Epistemic status: A definition I just learned, a preference statement, and some speculation

Yesterday I discovered that weather forecast probabilities aren't just the probability of rain in the forecast area, but also the probability that you'll be in a part of the forecast area where it's raining.

The National Weather Service defines the probability of precipitation (PoP) as:
PoP = C x A where "C" = the confidence that precipitation will occur somewhere in the forecast area, and where "A" = the percent of the area that will receive measurable precipitation (greater than or equal to 0.01"), if it occurs at all.
For example, if a meteorologist is 80% confident that at least 50% of the forecast area will see measurable precipitation then the PoP would be 40% (0.8 x 0.5 = 0.4 or 40%).

I have two thoughts about this right now:

First, I would strongly prefer they report these two numbers separately, so I can tell how much each factor is affecting the probability, and perhaps learn the parameter A over time myself from data. Hey, there's a good idea for a meta-weather app, if anyone wants to implement it.

Second, this might help explain something I've been wondering about: Why, when my weather app says there's a 20% chance of rain, does it always rain? It just seems very poorly calibrated. Since the geographic distribution of precipitation is uneven for various reasons, I may just be in a slice of the coverage area for predictions where it rains more often, and the PoP is being diluted by neighboring dry areas. Maybe. It's also possible I look at my weather app more often when it's more likely to rain (I dunno, maybe it smells different or something). Or perhaps I only remember instances when the app has predicted 20% and it rained anyway, because I got wet. I'd have to be a bit more careful to measure and record evenly if I really wanted to find out.