Tire Pressure Monitor System

[RMSAZ]

I was driving my H3 up a mountain (9000 ft elevation and about 30 degree temp drop). The tire pressure monitor warning came on when I was at the top of the mountain. It stayed on until I was back down to about 4000 ft. I didn't have a tire gauge available on the mountain, but when I checked the tires the next morning, they were all at 35psi. I expected to lose a couple of pounds of pressure on the climb, but not enough to set off the warning. Does anybody know the tolerance on the warning system?