Why Not Look Only at Model Output?. Good Web Site to Explore VV. http://www.twisterdata.com/. Comparison of Various Forms of the Q-G Omega Equation. Classic (Two terms: differential vorticity advection, Laplacian of the thermal wind)
Trenberth/Sutcliffe formulation (advection of absolute vorticity by the thermal wind) is more accurate since no cancellation problem.