Special Issue "Efficient Formulation and Implementation of Data Assimilation Methods"

A special issue of Atmosphere (ISSN 2073-4433).

Deadline for manuscript submissions: closed (31 December 2017).

Special Issue Editors

Guest Editor
Dr. Adrian Sandu

Department of Computer Science, Virginia Polytechnic Institute and State University 2202 Kraft Drive, Blacksburg, VA 24060, USA
Website | E-Mail
Interests: scientific computing; parallel computing; mathematical software development; numerical methods for stiff Ordinary Differential Equations (ODE), Differential Algebraic Equations (DAE); conservation laws; advection–diffusion–reaction equations; sparse linear algebra; sensitivity analysis; data assimilation; automatic differentiation; air quality modeling; computational biology
Guest Editor
Dr. Elias D. Niño-Ruiz

Department of Computer Science Universidad del Norte KM5 Via Puerto Colombia Barranquilla, Atlantico, Colombia
Website | E-Mail
Phone: (+57) 3005397765
Interests: data assimilation; covariance matrix estimation; inverse problems; high performance computing; numerical optimization.
Guest Editor
Dr. Haiyan Cheng

Computer Science Department, Willamette University 900 State Street, Salem, OR 97301, USA
Website | E-Mail
Interests: scientific computing; data assimilation techniques; hybrid numerical methods for data assimilation; uncertainty quantification and reduction techniques for large-scale simulations; polynomial chaos method; uncertainty apportionment; decision-making under uncertainty

Special Issue Information

Dear Colleagues,

Data Assimilation is the process by which imperfect numerical forecasts are adjusted according to real, noisy observations. In general, two families of methods are well-known in the data assimilation context: variational- and ensemble-based methods. In the context of ensemble data assimilation, the moments of the background error distribution are estimated via the empirical moments of an ensemble of model realizations. The resulting ensemble covariance matrix is well-known to be
flow-dependent and therefore, the estimated background-error correlations are driven by the physics and the dynamics of the numerical model. In operational data assimilation, model runs are computationally expensive, which implies that only a small ensemble size is feasible. Consequently, sampling errors impact the estimated background-error correlations and therefore, analysis innovations are poorly estimated by the ensemble covariance matrix. Likewise, in variational data assimilation methods, the actual state of a system is forecasted via the posterior mode of the error distribution. The assimilation process can be performed sequentially via the three dimensional variational (3D-Var) cost function or, given an assimilation window, for multiple observations, the four dimensional variational (4D-Var) cost function can be considered. In the last case, adjoint formulations are required, the computation of which is not trivial in practice. In recent years, the scientific community has centered its efforts on providing assimilation schemes wherein, information brought by ensemble members and optimization features of variational methods are exploited in order to reduce the impact of sampling errors over innovations and to provide efficient and practical implementations of robust data assimilation methods.

Papers are welcome on all aspects of ensemble data assimilation, including, but not restricted to:

  • Covariance matrix estimation in ensemble-based methods.

  • Ensemble 4D-Var data assimilation.

  • Parallel implementation of ensemble methods for data assimilation.

  • Domain localization in ensemble-based methods.

  • Ensemble data assimilation in highly non-linear models.

  • Ensemble-based methods for non-Gaussian data assimilation.

  • Efficient and practical implementations of ensemble-based methods.

  • Adjoint-free ensemble-based methods for 4D-Var data assimilation.

Dr. Adrian Sandu
Dr. Elias D. Niño-Ruiz
Dr. Haiyan Cheng
Guest Editors

Manuscript Submission Information

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Keywords

  • Variational data assimilation

  • Ensemble-based methods

  • Adjoint-free data assimilation

  • Covariance matrix estimation

  • Localization methods

  • Parallel data assimilation

Published Papers (6 papers)

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Editorial

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Open AccessEditorial
Efficient Formulation and Implementation of Data Assimilation Methods
Atmosphere 2018, 9(7), 254; https://doi.org/10.3390/atmos9070254
Received: 3 July 2018 / Accepted: 4 July 2018 / Published: 6 July 2018
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Abstract
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, [...] Read more.
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. Full article
(This article belongs to the Special Issue Efficient Formulation and Implementation of Data Assimilation Methods)

