JC99
The gamma pdf is a more general form of the equation for the ideal response of some number of equally-sized completely-mixed "tanks" arranged in series, to instantaneous input of an inert tracer. In such a circumstance the "shape" parameter alpha equals the number of such tanks, and the "mean" parameter tau equals the system's mean residence time. While the number-of-tanks is necessarily an integer property, the alpha parameter need not be. A surprising number of environmental transport phenomena (besides reactors in series) can be reasonably well characterized with gamma pdfs.