Two types of filtering failure are the well known filter divergence where errors may
exceed the size of the corresponding true chaotic attractor and the much more severe catastrophic
filter divergence where solutions diverge to machine infinity in finite time. In this paper, we demonstrate that
these failures occur in filtering the L-96 model, a nonlinear chaotic dissipative dynamical
system with the absorbing ball property and quasi-Gaussian unimodal statistics. In particular, catastrophic
filter divergence occurs in suitable parameter regimes for an ensemble Kalman filter when
the noisy turbulent true solution signal is partially observed at sparse regular spatial locations.
¶ With the above documentation, the main theme of this paper is to show that we can suppress
the catastrophic filter divergence with a judicious model error strategy, that is, through a suitable
linear stochastic model. This result confirms that the Gaussian assumption in the Kalman filter
formulation, which is violated by most ensemble Kalman filters through the nonlinearity in the model,
is a necessary condition to avoid catastrophic filter divergence. In a suitable range of chaotic regimes,
adding model errors is not the best strategy when the true model is known. However, we find that
there are several parameter regimes where the filtering performance in the presence of model errors
with the stochastic model supersedes the performance in the perfect model simulation of the best
ensemble Kalman filter considered here. Secondly, we also show that the advantage of the reduced
Fourier domain filtering strategy, A. Majda and M. Grote, Proceedings of the National Academy
of Sciences, 104, 1124-1129, 2007, E. Castronovo, J. Harlim and A. Majda, J. Comput. Phys.,
227(7), 3678-3714, 2008, J. Harlim and A. Majda, J. Comput. Phys., 227(10), 5304-5341, 2008 is
not simply through its numerical efficiency, but significant filtering accuracy is also gained through
ignoring the correlation between the appropriate Fourier coefficients when the sparse observations
are available in regular space locations.