A mechanism for catastrophic filter divergence in data assimilation for sparse observation networks

We study catastrophic filter divergence in data assimilation procedures whereby the forecast model develops severe numerical instabilities leading to a blow up of the solution. Catastrophic filter divergence occurs in sparse observational grids with small observational noise for intermediate 5 observation intervals and finite ensemble sizes. Using a minimal five dimensional model we establish that catastrophic filter divergence is caused by the filtering procedure producing analyses which are not consistent with the true dynamics, and stiffness caused by the fast attraction of the inconsistent 10 analyses towards the attractor during the forecast step.