study a general framework of the proper orthogonal decomposition (POD) method is considered and a cost-effective approach is proposed to incorporate DAS information into the orderreduction procedure. The sensitivities of the cost functional in 4DVAR data assimilation with respect to the time-varying model state are obtained from a backward integration of the adjoint model. This information is further used to define appropriate weights and to implement a dual-weighted proper orthogonal decomposition (DWPOD) method for order reduction. The use of a weighted ensemble data mean and weighted snapshots using the adjoint DAS is a novel element in reduced-order 4DVAR data assimilation. Numerical results are presented with a global shallow-water model based on the Lin-Rood flux-form semi-Lagrangian scheme. A simplified 4DVAR DAS is considered in the twin-experiment framework with initial conditions specified from the 40-yr ECMWF Re-Analysis (ERA-40) datasets. A comparative analysis with the standard POD method shows that the reduced DWPOD basis may provide an increased efficiency in representing an a priori specified forecast aspect and as a tool to perform reduced-order optimal control. This approach represents a first step toward the development of an order-reduction methodology that combines in an optimal fashion the model dynamics and the characteristics of the 4DVAR DAS.

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“…In a series of papers (see e.g. [31,36,37]) Navon et al proposed a dual-weighted POD method, where the weights assigned to each snapshot were derived from an adjoint related to the optimality system of a variational data assimilation problem in meteorology. It is also known that for compressible flows the choice of inner product and weighting of the different flow variables (velocity, pressure, speed of sound) in the snapshot matrix can have a large effect on the stability and accuracy of the ROM [14,35].…”

Section: "If It Is Not In the Snapshots It Is Not In The Rom"mentioning

confidence: 99%

Model Order Reduction in Fluid Dynamics: Challenges and Perspectives

Lassila

Manzoni

Quarteroni

et al. 2014

Reduced Order Methods for Modeling and Computational Reduction

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This chapter reviews techniques of model reduction of fluid dynamics systems. Fluid systems are known to be difficult to reduce efficiently due to several reasons. First of all, they exhibit strong nonlinearities -which are mainly related either to nonlinear convection terms and/or some geometric variability -that often cannot be treated by simple linearization. Additional difficulties arise when attempting model reduction of unsteady flows, especially when long-term transient behavior needs to be accurately predicted using reduced order models and more complex features, such as turbulence or multiphysics phenomena, have to be taken into consideration. We first discuss some general principles that apply to many parametric model order reduction problems, then we apply them on steady and unsteady viscous flows modelled by the incompressible Navier-Stokes equations. We address questions of inf-sup stability, certification through error estimation, computational issues and -in the unsteady case -long-time stability of the reduced model. Moreover, we provide an extensive list of literature references.

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Efficiency of a POD‐based reduced second‐order adjoint model in 4D‐Var data assimilation

Cited by 78 publications

References 45 publications

On the Sensitivity Equations of Four-Dimensional Variational (4D-Var) Data Assimilation

On the Sensitivity Equations of Four-Dimensional Variational (4D-Var) Data Assimilation

A Dual-Weighted Approach to Order Reduction in 4DVAR Data Assimilation

Model Order Reduction in Fluid Dynamics: Challenges and Perspectives

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