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The Ensemble Kalman filter assumes the observations to be Gaussian random variables with a pre-specified mean and variance. In practice, observations may also have detection limits, for instance when a gauge has a minimum or maximum value.…

Optimization and Control · Mathematics 2018-11-14 Abhishek Shah , Mohamad El Gharamti , Laurent Bertino

Data assimilation has been applied to coastal hydrodynamic models to better estimate system states or parameters by incorporating observed data into the model. Kalman Filter (KF) is one of the most studied data assimilation methods whose…

Atmospheric and Oceanic Physics · Physics 2016-07-05 Milad Hooshyar , Stephen C. Medeiros , Dingbao Wang , Scott C. Hagen

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

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

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

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

We explore the potential of Data-Assimilation (DA) within the multi-scale framework of a shell model of turbulence, with a focus on the Ensemble Kalman Filter (EnKF). The central objective is to understand how measuring mesoscales (i.e.,…

Fluid Dynamics · Physics 2026-01-15 Francesco Fossella , Luca Biferale , Alberto Carrassi , Massimo Cencini , Vikrant Gupta

An ensemble Kalman filter (EnKF)-based mixed model (EnKF-MM) is proposed for the subgrid-scale (SGS) closure in the large-eddy simulation (LES) of turbulence. The model coefficients are determined through the EnKF-based data assimilation…

Fluid Dynamics · Physics 2023-08-16 Yunpeng Wang , Zelong Yuan , Jianchun Wang

Data assimilation combines information from models, measurements, and priors to estimate the state of a dynamical system such as the atmosphere. The Ensemble Kalman filter (EnKF) is a family of ensemble-based data assimilation approaches…

Computational Engineering, Finance, and Science · Computer Science 2014-12-09 Ahmed Attia , Adrian Sandu

This study considers the data assimilation problem in coupled systems, which consists of two components (sub-systems) interacting with each other through certain coupling terms. A straightforward way to tackle the assimilation problem in…

Atmospheric and Oceanic Physics · Physics 2015-06-22 Xiaodong Luo , Ibrahim Hoteit

Data assimilation plays a key role in large-scale atmospheric weather forecasting, where the state of the physical system is estimated from model outputs and observations, and is then used as initial condition to produce accurate future…

Methodology · Statistics 2018-02-13 Azam Moosavi , Ahmed Attia , Adrian Sandu

The paper presents experiments of driving a physics-based thermosphere model by assimilating electron density (Ne) and temperature (Tn) data using the ensemble adjustment Kalman filter (EAKF) technique. This study not only helps to gauge…

Space Physics · Physics 2019-03-22 Timothy Kodikara , Kefei Zhang

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

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

Working with a two-stage ice sheet model, we explore how statistical data assimilation methods can be used to improve predictions of glacier melt and relatedly, sea level rise. We find that the EnKF improves model runs initialized using…

Dynamical Systems · Mathematics 2023-05-23 Emily Corcoran , Logan Knudsen , Talea Mayo , Hannah Park-Kaufmann , Alexander Robel

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

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

Ensemble-based data assimilation (DA) methods have become increasingly popular due to their inherent ability to address nonlinear dynamic problems. However, these methods often face a trade-off between analysis accuracy and computational…

Machine Learning · Computer Science 2026-05-26 Zhilin Li , Zhou Yao , Xianglong Li , Zeng Liu , Zhaokuan Lu , Shanlin Xu , Seungnam Kim , Guangyao Wang

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

Data assimilation (DA) aims to optimally combine model forecasts and observations that are both partial and noisy. Multi-model DA generalizes the variational or Bayesian formulation of the Kalman filter, and we prove that it is also the…

Methodology · Statistics 2023-01-23 Eviatar Bach , Michael Ghil
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