Asymptotic behavior of the forecast-assimilation process with unstable dynamics

Extensive numerical evidence shows that the assimilation of observations has a stabilizing effect on unstable dynamics, in numerical weather prediction, and elsewhere. In this paper, we apply mathematically rigorous methods to show why this is so. Our stabilization results do not assume a full set of observations and we provide examples where it suffices to observe the model's unstable degrees of freedom.

Automated summary

Extensive numerical evidence demonstrates that assimilating observations has a stabilizing effect on unstable dynamics, both in numerical weather prediction and other fields. In this paper, we employ mathematically rigorous methods to explain the underlying reasons behind this phenomenon. Our stabilization results do not necessitate a complete set of observations and we provide examples where observing only the unstable degrees of freedom of the model is sufficient.