Sensitivity of response functions in variational data assimilation for joint parameter and initial state estimation
| Autor: | Victor P. Shutyaev, E. I. Parmuzin, F.-X. Le Dimet |
|---|---|
| Přispěvatelé: | Institute of Numerical Mathematics [Moscou] (INM-RAS), Russian Academy of Sciences [Moscow] (RAS), Mathematics and computing applied to oceanic and atmospheric flows (AIRSEA), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Grenoble Alpes (UGA)-Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Centre National de la Recherche Scientifique (CNRS)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA) |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Hessian matrix
010504 meteorology & atmospheric sciences 010103 numerical & computational mathematics 01 natural sciences symbols.namesake optimal control Data assimilation [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph] Applied mathematics [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] Sensitivity (control systems) 0101 mathematics sea thermodynamics model Joint (geology) 0105 earth and related environmental sciences Mathematics [PHYS.PHYS.PHYS-AO-PH]Physics [physics]/Physics [physics]/Atmospheric and Oceanic Physics [physics.ao-ph] Estimation theory Applied Mathematics Function (mathematics) State (functional analysis) Optimal control sensitivity Computational Mathematics symbols parameter estimation |
| Zdroj: | Journal of Computational and Applied Mathematics Journal of Computational and Applied Mathematics, Elsevier, 2020, 373, pp.112368:1-14. ⟨10.1016/j.cam.2019.112368⟩ Journal of Computational and Applied Mathematics, 2020, 373, pp.112368:1-14. ⟨10.1016/j.cam.2019.112368⟩ |
| ISSN: | 0377-0427 |
| Popis: | International audience; The problem of variational data assimilation for a nonlinear evolution model is formulated as an optimal control problem to find simultaneously unknown parameters and initial state of the model. 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 gradient of the response function with respect to observations is related to the solution of a non-standard problem involving the coupled system of direct and adjoint equations. Based on the Hessian of the original cost function, the solvability of the non-standard problem is studied. An algorithm to compute the gradient of the response function with respect to observation data is formulated and justified. A numerical example is presented for variational data assimilation problem for the Baltic Sea thermodynamics model. |
| Databáze: | OpenAIRE |
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