Session S15 - Mathematics of Planet Earth

Wednesday, July 14, 18:00 ~ 18:25 UTC-3

Optimal observation placement in variational data assimilation models

Juan Carlos De los Reyes

MODEMAT, Escuela Politécnica Nacional, Ecuador   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

Variational data assimilation problems have been widely studied in numerical weather prediction as a technique for reconstruction of the atmosphere initial condition. Taking this problem as motivation, our goal consists in finding the solution to an optimal placement problem on a parabolic equation, such that the initial condition will be optimally reconstructed. Within the framework of supervised learning methods, we consider a bilevel optimization problem where the lower level task is the reconstruction of the initial condition of the system’s state, and the upper level solves the optimal placement. The training set is constituted by simulations of the initial condition and the state of the system. To solve the data assimilation problem we use the variational approach (4D−VAR). Existence and uniqueness of solutions to the data assimilation problem are proven using the direct method of the calculus of variations, whereas to derive the optimality system we used the Lagrangian approach. Due to the objective functional structure, an adjoint system with Borel measures on the right-hand side is obtained for the lower level problem. To show existence of a very weak solution we used the transposition method and extra regularity results for parabolic systems. To derive the optimality system for the upper-level problem, we again use the Lagrangian approach. The constraint in this case is given by the optimality system of the lower level problem, which contains regular Borel measures on the right hand side. Existence of Lagrange multipliers is justified.

Joint work with Paula Castro (MODEMAT, Escuela Politécnica Nacional, Ecuador).

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