Statistical functions used for spatial modelling due to assessment of landslide distribution and landscape-interaction factors in Iran

Landslides influence the capacity for safe and sustainable development of mountainous environments. This study explores the spatial distribution of and the interactions between landslides that are mapped using global positioning system (GPS) and extensive field surveys in Mazandaran Province, Iran. Point-pattern assessment is undertaken using several univariate summary statistical functions, including pair correlation, spherical-contact distribution, nearest-neighbor analysis, and O-ring analysis, as well as bivariate summary statistics, and a markcorrelation function. The maximum entropy method was applied to prioritize the factors controlling the incidence of landslides and the landslides susceptibility map. The validation processes were considered for separated 30% data applying the ROC curves, fourfold plot, and Cohen’s kappa index. The results show that pair correlation and O-ring analyses satisfactorily predicted landslides at scales from 1 to 150 m. At smaller scales, from 150 to 400 m, landslides were randomly distributed. The nearest-neighbor distribution function show that the highest distance to the nearest landslide occurred in the 355 m. The spherical-contact distribution revealed that the patterns were random up to a spatial scale of 80 m. The bivariate correlation functions revealed that landslides were positively linked to several linear features (including faults, roads, and rivers) at all spatial scales. The mark-correlation function showed that aggregated fields of landslides were positively correlated with measures of land use, lithology, drainage density, plan curvature, and aspect, when the numbers of landslides in the groups were greater than the overall average aggregation. The results of analysis of factor importance have showed that elevation (topography map scale: 1:25,000), distance to roads, and distance to rivers are the most important factors in the occurrence of landslides. The susceptibility model of landslides indicates an excellent accuracy, i.e., the AUC value of landslides was 0.860. The susceptibility map of landslides analyzed has shown that 35% of the area is low susceptible to landslides.