Sorted patterned ground: Numerical models exhibiting self-organization

Sorted patterned ground, decimeter- to meter-scale patterns of circular, polygonal, striped and labyrinthine stone and soil domains, form in Arctic, sub­Arctic and high alpine environments where the surface ground layer, the active layer, experiences cyclic freezing and thawing that drives transport by frost heave, which is soil expansion via ice lens formation. In numerical models encapsulating observed and inferred active layer processes, all forms of sorted patterned ground emerge from an interplay between two mechanisms: (i) lateral sorting occurs by frost heave transporting soil toward soil rich regions, and (ii) stone domain extension and thinning occurs by lateral frost heave squeezing elongate stone domains, thereby driving stone transport along the axis of stone domains. Sorted circles self-organize in a three-dimensional, cellular model of the active layer in which the first feedback is implemented by cyclic freezing and thawing driving transport of stone and soil particles via processes related to frost heave, gravity and water migration in soils. Modeled sorted circle size (~ 3 m), spacing (~ 4 m), and circulation time (~ 750 yr) are consistent with measurements from western Spitsbergen. The initial wavelength of perturbations on the stone/soil interface is accurately predicted using a linear stability analysis, but increase in wavelength through time reflects nonlinearities that control the spacing of soil plugs and sorted circles, namely, interactions and mergers between neighboring forms.In a two-dimensional numerical model abstracting both feedbacks, circles, labyrinths, and islands emerge when lateral sorting dominates (with increasing volumetric fraction of soil); polygons emerge when along-axis transport domi­nates. The first class of patterns transitions to the second as soil compressibility is decreased and freezing rate in stone domains is increased. Islands transition to stripes on hillslopes.The observed range of patterns also can be generated when the larger-scale properties of enhanced squeezing and rapid freezing of air cooled stone domains are included in the three-dimensional model. An increase in the volumetric fraction of soil, i:, causes transitions between circles (Vs < 0.47), labyrinths (0.4 7 < Vs < 0.66), and islands (Vs > 0.66). Polygons transition to labyrinths as the magnitude of squeezing decreases relative to processes associated with lateral sorting. Islands and polygons grade into stripes on hillslopes greater than 2° and 4°, respectively