Comments on "Application of ensemble transform data assimilation methods for parameter estimation in nonlinear problems"

2018 ◽  
Author(s):  
Anonymous
Keyword(s):  
Parameter Estimation ◽  
Data Assimilation ◽  
Nonlinear Problems ◽  
Ensemble Transform

scholarly journals Application of ensemble transform data assimilation methods for parameter estimation in nonlinear problems

2018 ◽  
Author(s):  
Sangeetika Ruchi ◽  
Svetlana Dubinkina
Keyword(s):  
Parameter Estimation ◽  
Data Assimilation ◽  
Nonlinear Problems ◽  
Model Parameters ◽  
Ensemble Size ◽  
Uncertain Model ◽  
Initial Ensemble ◽  
Non Gaussian ◽  
Posterior Estimation ◽  
Ensemble Transform

Abstract. Over the years data assimilation methods have been developed to obtain estimations of uncertain model parameters by taking into account a few observations of a model state. However, most of these computationally affordable methods have assumptions of Gaussianity, e.g. an Ensemble Kalman Filter. Ensemble Transform Particle Filter does not have the assumption of Gaussianity and has proven to be highly beneficial for an initial condition estimation and a small number of parameter estimation in chaotic dynamical systems with non-Gaussian distributions. In this paper we employ Ensemble Transform Particle Smoother (ETPS) and Ensemble Transform Kalman Smoother (ETKS) for parameter estimation in nonlinear problems with 1, 5, and 2500 uncertain parameters and compare them to importance sampling (IS). We prove that the updated parameters obtained by ETPS lie within the range of an initial ensemble, which is not the case for ETKS. We examine the performance of ETPS and ETKS in a twin experiment setup, where observations of pressure are synthetically created based on the know values of parameters. The numerical experiments demonstrate that the ETKS provides good estimations of the mean parameters but not of the posterior distributions and as the ensemble size increases the posterior does not improve. ETPS provides good approximations of the posterior and as the ensemble size increases the posterior converges to the posterior obtained by IS with a large ensemble. ETKS is very robust while ETPS is very sensitive with respect to the initial ensemble. An issue of an increase in the root mean square error after data assimilation is performed in ETPS for a high-dimensional test problem is resolved by applying distance-based localization, which however deteriorated the posterior estimation.

scholarly journals Application of ensemble transform data assimilation methods for parameter estimation in reservoir modeling

2018 ◽  
Vol 25 (4) ◽  
pp. 731-746 ◽  
Author(s):  
Sangeetika Ruchi ◽  
Svetlana Dubinkina
Keyword(s):  
Parameter Estimation ◽  
Kalman Filter ◽  
Data Assimilation ◽  
Particle Filter ◽  
Reservoir Modeling ◽  
Model Parameters ◽  
Uncertain Parameters ◽  
Initial Ensemble ◽  
Leading Mode ◽  
Ensemble Transform

Abstract. Over the years data assimilation methods have been developed to obtain estimations of uncertain model parameters by taking into account a few observations of a model state. The most reliable Markov chain Monte Carlo (MCMC) methods are computationally expensive. Sequential ensemble methods such as ensemble Kalman filters and particle filters provide a favorable alternative. However, ensemble Kalman filter has an assumption of Gaussianity. Ensemble transform particle filter does not have this assumption and has proven to be highly beneficial for an initial condition estimation and a small number of parameter estimations in chaotic dynamical systems with non-Gaussian distributions. In this paper we employ ensemble transform particle filter (ETPF) and ensemble transform Kalman filter (ETKF) for parameter estimation in nonlinear problems with 1, 5, and 2500 uncertain parameters and compare them to importance sampling (IS). The large number of uncertain parameters is of particular interest for subsurface reservoir modeling as it allows us to parameterize permeability on the grid. We prove that the updated parameters obtained by ETPF lie within the range of an initial ensemble, which is not the case for ETKF. We examine the performance of ETPF and ETKF in a twin experiment setup, where observations of pressure are synthetically created based on the known values of parameters. For a small number of uncertain parameters (one and five) ETPF performs comparably to ETKF in terms of the mean estimation. For a large number of uncertain parameters (2500) ETKF is robust with respect to the initial ensemble, while ETPF is sensitive due to sampling error. Moreover, for the high-dimensional test problem ETPF gives an increase in the root mean square error after data assimilation is performed. This is resolved by applying distance-based localization, which however deteriorates a posterior estimation of the leading mode by largely increasing the variance due to a combination of less varying localized weights, not keeping the imposed bounds on the modes via the Karhunen–Loeve expansion, and the main variability explained by the leading mode. A possible remedy is instead of applying localization to use only leading modes that are well estimated by ETPF, which demands knowledge of which mode to truncate.

scholarly journals Parameter Estimation Using Ensemble-Based Data Assimilation in the Presence of Model Error

