Journal ArticleDOI
Sampling strategies and square root analysis schemes for the EnKF
TLDR
In this paper, the authors examined how different sampling strategies and implementations of the analysis scheme influence the quality of the results in the EnKF and proposed a new computationally efficient square root algorithm which allows for the use of a low-rank representation of the measurement error covariance matrix.Abstract:
The purpose of this paper is to examine how different sampling strategies and implementations of the analysis scheme influence the quality of the results in the EnKF. It is shown that by selecting the initial ensemble, the model noise and the measurement perturbations wisely, it is possible to achieve a significant improvement in the EnKF results, using the same number of members in the ensemble. The results are also compared with a square root implementation of the EnKF analysis scheme where the analyzed ensemble is computed without the perturbation of measurements. It is shown that the measurement perturbations introduce sampling errors which can be reduced using improved sampling schemes in the standard EnKF or fully eliminated when the square root analysis algorithm is used. Further, a new computationally efficient square root algorithm is proposed which allows for the use of a low-rank representation of the measurement error covariance matrix. It is shown that this algorithm in fact solves the full problem at a low cost without introducing any new approximations.read more
Citations
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Journal ArticleDOI
Ensemble smoother with multiple data assimilation
TL;DR: This paper proposes to assimilate the same data multiple times with an inflated measurement error covariance matrix in order to improve the results obtained by the ensemble smoother, motivated by the equivalence between single and multiple data assimilation for the linear-Gaussian case.
Journal ArticleDOI
Review of the Ensemble Kalman Filter for Atmospheric Data Assimilation
P. L. Houtekamer,Fuqing Zhang +1 more
TL;DR: For the EnKF in general, but higher-resolution applications in particular, it is desirable to use a short assimilation window, and a focus on approaches for maintaining balance during the EnkF update is focused on.
Journal ArticleDOI
The ensemble Kalman filter for combined state and parameter estimation
TL;DR: In this paper, the authors provide a fundamental theoretical basis for understanding EnKF and serve as a useful text for future users, which is based on the assumption that measurement errors are independent in time and the model represents a Markov process, which allows for Bayes theorem to be written in a recursive form.
Journal ArticleDOI
Data assimilation in the geosciences: An overview of methods, issues, and perspectives
TL;DR: Data assimilation (DA) as mentioned in this paper is a state estimation theory in geosciences, which is commonly referred to as data assimilation in meteorology and weather prediction, and it has been applied in many other areas of climate, atmosphere, ocean, and environment modeling.
Journal ArticleDOI
Real-time groundwater flow modeling with the Ensemble Kalman Filter: Joint estimation of states and parameters and the filter inbreeding problem
TL;DR: In this paper, the Ensemble Kalman Filter (EnKF) approach is used to update states together with parameters by adopting an augmented state vector approach, and the performance of EnKF is investigated in a synthetic study with a two-dimensional transient groundwater flow model.
References
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Journal ArticleDOI
Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics
TL;DR: In this article, a new sequential data assimilation method is proposed based on Monte Carlo methods, a better alternative than solving the traditional and computationally extremely demanding approximate error covariance equation used in the extended Kalman filter.
Journal ArticleDOI
The Ensemble Kalman Filter: theoretical formulation and practical implementation
TL;DR: A fairly extensive discussion is devoted to the use of time correlated model errors and the estimation of model bias, and an ensemble based optimal interpolation scheme is presented as a cost-effective approach which may serve as an alternative to the EnKF in some applications.
Journal ArticleDOI
Analysis Scheme in the Ensemble Kalman Filter
TL;DR: In this article, it is shown that the observations must be treated as random variables at the analysis steps, which results in a completely consistent approach if the covariance of the ensemble of model states is interpreted as the prediction error covariance, and there are no further requirements on the ensemble Kalman filter method.
Journal ArticleDOI
An Ensemble Adjustment Kalman Filter for Data Assimilation
TL;DR: In this paper, an ensemble adjustment Kalman filter is proposed to estimate the probability distribution of the state of a model given a set of observations using Monte Carlo approximations to the nonlinear filter.
Journal ArticleDOI
Ensemble Data Assimilation without Perturbed Observations
TL;DR: In this paper, the EnSRF algorithm is proposed, which uses the traditional Kalman gain for updating the ensemble mean but uses a reduced loss to update deviations from the EnKF mean.