"The patterns form by self-organization, and the same fundamental processes are at work in the formation of all these different patterns," said Mark Kessler, a postdoctoral researcher in the Earth Sciences Department at the University of California, Santa Cruz.
As a graduate student working with Brad Werner, a professor of geophysics at UC San Diego, Kessler developed a numerical model of the processes involved in the self-organization of these patterns, known to geologists as "sorted patterned ground." Kessler and Werner reported their findings in a paper published in the January 17 issue of the journal Science.
Over the years, other scientists have proposed various explanations for these unusual patterns of stones and soil. But until now, no single explanation has been able to account for the full range of patterns seen in nature.
"The model I developed is essentially a hypothesis about what is important in the formation of patterned ground," Kessler said. "When you run the model on a computer, you can see the evolution of the pattern over time, and you can also see how small changes in key parameters result in a transition from one pattern to another."
According to Kessler, the patterns result primarily from the interaction of two mechanisms: lateral sorting, which moves soil toward areas of high soil concentration and stones toward areas of high stone concentration; and squeezing of stone domains, which causes stones to move within linear piles of stones and lengthens these lines of stones. The relative strengths of lateral sorting and squeezing, plus the slope of the ground and the ratio of stones to soil, are the factors that determine which pattern will emerge, Kessler said.
Driving the mechanisms of lateral sorting and squeezing is the phenomenon of frost heave--the expansion of fine-grained soils during freezing of wet ground. Frost heave results from the formation of discrete ice lenses in the soil. The soil near the surface expands because water flows up through the soil toward the ice lens as it forms (and to a lesser extent because the water expands as it freezes).
"If you start with a random layer of stones over a layer of soil, frost heave makes the soil layer unstable and deforms the interface between stones and soil," Kessler said.
As an ice lens grows near this interface, it pushes outward on the stones and also dessicates and compresses the soil below it. Where the interface between stones and soil is inclined, this causes lateral displacement of both stones and soil. When the ground thaws, the compressed soil reabsorbs water and expands. But the expansion occurs vertically, so it does not reverse the lateral displacement of soil by frost heave. Furthermore, the greater compressibility of soil-rich areas results in soil transport toward those areas.
Other processes are also involved in lateral sorting, but the end result is a positive feedback loop in which cycles of freezing and thawing cause soil-rich areas to attract more soil and stone-rich areas to attract more stones.
Once stones have been sorted into concentrated areas, or "stone domains," frost heave also squeezes and uplifts the stone domains. Differential uplift causes stones to migrate along the axis of a linear stone domain and lengthens the domain.
"The pattern depends on the relative strengths of lateral sorting, which actually brings stones back into areas of high stone concentration, and squeezing, which moves stones along," Kessler said. "One of the real mysteries to me was how you can get labyrinths or islands of stones in one location and polygons in another, when the ratio of stones to soil is the same in both places. Our model indicates that you get polygons when the squeezing is strong enough to counteract the effects of lateral sorting."
There are a variety of factors that can lead to differences in the relative strengths of squeezing and lateral sorting, he said. These include the compressibility of the soil and the size of the stones.
Another important factor is the extent to which the stone domains are confined by the soil, which determines whether squeezing will mainly cause stones to move along the stone domains or roll back onto the soil domains. In their model, Kessler and Werner can vary the degree of confinement, the concentration of stones, and the slope of the ground to produce circles, labyrinths, islands, stripes, and polygons of stones.
The researchers compared the patterns generated by the model with those observed in nature, using low-elevation aerial photographs of polygon networks in Alaska. Quantitative measurements of the natural and computer-generated polygons showed they were consistent. For example, one of the interesting features of polygon patterns, both in the model and in nature, is the tendency to form three-way intersections with equal angles between the intersecting lines, Kessler said.
One reason these patterns have remained unexplained for so long may be their occurence in remote areas, far from the temperate zone where most scientists live, Kessler said. "If these patterns were on the ground around here, I think we would have figured them out a long time ago. These landscapes are so amazing, it's the kind of thing that really calls out for an explanation."