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Data assimilation of observational data into full atmospheric states is essential for weather forecast model initialization. Recently, methods for deep generative data assimilation have been proposed which allow for using new input data…

Numerical weather prediction has long been constrained by the computational bottlenecks inherent in data assimilation and numerical modeling. While machine learning has accelerated forecasting, existing models largely serve as "emulators of…

Machine Learning · Computer Science 2026-03-17 Xiaoze Xu , Xiuyu Sun , Songling Zhu , Xiaohui Zhong , Yuanqing Huang , Zijian Zhu , Jun Liu , Hao Li

Artificial intelligence (AI)-based weather prediction research is growing rapidly and has shown to be competitive with the advanced dynamic numerical weather prediction models. However, research combining AI-based weather prediction models…

Machine Learning · Computer Science 2025-10-16 Shunji Kotsuki , Kenta Shiraishi , Atsushi Okazaki

Data assimilation is the process to fuse information from priors, observations of nature, and numerical models, in order to obtain best estimates of the parameters or state of a physical system of interest. Presence of large errors in some…

Numerical Analysis · Mathematics 2015-11-06 Vishwas Rao , Adrian Sandu , Michael Ng , Elias Nino-Ruiz

Data-driven prediction and physics-agnostic machine-learning methods have attracted increased interest in recent years achieving forecast horizons going well beyond those to be expected for chaotic dynamical systems. In a separate strand of…

Data Analysis, Statistics and Probability · Physics 2021-05-19 Georg A. Gottwald , Sebastian Reich

In meteorology, engineering and computer sciences, data assimilation is routinely employed as the optimal way to combine noisy observations with prior model information for obtaining better estimates of a state, and thus better forecasts,…

Geophysics · Physics 2009-08-12 M. J. Werner , K. Ide , D. Sornette

Weather forecasting is a crucial yet highly challenging task. With the maturity of Artificial Intelligence (AI), the emergence of data-driven weather forecasting models has opened up a new paradigm for the development of weather forecasting…

Atmospheric and Oceanic Physics · Physics 2024-05-21 Yi Xiao , Lei Bai , Wei Xue , Kang Chen , Tao Han , Wanli Ouyang

In numerical weather prediction (NWP), a large number of observations are used to create initial conditions for weather forecasting through a process known as data assimilation. An assessment of the value of these observations for NWP can…

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

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

Weather forecasting traditionally relies on numerical weather prediction (NWP) systems that integrates global observational systems, data assimilation (DA), and forecasting models. Despite steady improvements in forecast accuracy over…

Machine Learning · Computer Science 2026-03-17 Xiuyu Sun , Xiaohui Zhong , Xiaoze Xu , Yuanqing Huang , Hao Li , J. David Neelin , Deliang Chen , Jie Feng , Wei Han , Libo Wu , Yuan Qi

Data assimilation plays a crucial role in modern weather prediction, providing a systematic way to incorporate observational data into complex dynamical models. The paper addresses continuous data assimilation for a model arising as a…

Analysis of PDEs · Mathematics 2026-02-03 Eduard Feireisl , Piotr Gwiazda , Agnieszka Świerczewska-Gwiazda

Data assimilation is a core component of numerical weather prediction systems. The large quantity of data processed during assimilation requires the computation to be distributed across increasingly many compute nodes, yet existing…

Machine Learning · Computer Science 2025-01-15 Oscar Key , So Takao , Daniel Giles , Marc Peter Deisenroth

Data assimilation is a technique for increasing the accuracy of simulations of solutions to partial differential equations by incorporating observable data into the solution as time evolves. Recently, a promising new algorithm for data…

Analysis of PDEs · Mathematics 2018-12-06 Adam Larios , Collin Victor

Data assimilation combines information from physical observations and numerical simulation results to obtain better estimates of the state and parameters of a physical system. A wide class of physical systems of interest have solutions that…

Optimization and Control · Mathematics 2025-05-02 Amit N. Subrahmanya , Adrian Sandu

Increasing the resolution of a model can improve the performance of a data assimilation system: first because model field are in better agreement with high resolution observations, then the corrections are better sustained and, with…

Atmospheric and Oceanic Physics · Physics 2022-09-07 Sébastien Barthélémy , Julien Brajard , Laurent Bertino , François Counillon

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 combines (imperfect) knowledge of a flow's physical laws with (noisy, time-lagged, and otherwise imperfect) observations to produce a more accurate prediction of flow statistics. Assimilation by nudging (from 1964), while…

Numerical Analysis · Mathematics 2024-07-31 Aytekin Çıbık , Rui Fang , William Layton , Farjana Siddiqua

Satellite observation operators play an essential role in atmospheric data assimilation by translating model state variables into observation space. Previous work has shown that deep-learned emulators can effectively predict the outputs of…

Ensemble weather predictions require statistical post-processing of systematic errors to obtain reliable and accurate probabilistic forecasts. Traditionally, this is accomplished with distributional regression models in which the parameters…

Machine Learning · Statistics 2019-04-01 Stephan Rasp , Sebastian Lerch