Spectrum of Entrainment Rates

For some reason that last post really made the idea of the spectrum of entrainment rates make sense for me. In the bottom figure of the last post, we considered why the calculated green curve parcel profile didn't make sense, and drew an example of a curve that would make sense using green arrows. Just to fill that idea in, consider the following drawing, illustrating that many possible "green arrow" paths are possible. Could simulating a distribution of them improve the model? What would determine the proper distribution of the field?

What I'm wondering about now is how to handle the fact that there appears to be a problem of non-uniqueness...