Accounting for multi-scale vertical error correlation within ETKF through spectral-space covariance localization
Covariance localization is an indispensable component of any EnKF and it is most straightforwardly formulated as tapering of the sampled background covariance matrix by means of Schur product (B-loc).
However, within most (L)ETKF implementations, this operation is substituted by artificial inflation of R-matrix (R-loc) due to computational difficulty. Recent studies by (Bocquet et al. 2016; Bishop et al. 2017) have derived an efficient way to implement B-loc within cycled ETKF, so that B-loc within ETKF is now a feasible option.
In my last two talks at ISDA, I focused on the differences between B-loc and R-loc, and showed, with idealized 1D models, that (1) B-loc can increase the effective rank of the background covariance while R-loc cannot (RISDA2017) and (2) B-loc can more faithfully reproduce canonical KF analysis than R-loc does when the observation operator is nonlocal (ISDA2018).
However, in a more realistic 1D experiment using background profiles from operational EnKF, B-loc was found not to always beat R-loc, arguably because of the nonuniform vertical correlation scales of the background profiles. This talk will address how spectral-space localization can be formulated to improve this situation without much modification to the established model-space B-loc.
Dr. Daisuke Hotta Meteorological Research Institute, JMA