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Dive into the research topics where Victor P. Shutyaev is active.

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Featured researches published by Victor P. Shutyaev.


Izvestiya Atmospheric and Oceanic Physics | 2013

Observational data assimilation in the problem of Black Sea circulation and sensitivity analysis of its solution

V. I. Agoshkov; E. I. Parmuzin; Victor P. Shutyaev

The problem of the variational data assimilation of the sea-surface temperature for the model of the Black Sea dynamics has been formulated and numerically studied to reproduce surface heat fluxes. An analysis of sensitivity of the optimal solution to errors in observation data has been conducted. The results of numerical experiments have been presented.


Izvestiya Atmospheric and Oceanic Physics | 2010

Problems of Variational Assimilation of Observational Data for Ocean General Circulation Models and Methods for Their Solution

V. I. Agoshkov; V. M. Ipatova; V. B. Zalesnyi; E. I. Parmuzin; Victor P. Shutyaev

Problems of the variational assimilation of satellite observational data on the temperature and level of the ocean surface, as well as data on the temperature and salinity of the ocean from the ARGO system of buoys, are formulated with the use of the global three-dimensional model of ocean thermodynamics developed at the Institute of Numerical Mathematics, Russian Academy of Sciences (INM RAS). Algorithms for numerical solutions of the problems are developed and substantiated, and data assimilation blocks are developed and incorporated into the global three-dimensional model. Numerical experiments are performed with the use of the Indian Ocean or the entire World Ocean as examples. These numerical experiments support the theoretical conclusions and demonstrate that the use of a model with an assimilation block of operational observational data is expedient.


Computational Mathematics and Mathematical Physics | 2008

Numerical algorithm for variational assimilation of sea surface temperature data

V. I. Agoshkov; E. I. Parmuzin; Victor P. Shutyaev

The problem of variational assimilation of sea surface temperature data is formulated and studied. An algorithm for solving the problem is developed. Numerical results are presented.


Russian Journal of Numerical Analysis and Mathematical Modelling | 2015

Variational assimilation of observation data in the mathematical model of the Baltic Sea dynamics

Valeriy I. Agoshkov; E. I. Parmuzin; V. B. Zalesny; Victor P. Shutyaev; Natalia B. Zakharova; Anatoly V. Gusev

Abstract A mathematical model of the dynamics of the Baltic Sea is considered. A problem of variational assimilation of sea surface temperature (SST) data is formulated and studied. Based on variational assimilation of satellite observation data, an algorithm solving the inverse problem of heat flux restoration on the interface of two media is proposed. The results of numerical experiments reconstructing the heat flux functions in the problem of variational assimilation of SST observation data are presented. The influence of SST assimilation on other hydrodynamic parameters of the model is considered.


Russian Journal of Numerical Analysis and Mathematical Modelling | 2006

On error analysis in variational data assimilation problem for a nonlinear convection-diffusion model

E. I. Parmuzin; F.-X. Le Dimet; Victor P. Shutyaev

We consider the variational data assimilation problem to identify the initial condition for the 1D vertical heat exchange model governed by a non-stationary heat equation with nonlinear diffusion. We give the operator formulation of the problem and present solvability results. We derive an equation for the error of the optimal initial-value function through the errors of input data using the Hessian of the misfit functional. The fundamental control functions are used for error analysis. We obtain error sensitivity coefficients using singular vectors of the specific response operators in the error equation. Numerical examples are presented.


Russian Journal of Numerical Analysis and Mathematical Modelling | 2015

Variational assimilation of observation data in the mathematical model of the Black Sea taking into account the tide-generating forces

Valeriy I. Agoshkov; Maksim V. Assovskii; V. B. Zalesny; Natalia B. Zakharova; E. I. Parmuzin; Victor P. Shutyaev

Abstract A mathematical model of the dynamics of the Black and the Azov Seas is considered taking into account tide-generating forces. The problem of variational assimilation of sea surface temperature (SST) data is formulated and studied. Based on variational assimilation of satellite altimetry data, we propose an algorithm for solving the inverse problem of reconstruction of potential forces affecting the formation of the mean level and present a method of approximate solution of this problem.We also present numerical experiments concerning the study of the influence of tide-generating forces on the dynamics of the Black Sea and restoration of the heat flux function in the problem of variational data assimilation of SST observations


Russian Journal of Numerical Analysis and Mathematical Modelling | 2014

General sensitivity analysis in data assimilation

François-Xavier Le Dimet; Victor P. Shutyaev; Thu Ha Tran

Abstract The problem of variational data assimilation for a nonlinear evolution model is formulated as an optimal control problem to find the initial condition function (analysis). The operator of the model, and hence the optimal solution, depend on the parameters which may contain uncertainties. A response function is considered as a functional of the solution after assimilation. Based on the second-order adjoint techniques, the sensitivity of the response function to the parameters of the model is studied. The gradient of the response function is related to the solution of a non-standard problem involving the coupled system of direct and adjoint equations. The solvability of the non-standard problem is studied. Numerical algorithms for solving the problem are developed. The results are applied for 2D hydraulic and pollution models. Numerical examples on computation of the gradient of the response function are presented.


Russian Journal of Numerical Analysis and Mathematical Modelling | 2017

Sensitivity with respect to observations in variational data assimilation

Victor P. Shutyaev; François-Xavier Le Dimet; Elena Shubina

Abstract The problem of variational data assimilation for a nonlinear evolution model is formulated as an optimal control problem to find the initial condition function (analysis). The observation data, and hence the optimal solution, may contain uncertainties. A response function is considered as a functional of the optimal solution after assimilation. Based on the second-order adjoint techniques, the sensitivity of the response function to the observation data is studied. The gradient of the response function is related to the solution of a non-standard problem involving the coupled system of direct and adjoint equations. The solvability of the non-standard problem is studied, based on the Hessian of the original cost function. An algorithm to compute the gradient of the response function with respect to observations is developed and justified.


Russian Journal of Numerical Analysis and Mathematical Modelling | 2018

Adjoint equations in variational data assimilation problems

Victor P. Shutyaev

Abstract The problem of variational data assimilation for an evolution model is considered with the aim to identify the initial condition. The solvability of the optimality system is studied. Based on the adjoint equations, iterative algorithms for solving the problem are developed and justified.


Russian Journal of Numerical Analysis and Mathematical Modelling | 2018

Hessian-based covariance approximations in variational data assimilation

Igor Yu. Gejadze; Victor P. Shutyaev; François-Xavier Le Dimet

Abstract The problem of variational data assimilation (estimation) for a nonlinear model is considered in general operator formulation. Hessian-based methods are presented to compute the estimation error covariances. The importance of dynamic formulation and the role of the Hessian and its inverse are discussed.

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Igor Yu. Gejadze

Russian Academy of Sciences

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E. I. Parmuzin

Russian Academy of Sciences

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V. I. Agoshkov

Russian Academy of Sciences

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V. B. Zalesny

Russian Academy of Sciences

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F.-X. Le Dimet

Joseph Fourier University

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V. B. Zalesnyi

Russian Academy of Sciences

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V. M. Ipatova

Moscow Institute of Physics and Technology

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