Research

Jump to: Editorial

Open AccessArticle
Cluster Sampling Filters for Non-Gaussian Data Assimilation
Atmosphere 2018, 9(6), 213; https://doi.org/10.3390/atmos9060213
Received: 20 March 2018 / Revised: 2 May 2018 / Accepted: 2 May 2018 / Published: 31 May 2018
Cited by 2 | PDF Full-text (1308 KB) | HTML Full-text | XML Full-text
Abstract
This paper presents a fully non-Gaussian filter for sequential data assimilation. The filter is named the “cluster sampling filter”, and works by directly sampling the posterior distribution following a Markov Chain Monte-Carlo (MCMC) approach, while the prior distribution is approximated using [...] Read more.
This paper presents a fully non-Gaussian filter for sequential data assimilation. The filter is named the “cluster sampling filter”, and works by directly sampling the posterior distribution following a Markov Chain Monte-Carlo (MCMC) approach, while the prior distribution is approximated using a Gaussian Mixture Model (GMM). Specifically, a clustering step is introduced after the forecast phase of the filter, and the prior density function is estimated by fitting a GMM to the prior ensemble. Using the data likelihood function, the posterior density is then formulated as a mixture density, and is sampled following an MCMC approach. Four versions of the proposed filter, namely C MCMC , C HMC , MC- C HMC , and MC- C HMC are presented. C MCMC uses a Gaussian proposal density to sample the posterior, and C HMC is an extension to the Hamiltonian Monte-Carlo (HMC) sampling filter. MC- C MCMC and MC- C HMC are multi-chain versions of the cluster sampling filters C MCMC and C HMC respectively. The multi-chain versions are proposed to guarantee that samples are taken from the vicinities of all probability modes of the formulated posterior. The new methodologies are tested using a simple one-dimensional example, and a quasi-geostrophic (QG) model with double-gyre wind forcing and bi-harmonic friction. Numerical results demonstrate the usefulness of using GMMs to relax the Gaussian prior assumption especially in the HMC filtering paradigm. Full article
(This article belongs to the Special Issue Efficient Formulation and Implementation of Data Assimilation Methods)
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Open AccessArticle
A Robust Non-Gaussian Data Assimilation Method for Highly Non-Linear Models
Atmosphere 2018, 9(4), 126; https://doi.org/10.3390/atmos9040126
Received: 5 January 2018 / Revised: 14 March 2018 / Accepted: 20 March 2018 / Published: 26 March 2018
Cited by 2 | PDF Full-text (1287 KB) | HTML Full-text | XML Full-text
Abstract
In this paper, we propose an efficient EnKF implementation for non-Gaussian data assimilation based on Gaussian Mixture Models and Markov-Chain-Monte-Carlo (MCMC) methods. The proposed method works as follows: based on an ensemble of model realizations, prior errors are estimated via a Gaussian Mixture [...] Read more.
In this paper, we propose an efficient EnKF implementation for non-Gaussian data assimilation based on Gaussian Mixture Models and Markov-Chain-Monte-Carlo (MCMC) methods. The proposed method works as follows: based on an ensemble of model realizations, prior errors are estimated via a Gaussian Mixture density whose parameters are approximated by means of an Expectation Maximization method. Then, by using an iterative method, observation operators are linearized about current solutions and posterior modes are estimated via a MCMC implementation. The acceptance/rejection criterion is similar to that of the Metropolis-Hastings rule. Experimental tests are performed on the Lorenz 96 model. The results show that the proposed method can decrease prior errors by several order of magnitudes in a root-mean-square-error sense for nearly sparse or dense observational networks. Full article
(This article belongs to the Special Issue Efficient Formulation and Implementation of Data Assimilation Methods)
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Open AccessArticle
Assessing the Impact of Surface and Upper-Air Observations on the Forecast Skill of the ACCESS Numerical Weather Prediction Model over Australia
Atmosphere 2018, 9(1), 23; https://doi.org/10.3390/atmos9010023
Received: 15 December 2017 / Revised: 11 January 2018 / Accepted: 12 January 2018 / Published: 16 January 2018
Cited by 1 | PDF Full-text (10732 KB) | HTML Full-text | XML Full-text
Abstract
The impact of the Australian Bureau of Meteorology’s in situ observations (land and sea surface observations, upper air observations by radiosondes, pilot balloons, wind profilers, and aircraft observations) on the short-term forecast skill provided by the ACCESS (Australian Community Climate and Earth-System Simulator) [...] Read more.
The impact of the Australian Bureau of Meteorology’s in situ observations (land and sea surface observations, upper air observations by radiosondes, pilot balloons, wind profilers, and aircraft observations) on the short-term forecast skill provided by the ACCESS (Australian Community Climate and Earth-System Simulator) global numerical weather prediction (NWP) system is evaluated using an adjoint-based method. This technique makes use of the adjoint perturbation forecast model utilized within the 4D-Var assimilation system, and is able to calculate the individual impact of each assimilated observation in a cycling NWP system. The results obtained show that synoptic observations account for about 60% of the 24-h forecast error reduction, with the remainder accounted for by aircraft (12.8%), radiosondes (10.5%), wind profilers (3.9%), pilot balloons (2.8%), buoys (1.7%) and ships (1.2%). In contrast, the largest impact per observation is from buoys and aircraft. Overall, all observation types have a positive impact on the 24-h forecast skill. Such results help to support the decision-making process regarding the evolution of the observing network, particularly at the national level. Consequently, this 4D-Var-based approach has great potential as a tool to assist the design and running of an efficient and effective observing network. Full article
