A novel hybrid bivariate statistical method entitled FROC for landslide susceptibility assessment

For creating landslide susceptibility maps (LSMs), bivariate statistical methods are used frequently; however, these kinds of methods have one major disadvantage that they can only calculate the weights of the classes of a factor not the weight of the landslide causative factor itself. In this study, therefore, a novel bivariate statistical method entitled FROC is introduced, which is able to calculate the weights of the factors (using the new parameter of LFW) in addition to the weights of the classes (using CW parameter). This method can also measure the reliability of the produced LSMs directly using the mentioned parameters. For comparison, two other proposed methods for estimating the factors' weights (weighting factor, WF, and predictor rating, PR) were also employed. The LSMs of the three methods were produced by multiplying the CWs of the classes (calculated based on the 60% of randomly selected pixels of the 166 detected shallow translational slides) by the LFW, WF, and PR weights of each factor (altitude, slope degree, slope aspect, lithology, land use/land cover, precipitation, and distance to stream network, roads, and faults). To measure the LSMs' validity, their success and prediction rates were calculated using the LFW parameter (by engaging the mentioned 60% landslide pixels and the remaining landslide pixels, respectively). Both rates were equal to 0.86 for FROC LSM, 0.85 for WF, and about 0.84 for PR, showing that the FROC model achieved the best results. Based on the Cohen's kappa index, the spatial patterns of the LSMs were about 20% different. In this respect also, the FROC LSM was superior to the WF and PR LSMs because the density of landslides (calculated by the CW parameter) in the high and very high susceptible zones of this map was comparatively higher.