When Enough Is Really Enough? On the Minimum Number of Landslides to Build Reliable Susceptibility Models
<p>Panel (<b>a</b>) locates Tajikistan in yellow. Panel (<b>b</b>) shows the study area corresponding to the western sector of Tajikistan. Panel (<b>c</b>) reports the Landslide Identification Points (LIP) for the mapped landslides.</p> "> Figure 2
<p>Four of the nine covariates used in this study: (<b>a</b>) Land use, (<b>b</b>) lithology, (<b>c</b>) PGA maps of the 475-year Return Period, and (<b>d</b>) average annual precipitation (over a 10-year period).</p> "> Figure 3
<p>Landslide distribution per UCU.</p> "> Figure 4
<p>(<b>a</b>) Landslide susceptibility map of Tajikistan. (<b>b</b>) 95% of Confidence Interval (CI) of the landslide susceptibility map of Tajikistan.</p> "> Figure 5
<p>Performance of the single covariate used to model the landslide susceptibility map: (<b>a</b>) slope, (<b>b</b>) relative relief, (<b>c</b>) annual precipitation, (<b>d</b>) covariates modeled as fixed effects, (<b>e</b>) land use, (<b>f</b>) lithology. See <a href="#geosciences-11-00469-t001" class="html-table">Table 1</a> for the explanation of the abbreviations of the covariates.</p> "> Figure 6
<p>(<b>a</b>) Tajikistan landslide susceptibility map classified by maximizing the AUC and the relative ROC curves with respect to the unstable UCUs. (<b>c</b>) Tajikistan landslide susceptibility map classified by maximizing the AUC of the area-weighted ROC curve and the relative ROC curves. Panels (<b>b</b>,<b>d</b>) show the corresponding classification schemes and the relative percentage area per class.</p> "> Figure 7
<p>(<b>a</b>) 3D representations of the landslides distribution on the classified, area-based (<a href="#geosciences-11-00469-f006" class="html-fig">Figure 6</a>c) susceptibility map. (<b>b</b>) 3D representation of the landslides distribution and of the relative relief.</p> "> Figure 8
<p>Distribution of the Area Under the ROC Curve (AUC) values of the 2000 model runs with different proportions of number presence condition.</p> "> Figure 9
<p>(<b>a</b>) 10-runs median susceptibility map with 100% of total landslide inventory (AUC = 0.87) classified in quartiles and the contour lines of the landslides density distribution; (<b>b</b>) 10-runs median susceptibility map with 5% of total landslide inventory (AUC = 0.79) classified in quartiles and the contour lines of the landslides density distribution.</p> "> Figure 10
<p>Example of covariate effects estimated at a varying proportion of landslide presence data for: (<b>a</b>) Area, (<b>b</b>) annual rainfall, (<b>c</b>) lithology, (<b>d</b>) slope, (<b>e</b>) land use, and (<b>f</b>) relative relief.</p> "> Figure 11
<p>Graph in dots of the median AUC also visible in <a href="#geosciences-11-00469-f008" class="html-fig">Figure 8</a> and the relative <span class="html-italic">f</span> function (Equation (2)) which measure how much the trend of the median graph varies.</p> "> Figure A1
<p>Flow-chart summarizing the analytical protocol we implemented.</p> "> Figure A2
<p>PGA, area, profile curvature, and plan curvature effects graphical summary at a varying proportion of landslide presence data.</p> "> Figure A3
<p>Mean slope effect graphical summary at a varying proportion of landslide presence data.</p> "> Figure A4
<p>Mean relative relief effect graphical summary at a varying proportion of landslide presence data.</p> "> Figure A5
<p>Mean annual precipitation effect graphical summary at a varying proportion of landslide presence data.</p> "> Figure A6
<p>Lithology effect graphical summary at a varying proportion of landslide presence data.</p> "> Figure A7
<p>Land use effect graphical summary at a varying proportion of landslide presence data.</p> "> Figure A8
<p>ROC curves from the 1st to 10th run at a varying proportion of landslide presence data. Each figure shows 10 ROC curves of cross-validation per 20 different landslide presence proportions (200 curves in each figure).</p> ">
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
APA StyleTitti, G., van Westen, C., Borgatti, L., Pasuto, A., & Lombardo, L. (2021). When Enough Is Really Enough? On the Minimum Number of Landslides to Build Reliable Susceptibility Models. Geosciences, 11(11), 469. https://doi.org/10.3390/geosciences11110469