A Tower Local Controller reported they cleared an aircraft onto the runway with another aircraft on short final.

Narrative

5 minutes after taking position from previous controller; splitting off LC2 (Local Control) to accommodate increasing volume of traffic. After briefing given to parallel controller and while monitoring departures from the south runway to switch pattern traffic to a different frequency; Aircraft X calls ready for departure. Radar tag for Aircraft Y was observed dropping off of the scope; which usually correlates with the aircraft touching down on the runway; and Aircraft X was issued LUAW (Line Up and Wait) instruction. As they read it back; I see Aircraft Y about to touch down; so at first I attempt to make Aircraft X stop; but they have immediately begun moving at near takeoff speed to taxi onto the runway and ignore this transmission; so I instead tell Aircraft Y to go around; with which they comply. No further issues arise and Aircraft Y comes back around to land without issue after Aircraft X is cleared for takeoff.During winter months when there is snow on the ground it is extremely difficult to see aircraft on final for Runway 30R once they pass below the horizon. If it is possible to change the tolerance of the radar to keep tags on the scope until they touch the surface it would be very beneficial for keeping our increasing volume of traffic in proper sequence. Additionally this was during a back-to-back briefing situation with CIC (Controller in Charge) combined with GC; so no available oversight to catch mistakes; we need greater staffing numbers in order to keep all of our positions open so these things can be caught more easily.