Small Aircraft
Air Traffic Control Fully Certified
Situational Awareness
ATC Issue All Types; Deviation / Discrepancy - Procedural Clearance; Ground Incursion Taxiway
Air Traffic Control Issued Advisory / Alert; Flight Crew Became Reoriented
Airport; Human Factors
Small aircraft on his first trip in the pattern [in] left closed traffic [for] Runway (RWY) 13. Aircraft appeared to be lined up on final for RWY 13 with no conflicts. I turned my attention to Ground Control duties for a moment (marking a strip); and when I looked back up; the [aircraft] was executing a touch-and-go on the parallel taxiway (Taxiway E). Once the aircraft was airborne; I inquired if he realized what had just happened. He replied 'Yes; I'm sorry.' Given that there was no other traffic and the situation had passed without incident; I decided not to issue a brasher warning. He continued in the pattern for a while longer before landing and returning to parking without incident.The pilot did call the tower a while later; just to apologize for the mistake. I did not take that phone call. It is my understanding that this is not the first aircraft to land on Taxiway E by mistake.Remove white splotches in concrete on Taxiway E that look a LOT like touchdown zone markers.  Paint a 'TAXI' sign at the NW corner of Taxiway E; abeam the RWY 13 numbers. Re-paint the RWY 13 markings if necessary to make the runway stand out. This is a new; wide taxiway with fresh; bright concrete. I can completely understand how a pilot could confuse it with RWY 13.
CID Tower Controller reports a small aircraft pilot performing a touch and go on Taxiway E thinking it is Runway 13 which he had been cleared for. This is a new; wide taxiway with fresh; bright concrete and white splotches that look similar to touchdown zone markers.