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The ensemble Kalman filter (EnKF) is a recursive filter suitable for problems with a large number of variables, such as discretizations of partial differential equations in geophysical models. The EnKF originated as a version of the Kalman…

Atmospheric and Oceanic Physics · Physics 2009-01-26 Jan Mandel

Ensemble methods such as the Ensemble Kalman Filter (EnKF) are widely used for data assimilation in large-scale geophysical applications, as for example in numerical weather prediction (NWP). There is a growing interest for physical models…

Applications · Statistics 2018-08-01 Sylvain Robert , Hans R. Künsch

Ensemble data assimilation methods such as the Ensemble Kalman Filter (EnKF) are a key component of probabilistic weather forecasting. They represent the uncertainty in the initial conditions by an ensemble which incorporates information…

Applications · Statistics 2018-10-17 Sylvain Robert , Daniel Leuenberger , Hans R. Künsch

The Ensemble Kalman Filter (EnKF), as a fundamental data assimilation approach, has been widely used in many fields of the sciences and engineering. When the state variable is of high dimensional accompanied with high resolution…

Methodology · Statistics 2025-09-18 Shouxia Wang , Hao-Xuan Sun , Song Xi Chen

The Ensemble Kalman Filter (EnKF) is a widely used method for data assimilation in high-dimensional systems, with an ensemble update step equivalent to an empirical version of the Matheron update popular in Gaussian process regression -- a…

Machine Learning · Computer Science 2025-09-19 Dan MacKinlay

Ensemble Kalman filter (EnKF) is an important data assimilation method for high dimensional geophysical systems. Efficient implementation of EnKF in practice often involves the localization technique, which updates each component using only…

Probability · Mathematics 2018-04-04 Xin T. Tong

The ensemble Kalman filter (EnKF) is widely used for data assimilation in high-dimensional systems, but its performance often deteriorates for strongly nonlinear dynamics due to the structural mismatch between the Kalman update and the…

Machine Learning · Computer Science 2026-04-30 Xin T. Tong , Yanyan Wang , Liang Yan

The ensemble Kalman filter is a well-known and celebrated data assimilation algorithm. It is of particular relevance as it used for high-dimensional problems, by updating an ensemble of particles through a sample mean and covariance…

Numerical Analysis · Mathematics 2022-07-27 Neil K. Chada

Data assimilation (DA) is a key component of many forecasting models in science and engineering. DA allows one to estimate better initial conditions using an imperfect dynamical model of the system and noisy/sparse observations available…

Machine Learning · Computer Science 2023-02-01 Ashesh Chattopadhyay , Ebrahim Nabizadeh , Eviatar Bach , Pedram Hassanzadeh

Ensemble Kalman Filtering (EnKF) is a popular technique for data assimilation, with far ranging applications. However, the vanilla EnKF framework is not well-defined when perturbations are nonlinear. We study two non-linear extensions of…

Machine Learning · Statistics 2024-09-24 Zachariah Malik , Romit Maulik

We present a new type of the EnKF for data assimilation in spatial models that uses diagonal approximation of the state covariance in the wavelet space to achieve adaptive localization. The efficiency of the new method is demonstrated on an…

Dynamical Systems · Mathematics 2011-03-01 Jonathan D. Beezley , Jan Mandel , Loren Cobb

The ensemble Kalman filter (EnKF) is a Monte Carlo based implementation of the Kalman filter (KF) for extremely high-dimensional, possibly nonlinear and non-Gaussian state estimation problems. Its ability to handle state dimensions in the…

Methodology · Statistics 2018-02-12 Michael Roth , Gustaf Hendeby , Carsten Fritsche , Fredrik Gustafsson

Although data assimilation originates from control theory, the relationship between modern data assimilation methods in geoscience and model predictive control has not been extensively explored. In the present paper, I discuss that the…

Geophysics · Physics 2024-10-21 Yohei Sawada

Machine learning techniques have seen a tremendous rise in popularity in weather and climate sciences. Data assimilation (DA), which combines observations and numerical models, has great potential to incorporate machine learning and…

Machine Learning · Computer Science 2024-03-20 Feiyu Lu

Parameter estimation has a high importance in the geosciences. The ensemble Kalman filter (EnKF) allows parameter estimation for large, time-dependent systems. For large systems, the EnKF is applied using small ensembles, which may lead to…

Applications · Statistics 2021-08-05 Johannes Keller , Harrie-Jan Hendricks Franssen , Wolfgang Nowak

The ensemble Kalman filter (EnKF) (Evensen, 2009) has proven effective in quantifying uncertainty in a number of challenging dynamic, state estimation, or data assimilation, problems such as weather forecasting and ocean modeling. In these…

We propose a new type of the Ensemble Kalman Filter (EnKF), which uses the Fast Fourier Transform (FFT) for covariance estimation from a very small ensemble with automatic tapering, and for a fast computation of the analysis ensemble by…

Atmospheric and Oceanic Physics · Physics 2011-08-01 Jan Mandel , Jonathan D. Beezley , Volodymyr Y. Kondratenko

We study the ensemble Kalman filter (EnKF) algorithm for sequential data assimilation in a general situation, that is, for nonlinear forecast and measurement models with non-additive and non-Gaussian noises. Such applications traditionally…

Methodology · Statistics 2018-08-17 Weixuan Li , W. Steven Rosenthal , Guang Lin

The ensemble Kalman filter (EnKF) is a reliable data assimilation tool for high-dimensional meteorological problems. On the other hand, the EnKF can be interpreted as a particle filter, and particle filters collapse in high-dimensional…

Numerical Analysis · Mathematics 2016-06-01 Matthias Morzfeld , Daniel Hodyss , Chris Snyder

The ensemble Kalman filter (EnKF) is a data assimilation technique that uses an ensemble of models, updated with data, to track the time evolution of a usually non-linear system. It does so by using an empirical approximation to the…

Applications · Statistics 2021-03-12 Elizabeth Hou , Earl Lawrence , Alfred O. Hero
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