2015 ◽  
Vol 143 (5) ◽  
pp. 1568-1582 ◽  
Author(s):  
Juan Ruiz ◽  
Manuel Pulido
Keyword(s):  
Parameter Estimation ◽  
Data Assimilation ◽  
Model Error ◽  
Forecast Skill ◽  
Moist Convection ◽  
Treatment Techniques ◽  
Correction Technique ◽  
Error Treatment ◽  
Data Assimilation System ◽  
Assimilation System

Abstract This work explores the potential of online parameter estimation as a technique for model error treatment under an imperfect model scenario, in an ensemble-based data assimilation system, using a simple atmospheric general circulation model, and an observing system simulation experiment (OSSE) approach. Model error is introduced in the imperfect model scenario by changing the value of the parameters associated with different schemes. The parameters of the moist convection scheme are the only ones to be estimated in the data assimilation system. In this work, parameter estimation is compared and combined with techniques that account for the lack of ensemble spread and for the systematic model error. The OSSEs show that when parameter estimation is combined with model error treatment techniques, multiplicative and additive inflation or a bias correction technique, parameter estimation produces a further improvement of analysis quality and medium-range forecast skill with respect to the OSSEs with model error treatment techniques without parameter estimation. The improvement produced by parameter estimation is mainly a consequence of the optimization of the parameter values. The estimated parameters do not converge to the value used to generate the observations in the imperfect model scenario; however, the analysis error is reduced and the forecast skill is improved.

scholarly journals Gain Form of the Ensemble Transform Kalman Filter and Its Relevance to Satellite Data Assimilation with Model Space Ensemble Covariance Localization

2017 ◽  
Vol 145 (11) ◽  
pp. 4575-4592 ◽  
Author(s):  
Craig H. Bishop ◽  
Jeffrey S. Whitaker ◽  
Lili Lei
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Satellite Data ◽  
Localization Length ◽  
Model Space ◽  
Ensemble Size ◽  
Length Scales ◽  
Ensemble Transform Kalman Filter ◽  
Ensemble Transform ◽  
Expanded Ensemble

To ameliorate suboptimality in ensemble data assimilation, methods have been introduced that involve expanding the ensemble size. Such expansions can incorporate model space covariance localization and/or estimates of climatological or model error covariances. Model space covariance localization in the vertical overcomes problematic aspects of ensemble-based satellite data assimilation. In the case of the ensemble transform Kalman filter (ETKF), the expanded ensemble size associated with vertical covariance localization would also enable the simultaneous update of entire vertical columns of model variables from hyperspectral and multispectral satellite sounders. However, if the original formulation of the ETKF were applied to an expanded ensemble, it would produce an analysis ensemble that was the same size as the expanded forecast ensemble. This article describes a variation on the ETKF called the gain ETKF (GETKF) that takes advantage of covariances from the expanded ensemble, while producing an analysis ensemble that has the required size of the unexpanded forecast ensemble. The approach also yields an inflation factor that depends on the localization length scale that causes the GETKF to perform differently to an ensemble square root filter (EnSRF) using the same expanded ensemble. Experimentation described herein shows that the GETKF outperforms a range of alternative ETKF-based solutions to the aforementioned problems. In cycling data assimilation experiments with a newly developed storm-track version of the Lorenz-96 model, the GETKF analysis root-mean-square error (RMSE) matches the EnSRF RMSE at shorter than optimal localization length scales but is superior in that it yields smaller RMSEs for longer localization length scales.

scholarly journals Genetic Operator-Based Particle Filter Combined with Markov Chain Monte Carlo for Data Assimilation in a Crop Growth Model

Agriculture ◽  
2020 ◽  
Vol 10 (12) ◽  
pp. 606
Author(s):  
Alaa Jamal ◽  
Raphael Linker
Keyword(s):  
Monte Carlo ◽  
Parameter Estimation ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Data Assimilation ◽  
Particle Filter ◽  
Sequential Estimation ◽  
Measurement Noise ◽  
Genetic Operators ◽  
True Value

Particle filter has received increasing attention in data assimilation for estimating model states and parameters in cases of non-linear and non-Gaussian dynamic processes. Various modifications of the original particle filter have been suggested in the literature, including integrating particle filter with Markov Chain Monte Carlo (PF-MCMC) and, later, using genetic algorithm evolutionary operators as part of the state updating process. In this work, a modified genetic-based PF-MCMC approach for estimating the states and parameters simultaneously and without assuming Gaussian distribution for priors is presented. The method was tested on two simulation examples on the basis of the crop model AquaCrop-OS. In the first example, the method was compared to a PF-MCMC method in which states and parameters are updated sequentially and genetic operators are used only for state adjustments. The influence of ensemble size, measurement noise, and mutation and crossover parameters were also investigated. Accurate and stable estimations of the model states were obtained in all cases. Parameter estimation was more challenging than state estimation and not all parameters converged to their true value, especially when the parameter value had little influence on the measured variables. Overall, the proposed method showed more accurate and consistent parameter estimation than the PF-MCMC with sequential estimation, which showed highly conservative behavior. The superiority of the proposed method was more pronounced when the ensemble included a large number of particles and the measurement noise was low.

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