Thanks for checking.  Here's another example of a precipitation rate figure from NOAA PSL:

https://www.psl.noaa.gov/map/images/rnl/prate_01a.rnl.anim.html

I realize "kilograms per meter squared per second" is a little odd to think about, but it is a "rate" (change in quantity over time).  This particular unit is sometimes shown because it's standard output from many of our models and analysis.