Articles | Volume 20, issue 5
Nonlin. Processes Geophys., 20, 705–712, 2013
https://doi.org/10.5194/npg-20-705-2013

Special issue: Ensemble methods in geophysical sciences

Nonlin. Processes Geophys., 20, 705–712, 2013
https://doi.org/10.5194/npg-20-705-2013

Research article 25 Sep 2013

Research article | 25 Sep 2013

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

G. A. Gottwald1 and A. J. Majda2 G. A. Gottwald and A. J. Majda
  • 1School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia
  • 2Department of Mathematics and Center for Atmosphere Ocean Science, Courant Institute of Mathematical Sciences, New York University, USA

Abstract. 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 can occur in sparse observational grids with small observational noise for intermediate observation intervals and finite ensemble sizes. Using a minimal five-dimensional model, we establish that catastrophic filter divergence is a numerical instability of the underlying forecast model 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 analyses towards the attractor during the forecast step.