A Model for Sorted Patterned-Ground Regularity

Abstract

Abstract Sorted patterned ground refers to polygons, nets, or stripes defined by rocky borders which are the result of sorting in soil subjected to frost action. This paper presents a model in which convection cells, driven by unstable density stratification in the aqueous phase, result in uneven melting of the underlying ice front during thawing. The resulting undulatory ice front with regularly spaced peaks and troughs provides the pattern which results in the regularity observed for certain types of patterned ground. In addition, the model predicts the width to depth-of-sorting ratio for both polygons and stripes, and explains the characteristic hexagonal shape of sorted polygons, the transition from sorted polygons to sorted stripes on sloped terrain, and the formation of sorted polygons under water. The predicted ratio of width to depth-of-sorting of 3.81 for sorted polygons is compared with the ratio of width to depth-of-sorting of 3.57 found from a linear regression analysis of 18 field study data.