If the National Weather Service website shows increasing probability of precipitation (POP) over a 6 hour period (e.g. 10% rising gradually to 60%), what is the POP in this time interval if the confidence percentage is unknown?
The Probability Of Precipitation or POP is the exceedance probability over a given area for a given duration. The exceedance amount is generally taken as 0.25 mm, but may be any specified value. Again, the time $t$ must be specified, and is usually 3, 6, 12 or 24 hours.
Strictly speaking, the POP is meaningless unless the area under consideration is also specified, although in public weather forecasts this is seldom indicated. Individual storm cells generally have a footprint only a few kilometers wide, so obviously, the larger the area the higher the probability of precipitation, but the lower the average rainfall.
As for the confidence, this is a function of rainfall record duration and continuity, and raingauge network density.