In short: how large a diameter does a gauge need to have for it to be giving an accurate indication? I’m surprisingly confused by the fact that water is distributed in discrete drops, which makes me think that a given spot might receive less water in a given period than a spot right next to it. Does the ~1-inch diameter of my little rain gauge account for this?
The problem is that rain arrives in discrete drops and that makes a rain gage’s measurement change in that size increment. If you add one drop to your gage, how much does it change? Even a one inch diameter gage is not going to look much different after the arrival of one more drop.
A spot on the ground can receive different water for this reason. That’s why if it barely sprinkles, the patio becomes polka-dotted. But rain of this quantity is generally not important anyway. To the extent that rain waters the plants, the ground absorbs and distributes water on a larger-than-droplet scale. To the extent that it warms or cools or cleans the air, that’s always mixing around anyway.