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The 4D-Var method for filtering partially observed nonlinear chaotic dynamical systems consists of finding the maximum a-posteriori (MAP) estimator of the initial condition of the system given observations over a time window, and…

Methodology · Statistics 2021-01-19 Daniel Paulin , Ajay Jasra , Alexandros Beskos , Dan Crisan

Data assimilation techniques, developed in the last two decades mainly for weather prediction, produce better forecasts by taking advantage of both theoretical/numerical models and real-time observations. In this paper, we explore the…

Astrophysics · Physics 2015-05-13 Eric Bélanger , Alain Vincent , Paul Charbonneau

The Strong Constraint 4D Variational (SC-4DVAR) data assimilation method is widely used in climate and weather applications. SC-4DVAR involves solving a minimization problem to compute the maximum a posteriori estimate, which we tackle…

Numerical Analysis · Mathematics 2025-06-16 Amit N. Subrahmanya , Vishwas Rao , Arvind K. Saibaba

This study demonstrates how the incremental 4D-Var data assimilation method can be applied efficiently preconditione d in an application to an oceanographic problem. The approach consists in performing a few iterations of the reduced-order…

Geophysics · Physics 2007-09-19 Céline Robert , Eric Blayo , Jacques Verron

Constraining a numerical weather prediction (NWP) model with observations via 4D variational (4D-Var) data assimilation is often difficult to implement in practice due to the need to develop and maintain a software-based tangent linear…

Machine Learning · Computer Science 2024-08-07 Kylen Solvik , Stephen G. Penny , Stephan Hoyer

Four-dimensional variational data assimilation (4DVar) has become an increasingly important tool in data science with wide applications in many engineering and scientific fields such as geoscience1-12, biology13 and the financial…

Data Analysis, Statistics and Probability · Physics 2018-05-28 Xiangjun Tian , Aiguo Dai , Xiaobing Feng , Hongqin Zhang , Rui Han , Lu Zhang

Extreme weather events pose significant challenges, thereby demanding techniques for accurate analysis and precise forecasting to mitigate its impact. In recent years, deep learning techniques have emerged as a promising approach for…

Atmospheric and Oceanic Physics · Physics 2023-08-23 Shikha Verma , Kuldeep Srivastava , Akhilesh Tiwari , Shekhar Verma

We propose a certified reduced basis approach for the strong- and weak-constraint four-dimensional variational (4D-Var) data assimilation problem for a parametrized PDE model. While the standard strong-constraint 4D-Var approach uses the…

Optimization and Control · Mathematics 2018-02-08 Mark Kärcher , Sébastien Boyaval , Martin A. Grepl , Karen Veroy

Data assimilation combines prior (or background) information with observations to estimate the initial state of a dynamical system over a given time-window. A common application is in numerical weather prediction where a previous forecast…

Optimization and Control · Mathematics 2021-07-27 Coralia Cartis , Maha H. Kaouri , Amos S. Lawless , Nancy K. Nichols

Dynamic downscaling typically involves using numerical weather prediction (NWP) solvers to refine coarse data to higher spatial resolutions. Data-driven models such as FourCastNet have emerged as a promising alternative to the traditional…

Atmospheric and Oceanic Physics · Physics 2025-03-05 Philip Dinenis , Vishwas Rao , Mihai Anitescu

Four-dimensional variational data assimilation (4D-Var) on a seasonal-to-interdecadal time scale under the existence of unstable modes can be viewed as an optimization problem of synchronized, coupled chaotic systems. The problem is tackled…

Data Analysis, Statistics and Probability · Physics 2015-11-17 Nozomi Sugiura , Shuhei Masuda , Yosuke Fujii , Masafumi Kamachi , Yoichi Ishikawa , Toshiyuki Awaji

This work introduces a new class of four-dimensional variational data assimilation (4D-Var) methods grounded in data-consistent inversion (DCI) theory. The methods extend classical 4D-Var by incorporating a predictability-aware…

Numerical Analysis · Mathematics 2025-11-04 Rylan Spence , Troy Butler , Clint Dawson

Variational data assimilation estimates the dynamical system states by minimizing a cost function that fits the numerical models with the observational data. Although four-dimensional variational assimilation (4D-Var) is widely used, it…

Machine Learning · Computer Science 2025-06-16 Yiming Yang , Xiaoyuan Cheng , Daniel Giles , Sibo Cheng , Yi He , Xiao Xue , Boli Chen , Yukun Hu

Intelligent transportation systems require accurate and reliable sensing. However, adverse environments, such as rain, snow, and fog, can significantly degrade the performance of LiDAR and cameras. In contrast, 4D mmWave radar not only…

Computer Vision and Pattern Recognition · Computer Science 2025-07-08 Xiangyuan Peng , Miao Tang , Huawei Sun , Kay Bierzynski , Lorenzo Servadei , Robert Wille

This paper addresses the impact of assimilating data from the Earth Networks Total Lightning Network (ENTLN) during two cases of severe weather. Data from the ENTLN serve as a substitute for those from the upcoming launch of the GOES…

Optimization and Control · Mathematics 2013-06-11 Razvan Stefanescu , I. Michael Navon , Henry Fuelberg , Max Marchand

Accurately forecasting the weather is an important task, as many real-world processes and decisions depend on future meteorological conditions. The NeurIPS 2022 challenge entitled Weather4cast poses the problem of predicting rainfall events…

Computer Vision and Pattern Recognition · Computer Science 2022-12-06 Yury Belousov , Sergey Polezhaev , Brian Pulfer

Understanding the combined influences of meteorological and hydrological factors on water level and flood events is essential, particularly in today's changing climate environments. Transformer, as one kind of the cutting-edge deep learning…

Machine Learning · Computer Science 2024-05-24 Mingyu Liu , Nana Bao , Xingting Yan , Chenyang Li , Kai Peng

To mitigate the impacts associated with adverse weather conditions, meteorological services issue weather warnings to the general public. These warnings rely heavily on forecasts issued by underlying prediction systems. When deciding which…

Applications · Statistics 2022-09-13 Sam Allen , Jonas Bhend , Olivia Martius , Johanna Ziegel

This paper presents a practical computational approach to quantify the effect of individual observations in estimating the state of a system. Such an analysis can be used for pruning redundant measurements, and for designing future sensor…

Computational Engineering, Finance, and Science · Computer Science 2013-07-22 Alexandru Cioaca , Adrian Sandu , Eric de Sturler

Predictions of thunderstorm-related hazards are needed in several sectors, including first responders, infrastructure management and aviation. To address this need, we present a deep learning model that can be adapted to different hazard…

Atmospheric and Oceanic Physics · Physics 2023-03-16 Jussi Leinonen , Ulrich Hamann , Ioannis V. Sideris , Urs Germann
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