(This article belongs to the Special Issue Efficient Formulation and Implementation of Data Assimilation Methods)
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Open AccessArticle
Evaluating the Role of the EOF Analysis in 4DEnVar Methods
Atmosphere 2017, 8(8), 146; https://doi.org/10.3390/atmos8080146
Received: 30 June 2017 / Revised: 6 August 2017 / Accepted: 9 August 2017 / Published: 15 August 2017
Cited by 2 | PDF Full-text (3041 KB) | HTML Full-text | XML Full-text
Abstract
The four-dimensional variational data assimilation (4DVar) method is one of the most popular techniques used in numerical weather prediction. Nevertheless, the needs of the adjoint model and the linearization of the forecast model largely limit the wider applications of 4DVar. 4D ensemble-variational data [...] Read more.
The four-dimensional variational data assimilation (4DVar) method is one of the most popular techniques used in numerical weather prediction. Nevertheless, the needs of the adjoint model and the linearization of the forecast model largely limit the wider applications of 4DVar. 4D ensemble-variational data assimilation methods (4DEnVars) exploit the strengths of the Ensemble Kalman Filter and 4DVar, and use the ensemble trajectories to directly estimate four-dimensional background error covariance. This study evaluates the role of the empirical orthogonal function (EOF) analysis in 4DEnVars. The widely-recognized 4DEnVar method DRP-4DVar (the Dimension-reduced projection 4DVar) is adopted as the representation of EOF analyses in this study. The performance of the Dimension-reduced projection 4DVar (DRP-4DVar), 4DEnVar (i.e., another traditional 4DEnVar scheme without EOF transformation), and the Ensemble Transform Kalman Filter (ETKF) was compared to demonstrate the effect of the EOF analysis in DRP-4DVar. Sensitivity experiments indicate that EOF analyses construct basis vectors in eigenvalue space and the dimension reduction in the DRP-4DVar approach helps improve computational efficiency and analysis accuracy. When compared with 4DEnVar and the ETKF, the DRP-4DVar demonstrates similar analysis root-mean-square error (RMSE) to 4DEnVar, whereas it surpasses the ETKF by 22.3%. In addition, sensitivity experiments of DRP-4DVar on the ensemble size, the assimilation window length, and the standard deviation of the initial perturbation imply that the DRP-4DVar with the optimized EOF truncation number is robust to a wide range of the parameters, but extremely low values should be avoided. The results presented here suggest the potential wide application of EOF analysis in the hybrid 4DEnVar methods. Full article
(This article belongs to the Special Issue Efficient Formulation and Implementation of Data Assimilation Methods)
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Open AccessArticle
A Matrix-Free Posterior Ensemble Kalman Filter Implementation Based on a Modified Cholesky Decomposition
Atmosphere 2017, 8(7), 125; https://doi.org/10.3390/atmos8070125
Received: 31 March 2017 / Revised: 10 July 2017 / Accepted: 12 July 2017 / Published: 18 July 2017
Cited by 5 | PDF Full-text (541 KB) | HTML Full-text | XML Full-text
Abstract
In this paper, a matrix-free posterior ensemble Kalman filter implementation based on a modified Cholesky decomposition is proposed. The method works as follows: the precision matrix of the background error distribution is estimated based on a modified Cholesky decomposition. The resulting estimator can [...] Read more.
In this paper, a matrix-free posterior ensemble Kalman filter implementation based on a modified Cholesky decomposition is proposed. The method works as follows: the precision matrix of the background error distribution is estimated based on a modified Cholesky decomposition. The resulting estimator can be expressed in terms of Cholesky factors which can be updated based on a series of rank-one matrices in order to approximate the precision matrix of the analysis distribution. By using this matrix, the posterior ensemble can be built by either sampling from the posterior distribution or using synthetic observations. Furthermore, the computational effort of the proposed method is linear with regard to the model dimension and the number of observed components from the model domain. Experimental tests are performed making use of the Lorenz-96 model. The results reveal that, the accuracy of the proposed implementation in terms of root-mean-square-error is similar, and in some cases better, to that of a well-known ensemble Kalman filter (EnKF) implementation: the local ensemble transform Kalman filter. In addition, the results are comparable to those obtained by the EnKF with large ensemble sizes. Full article
(This article belongs to the Special Issue Efficient Formulation and Implementation of Data Assimilation Methods)
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