Lessons from a Mixed Deterministic Stochastic Model of Periglacial Gnamma Development.

A theory of periglacial gnamma development in Chile, Minnesota, and Portugal claims that the maximum depth of gnammas (h) divided by the maximum depth of water which can be held by the gnammas (u) can be used to identify numerous periods of gnamma initiation on the rock surfaces. Surprisingly, h and u are positively correlated in the real data but must be negatively correlated in the theory. A deterministic computer model shows that if the rate of deepening of the gnamma is more rapid than in the spillway connected to the gnamma, h and u must be positively correlated as in the data. The simulations also show that it is more likely that all the gnammas on a surface develop at about the same time, a few centuries after the surface is exposed, and after that, few if any new gnammas are formed. The models also explain why the frequency distributions of h/u are asymmetric and skewed toward the small size gnammas. In the simulations, and on the outcrop, h/u approaches a steady state after thousands of years that is a function of the average rate of weathering of rock, not the initiation of new sets of gnammas.