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The integration of observational data into numerical models, known as data assimilation (DA), is fundamental for making Numerical Weather Prediction (NWP) possible, with breathtaking success over the past 60 years (Bauer et al. 2015).…

Atmospheric and Oceanic Physics · Physics 2024-06-04 Jan D. Keller , Roland Potthast

We introduce a data assimilation strategy aimed at accurately capturing key non-Gaussian structures in probability distributions using a small ensemble size. A major challenge in statistical forecasting of nonlinearly coupled multiscale…

Numerical Analysis · Mathematics 2025-04-01 Di Qi , Jian-Guo Liu

Data assimilation (DA) aims to estimate the full state of a dynamical system by combining partial and noisy observations with a prior model forecast, commonly referred to as the background. In atmospheric applications, this problem is…

Atmospheric and Oceanic Physics · Physics 2025-05-29 Jing-An Sun , Hang Fan , Junchao Gong , Ben Fei , Kun Chen , Fenghua Ling , Wenlong Zhang , Wanghan Xu , Li Yan , Pierre Gentine , Lei Bai

Data assimilation (DA) plays a pivotal role in diverse applications, ranging from climate predictions and weather forecasts to trajectory planning for autonomous vehicles. A prime example is the widely used ensemble Kalman filter (EnKF),…

Dynamical Systems · Mathematics 2024-01-03 Mohamad Abed El Rahman Hammoud , Naila Raboudi , Edriss S. Titi , Omar Knio , Ibrahim Hoteit

Data assimilation is a central problem in many geophysical applications, such as weather forecasting. It aims to estimate the state of a potentially large system, such as the atmosphere, from sparse observations, supplemented by prior…

Machine Learning · Computer Science 2024-06-24 Matthieu Blanke , Ronan Fablet , Marc Lelarge

There has been a recent surge in development of accurate machine learning (ML) weather prediction models, but evaluation of these models has mainly been focused on medium-range forecasts, not their performance in cycling data assimilation…

Atmospheric and Oceanic Physics · Physics 2024-12-25 Laura C. Slivinski , Jeffrey S. Whitaker , Sergey Frolov , Timothy A. Smith , Niraj Agarwal

Data Assimilation is the process in which we improve the representation of the state of a physical system by combining information coming from a numerical model, real-world observations, and some prior modelling. It is widely used to model…

Optimization and Control · Mathematics 2025-01-09 Victor Trappler , Arthur Vidard

Data Assimilation is a cornerstone of atmospheric system modeling, tasked with reconstructing system states by integrating sparse, noisy observations with prior estimation. While traditional approaches like variational and ensemble Kalman…

Machine Learning · Computer Science 2025-11-04 Hao Wang , Zixuan Weng , Jindong Han , Wei Fan , Hao Liu

Data assimilation (DA) is a fundamental component of modern weather prediction, yet it remains a major computational bottleneck in machine learning (ML)-based forecasting pipelines due to reliance on traditional variational methods. Recent…

Machine Learning · Computer Science 2026-02-09 Ran Cheng , Lailai Zhu

Continuous data assimilation (CDA) is a method that continuously integrates observational data into a dynamical system to improve model accuracy in real-time. The AOT algorithm is one of the most widely used methods in CDA due to its…

Optimization and Control · Mathematics 2024-07-25 Ning Ning , Collin Victor

Data assimilation (DA) improves prediction of chaotic systems by combining model forecasts with sparse, noisy observations. Many DA methods are inherently probabilistic, but accurate probabilistic DA is often computationally expensive…

Fluid Dynamics · Physics 2026-04-24 Aditya Sai Pranith Ayapilla , Kazuya Miyashita , Yuki Yasuda , Ryo Onishi

Data assimilation (DA) integrates observations with model forecasts to produce optimized atmospheric states, whose physical consistency is critical for stable weather forecasting and reliable climate research. Traditional Bayesian DA…

Atmospheric and Oceanic Physics · Physics 2026-03-05 Hang Fan , Lei Bai , Ben Fei , Yi Xiao , Kun Chen , Yubao Liu , Yongquan Qu , Fenghua Ling , Pierre Gentine

Data-space inversion (DSI) and related procedures represent a family of methods applicable for data assimilation in subsurface flow settings. These methods differ from model-based techniques in that they provide only posterior predictions…

Machine Learning · Statistics 2020-05-08 Su Jiang , Louis J. Durlofsky

The recent surge in machine learning (ML) methods for geophysical modeling has raised the question of how these methods might be applied to data assimilation (DA). We focus on diffusion modeling (a form of generative artificial…

Atmospheric and Oceanic Physics · Physics 2025-08-29 Daniel Hodyss , Matthias Morzfeld

Data assimilation (DA) combines partial observations with dynamical models to improve state estimation. Filter-based DA uses only past and present data and is the prerequisite for real-time forecasts. Smoother-based DA exploits both past…

Systems and Control · Electrical Eng. & Systems 2026-01-21 Marios Andreou , Nan Chen , Yingda Li

Research on Artificial Intelligence (AI)-based Data Assimilation (DA) is expanding rapidly. However, the absence of an objective, comprehensive, and real-world benchmark hinders the fair comparison of diverse methods. Here, we introduce…

Machine Learning · Computer Science 2026-02-17 Wuxin Wang , Weicheng Ni , Ben Fei , Tao Han , Lilan Huang , Taikang Yuan , Xiaoyong Li , Lei Bai , Boheng Duan , Kaijun Ren

Starting from limited measurements of a turbulent flow, data assimilation (DA) attempts to estimate all the spatio-temporal scales of motion. Success is dependent on whether the system is observable from the measurements, or how much of the…

Fluid Dynamics · Physics 2026-02-16 Andrew Cleary , Qi Wang , Tamer A. Zaki

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

Data assimilation is a method that combines observations (that is, real world data) of a state of a system with model output for that system in order to improve the estimate of the state of the system and thereby the model output. The model…

Numerical Analysis · Mathematics 2020-05-18 Melina A. Freitag

We introduce a framework for Data Assimilation (DA) in which the data is split into multiple sets corresponding to low-rank projections of the state space. Algorithms are developed that assimilate some or all of the projected data,…

Computation · Statistics 2020-05-19 John Maclean , Erik S Van Vleck