An optimization framework to improve 4D-Var data assimilation system performance

Cioaca, Alexandru; Sandu, Adrian

doi:10.1016/j.jcp.2014.07.005

Cited by 19 publications

(17 citation statements)

References 44 publications

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“…Mathematically this results in analyzing the sensitivity of states with respect to the data, and eventually in a large linear system to solve. For more information and solution methods, including low-rank approaches, we refer to [43,44,169] and references therein.…”

Section: Bayesian Inference and Tikhonov Regularization And Other Asmentioning

confidence: 99%

Numerical linear algebra in data assimilation

Freitag

2020

GAMM-Mitteilungen

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Data assimilation is a method that combines observations (ie, real world data) of a state of a system with model output for that system in order to improve the estimate of the state of the system and thereby the model output. The model is usually represented by a discretized partial differential equation. The data assimilation problem can be formulated as a large scale Bayesian inverse problem. Based on this interpretation we will derive the most important variational and sequential data assimilation approaches, in particular three‐dimensional and four‐dimensional variational data assimilation (3D‐Var and 4D‐Var) and the Kalman filter. We will then consider more advanced methods which are extensions of the Kalman filter and variational data assimilation and pay particular attention to their advantages and disadvantages. The data assimilation problem usually results in a very large optimization problem and/or a very large linear system to solve (due to inclusion of time and space dimensions). Therefore, the second part of this article aims to review advances and challenges, in particular from the numerical linear algebra perspective, within the various data assimilation approaches.

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Section: Bayesian Inference and Tikhonov Regularization And Other Asmentioning

confidence: 99%

Numerical linear algebra in data assimilation

Freitag

2020

GAMM-Mitteilungen

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“…The methodology for building and using various adjoint models for optimization, sensitivity analysis, and uncertainty quantification is discussed in [6,27]. Various strategies to improve the the 4D-Var data assimilation system are described in [7]. The procedure to estimate the impact of observation and model errors is developed in [22,23].…”

Section: Four-dimensional Variational Data Assimilationmentioning

confidence: 99%

Robust Data Assimilation Using $L_1$ and Huber Norms

Rao

Sandu

Ng³

et al. 2017

SIAM J. Sci. Comput.

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Abstract. Data assimilation is the process to fuse information from priors, observations of nature, and numerical models, in order to obtain best estimates of the parameters or state of a physical system of interest. Presence of large errors in some observational data, e.g., data collected from a faulty instrument, negatively affect the quality of the overall assimilation results. This work develops a systematic framework for robust data assimilation. The new algorithms continue to produce good analyses in the presence of observation outliers. The approach is based on replacing the traditional L 2 norm formulation of data assimilation problems with formulations based on L 1 and Huber norms. Numerical experiments using the Lorenz-96 and the shallow water on the sphere models illustrate how the new algorithms outperform traditional data assimilation approaches in the presence of data outliers.1. Introduction. Dynamic data-driven application systems (DDDAS [3]) integrate computational simulations and physical measurements in symbiotic and dynamic feedback control systems. Within the DDDAS paradigm, data assimilation (DA) defines a class of inverse problems that fuses information from an imperfect computational model based on differential equations (which encapsulates our knowledge of the physical laws that govern the evolution of the real system), from noisy observations (sparse snapshots of reality), and from an uncertain prior (which encapsulates our current knowledge of reality). Data assimilation integrates these three sources of information and the associated uncertainties in a Bayesian framework to provide the posterior, i.e., the probability distribution conditioned on the uncertainties in the model and observations. Two approaches to data assimilation have gained widespread popularity: ensemblebased estimation and variational methods. The ensemble-based methods are rooted in statistical theory, whereas the variational approach is derived from optimal control theory. The variational approach formulates data assimilation as a nonlinear optimization problem constrained by a numerical model. The initial conditions (as well as boundary conditions, forcing, or model parameters) are adjusted to minimize the discrepancy between the model trajectory and a set of time-distributed observations. In real-time operational settings the data assimilation process is performed in cycles: observations within an assimilation window are used to obtain an optimal trajectory, which provides the initial condition for the next time window, and the process is repeated in the subsequent cycles.Large errors in some observations can adversely impact the overall solution to the data assimilation system, e.g., can lead to spurious features in the analysis [15]. Various factors contribute to uncertainties in observations. Faulty and malfunctioning

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“…Let x { } be the solution obtained by solving the optimization problem (12) for particular values of µ { } and λ { } . Apply the classical update (13) to obtain µ { +1} and λ { +1} . 3.…”

Section: Updating Lagrange Multipliersmentioning

confidence: 99%

A time-parallel approach to strong-constraint four-dimensional variational data assimilation

Rao

Sandu

2016

Journal of Computational Physics

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A parallel-in-time algorithm based on an augmented Lagrangian approach is proposed to solve four-dimensional variational (4D-Var) data assimilation problems. The assimilation window is divided into multiple subintervals that allows parallelization of cost function and gradient computations. The solution to the continuity equations across interval boundaries are added as constraints. The augmented Lagrangian approach leads to a different formulation of the variational data assimilation problem than the weakly constrained 4D-Var. A combination of serial and parallel 4D-Vars to increase performance is also explored. The methodology is illustrated on data assimilation problems involving the Lorenz-96 and the shallow water models.

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An optimization framework to improve 4D-Var data assimilation system performance

Cited by 19 publications

References 44 publications

Numerical linear algebra in data assimilation

Numerical linear algebra in data assimilation

Robust Data Assimilation Using $L_1$ and Huber Norms

A time-parallel approach to strong-constraint four-dimensional variational data assimilation

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