Search Results
Abstract
The sensitivity of model forecasts to uncertainties in control variables is evaluated using the adjoint technique and the ensemble generated by the reduced-order four-dimensional variational data assimilation (R4DVAR) algorithm within the framework of twin-data experiments with a quasigeostrophic model. To simulate real applications where the true state is unknown, the sensitivities were estimated using model solutions that were obtained after assimilating sparse observations extracted from the true solutions. The numerical experiments were conducted in the linear, weakly nonlinear, and strongly nonlinear (NL) regimes with special emphasis on the NL case characterized by the instability of the tangent linear model. It is shown that the ensemble-based R4DVAR method provides better sensitivity estimates in the NL case, primarily due to the better accuracy of the optimized solutions. The concept of sensitivity in the NL case is also considered within the statistical framework. Using analytical arguments and numerical experimentation, averaging the adjoint sensitivity estimates over an ensemble of model trajectories generated by finite perturbations of the optimal control is shown to provide an estimate similar to that obtained with the adjoint model stabilized by enhanced dissipation. This observation allows for evaluation of the sensitivities of strongly nonlinear optimal solutions by using both the adjoint (4DVAR) and ensemble (R4DVAR) optimization algorithms.
Abstract
The sensitivity of model forecasts to uncertainties in control variables is evaluated using the adjoint technique and the ensemble generated by the reduced-order four-dimensional variational data assimilation (R4DVAR) algorithm within the framework of twin-data experiments with a quasigeostrophic model. To simulate real applications where the true state is unknown, the sensitivities were estimated using model solutions that were obtained after assimilating sparse observations extracted from the true solutions. The numerical experiments were conducted in the linear, weakly nonlinear, and strongly nonlinear (NL) regimes with special emphasis on the NL case characterized by the instability of the tangent linear model. It is shown that the ensemble-based R4DVAR method provides better sensitivity estimates in the NL case, primarily due to the better accuracy of the optimized solutions. The concept of sensitivity in the NL case is also considered within the statistical framework. Using analytical arguments and numerical experimentation, averaging the adjoint sensitivity estimates over an ensemble of model trajectories generated by finite perturbations of the optimal control is shown to provide an estimate similar to that obtained with the adjoint model stabilized by enhanced dissipation. This observation allows for evaluation of the sensitivities of strongly nonlinear optimal solutions by using both the adjoint (4DVAR) and ensemble (R4DVAR) optimization algorithms.
Abstract
Many background error correlation (BEC) models in data assimilation are formulated in terms of a smoothing operator 
In this study approximate renormalization techniques based on the Monte Carlo (MC) and Hadamard matrix (HM) methods and on the analytic approximations derived under the assumption of the local homogeneity (LHA) of 
Abstract
Many background error correlation (BEC) models in data assimilation are formulated in terms of a smoothing operator
In this study approximate renormalization techniques based on the Monte Carlo (MC) and Hadamard matrix (HM) methods and on the analytic approximations derived under the assumption of the local homogeneity (LHA) of
Abstract
Improving the performance of ensemble filters applied to models with many state variables requires regularization of the covariance estimates by localizing the impact of observations on state variables. A covariance localization technique based on modeling of the sample covariance with polynomial functions of the diffusion operator (DL method) is presented. Performance of the technique is compared with the nonadaptive (NAL) and adaptive (AL) ensemble localization schemes in the framework of numerical experiments with synthetic covariance matrices in a realistically inhomogeneous setting. It is shown that the DL approach is comparable in accuracy with the AL method when the ensemble size is less than 100. With larger ensembles, the accuracy of the DL approach is limited by the local homogeneity assumption underlying the technique. Computationally, the DL method is comparable with the NAL technique if the ratio of the local decorrelation scale to the grid step is not too large.
Abstract
Improving the performance of ensemble filters applied to models with many state variables requires regularization of the covariance estimates by localizing the impact of observations on state variables. A covariance localization technique based on modeling of the sample covariance with polynomial functions of the diffusion operator (DL method) is presented. Performance of the technique is compared with the nonadaptive (NAL) and adaptive (AL) ensemble localization schemes in the framework of numerical experiments with synthetic covariance matrices in a realistically inhomogeneous setting. It is shown that the DL approach is comparable in accuracy with the AL method when the ensemble size is less than 100. With larger ensembles, the accuracy of the DL approach is limited by the local homogeneity assumption underlying the technique. Computationally, the DL method is comparable with the NAL technique if the ratio of the local decorrelation scale to the grid step is not too large.
Abstract
A hybrid background error covariance (BEC) model for three-dimensional variational data assimilation of glider data into the Navy Coastal Ocean Model (NCOM) is introduced. Similar to existing atmospheric hybrid BEC models, the proposed model combines low-rank ensemble covariances 
The BEC model is validated by assimilation experiments with simulated and real data obtained during a glider survey of the Monterey Bay in August 2003. It is shown that the proposed hybrid scheme substantially improves the forecast skill of the heuristic covariance model.
Abstract
A hybrid background error covariance (BEC) model for three-dimensional variational data assimilation of glider data into the Navy Coastal Ocean Model (NCOM) is introduced. Similar to existing atmospheric hybrid BEC models, the proposed model combines low-rank ensemble covariances
The BEC model is validated by assimilation experiments with simulated and real data obtained during a glider survey of the Monterey Bay in August 2003. It is shown that the proposed hybrid scheme substantially improves the forecast skill of the heuristic covariance model.
Abstract
A version of the reduced control space four-dimensional variational method (R4DVAR) of data assimilation into numerical models is proposed. In contrast to the conventional 4DVAR schemes, the method does not require development of the tangent linear and adjoint codes for implementation. The proposed R4DVAR technique is based on minimization of the cost function in a sequence of low-dimensional subspaces of the control space. Performance of the method is demonstrated in a series of twin-data assimilation experiments into a nonlinear quasigeostrophic model utilized as a strong constraint. When the adjoint code is stable, R4DVAR’s convergence rate is comparable to that of the standard 4DVAR algorithm. In the presence of strong instabilities in the direct model, R4DVAR works better than 4DVAR whose performance is deteriorated because of the breakdown of the tangent linear approximation. Comparison of the 4DVAR and R4DVAR also shows that R4DVAR becomes advantageous when observations are sparse and noisy.
Abstract
A version of the reduced control space four-dimensional variational method (R4DVAR) of data assimilation into numerical models is proposed. In contrast to the conventional 4DVAR schemes, the method does not require development of the tangent linear and adjoint codes for implementation. The proposed R4DVAR technique is based on minimization of the cost function in a sequence of low-dimensional subspaces of the control space. Performance of the method is demonstrated in a series of twin-data assimilation experiments into a nonlinear quasigeostrophic model utilized as a strong constraint. When the adjoint code is stable, R4DVAR’s convergence rate is comparable to that of the standard 4DVAR algorithm. In the presence of strong instabilities in the direct model, R4DVAR works better than 4DVAR whose performance is deteriorated because of the breakdown of the tangent linear approximation. Comparison of the 4DVAR and R4DVAR also shows that R4DVAR becomes advantageous when observations are sparse and noisy.
