Subramanian, A. C., I. Hoteit, B. Cornuelle, A. J. Miller and H. Song, 2012:
Linear vs. nonlinear filtering with scale selective corrections for
balanced dynamics in a simple atmospheric model
Journal of the Atmospheric Sciences, 69, 3405-3419.
We investigate the role of the linear analysis step of the ensemble Kalman Filters (EnKF)
in disrupting the balanced dynamics in a simple atmospheric model and compare it to a
fully nonlinear particle-based filter (PF). The filters have a very similar forecast step but the
analysis step of the PF solves the full Bayesian filtering problem while the EnKF analysis
only applies to Gaussian distributions. We compare the EnKF to two
flavors of the particle
filter with different sampling strategies, the Sequential Importance Resampling Filter (SIRF)
and the Sequential Kernel Resampling Filter (SKRF).
The model admits a chaotic vortical
mode coupled to a comparatively fast gravity wave mode. It can also either be configured to
evolve on a so-called slow manifold, where the fast motion is suppressed or such that the fast
varying variables are diagnosed from the slow-varying variables as slaved modes. Identical
twin experiments show that EnKF and PF capture the variables on the slow manifold well
as the dynamics is very stable. PFs, especially the SKRF, capture slaved modes better than
the EnKF implying a full Bayesian analysis estimates the nonlinear model variables better.
The PFs perform significantly better in the fully coupled nonlinear model where fast and
slow variables modulate each other. This suggests that the analysis step in the PFs maintain
the balance in both variables much better than the EnKF. It is also shown that increasing
the ensemble size generally improves the performance of the PFs but has less impact on the
EnKF after a suppressedcient number of members has been used.