From AMS Glossary
A numerical forecast model based on discrete advection terms only, with less or no emphasis on forcing, dissipation, and physics.
Advective models are most appropriately applied to nearly conserved quantities in the atmosphere or ocean, such as potential vorticity. Advective models are usually for one level only, or for a vertically integrated fluid. Historically, the barotropic model has been remarkably successful given its simplicity. A more recent example of an advective model is the divergent anomaly vorticity advection model.
Qin, J., and H. M. van den Dool 1996. Simple extensions of an NWP model. Mon. Wea. Rev.. 124. 277–287.