Cessna 172 student pilot reported a runway excursion while landing at a tower-controlled airport in daylight visual conditions. The student pilot veered off the runway; across the grass and applied braking; then stopped safely on the taxiway; with no aircraft or airport damage; then taxied to parking.

Narrative

I was doing touch and goes at ZZZ and did not leave the pattern. Prior to the incident I did a total of 8 touch and goes with 2 additional go arounds one of which was ordered by ATC to the left side of the runway. The landing in which the incident occurred was intend to be a full stop landing and the last one for the day. The approach on final was very stable and probably one of the most stable that I had all day. I was able to maintain close to 61-65 kts. for the final mile with a good glideslope into the runway. What I did notice during the last few landings attempts was that the airplane was sinking very quickly as it approached the threshold. It was sinking so quickly that in each case I had to add considerable power to ensure the I cleared the blast wall. For the final landing I flared and was able touched down with the main gear first and everything appeared to be normal until the nose gear touched down then the aircraft started to veered to the left. The aircraft seem to have much more speed on the ground roll than in the prior landings. I retracted the flaps and maintained some back pressure but was hesitant to apply heavy braking or heavy right rudder fearing that might tip the airplane over at the speed that it moving. I believe the airplane entered the grass median between [Taxiway] 1 and 2; cross through the median without striking the lights or signs and entered the 3 taxiway before I applied enough brake to stop the plane. I stopped the airplane on the taxiway and waited for ATC to contact me. They radioed about 10-15 seconds later and asked if I was doing OK which I replied to the affirmative. They cleared me to continue on 3 to my parking destination. Upon; parking the aircraft I inspected the exterior of the plane for damage and found no obvious damage. When I took off the ATIS was reporting the winds from 320 at 13 kts. The METAR was reporting the winds to be 340 at 11 kts. at approximately 1800. The METAR was reporting some gust earlier in the day but did not have any when I took off. The wind speeds where within the limits prescribed in my solo endorsement from my CFI which was 14 kts. with a 6 kt. crosswind. I am not completely familiar with the signs of windshear but since I had to add considerable power just before touchdown in order to arrest my sink rate this contributed to a fairly high groundspeed by the time I touched down.