Perspectives on the Probability of Precipitation

It is now May 11th and although we got a trace of rain last night at the Salt Lake City International Airport, we have yet to record measurable (.01" or greater) precipitation so far this month.  In fact, the last measurable rain fell on April 16. 

Some rain is possible this week, but not a lead-pipe cinch.  At about 7:45 AM this morning, I pulled up the forecast below for the airport and it shows a 20% chance late Thursday night, a 20% chance Wednesday, and a 20% chance Thursday.

But what does this really mean? 

Some people thing that it means 20% of the area will get precipitation or that it will rain 20% of the time, but neither of those is true.

Instead, the National Weather Service Probability of Precipitation is "the probability that the location in question will receive at least .01" of rain."  A 20% chance would mean there's a 1 in 5 chance that there will be measurable precipitation during the forecast period.

So, Probability of Precipitation tells you nothing about how much it is going to rain. 

Additionally, the forecast above is for a specific location, the Salt Lake City International Airport.  If I switch instead to the University of Utah, the forecast is slightly different.  Note, for example, the higher Probability of Precipitation on Thursday. 

In some instances, that makes sense.  The University of Utah is wetter than the airport. 

There are some aspects of the National Weather Service Forecast Probability of Precipitation that I find confusing.  For instance, when they split the day as they do on Thursday in the forecast above for the University of Utah, 30% is indicated in the left hand side of the icon and 40% in the right hand side.  The text below then says "chance rain" and "chance T-storms."

Does this mean a 30% chance of measurable rain and then a 40% chance of a thunderstorm?  Does it mean a 30% chance of rain in the morning and a 40% chance in the afternoon?

The more detailed accompanying text forecast is below and it does not provide thunderstorm probabilities, but does say that the chance of precipitation is 40%. 

So, it must be 30% chance in the morning and 40% chance in the afternoon, right?  Well, that doesn't make sense statistically.  If you have a 30% chance of something happening in the morning and a 40% chance of it happening in the afternoon, there's actually a 58% chance that it happens at any point during the day. 

Personally, I hope we either end up dry so we can claim some sort of streak or record, or we get a dousing so that the plants can take advantage.  Anything in between would just be a teaser.