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Nonlin. Processes Geophys., 25, 429-439, 2018
https://doi.org/10.5194/npg-25-429-2018
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.
Research article
21 Jun 2018
Sensitivity analysis with respect to observations in variational data assimilation for parameter estimation
Victor Shutyaev1,2,3, Francois-Xavier Le Dimet4, and Eugene Parmuzin1,3 1Institute of Numerical Mathematics, Russian Academy of Sciences, Gubkina 8, Moscow 119333, Russia
2Federal State Budget Scientific Institution “Marine Hydrophysical Institute of RAS”, Kapitanskaya 2, Sevastopol
3Moscow Institute for Physics and Technology, 9 Institutskiy per., Dolgoprudny, Moscow Region, 141701, Russia
4LJK, Université Grenoble Alpes, 700 Avenue Centrale, 38401 Domaine Universitaire de Saint-Martin-d'Hères, Grenoble, France
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.
Citation: Shutyaev, V., Le Dimet, F.-X., and Parmuzin, E.: Sensitivity analysis with respect to observations in variational data assimilation for parameter estimation, Nonlin. Processes Geophys., 25, 429-439, https://doi.org/10.5194/npg-25-429-2018, 2018.
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Short summary
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. The sensitivity of the response function to the observation data is studied. The results are relevant for monitoring and prediction of sea and ocean states.
The problem of variational data assimilation for a nonlinear evolution model is formulated as an...
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