Scale-Dependent Weighting and Localization for the NCEP GFS Hybrid 4D EnVar Scheme

Following the successful transition to hybrid 4D EnVar into NCEP for the Global Forecast System (GFS) and Global Data Assimilation System (GDAS), work has begun to improve several aspects of the algorithm.  The current hybrid scheme in use for the NCEP GDAS utilizes single global weighting parameters to prescribe the contributions from the ensemble and static error covariances.  Furthermore, the localization applied to the control variable to prescribe the ensemble-based analysis increment is assumed to be Gaussian, with the horizontal localization varying only by vertical level.  Several studies have already shown that spectral and scale-dependent localization can be more effective within the context of EnVar (Buehner 2012, Buehner and Shlyaeva 2015).  Here, we will describe an effort toward applying waveband dependent localization as well as weighting between the static and ensemble contributions within a hybrid assimilation paradigm.  Results from a toy model as well as a low-resolution prototype of the NCEP GFS will be presented.  Within the context of the GFS, we will further explore the use of variable-dependent localization as a potential alternative or supplement to scale-dependent localization.