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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

The filtering distribution in hidden Markov models evolves according to the law of a mean-field model in state-observation space. The ensemble Kalman filter (EnKF) approximates this mean-field model with an ensemble of interacting…

Machine Learning · Statistics 2025-12-25 Eviatar Bach , Ricardo Baptista , Edoardo Calvello , Bohan Chen , Andrew Stuart

Various types of measurement techniques, such as Light Detection and Ranging (LiDAR) devices, anemometers, and wind vanes, are extensively utilized in wind energy to characterize the inflow. However, these methods typically gather data at…

Fluid Dynamics · Physics 2025-02-13 Chang Yan , Shengfeng Xu , Zhenxu Sun , Thorsten Lutz , Dilong Guo , Guowei Yang

Due to climate and land-use change, natural disasters such as flooding have been increasing in recent years. Timely and reliable flood detection and mapping can help emergency response and disaster management. In this work, we propose a…

Computer Vision and Pattern Recognition · Computer Science 2022-12-13 Ritu Yadav , Andrea Nascetti , Yifang Ban

Errors in the representation of clouds in convection-permitting numerical weather prediction models can be introduced by different sources. These can be the forcing and boundary conditions, the representation of orography, the accuracy of…

Atmospheric and Oceanic Physics · Physics 2022-03-14 Stefanie Legler , Tijana Janjic

Data assimilation (DA) aims at forecasting the state of a dynamical system by combining a mathematical representation of the system with noisy observations taking into account their uncertainties. State of the art methods are based on the…

Machine Learning · Computer Science 2023-05-26 Pierre Boudier , Anthony Fillion , Serge Gratton , Selime Gürol , Sixin Zhang

During the night between 9 and 10 September 2017, multiple flash floods associated to a heavy-precipitation event affected the town of Livorno, located in Tuscany, Italy. Accumulated precipitation exceeding 200 mm in two hours, associated…

Atmospheric and Oceanic Physics · Physics 2021-05-03 Valerio Capecchi , Andrea Antonini , Riccardo Benedetti , Luca Fibbi , Samantha Melani , Luca Rovai , Antonio Ricchi , Diego Cerrai

Contemporary data assimilation often involves more than a million prediction variables. Ensemble Kalman filters (EnKF) have been developed by geoscientists. They are successful indispensable tools in science and engineering, because they…

Probability · Mathematics 2017-05-26 Andrew J. Majda , Xin T. Tong

This work discusses how to choose performance measures to compare numerical simulations of a flood event with one satellite image, e.g., in a model calibration or validation procedure. A series of criterion are proposed to evaluate the…

Recent advances in data assimilation (DA) have focused on developing more flexible approaches that can better accommodate nonlinearities in models and observations. However, it remains unclear how the performance of these advanced methods…

Atmospheric and Oceanic Physics · Physics 2025-05-08 Zixiang Xiong , Siming Liang , Feng Bao , Guannan Zhang , Hristo G. Chipilski

Present forecasting efforts rely on assimilation techniques that adjust the model basic state, meaning that profiles of temperature and salinity are used as measured or converted to temperature and salinity through statistical…

Atmospheric and Oceanic Physics · Physics 2026-04-21 Justin Cooke , Kathleen Donohue , Clark D Rowley , Prasad G Thoppil , D Randolph Watts

In recent years, climate extremes such as floods have created significant environmental and economic hazards for Australia. Deep learning methods have been promising for predicting extreme climate events; however, large flooding events…

Machine Learning · Computer Science 2025-02-12 Rohitash Chandra , Arpit Kapoor , Siddharth Khedkar , Jim Ng , R. Willem Vervoort

The ensemble Kalman filter (EnKF) is widely used to sample a probability density function (pdf) generated by a stochastic model conditioned by noisy data. This pdf can be either a joint posterior that describes the evolution of the state of…

Data Analysis, Statistics and Probability · Physics 2016-08-08 Matthias Morzfeld , Daniel Hodyss

Integration of renewable power sources into grids remains an active research and development area, particularly for less developed renewable energy technologies such as wave energy converters (WECs). WECs are projected to have strong early…

Atmospheric and Oceanic Physics · Physics 2022-10-03 Mohammad Khalil , Carlos Michelén Ströfer , Kaustubha Raghukumar , Ann Dallman

The majority of data assimilation (DA) methods in the geosciences are based on Gaussian assumptions. While these assumptions facilitate efficient algorithms, they cause analysis biases and subsequent forecast degradations. Non-parametric,…

Methodology · Statistics 2025-05-12 Hristo G. Chipilski

We demonstrate that combining machine learning with data assimilation leads to a major improvement in phytoplankton short-range (1-5 day) forecasts for the North-West European Shelf (NWES) seas. We show that excess nitrate concentrations…

Quantitative Methods · Quantitative Biology 2025-08-05 Deep S Banerjee , Jozef Skakala , David Ford

We investigate the combined use of a Kinect depth sensor and of a stochastic data assimilation method to recover free-surface flows. More specifically, we use a Weighted ensemble Kalman filter method to reconstruct the complete state of…

Fluid Dynamics · Physics 2016-01-05 Benoit Combès , Dominique Heitz , Anthony Guibert , Etienne Mémin

The reconstruction of the dynamics of an observed physical system as a surrogate model has been brought to the fore by recent advances in machine learning. To deal with partial and noisy observations in that endeavor, machine learning…

Machine Learning · Statistics 2020-10-06 Marc Bocquet , Alban Farchi , Quentin Malartic

We propose a Dynamical Low-Rank Ensemble Kalman Filter (DLR-ENKF) for efficient joint state-parameter estimation in high-dimensional dynamical systems. The method extends the DLR-ENKF formulation of arXiv:2509.11210 to the augmented…

Numerical Analysis · Mathematics 2026-02-09 Fabio Nobile , Sébastien Riffaud , Thomas Trigo Trindade

Satellite observations play a critical role in numerical weather prediction where they are assimilated through an observation operator that maps model states to radiances. In the traditional Ensemble Kalman Filter, these observations are…

Atmospheric and Oceanic Physics · Physics 2026-03-24 Gian Luca Buono , Stefanie Hollborn , Roland Potthast , Jörg Schäfer , Martin Simon