When Enough Is Really Enough? On the Minimum Number of Landslides to Build Reliable Susceptibility Models
Abstract
:1. Introduction
2. Materials and Methods
2.1. Tajikistan and Its Reference Landslide Inventory
2.2. Covariates
2.3. Mapping Units
2.4. Modeling Strategy
2.4.1. Generalized Additive Model
- is the logit link;
- P is the probability of landslide occurrence;
- is the global intercept;
- are the jth regression coefficients estimated for the xth covariates which we modeled as fixed effects (or linear properties);
- and are two random effects (non linear properties), which we modeled as independent and identically distributed (iid) covariates. This implies that the regression coefficient associated with each class is estimated independently from the other classes;
- and are two random effects (non linear properties) that we modeled as random walks of the first order () covariates. This implies that the regression coefficient associated with each class is estimated with an adjacent class dependence. In other words, the coefficient of a single class depends on the coefficient estimated for the class before and after. The use of a random walk allows one to retain the ordinal structure of a covariate that was originally continuous in nature, which we reclassified to obtain a non linear function of the same.
2.4.2. Performance Assessment
2.4.3. Fitting Different Presence Data Proportions
3. Results and Discussion
3.1. Reference Susceptibility Model
3.2. First set of Cross-Validations
3.3. Sensitivity Analyses at Varying Landslide Presence
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Appendix A
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Covariate | Original Type | Acronym | Unit |
---|---|---|---|
Slope degree | Continuous | Slope | degree (°) |
Relative relief | Continuous | Rlf | m |
Plan curvature | Continuous | PlC | |
Profile curvature | Continuous | PrC | |
Peak Ground Acceleration | Continuous | PGA | |
Annual precipitation | Continuous | Rn | mm/y |
Land use | Categorical | LU | unitless |
Lithology | Categorical | Litho | unitless |
Area with Slope > 10° per map unit | Continuous | Area |
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Titti, G.; van Westen, C.; Borgatti, L.; Pasuto, A.; Lombardo, L. When Enough Is Really Enough? On the Minimum Number of Landslides to Build Reliable Susceptibility Models. Geosciences 2021, 11, 469. https://doi.org/10.3390/geosciences11110469
Titti G, van Westen C, Borgatti L, Pasuto A, Lombardo L. When Enough Is Really Enough? On the Minimum Number of Landslides to Build Reliable Susceptibility Models. Geosciences. 2021; 11(11):469. https://doi.org/10.3390/geosciences11110469
Chicago/Turabian StyleTitti, Giacomo, Cees van Westen, Lisa Borgatti, Alessandro Pasuto, and Luigi Lombardo. 2021. "When Enough Is Really Enough? On the Minimum Number of Landslides to Build Reliable Susceptibility Models" Geosciences 11, no. 11: 469. https://doi.org/10.3390/geosciences11110469