On optimal solution error covariances in variational data assimilation

2008 ◽  
Vol 23 (2) ◽  
Author(s):  
V. Shutyaev ◽  
F.-X. Le Dimet ◽  
I. Gejadze
Keyword(s):  
Data Assimilation ◽  
Optimal Solution ◽  
Variational Data Assimilation

scholarly journals Sensitivity analysis with respect to observations in variational data assimilation for parameter estimation

2018 ◽  
Vol 25 (2) ◽  
pp. 429-439 ◽  
Author(s):  
Victor Shutyaev ◽  
Francois-Xavier Le Dimet ◽  
Eugene Parmuzin
Keyword(s):  
Data Assimilation ◽  
Response Function ◽  
Optimal Solution ◽  
Coupled System ◽  
Variational Data Assimilation ◽  
Adjoint Equations ◽  
Observation Data ◽  
Unknown Parameters ◽  
The Baltic ◽  
Nonstandard Problem

Abstract. The problem of variational data assimilation for a nonlinear evolution model is formulated as an optimal control problem to find unknown parameters of the model. 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 nonstandard problem involving the coupled system of direct and adjoint equations. The nonstandard 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 presented. A numerical example is given for the variational data assimilation problem related to sea surface temperature for the Baltic Sea thermodynamics model.

Sensitivity with respect to observations in variational data assimilation

2017 ◽  
Vol 32 (1) ◽  
Author(s):  
Victor Shutyaev ◽  
Francois-Xavier Le Dimet ◽  
Elena Shubina
Keyword(s):  
Data Assimilation ◽  
Response Function ◽  
Nonlinear Evolution ◽  
Function Analysis ◽  
Optimal Solution ◽  
Coupled System ◽  
Variational Data Assimilation ◽  
Adjoint Equations ◽  
Observation Data ◽  
Standard Problem

AbstractThe 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.

scholarly journals Optimal solution error covariance in highly nonlinear problems of variational data assimilation

2012 ◽  
Vol 19 (2) ◽  
pp. 177-184 ◽  
Author(s):  
V. Shutyaev ◽  
I. Gejadze ◽  
G. J. M. Copeland ◽  
F.-X. Le Dimet
Keyword(s):  
Nonlinear Dynamics ◽  
Data Assimilation ◽  
Optimal Solution ◽  
Nonlinear Problems ◽  
Variational Data Assimilation ◽  
Model Parameters ◽  
Efficient Computation ◽  
Viscous Term ◽  
Highly Nonlinear ◽  
The Cost

Abstract. The problem of variational data assimilation (DA) for a nonlinear evolution model is formulated as an optimal control problem to find the initial condition, boundary conditions and/or model parameters. The input data contain observation and background errors, hence there is an error in the optimal solution. For mildly nonlinear dynamics, the covariance matrix of the optimal solution error can be approximated by the inverse Hessian of the cost function. For problems with strongly nonlinear dynamics, a new statistical method based on the computation of a sample of inverse Hessians is suggested. This method relies on the efficient computation of the inverse Hessian by means of iterative methods (Lanczos and quasi-Newton BFGS) with preconditioning. Numerical examples are presented for the model governed by the Burgers equation with a nonlinear viscous term.

scholarly journals Sensitivity of functionals of variational data assimilation problems

2019 ◽  
Vol 486 (4) ◽  
pp. 421-425
Author(s):  
V. P. Shutyaev ◽  
F.-X. Le Dimet
Keyword(s):  
Data Assimilation ◽  
Observational Data ◽  
Response Function ◽  
Optimal Solution ◽  
Evolutionary Model ◽  
Variational Data Assimilation ◽  
Adjoint Equations ◽  
Unknown Parameters ◽  
Initial State ◽  
Nonstandard Problem

The problem of variational data assimilation for a nonlinear evolutionary model is formulated as an optimal control problem to find simultaneously unknown parameters and the initial state of the model. The response function is considered as a functional of the optimal solution found as a result of assimilation. The sensitivity of the functional to observational data is studied. The gradient of the functional with respect to observations is associated with the solution of a nonstandard problem involving a system of direct and adjoint equations. On the basis of the Hessian of the original cost function, the solvability of the nonstandard problem is studied. An algorithm for calculating the gradient of the response function with respect to observational data is formulated and justified.

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

2019 ◽  
Vol 55 (1) ◽  
pp. 17-34
Author(s):  
V. P. Shutyaev
Keyword(s):  
Data Assimilation ◽  
Variational Methods ◽  
Observational Data ◽  
Optimal Solution ◽  
Variational Data Assimilation ◽  
Optimality System ◽  
Weak Formulation ◽  
Variational Assimilation ◽  
Geophysical Hydrodynamics

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.

scholarly journals On optimal solution error covariances in variational data assimilation problems

2010 ◽  
Vol 229 (6) ◽  
pp. 2159-2178 ◽  
Author(s):  
I.Yu. Gejadze ◽  
F.-X. Le Dimet ◽  
V. Shutyaev
Keyword(s):  
Data Assimilation ◽  
Optimal Solution ◽  
Variational Data Assimilation

Sensitivity of functionals with respect to observations in variational data assimilation

2016 ◽  
Vol 31 (2) ◽  
Author(s):  
François-Xavier Le Dimet ◽  
Victor Shutyaev ◽  
Eugene Parmuzin
Keyword(s):  
Data Assimilation ◽  
Optimal Solution ◽  
Coupled System ◽  
Variational Data Assimilation ◽  
Adjoint Equations ◽  
Boundary Values ◽  
The Baltic Sea ◽  
Standard Problem ◽  
The Mean ◽  
The Baltic

AbstractThe problem of variational data assimilation for a model of ocean thermodynamics is formulated as an optimal control problem to find the boundary heat flux. The sensitivity of functionals of the optimal solution with respect to observations is studied. Computing the gradient of the functionals is reduced to the solution of a non-standard problem which is a coupled system involving direct and adjoint equations with mutually dependent boundary values. Solvability of the non-standard problem is studied based on the Hessian of the original cost function. An algorithm for computing the gradient of the response function related to the mean surface temperature is developed and justified. Numerical examples are presented for the Baltic Sea thermodynamics model.

Stability analysis of functionals in variational data assimilation with respect to uncertainties of input data for a sea thermodynamics model

2021 ◽  
Vol 36 (6) ◽  
pp. 347-357
Author(s):  
Victor Shutyaev ◽  
Eugene Parmuzin ◽  
Igor Gejadze
Keyword(s):  
Stability Analysis ◽  
Data Assimilation ◽  
Response Function ◽  
Input Data ◽  
Optimal Solution ◽  
Coupled System ◽  
Variational Data Assimilation ◽  
Adjoint Equations ◽  
Observation Data ◽  
Initial State

Abstract The problem of stability and sensitivity of functionals of the optimal solution of the variational data assimilation of sea surface temperature for the model of sea thermodynamics is considered. The variational data assimilation problem is formulated as an optimal control problem to find the initial state and the boundary heat flux. The sensitivity of the response functions as functionals of the optimal solution with respect to the observation data is studied. Computing the gradient of the response function reduces to the solution of a non-standard problem being a coupled system of direct and adjoint equations with mutually dependent initial and boundary values. The algorithm to compute the gradient of the response function is presented, based on the Hessian of the original cost functional. Stability analysis of the response function with respect to uncertainties of input data is given. Numerical examples are presented for the Black and Azov seas thermodynamics model.

Sign in / Sign up

Export Citation Format

Share Document