Landslide susceptibility assessment by bivariate methods at large scales: Application to a complex mountainous environment

TL;DR: In this article, the authors presented a procedure to identify the best variables for landslide susceptibility assessment through a bivariate technique (weights of evidence, WOE) and discussed the best way to minimize conditional independence (CI) between the predictive variables.

About: This article is published in Geomorphology.The article was published on 2007-11-15 and is currently open access. It has received 243 citations till now. The article focuses on the topics: Landslide classification & Landslide.

Summary

2.1. Geomorphology of the Barcelonnette Basin

• The western unit (ca. 60 km 2 ), drained by four main torrents, presents an irregular topography of alternating steep convex slopes, planar slopes and hummocky slopes.
• The steepest convex slopes (>35°) are carved in black marl outcrops, and are very commonly gullied into badlands, or affected by rock-block or complex slides (Malet et al., 2005) .
• The planar slopes (5-30°) composed of thick moraine deposits (from 6 to 20 m), are very often cultivated and affected by rotational or translational slides.
• The hummocky slopes are generally covered by forests and/or natural grasslands (Fig. 2 ), and affected by large relict landslides and/or surficial soil creep.
• Most landslides within the western unit are located along streams or on gentle slopes, where the contact of moraine deposits and black marls creates a hydrological discontinuity favourable for slope movements.

2.2. Landslide data

• This procedure offers some advantages because it does not take into account the landslide boundaries and it does not attribute a too large influence to the largest landslides which exhibit more diversity in predisposing factors.
• If the results based on one cell at the centre of the triggering zone can be satisfactory, the final probabilities are not necessarily representative of the predisposing conditions at the onset of the landslide.
• Defining the most appropriate part of the landslide to compute the probabilities is therefore a prerequisite to understand how it influences the model results.

3.1.1. WOE method

• The WOE for all PVs is combined using the natural logarithm of the odds , in order to estimate the conditional probability of landslide occurrence.
• When several PVs are combined, areas with high or low weights correspond to high or low probabilities of presence of the RV.

3.1.2. Hypothesis of the WOE method

• The WOE method requires the assumption that input maps are conditionally independent.
• To meet this need, many statistical tests may be used (e.g., χ 2 -test, omnibus test, and new omnibus test).
• In case of violation of conditional independence, PVs which are dependent can be combined into a neo-variable (nPV) which is then used in the WOE method (Thiart et al., 2003) .
• The weighted-logistic-regression method (WLR) may also be used to bypass the violation of conditional independence.

3.2.2. Identification of the predictive variables (PVs)

• (ii) Analysis of CI violation between each PV and the RV.
• The Cramer's V is considered as the more robust association test because of its possibility to assess large and complex contingency tables (Howell, 1997) .
• The coefficient provides a standardized measure in the range [0-1]; the closer V → 1, the stronger is the association between two PVs.
• Finally, the performance of each PV and nPV is assessed by introducing the variables iteratively in the statistical model.

3.2.3. Evaluation of performance of the indirect susceptibility maps

• Because the direct susceptibility map had been produced by the French Official Method of Landslide Risk Zoning (MATE/METL, 1999) independently of the landslide types, a unified indirect susceptibility map was produced by combining the indirect susceptibility maps obtained for the three landslide types.
• The four classes of the indirect susceptibility maps were merged, and for each cell, more weight was systematically given to the higher susceptibility class (Fig. 8 ).
• Confusion matrices were calculated and several statistical tests -17 -were performed for the direct and unified indirect susceptibility maps (Tables 5 and 6 ).
• The Kappa (Κ) coefficient was used to assess the improvement of the model predictions over chance (Table 6 ).
• Κ values higher than 0.4 signify a good statistical agreement between maps (Fielding and Bell, 1997) .

