What is a raindrop size distribution?

It is commonly understood that the number of drops that one happens to meas ure as a function of diameter in some sample represents the drop size distr ibution. However, recent observations show that rain is "patchy" suggesting that such a seemingly "obvious" definition is incomplete. That is, rain co nsists of patches of elementary drop size distributions over a range of dif ferent scales. All measured drop size distributions, then, are statistical mixtures of these patches. Moreover, it is shown that the interpretation of the measured distribution depends upon whether the rain is statistically homogeneous or not. It is ar gued and demonstrated using Monte Carlo simulations that in statistically h omogeneous rain, as the number of patches included increases, the observed spectrum of drop sizes approaches a "steady" distribution. On the other han d, it is argued and demonstrated using video disdrometer data that in stati stically inhomogeneous rain, there is no such steady distribution. Rather a s long as one keeps measuring,; the drop size distribution continues to cha nge. What is observed, then, depends on when one chooses to stop adding mea surements. Consequently, the distributions measured in statistically inhomogeneous rai n are statistical entities of mean drop concentrations best suited to stati stical interpretations. In contrast, steady distributions in statistically homogeneous rain are more amenable to deterministic interpretations since t hey depend upon factors independent of the measurement process. These findings have implications addressed in two additional questions, nam ely, Are computer-created virtual drop size distributions really the same as tho se observed? What is the appropriate drop size distribution when several measurements us ed in an algorithm for rain estimations are made at different resolutions?.