A comparative study of the performance of high resolution advection schemes in the context of data assimilation

Akella, Santha; Navon, I. M.

doi:10.1002/fld.1145

Cited by 12 publications

(13 citation statements)

References 70 publications

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“…The sensitivities of J with respect to the ensemble DAS input [y i , R i , x b , B] were evaluated by performing the computational stages S1-S5. The first-order adjoint of the finite volume SW model used in this study was developed in the work of Akella and Navon (2006). The simplicity of the SW model allowed us to implement an SOA model with the aid of automatic differentiation software (Giering and Kaminski 1998).…”

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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“…The finite-volume FFSL scheme is of particular importance since it provides the horizontal discretization to the finite-volume dynamical core of the National Center for Atmospheric Research (NCAR) Community Atmosphere Model (CAM) and the National Aeronautics and Space Administration (NASA) Goddard Earth Observing System-5 (GEOS-5) data assimilation and forecasting system (Lin 2004). The adjoint model to the SW-FFSL scheme used in this study was developed in the work of Akella and Navon (2006) with the aid of automatic differentiation software (Giering and Kaminski 1998).…”

Section: Numerical Experimentsmentioning

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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“…Issues with discrete adjoints can come not only from the hyperbolic discretization, but also from the inclusion in the models of physical processes with parameterized discontinuities [10]. Despite the importance of such schemes in many fields, the impact of discretization techniques for advection/hyperbolic term(s) in the framework of inverse problems and data assimilation has not been extensively studied to date [11].…”

Section: G(c(t X)) DX Dt + P(c(tmentioning

confidence: 99%

“…There are many discretization techniques that have proved very useful in geoscience applications and are not discussed here. Among them there are the piecewise parabolic method [27] (whose discrete adjoint performance is discussed in [11]), the Rood advection scheme [7], etc. as well as the discontinuous Galerkin approach [18].…”

Section: Nonlinear Discretization Schemesmentioning

confidence: 99%

“…The properties of discrete adjoints for different classes of numerical schemes have been discussed in the literature. They include non-oscillatory advection schemes [16], Euler equations [17], discontinuous Galerkin methods [18], streamline upwind/Petrov Galerkin methods [19], high-resolution methods [11], domain decomposition methods [20], and various advection methods in MITGCM [21]. The correct behaviour of discrete 772 Z. LIU AND A. SANDU adjoints is very important in optimal control of systems with distributed parameters [22,23] and in data assimilation [24,25].…”

Section: G(c(t X)) DX Dt + P(c(tmentioning

confidence: 99%

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On the properties of discrete adjoints of numerical methods for the advection equation

Liu

Sandu

2007

Numerical Methods in Fluids

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SUMMARYThis paper discusses several aspects related to the consistency of the discrete adjoints of upwind numerical schemes. Both linear (finite differences, finite volumes) and nonlinear (slope and flux-limited) discretizations of the one-dimensional advection equation are considered. The analysis is focused on uniform meshes and on explicit numerical schemes. We show that the discrete adjoints may lose consistency near the points where upwinding changes, near inflow boundaries where another numerical scheme is employed, and near the locations where the slope/flux limiter is active in the forward simulation. Numerical results are presented to support the theoretical analysis.

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A comparative study of the performance of high resolution advection schemes in the context of data assimilation

Cited by 12 publications

References 70 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

On the properties of discrete adjoints of numerical methods for the advection equation

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