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Data assimilation (DA) in the geophysical sciences remains the cornerstone of robust forecasts from numerical models. Indeed, DA plays a crucial role in the quality of numerical weather prediction, and is a crucial building block that has…

Data assimilation is an iterative approach to the problem of estimating the state of a dynamical system using both current and past observations of the system together with a model for the system's time evolution. Rather than solving the…

Data Analysis, Statistics and Probability · Physics 2007-05-23 Brian R. Hunt , Eric J. Kostelich , Istvan Szunyogh

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 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

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

Using a very cheap Data Assimilation (DA) method, I show an alternative approach to classical DA for numerical climate models which produce a large amount of "big data". The problematic features of state-of-the-art high resolution Regional…

Applications · Statistics 2016-10-12 Bijan Fallah

Data assimilation (DA) is a fundamental computational technique that integrates numerical simulation models and observation data on the basis of Bayesian statistics. Originally developed for meteorology, especially weather forecasting, DA…

Data assimilation (DA) aims at optimally merging observational data and model outputs to create a coherent statistical and dynamical picture of the system under investigation. Indeed, DA aims at minimizing the effect of observational and…

Data Analysis, Statistics and Probability · Physics 2022-01-05 Yumeng Chen , Alberto Carrassi , Valerio Lucarini

Data assimilation (DA) is a cornerstone of scientific and engineering applications, combining model forecasts with sparse and noisy observations to estimate latent system states. Classical high-dimensional DA methods, such as the ensemble…

Machine Learning · Statistics 2026-05-28 Martin Andrae , Erik Wikingsson , So Takao , Tomas Landelius , Fredrik Lindsten

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

We describe a new approach allowing for systematic causal attribution of weather and climate-related events, in near-real time. The method is purposely designed to facilitate its implementation at meteorological centers by relying on data…

Data assimilation (DA) enables hydrologic models to update their internal states using near-real-time observations for more accurate forecasts. With deep neural networks like long short-term memory (LSTM), using either lagged observations…

Fluid Dynamics · Physics 2025-02-25 Amirmoez Jamaat , Yalan Song , Farshid Rahmani , Jiangtao Liu , Kathryn Lawson , Chaopeng Shen

Variational data assimilation optimizes for an initial state of a dynamical system such that its evolution fits observational data. The physical model can subsequently be evolved into the future to make predictions. This principle is a…

Machine Learning · Computer Science 2021-05-21 Thomas Frerix , Dmitrii Kochkov , Jamie A. Smith , Daniel Cremers , Michael P. Brenner , Stephan Hoyer

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

Chaos is ubiquitous in physical systems. The associated sensitivity to initial conditions is a significant obstacle in forecasting the weather and other geophysical fluid flows. Data assimilation is the process whereby the uncertainty in…

Data Analysis, Statistics and Probability · Physics 2020-11-03 Alberto Carrassi , Marc Bocquet , Jonathan Demaeyer , Colin Grudzien , Patrick Raanes , Stephane Vannitsem

Data assimilation (DA) addresses the problem of sequentially estimating the state of a dynamical system from noisy and incomplete observations. In this work, we employ a diffusion model as a world model to simulate and predict the system's…

Machine Learning · Statistics 2026-05-26 Lifu Wei , Yinuo Ren , Naichen Shi , Yiping Lu

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

In this study, two classes of methods including statistical and variational data assimilation algorithms will be described. In statistical methods, the model state is updated sequentially based on the previous estimate. Variational methods,…

Systems and Control · Electrical Eng. & Systems 2021-10-25 Loc Luong

We review the field of data assimilation (DA) from a Bayesian perspective and show that, in addition to its by now common application to state estimation, DA may be used for model selection. An important special case of the latter is the…

Applications · Statistics 2017-04-05 Alberto Carrassi , Marc Bocquet , Alexis Hannart , Michael Ghil
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