I can't find anything certifying this, but from what I understand, a "P1" simply refers to a regular viewer or listener of a broadcast. In the case of The Weather Channel, I would imagine the P1's tuning in at the same time are doing so right before they leave for work, or before shutting it down for the night to find out what conditions lie ahead the next day.
I hope my explanation helped, as I was not able to locate a concrete definition. (Who knew there would come a time when Google was not your friend?)