Underlying physical basis of an exponential distribution My data set of upper atmospheric cloud occurrences $N$ versus their thickness (or optical brightness, say $B$) show an exponential variation over more than two orders of magnitude - that is $N$ varies as $\mathrm{e}^{-cB}$. The quantity $c$ can vary from location to location. More than one first-principle model shows the identical exponential law. This behavior is clearly robust, but I have no idea as to what would cause such a beautiful distribution of such complicated animals, like clouds. Where would I start to try to understand the underlying physical principle? There must be something basic here that I am missing.
 A: This wiki article on the exponential covers a lot of ground. For physics solutions:

The exponential function is used to model a relationship in which a constant change in the independent variable gives the same proportional change (i.e. percentage increase or decrease) in the dependent variable.

Examples of this statement are given here

Consider the case of a nuclide A decaying into another B by some process A → B (emission of other particles, like electron neutrinos $\nu_e$ and electrons $e^-$ in beta decay, are irrelevant in what follows). The decay of an unstable nucleus is entirely random and it is impossible to predict when a particular atom will decay. However, it is equally likely to decay at any time. Therefore, given a sample of a particular radioisotope, the number of decay events −dN expected to occur in a small interval of time dt is proportional to the number of atoms present N, that is
$$-\frac{\mathrm{d}N}{\mathrm{d}t}\propto N$$
$$-\frac{\mathrm{d}N}{\mathrm{d}t}\propto \lambda\mathrm{d}t$$
The negative sign indicates that $N$ decreases as time increases, as each decay event follows one after another. The solution to this first-order differential equation is the function:
$$N(t) = N_0 e^{-\lambda t} = N_0 e^{-t/\tau}$$

In physics such assumptions can apply in many situation where the differential changes, in thickness or absorption or... can be modeled as above.
