Data assimilation by delay-coordinate nudging

A new nudging method for data assimilation, delay-coordinate nudging, is presented. Delay-coordinate nudging makes explicit use of present and past observations in the formulation of the forcing driving the model evolution at each time step. Numerical experiments with a low-order chaotic system show that the new method systematically outperforms standard nudging in different model and observational scenarios, also when using an unoptimized formulation of the delay-nudging coefficients. A connection between the optimal delay and the dominant Lyapunov exponent of the dynamics is found based on heuristic arguments and is confirmed by the numerical results, providing a guideline for the practical implementation of the algorithm. Delay-coordinate nudging preserves the easiness of implementation, the intuitive functioning and the reduced computational cost of the standard nudging, making it a potential alternative especially in the field of seasonal-to-decadal predictions with large Earth system models that limit the use of more sophisticated data assimilation procedures.