A Robust Non-Gaussian Data Assimilation Method for Highly Non-Linear Models

Niño-Ruiz, Elías D.; Cheng, Haiyan; Beltran, Rolando

doi:10.3390/atmos9040126

Cited by 12 publications

(6 citation statements)

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“…For the experiments, we consider non-linear observation operators, a current challenge in the context of DA [6,24]. We make use of the Lorenz-96 model [25] as our surrogate model during the experiments.…”

Section: Resultsmentioning

confidence: 99%

A Random Line-Search Optimization Method via Modified Cholesky Decomposition for Non-linear Data Assimilation

Niño-Ruiz

2020

Lecture Notes in Computer Science

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This paper proposes a line-search optimization method for non-linear data assimilation via random descent directions. The iterative method works as follows: at each iteration, quadratic approximations of the Three-Dimensional-Variational (3D-Var) cost function are built about current solutions. These approximations are employed to build sub-spaces onto which analysis increments can be estimated. We sample search-directions from those sub-spaces, and for each direction, a line-search optimization method is employed to estimate its optimal step length. Current solutions are updated based on directions along which the 3D-Var cost function decreases faster. We theoretically prove the global convergence of our proposed iterative method. Experimental tests are performed by using the Lorenz-96 model, and for reference, we employ a Maximum-Likelihood-Ensemble-Filter (MLEF) whose ensemble size doubles that of our implementation. The results reveal that, as the degree of observational operators increases, the use of additional directions can improve the accuracy of results in terms of 2-norm of errors, and even more, our numerical results outperform those of the employed MLEF implementation.

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Section: Resultsmentioning

confidence: 99%

A Random Line-Search Optimization Method via Modified Cholesky Decomposition for Non-linear Data Assimilation

Niño-Ruiz

2020

Lecture Notes in Computer Science

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“…Furthermore, the convergence of MCMC is sped up by using Verlet integrators. On the other hand, Nino-Ruiz et al [15] proposes "A Robust Non-Gaussian Data Assimilation Method for Highly Non-Linear Models" wherein prior errors are modeled by fitting GMMs while gradient approximations of the three-dimensional variational cost function are exploited for accelerating its convergence towards posterior modes. 3.…”

Section: Efficient Formulation and Implementation Of Data Assimilatiomentioning

confidence: 99%

Efficient Formulation and Implementation of Data Assimilation Methods

2018

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This Special Issue presents efficient formulations and implementations of sequential and variational data assimilation methods. The methods address three important issues in the context of operational data assimilation: efficient implementation of localization methods, sampling methods for approaching posterior ensembles under non-linear model errors, and adjoint-free formulations of four dimensional variational methods.

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“…There is a group of methods that aims to extend EnKF to improve performance in problems with non-Gaussian distributions and nonlinear observations while retaining algorithmic similarity to EnKFs. This group includes Gaussian mixture methods [12,16,45,88,35,60,68], methods based on gamma/inversegamma distributions [18,72], methods that target higher moments of the posterior [43,44], methods based on rank statistics [9,64,10,11], and 'Gaussian Anamorphosis' methods [17,20,94,21,83]. Gaussian anamorphosis (GA) methods were originally motivated by the desire to keep certain state variables -like concentration, mass, or volume -positive, a constraint not respected by EnKFs.…”

Section: Introductionmentioning

confidence: 99%

A comparison of nonlinear extensions to the ensemble Kalman filter: Gaussian Anamorphosis and Two-Step Ensemble Filters

Grooms

2021

Preprint

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This paper reviews two nonlinear, non-Gaussian extensions of the Ensemble Kalman Filter: Gaussian anamorphosis (GA) methods and two-step updates, of which the rank histogram filter (RHF) is a prototypical example. GA-EnKF methods apply univariate transforms to the state and observation variables to make their distribution more Gaussian before applying an EnKF. The two-step methods use a scalar Bayesian update for the first step, followed by linear regression for the second step. The connection of the two-step framework to the full Bayesian problem is made, which opens the door to more advanced two-step methods in the full Bayesian setting. A new method for the first part of the two-step framework is proposed, with a similar form to the RHF but a different motivation, called the 'improved RHF' (iRHF). A suite of experiments with the Lorenz-'96 model demonstrate situations where the GA-EnKF methods are similar to EnKF, and where they outperform EnKF. The experiments also strongly support the accuracy of the RHF and iRHF filters for nonlinear and non-Gaussian observations; these methods uniformly beat the EnKF and GA-EnKF methods in the experiments reported here. The new iRHF method is only more accurate than RHF at small ensemble sizes in the experiments reported here.

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A Robust Non-Gaussian Data Assimilation Method for Highly Non-Linear Models

Cited by 12 publications

References 50 publications

A Random Line-Search Optimization Method via Modified Cholesky Decomposition for Non-linear Data Assimilation

A Random Line-Search Optimization Method via Modified Cholesky Decomposition for Non-linear Data Assimilation

Efficient Formulation and Implementation of Data Assimilation Methods

A comparison of nonlinear extensions to the ensemble Kalman filter: Gaussian Anamorphosis and Two-Step Ensemble Filters

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