Distribution of polygon characteristic scale in Martian patterned ground terrain in the northern hemisphere using the Fourier transform

Permafrost patterned ground forms on the surface of nearly all landscapes between 50 degrees N and 70 degrees N on Mars. This landform appears in satellite imagery as an interconnected network of polygonal shapes. Previous studies used geomorphologic observations to characterize patterned ground terrains on Mars. These classification systems prove useful but suffer from somewhat subjective methods. We find objective analysis of the polygons comprising patterned ground terrains on the surface of Mars feasible using High Resolution Imaging Science Experiment imagery acquired from orbit. We perform a two-dimensional Fourier transform on 124 images of patterned surfaces to characterize the spatial scale pertinent to scenes and analyze the distribution of these properties on the surface of Mars between 50 degrees N and 70 degrees N. We find two distinct sets of polygons: large polygons which form below 60 degrees N and small polygons primarily above 60 degrees N with exception for sites within Acidalia Planitia. Our findings show similar trends to those found in previous studies but also fundamental differences in the populations of polygons above and below 60 degrees N. The polygons within 60 degrees N-70 degrees N share roughly the same polygonal scale, implying that seasonal temperature change is not the only factor forcing polygon development as previous models found. In some cases, our method indicates the presence of multiple scales of polygons, although it cannot quantify the larger scale. This method in conjunction with observational analysis improves our ability to characterize surfaces and examine patterned ground terrains on Mars.