scholarly journals Sensitivity of response functions in variational data assimilation for joint parameter and initial state estimation

2020 ◽  
Vol 373 ◽  
pp. 112368
Author(s):  
V. Shutyaev ◽  
F.-X. Le Dimet ◽  
E. Parmuzin
Keyword(s):  
Data Assimilation ◽  
State Estimation ◽  
Variational Data Assimilation ◽  
Response Functions ◽  
Initial State

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.

State Estimation of the North Pacific Ocean by a Four-Dimensional Variational Data Assimilation Experiment

2003 ◽  
Vol 59 (6) ◽  
pp. 931-943 ◽  
Author(s):  
Toshiyuki Awaji ◽  
Shuhei Masuda ◽  
Yoichi Ishikawa ◽  
Nozomi Sugiura ◽  
Takahiro Toyoda ◽  
...  
Keyword(s):  
Pacific Ocean ◽  
Data Assimilation ◽  
State Estimation ◽  
North Pacific ◽  
North Pacific Ocean ◽  
Variational Data Assimilation ◽  
Assimilation Experiment ◽  
The North ◽  
The North Pacific

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.

Numerical solution of the problem of variational data assimilation to restore heat fluxes and initial state for the ocean thermodynamics model

2021 ◽  
Vol 36 (1) ◽  
pp. 43-53
Author(s):  
Victor P. Shutyaev ◽  
Eugene I. Parmuzin
Keyword(s):  
Data Assimilation ◽  
Black Sea ◽  
Numerical Experiments ◽  
Iterative Solution ◽  
System Justification ◽  
Heat Fluxes ◽  
Variational Data Assimilation ◽  
The Black Sea ◽  
Initial State ◽  
Solution Algorithms

Abstract For the model of ocean thermodynamics developed at the Institute of Numerical Mathematics of RAS, the problem of variational data assimilation is considered in order to restore heat fluxes on the ocean surface and initial state of the model. Iterative solution algorithms are proposed for the optimality system, justification of these algorithms is given based on properties of the control operator. The results of numerical experiments for the model of the Black Sea dynamics are presented.

scholarly journals Sensitivity of functionals in variational data assimilation for a sea thermodynamics model

2021 ◽  
Vol 2099 (1) ◽  
pp. 012031
Author(s):  
V P Shutyaev ◽  
E I Parmuzin ◽  
I Yu Gejadze
Keyword(s):  
Data Assimilation ◽  
Response Function ◽  
Optimal Solution ◽  
Coupled System ◽  
Variational Data Assimilation ◽  
Adjoint Equations ◽  
The Black Sea ◽  
Observation Data ◽  
Initial State ◽  
Standard Problem

Abstract The sensitivity of functionals of the optimal solution to a variational data assimilation problem for the sea thermodynamics model is studied. The variational data assimilation problem is formulated as an optimal control problem to find the initial state and the boundary condition. The sensitivity of the response functions as functionals of the optimal solution with respect to the observation data is determined by the gradient of the response function and 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. The sensitivity analysis of the response function with respect to errors of observation data is carried out. Numerical examples are presented for the Black Sea thermodynamics model.

scholarly journals Diffusion Filters for Variational Data Assimilation of Sea Surface Temperature in an Intermediate Climate Model

2015 ◽  
Vol 2015 ◽  
pp. 1-17
Author(s):  
Xuefeng Zhang ◽  
Dong Li ◽  
Peter C. Chu ◽  
Lianxin Zhang ◽  
Wei Li
Keyword(s):  
Data Assimilation ◽  
Surface Temperature ◽  
Sea Surface Temperature ◽  
State Estimation ◽  
The State ◽  
Variational Data Assimilation ◽  
Sea Surface ◽  
Superior Performance ◽  
Assimilation Experiment ◽  
Gradient Diffusion

Sequential, adaptive, and gradient diffusion filters are implemented into spatial multiscale three-dimensional variational data assimilation (3DVAR) as alternative schemes to model background error covariance matrix for the commonly used correction scale method, recursive filter method, and sequential 3DVAR. The gradient diffusion filter (GDF) is verified by a two-dimensional sea surface temperature (SST) assimilation experiment. Compared to the existing DF, the new GDF scheme shows a superior performance in the assimilation experiment due to its success in extracting the spatial multiscale information. The GDF can retrieve successfully the longwave information over the whole analysis domain and the shortwave information over data-dense regions. After that, a perfect twin data assimilation experiment framework is designed to study the effect of the GDF on the state estimation based on an intermediate coupled model. In this framework, the assimilation model is subject to “biased” initial fields from the “truth” model. While the GDF reduces the model bias in general, it can enhance the accuracy of the state estimation in the region that the observations are removed, especially in the South Ocean. In addition, the higher forecast skill can be obtained through the better initial state fields produced by the GDF.

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