The details of the model are presented in the ncep office notes at
The GFS model, formerly known as the Medium Range Forecast model (MRF) was initially developed by J. Sela(1980,1982).
The introduction of gocart aerosol module is described in the ncep technical note
It clearly mentions that the model is incapable of carrying advection and other dynamics and operates similar to an offine model coupled with the physics module through a coupler.
The introduction of sigma hybrid pressure levels into the gfs
Understanding Spectral Modelling
The COLA-Atmosphere-Biosphere General Circulation Model
Recent Changes into the Global Forecast System
The NCEP Climate Forecast System Version 2
Changes to the NCEP GFS by Srinivas Moorthy
The NCEP Climate Forecast System