Publikationen des Lehrstuhls Datenassimilation

Time-limited Balanced Truncation within Incremental Four-Dimensional Variational Data Assimilation

Autoren: J. König, M.A. Freitag (2023)

Four-dimensional variational data assimilation (4D-Var) is a data assimilation method often used in weather forecasting. Based on a numerical model and observations of a system, it predicts the system state beyond the last time of measurement. This requires the minimisation of a functional. At each step of the optimisation algorithm, a full nonlinear model evaluation and its adjoint is required. This quickly becomes very costly, especially in high dimensions. For this reason, a surrogate model is needed that approximates the full model well, but requires significantly less computational effort. In this paper, we propose time-limited balanced truncation to build such a reduced-order model. Our approach is able to deal with unstable system matrices. We demonstrate its performance in experiments and compare it with α-bounded balanced truncation, which is an another reduction approach for unstable systems.

Proceedings in Applied Mathematics and Mechanics

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