Sequential data assimilation for a subsurface flow model with the ensemble Kalman filter

2014 ◽  
pp. 1347-1354
Author(s):  
S Yamamoto ◽  
M Honda ◽  
M Suzuki ◽  
H Sakurai
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Flow Model ◽  
Subsurface Flow ◽  
Sequential Data ◽  
Sequential Data Assimilation

TREATMENT OF THE ERROR DUE TO UNRESOLVED SCALES IN SEQUENTIAL DATA ASSIMILATION

2011 ◽  
Vol 21 (12) ◽  
pp. 3619-3626 ◽  
Author(s):  
ALBERTO CARRASSI ◽  
STÉPHANE VANNITSEM
Keyword(s):  
Dynamical System ◽  
Kalman Filter ◽  
Data Assimilation ◽  
Large Scale ◽  
Model Error ◽  
Environmental Modeling ◽  
Sequential Data ◽  
Chaotic Dynamical System ◽  
Error Covariance ◽  
Sequential Data Assimilation

In this paper, a method to account for model error due to unresolved scales in sequential data assimilation, is proposed. An equation for the model error covariance required in the extended Kalman filter update is derived along with an approximation suitable for application with large scale dynamics typical in environmental modeling. This approach is tested in the context of a low order chaotic dynamical system. The results show that the filter skill is significantly improved by implementing the proposed scheme for the treatment of the unresolved scales.

Fast linearized forecasts for subsurface flow data assimilation with ensemble Kalman filter

2016 ◽  
Vol 20 (5) ◽  
pp. 929-952 ◽  
Author(s):  
Mohammadali Tarrahi ◽  
Siavash Hakim Elahi ◽  
Behnam Jafarpour
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Subsurface Flow ◽  
Flow Data

scholarly journals Coupling the K-nearest neighbors and locally weighted linear regression with ensemble Kalman filter for data-driven data assimilation

2021 ◽  
Vol 13 (1) ◽  
pp. 1395-1413
Author(s):  
Manhong Fan ◽  
Yulong Bai ◽  
Lili Wang ◽  
Lihong Tang ◽  
Lin Ding
Keyword(s):  
Kalman Filter ◽  
Linear Regression ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Nearest Neighbor ◽  
Nearest Neighbors ◽  
Forecast Model ◽  
Data Driven ◽  
Sequential Data ◽  
Weighted Linear Regression

Abstract Machine learning-based data-driven methods are increasingly being used to extract structures and essences from the ever-increasing pool of geoscience-related big data, which are often used in relation to the atmosphere, oceans, and land surfaces. This study focuses on applying a data-driven forecast model to the classical ensemble Kalman filter process to reconstruct, analyze, and elucidate the model. In this study, a nonparametric sampler from a catalog of historical datasets, namely, a nearest neighbor or analog sampler, is given by numerical simulations. Based on this catalog (sampler), the dynamics physics model is reconstructed using the K-nearest neighbors algorithm. The optimal values of the surrogate model are found, and the forecast step is performed using locally weighted linear regression. Several numerical experiments carried out using the Lorenz-63 and Lorenz-96 models demonstrate that the proposed approach performs as good as the ensemble Kalman filter for larger catalog sizes. This approach is restricted to the ensemble Kalman filter form. However, the basic strategy is not restricted to any particular version of the Kalman filter. It is found that this combined approach can outperform the generally used sequential data assimilation approach when the size of the catalog is substantially large.

scholarly journals Robust Ensemble Filtering and Its Relation to Covariance Inflation in the Ensemble Kalman Filter

2011 ◽  
Vol 139 (12) ◽  
pp. 3938-3953 ◽  
Author(s):  
Xiaodong Luo ◽  
Ibrahim Hoteit
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Estimation Error ◽  
Minimum Variance ◽  
Global Constraints ◽  
Original Form ◽  
Sequential Data ◽  
Special Cases ◽  
Ensemble Filtering ◽  
Sequential Data Assimilation

Abstract A robust ensemble filtering scheme based on the H∞ filtering theory is proposed. The optimal H∞ filter is derived by minimizing the supremum (or maximum) of a predefined cost function, a criterion different from the minimum variance used in the Kalman filter. By design, the H∞ filter is more robust than the Kalman filter, in the sense that the estimation error in the H∞ filter in general has a finite growth rate with respect to the uncertainties in assimilation, except for a special case that corresponds to the Kalman filter. The original form of the H∞ filter contains global constraints in time, which may be inconvenient for sequential data assimilation problems. Therefore a variant is introduced that solves some time-local constraints instead, and hence it is called the time-local H∞ filter (TLHF). By analogy to the ensemble Kalman filter (EnKF), the concept of ensemble time-local H∞ filter (EnTLHF) is also proposed. The general form of the EnTLHF is outlined, and some of its special cases are discussed. In particular, it is shown that an EnKF with certain covariance inflation is essentially an EnTLHF. In this sense, the EnTLHF provides a general framework for conducting covariance inflation in the EnKF-based methods. Some numerical examples are used to assess the relative robustness of the TLHF–EnTLHF in comparison with the corresponding KF–EnKF method.

scholarly journals Merging particle filter for sequential data assimilation

2007 ◽  
Vol 14 (4) ◽  
pp. 395-408 ◽  
Author(s):  
S. Nakano ◽  
G. Ueno ◽  
T. Higuchi
Keyword(s):  
Data Assimilation ◽  
Particle Filter ◽  
Ensemble Kalman Filter ◽  
Computational Cost ◽  
Sequential Data ◽  
Filtering Technique ◽  
The Mean ◽  
Multiple Samples ◽  
Filtering Procedure ◽  
Sequential Data Assimilation

Abstract. A new filtering technique for sequential data assimilation, the merging particle filter (MPF), is proposed. The MPF is devised to avoid the degeneration problem, which is inevitable in the particle filter (PF), without prohibitive computational cost. In addition, it is applicable to cases in which a nonlinear relationship exists between a state and observed data where the application of the ensemble Kalman filter (EnKF) is not effectual. In the MPF, the filtering procedure is performed based on sampling of a forecast ensemble as in the PF. However, unlike the PF, each member of a filtered ensemble is generated by merging multiple samples from the forecast ensemble such that the mean and covariance of the filtered distribution are approximately preserved. This merging of multiple samples allows the degeneration problem to be avoided. In the present study, the newly proposed MPF technique is introduced, and its performance is demonstrated experimentally.

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