A 4-dimensional variational ensemble data assimilation (DA) scheme is introduced that (a) find the analysis corrections in a global variational solve, and (b) uses flow adaptive propagating error covariance localization in order to allow for long-time window DA. The scheme is based on a new method for inexpensively generating the square root of an adaptively localized global 4-dimensional error covariance model in terms of products or modulations of smoothed ensemble members with themselves and with raw ensemble members. The columns of the square root of this matrix may be interpreted as members of a modulation ensemble. For a 100 member raw ensemble, the modulation ensemble contains one million members. With the help of a global numerical weather prediction (NWP) model we (a) show that this million member ensemble provides a plausible model of 4-dimensional forecast error covariances (b) show that the initial time error covariance model provided by this covariance model is superior to that used by the operational (3D-VAR) DA scheme of the US Navy, and (c) show that the statistical Tangent Linear Model (TLM) implied by the 4D covariances is of comparable accuracy to those used in 4D-VAR data assimilation schemes. If time allows, I will also discuss (a) the deleterious effect of radiance space localization for EnKFs satellite DA and (b) ways in which some of the DAMES ideas can be incorporated into the LETKF.

Speaker Information: Dr. Craig H. Bishop
Naval Research Laboratory, Marine Meteorology Division
7 Grace Hopper Ave, Stop 2, Building 702, Room 212
Monterey, CA 93943-5502
E-mail: bishop@nrlmry.navy.mil