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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…

We mathematically derive the sensitivity of data assimilation results for tsunami modelling, to perturbations in the observation operator. We consider results of variational data assimilation schemes on the one dimensional shallow water…

Numerical Analysis · Mathematics 2020-03-24 N. K. -R. Kevlahan , R. A. Khan

Data assimilation algorithms are used to estimate the states of a dynamical system using partial and noisy observations. The ensemble Kalman filter has become a popular data assimilation scheme due to its simplicity and robustness for a…

Numerical Analysis · Mathematics 2021-06-23 Gottfried Hastermann , Maria Reinhardt , Rupert Klein , Sebastian Reich

The accuracy of simulation-based forecasting in chaotic systems is heavily dependent on high-quality estimates of the system state at the time the forecast is initialized. Data assimilation methods are used to infer these initial conditions…

Machine Learning · Computer Science 2021-11-02 Michael McCabe , Jed Brown

Satellite radar altimeters are a key source of observation of ocean surface dynamics. However, current sensor technology and mapping techniques do not yet allow to systematically resolve scales smaller than 100km. With their new sensors,…

Machine Learning · Computer Science 2023-09-28 Quentin Febvre , Ronan Fablet , Julien Le Sommer , Clément Ubelmann

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

We present a new continuous data assimilation algorithm based on ideas that have been developed for designing finite-dimensional feedback controls for dissipative dynamical systems, in particular, in the context of the incompressible…

Analysis of PDEs · Mathematics 2015-06-15 Abderrahim Azouani , Eric Olson , Edriss S. Titi

The accurate prediction of oceanographic variables is crucial for understanding climate change, managing marine resources, and optimizing maritime activities. Traditional ocean forecasting relies on numerical models; however, these…

Machine Learning · Computer Science 2025-10-30 Víctor Medina , Giovanny A. Cuervo-Londoño , Javier Sánchez

The use of data assimilation technique to identify optimal topography is discussed in frames of time-dependent motion governed by non-linear barotropic ocean model. Assimilation of artificially generated data allows to measure the influence…

Atmospheric and Oceanic Physics · Physics 2009-12-08 Eugene Kazantsev

Variational data assimilation technique applied to identification of optimal approximations of derivatives near boundary is discussed in frames of one-dimensional wave equation. Simplicity of the equation and of its numerical scheme allows…

Mathematical Physics · Physics 2015-05-13 Eugene Kazantsev

Long distance imaging is subject to the impact of the turbulent atmosphere. This results into geometric distortions and some blur effect in the observed frames. Despite the existence of several turbulence mitigation algorithms in the…

Computer Vision and Pattern Recognition · Computer Science 2024-10-31 Nicholas B. Ferrante , Jerome Gilles

The reconstruction of ocean subsurface temperature (OST) using satellite remote sensing data holds significant scientific value for advancing the understanding of ocean dynamics and climate variability. However, the scarcity of subsurface…

Atmospheric and Oceanic Physics · Physics 2026-05-05 Ming Shan Loo , Wengen Li , Xudong Jiang , Hailiang Cheng , Zhifei Zhang , Jihong Guan , Yichao Zhang

Through ensemble-based data assimilation (DA), we address one of the most notorious difficulties in phase-resolved ocean wave forecast, regarding the deviation of numerical solution from the true surface elevation due to the chaotic nature…

Atmospheric and Oceanic Physics · Physics 2021-07-01 Guangyao Wang , Yulin Pan

For oceanographic applications, probabilistic forecasts typically have to deal with i) high-dimensional complex models, and ii) very sparse spatial observations. In search-and-rescue operations at sea, for instance, the short-term…

Applications · Statistics 2023-02-15 Florian Beiser , Håvard Heitlo Holm , Jo Eidsvik

Forecasting ocean drift trajectories are important for many applications, including search and rescue operations, oil spill cleanup and iceberg risk mitigation. In an operational setting, forecasts of drift trajectories are produced based…

Computation · Statistics 2020-03-26 Håvard Heitlo Holm , Martin Lilleeng Sætra , Peter Jan van Leeuwen

AI and data-driven models have large potential for data assimilation applications by creating fast and accurate forecasts. Their tendency to produce spurious inaccurate, nonphysical results -- hallucination -- however, raises a serious…

Computational Engineering, Finance, and Science · Computer Science 2026-04-28 Andrey A. Popov

Adaptive variational quantum simulation algorithms use information from the quantum computer to dynamically create optimal trial wavefunctions for a given problem Hamiltonian. A key ingredient in these algorithms is a predefined operator…

AOSAT is a python package for the analysis of single-conjugate adaptive optics (SCAO) simulation results. Python is widely used in the astronomical community these days, and AOSAT may be used stand-alone, integrated into a simulation…

Instrumentation and Methods for Astrophysics · Physics 2021-02-08 Markus Feldt , Stefan Hippler , Faustine Cantalloube , Thomas Bertram , Andreas Obereder , Horst Steuer , Olivier Absil , Miska Le Louarn

The review describes the development of ideas Gury Ivanovich Marchuk in the field of variational data assimilation for ocean models applied in particular in coupled models for long-range weather forecasts. Particular attention is paid to…

Atmospheric and Oceanic Physics · Physics 2016-01-07 Christine Kazantsev , Eugene Kazantsev , Mikhail Tolstykh

The amount of Adaptive Optics (AO) telemetry generated by VIS/NIR ground-based observatories is ever greater, leading to a growing need for a standardised data exchange format to support performance analysis and AO research and development…