We showed in earlier work that this problem can be somewhat alleviated by a suitable change of analysis variable, which is defined by a background-dependent scaling of the specific humidity. In this new variable, time- and space averaging of the errors becomes more meaningful, so that simple covariance models based on statistical averages do present some useful information about local errors.
With this as a starting point, we embarked upon an effort to further improve the description of moisture errors by modeling the three main dynamic effects on the error covariances in the assimilation cycle: (1) advection of initial errors, (2) error growth due to model defects, and (3) error reduction due to the incorporation of observations. We have formulated simple representations of each of these effects, which are intended to be incorporated in the moisture error covariance specification of the Physical-space/Finite-volume Data Assimilation System (fvDAS) at NASA's Data Assimilation Office. We plan to present the results of initial assimilation experiments with this scheme.