Optimal solution error quantification in variational data assimilation involving imperfect models

Shutyaev, V. P.; Gejadze, Igor; Vidard, Arthur; Dimet, F.‐X. Le

doi:10.1002/fld.4266

Cited by 3 publications

(2 citation statements)

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“…Ошибки модели могут быть связаны с дискретизацией, с неточным описанием физических процессов, с погрешностями исходных данных. Чтобы учесть возможные ошибки модели, рассматривают так называемую слабую формули-ровку, или постановку со слабыми ограничениями (weak constraint) [51][52][116][117][118][119][120][121][122][123][124][125].…”

Section: слабая формулировка вариационного усвоения данныхunclassified

Methods for assimilation of observational data in problems of the physics of the atmosphere and the ocean

Shutyaev

2019

Известия Российской академии наук. Физика атмосферы и океана

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In this paper we review and analyze approaches to data assimilation in geophysical hydrodynamics problems, starting with the simplest successive schemes of assimilation and ending with modern variational methods. Special attention is paid to the the study of the problem of variational assimilation in the weak formulation and construction of covariance error matrices of the optimal solution. This is a new direction, to which the author made a contribution: an optimality system is formulated for the problem of variational data assimilation in a weak formulation and algorithms for deriving the covariance error matrices of the optimal solution are developed.

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Section: слабая формулировка вариационного усвоения данныхunclassified

Methods for assimilation of observational data in problems of the physics of the atmosphere and the ocean

Shutyaev

2019

Известия Российской академии наук. Физика атмосферы и океана

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“…An uncertainty quantification research proposed by Shutyaev et al . focuses on evaluating the analysis error covariance matrix for weak constraint variational data assimilation problems. Besides the inverse Hessian of an associated objective function, the analysis error includes an additional component associated to the model error.…”

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Model reduction and inverse problems and data assimilation with geophysical applications. A special issue in honor of I. Michael Navon's 75th birthday

Ştefanescu

Noack

Sandu

2016

Numerical Methods in Fluids

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EDITORIALModel reduction and inverse problems and data assimilation with geophysical applications. A special issue in honor of I. Michael Navon's 75th birthdayProfessor Ionel Michael Navon retired in September 2014 from the Scientific Computing Department, Florida State University, Tallahassee, Florida, after a brilliant academic career. Since 1997, he is a fellow of the American Meteorological Society, and recently, he became an honorary member of the Academy of Romanian Scientists. His distinguished pioneering achievements in the domains of data assimilation, inverse problems, and reduced order modeling during the last few decades have greatly contributed to the establishment and development of these aforementioned fields. In particular, his rich interdisciplinary expertise allowed him to advance the science reduced order modeling and inverse modeling as core techniques for data-driven modeling. He generalized predictive computational modeling leading to fast novel solution approaches for real-world inverse problems of oceanography and weather forecast. At the same time, Professor Ionel Michael Navon has been an outstanding mentor, advisor, role model, and friend to his 9 PhD students and 11 postdoctoral scholars, with the large majority of them pursuing successful academic, scientific, and industry careers. This year Professor Ionel Michael Navon celebrates his 75th anniversary, and this special issue recognizes his accomplishments. The contributors to this special issue are former students, postdoctoral scholars, colleagues, close collaborators, and friends of Professor Ionel Michael Navon. The next three paragraphs describe his most important contributions to data assimilation and reduced order modeling fields in the last 10 years, while the last part of the editorial focuses on the special issue's contributions.Professor Navon's work addressed fundamental issues in both variational and statistical data assimilation with applications in fluid dynamics and atmospheric flows. Professor Navon extended and proposed frameworks to tackle non-differentiability in models and objective functions. For example, he formulated the maximum likelihood ensemble filter (MLEF) equations without the differentiability requirement for the prediction model and for the observation operators [1] and measured the impact of non-smooth observation operators on variational and sequential data assimilation [2]. Other efforts include coupling a Gaussian resampling method to generate more effective and efficient Particle Filter posterior analysis ensembles [3], improvement on the ensemble Kalman filters [4][5][6][7], and MLEF [8]. Professor Navon is also the co-author of a recent book [9] and several book chapters [10][11][12][13] describing the recent advancements and methodologies in variational data assimilation and non-linear sensitivity analysis. Goal-oriented adjoint sensitivity methods were proposed to guide to the adaptivity of finite element meshes [14,15]. Moreover, he developed different approaches to model error formulation [...

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Methods for Observation Data Assimilation in Problems of Physics of Atmosphere and Ocean

Shutyaev

2019

Izv. Atmos. Ocean. Phys.

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Optimal solution error quantification in variational data assimilation involving imperfect models

Cited by 3 publications

References 29 publications

Methods for assimilation of observational data in problems of the physics of the atmosphere and the ocean

Methods for assimilation of observational data in problems of the physics of the atmosphere and the ocean

Model reduction and inverse problems and data assimilation with geophysical applications. A special issue in honor of I. Michael Navon's 75th birthday

Methods for Observation Data Assimilation in Problems of Physics of Atmosphere and Ocean

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