Is there a standardized way to define weather icons based on quantifiable data? Weather APIs often provide weather icons which symbolize the state of the sky at a given point, or as an average.

Is there a standardized way to define what the icon should be, based on quantifiable data such as cloud coverage or rain level (the idea being that, say, with over 50% cloud coverage a "cloud" is used, then with > 1 mm rain, "drops" are added etc.) -- or is it left purely as an interpretation to the user?
The icons that are used are really just a visual way of describing the phrasing that is used in the forecast.  You can see an example of one set of icons offered by Weather Underground here.  And they have many different icon sets that you could choose from.  The phrases themselves are linked to specific ranges of probability of precipitation, cloud cover, or other factor.  This site shows some nice tables that give some of those ranges (sample shown below):