On optimal solution error covariances in variational data assimilation problems

DOI10.1016/j.jcp.2009.11.028zbMath1185.65106OpenAlexW2079159741MaRDI QIDQ2270063

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

Publication date: 12 March 2010

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://strathprints.strath.ac.uk/16315/

zbMATH Keywords

optimal controlparameter estimationnumerical examplesvariational data assimilationconvection-diffusion modelHessian preconditioningnonlinear evolution modeloptimal solution error covariancesquasi-Newton Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Newton-type methods (49M15) Existence theories for optimal control problems involving partial differential equations (49J20)

Related Items (22)

Stability analysis of functionals in variational data assimilation with respect to uncertainties of input data for a sea thermodynamics model ⋮ Sensitivity of functionals with respect to observations in variational data assimilation ⋮ On model error in variational data assimilation ⋮ Sensitivity of functionals to observation data in a variational assimilation problem for the sea thermodynamics model ⋮ Sensitivity of functionals of the solution of a variational data assimilation problem with simultaneous reconstruction of heat fluxes and the initial state for the sea thermodynamics model ⋮ A Posteriori Error Estimates for the Solution of Variational Inverse Problems ⋮ An optimization framework to improve 4D-Var data assimilation system performance ⋮ On Gauss-verifiability of optimal solutions in variational data assimilation problems with nonlinear dynamics ⋮ Sensitivity with respect to observations in variational data assimilation ⋮ Design of the control set in the framework of variational data assimilation ⋮ Recovering the observable part of the initial data of an infinite-dimensional linear system with skew-adjoint generator ⋮ The study of the local sensitivity of functionals of the optimal solution to observational data and the heat flux input data in a variational assimilation problem for the sea thermodynamics model ⋮ Reconstructing the initial state of the linear system and estimating its error in discretization ⋮ Sensitivity of functionals of the solution to the variational assimilation problem to the input data on the heat flux for a model of sea thermodynamics ⋮ Computation of the analysis error covariance in variational data assimilation problems with nonlinear dynamics ⋮ Hessian-based covariance approximations in variational data assimilation ⋮ State reconstruction of the wave equation with general viscosity and non-collocated observation and control ⋮ Adjoint equations and iterative algorithms in problems of variational data assimilation ⋮ A Multilevel Approach for Computing the Limited-Memory Hessian and its Inverse in Variational Data Assimilation ⋮ Optimal sensor placement for joint parameter and state estimation problems in large-scale dynamical systems with applications to thermo-mechanics ⋮ Sensitivity of functionals of variational data assimilation problems ⋮ Sensitivity of functionals of the solution to a variational data assimilation problem with heat flux reconstruction for the sea thermodynamics model

Uses Software

• L-BFGS
• TAPENADE

Cites Work

• Discrete second order adjoints in atmospheric chemical transport modeling
• Data assimilation in weather forecasting: a case study in PDE-constrained optimization
• Optimization. Algorithms and consistent approximations
• A posteriori error covariances in variational data assimilation
• On Analysis Error Covariances in Variational Data Assimilation
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