Time‐limited balanced truncation within incremental four‐dimensional variational data assimilation

Abstract

AbstractFour‐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.