Looking at the Trenberth Equation with the thermal wind calculated between 1000-500 mb and the absolute geostrophic vorticity advection by the thermal wind at 700 mb. The thermal wind flows parallel to the isotherms, with warmer air to the right, so the thermal wind is flowing eastward into Missouri. While the thermal wind is flowing eastward, it passes through a vort max associated with the trough, and thus the higher values of vorticity are advected into Missouri.
The Trenberth form of the omega equation indicates rising motion throughout Missouri and Illinois, extending into nearby states. It indicates sinking motion around the Texas panhandle into New Mexico. There is also a Vorticity maxima in north central Oklahoma.