Bivariate Landslide Susceptibility Analysis: Clarification, Optimization, Open Software, and Preliminary Comparison

Abstract

Bivariate data-driven methods have been widely used in landslide susceptibility analysis. However, the names, principles, and correlations of bivariate methods are still confused. In this paper, the names, principles, and correlations of bivariate methods are first clarified based on a comprehensive and in-depth survey. A total of eleven prevalent bivariate methods are identified, nominated, and elaborated in a general framework, constituting a well-structured bivariate method family. We show that all prevalent bivariate methods depend on empirical conditional probabilities of landslide occurrence to calculate landslide susceptibilities, either exclusively or inclusively. It is clarified that those eight “conditional-probability-based” bivariate methods, which exclusively depend on empirical conditional probabilities, are particularly strongly correlated in principle, and therefore are expected to have a very close or even the same performance. It is also suggested that conditional-probability-based bivariate methods apply to a “classification-free” modification, in which factor classifications are avoided and the result is dominated by a single parameter, “bin width”. Then, a general optimization framework for conditional-probability-based bivariate methods, based on the classification-free modification and obtaining optimum results by optimizing the dominant parameter bin width, is proposed. The open software Automatic Landslide Susceptibility Analysis (ALSA) is updated to implement the eight conditional-probability-based bivariate methods and the general optimization framework. Finally, a case study is presented, which confirms the theoretical expectation that different conditional-probability-based bivariate methods have a very close or even the same performance, and shows that optimal bivariate methods perform better than conventional bivariate methods regarding both the prediction rate and the ability to reveal the quasi-continuous varying pattern of sensibilities to landslides for individual predisposing factors. The principles and open software presented in this study provide both theoretical and practical foundations for applications and explorations of bivariate methods in landslide susceptibility analysis.