Variational Data Assimilation Technique in Mathematical Modeling of Ocean Dynamics

2011 ◽  
Vol 169 (3) ◽  
pp. 555-578 ◽  
Author(s):  
V. I. Agoshkov ◽  
V. B. Zalesny
Keyword(s):  
Mathematical Modeling ◽  
Data Assimilation ◽  
Variational Data Assimilation ◽  
Ocean Dynamics ◽  
Data Assimilation Technique

scholarly journals Numerical Modeling of Marine Circulation with 4D Variational Data Assimilation

2020 ◽  
Vol 8 (7) ◽  
pp. 503
Author(s):  
Vladimir Zalesny ◽  
Valeriy Agoshkov ◽  
Victor Shutyaev ◽  
Eugene Parmuzin ◽  
Natalia Zakharova
Keyword(s):  
Data Assimilation ◽  
Finite Difference Methods ◽  
Variational Data Assimilation ◽  
Adjoint Equations ◽  
Special Choice ◽  
Modeling And Prediction ◽  
Solving Equations ◽  
The Baltic ◽  
Academy Of Sciences ◽  
Data Assimilation Technique

The technology is presented for modeling and prediction of marine hydrophysical fields based on the 4D variational data assimilation technique developed at the Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences (INM RAS). The technology is based on solving equations of marine hydrodynamics using multicomponent splitting, thereby solving an optimality system that includes adjoint equations and covariance matrices of observation errors. The hydrodynamic model is described by primitive equations in the sigma-coordinate system, which is solved by finite-difference methods. The technology includes original algorithms for solving the problems of variational data assimilation using modern iterative processes with a special choice of iterative parameters. The methods and technology are illustrated by the example of solving the problem of circulation of the Baltic Sea with 4D variational data assimilation of sea surface temperature information.

scholarly journals Strong Solvability of a Variational Data Assimilation Problem for the Primitive Equations of Large-Scale Atmosphere and Ocean Dynamics

2021 ◽  
Vol 31 (3) ◽  
Author(s):  
Peter Korn
Keyword(s):  
Data Assimilation ◽  
Large Scale ◽  
Initial Conditions ◽  
Strong Solutions ◽  
Variational Data Assimilation ◽  
Ocean Dynamics ◽  
Primitive Equations ◽  
Cost Functional ◽  
Strong Solvability ◽  
Gradient Based

AbstractFor the primitive equations of large-scale atmosphere and ocean dynamics, we study the problem of determining by means of a variational data assimilation algorithm initial conditions that generate strong solutions which minimize the distance to a given set of time-distributed observations. We suggest a modification of the adjoint algorithm whose novel elements is to use norms in the variational cost functional that reflects the $$H^1$$ H 1 -regularity of strong solutions of the primitive equations. For such a cost functional, we prove the existence of minima and a first-order adjoint condition for strong solutions that provides the basis for computing these minima. We prove the local convergence of a gradient-based descent algorithm to optimal initial conditions using the second-order adjoint primitive equations. The algorithmic modifications due to the $$H^1$$ H 1 -norms are straightforwardly to implement into a variational algorithm that employs the standard $$L^2$$ L 2 -metrics.

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