EGU General Assembly 2022
© Author(s) 2022. This work is distributed under
the Creative Commons Attribution 4.0 License.

Asymptotic behavior of the forecast-assimilation process with unstable dynamics

Dan Crisan1 and Michael Ghil2
Dan Crisan and Michael Ghil
  • 1Imperial College London, Faculty of Natural Sciences, Mathematics, London, United Kingdom of Great Britain – England, Scotland, Wales (
  • 2Ecole Normale Supérieure, Laboratoire de Météorologie Dynamique, Paris, France ( University of California, Los Angeles (UCLA)

Extensive numerical evidence for real and/or simulated data shows that the assimilation of observations has a stabilizing effect on unstable dynamics in numerical weather prediction and elsewhere.  In this talk, I will discuss mathematically rigorous considerations showing why this is so. In particular we prove that the expected value of the Wasserstein distance between the forecast-assimilation (FA) process starting from the true initial conditions and FA process wrongly initialized can be controlled uniformly in time. Under suitable circumstances, the number of observations required to achieve this stabilization can be much smaller than the number of model variables. In particular, it suffices to observe the model's unstable degrees of freedom. 

How to cite: Crisan, D. and Ghil, M.: Asymptotic behavior of the forecast-assimilation process with unstable dynamics, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-8659,, 2022.