4.1. Best response variable

• The minimum number of cells representing the variability of the predisposing factors within the LTZs was identified from the 460 cells.
• The relation between the number of LTZs cells introduced in the model and ξ for each landslide type is presented in Fig. 7 .
• A threshold comparable to 50% of the 460 cells was identified to stabilize ξ for the 'sampling area', and the simulations with RV-3 to RV-7 were performed with the 230 cells.
• Table 4 indicates that the simulations with RV-2 and RV-3 are not acceptable, confirming that using only one or a few cells around the centre of a LTZ mass underestimates PriorP and PostP.
• Table 4 also indicates the influence of LTZ sizes on the results, and highlights that the best results are obtained with the use of the cells representing the most frequent combination of PVs observed in LTZs (RV-7).

4.2. Best predictive variables

• The first four axes of the MCA (multiple correspondence analysis) explain 40.5%, 49.3% and 46.0% of the total variance for the shallow translational slides, rotational slides and translational slides, respectively.
• Some useful information is still highlighted by the MCA.
• Thus, the MCA gives some indications on the possible combination of classes for each PV, and allows us to justify the definition of an nPV with both a geomorphological meaning and a low redundancy of information.
• Table 8 summarizes the results of the MCA for the three landslide types.

5. Discussion

• The proposed procedure follows the guidelines suggested by van Westen et al. (2003) and Guzzetti et al. (2006) for the validation of indirect susceptibility maps.
• Guzetti et al. (2006) proposed a set of criteria for ranking and comparing the quality of landslide susceptibility assessments, i.e., the quality of the input data and the use of different statistical tests.
• In terms of these criteria, the susceptibility maps obtained with the procedure used in this study have the highest quality (level 7).

Figures

Table 6. Statistics derived from the confusion matrix. N: number of cells in the study area. a: true positives; b: false positives; c: false negatives; d: true negatives.

Table 4. Characteristics of the response variable (RV) introduced in the statistical model to identify the most relevant spatial locations of cells to represent the variability of predisposing factors within LTZs, and relative error associated with the simulations. The simulations were performed with the predictive variables (PVs) SLO, SF, LIT and LAND (Table 2). STS: shallow translational slides; RS: rotational slides; TS: translational s lides.

Table 5. Confusion matrix. a: true positives; b: false positives; c: false negatives; d: true negatives.

Table 1. Morphometric characteristics of active landslides inventoried with a high mapping confidence index (MCI). µ is geometric average; σ is standard deviation.

Table 2. Thematic data used in the statistical model.

Table 3. Expert rules and associated environmental conditions used to define the direct susceptibility map. SLO: slope gradient; LAD: land use; CUR: slope curvature.

Table 7. Example of association measures between RV-7 and PVs for the translational slides. The PVs CUR, HYD and BED are not introduced in the model because there is no causal relation between the occurrence of the translational slides and these PVs. The bold font indicates the PV used to build an nPV. χ2-test: from left to right, calculated χ2, theoretical χ2, and degree of freedom. The grey-coloured box represents the conditional dependence between PVs and the null hypothesis H0 rejected for a level of significance α = 0.05. Cramer’s V coefficient: the bold font indicates moderate to high association between the variables.

Table 8. Contribution of PVs on the explained variance of the axes F1 to F4 for three landslide types. The most contributive PVs for each axis are indicated in grey and are used to define nPVs. The classes chosen to build nPVs are detailed in the last column.

Table 10. Relative error ξ of the best simulations for the ‘sampling area’ and the total study area. Results are indicated for the LTZ and the total area of landslide (L). Simulations are computed with RV-7.

Table 11. Statistical accuracy tests between the indirect and direct susceptibility maps. ccr is the correct classification rate; mcr is misclassification rate.

Table 9. Relative error ξ and CI results for the best combination of PVs and nPVs

Frequently asked questions

Q1. What are the contributions in "Landslide susceptibility assessment by bivariate methods at large scales: application to a complex mountainous environment" ?

This paper presents a procedure to identify the best variables for landslide susceptibility assessment through a bivariate technique ( weights of evidence, WOE ) and discusses the best way to minimize conditional independence ( CI ) between the predictive variables. The study site is the north-facing hillslope of the Barcelonnette Basin ( France ), affected by several types of landslides and characterized by a complex morphology.