An application of different summary statistics for modelling piping collapses and gully headcuts to evaluate their geomorphological interactions in Golestan Province, Iran

The quantitative characterizations of piping collapses (PCs) and gully headcuts (GHS) are an important part of the study of geomorphological processes under different types of climate such as arid, semiarid, and temperate and non-climatic conditions like land use changes and agricultural machinery. The present study aimed to evaluate summary statistics to characterize PCs and/or GHS structure by using numerical functions as well as understanding the interaction of gully head features and collapse pipes by applying univariate and bivariate summary statistics. To this end, a 703.36 ha area was first selected in the loess-covered hilly region of Golestan Province, eastern-north of Iran. Then, the maps of 345 PCs and 133 GHS were obtained by a detailed reconnaissance surveys in the field by using an unmanned aerial vehicle (UAV) photography. Finally, the univariate (L, g, and O-ring functions) and bivariate (L12, g12, O12, g22(r) _ g11(r), g12(r) _g11(r), and g1,1+2_g2,1+2 functions) summary statistics were used to investigate the statistical analyses of PCs and GHS, separately. Based on the results of the univariate summary statistics, the PCs had a clustered distribution and the pattern of GHs was aggregate. Based on bivariate summary statistics, gully headcuts were positively related to collapse pipes. In addition, PCs had more aggregation compared to the GHS. The neighborhood density of PCs was relatively less frequent around GHs than PCs. The PCs were spatially located in more dense parts of the study area. It means that PCs are positively correlated with each other and generally multi PCs should be put together to form one gully headcut. In general, the proposed summary statistics lead to a better understanding of the studied soil erosion processes in the study area.