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Estimating landslide susceptibility areas considering the uncertainty inherent in modeling methods

Abstract

Landslides are one of the most dangerous types of natural disasters, and damage due to landslides has been increasing in certain regions of the world because of increased precipitation. Policy decision makers require reliable information that can be used to establish spatial adaptation plans to protect people from landslide hazards. Researchers presently identify areas susceptible to landslides using various spatial distribution models. However, such data are associated with a high amount of uncertainty. This study focuses on quantifying the uncertainty of several spatial distribution models and identifying the effectiveness of various ensemble methods that can be used to provide reliable information to support policy decisions. The area of study was Inje-gun, Republic of Korea. Ten models were selected to assess landslide susceptibility. Moreover, five ensemble methods were selected for the aggregated results of the 10 models. The uncertainty was quantified using the coefficient of variation and the uncertainty map we developed revealed areas with strongly differing values among single models. A matrix map was created using an ensemble map and a coefficient of variation map. Using matrix analysis, we identified the areas that are most susceptible to landslides according to the ensemble model with a low uncertainty. Thus, the ensemble model can be a useful tool for supporting decision makers. The framework of this study can also be employed to support the establishment of landslide adaptation plans in other areas of the Republic of Korea and in other countries.

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Notes

  1. 1.

    An ROC curve is a plot graph that shows the diagnostic ability of a binary classification method considering a threshold value. ROC curves are created by plotting the true positive rate (TPR) against the false positive rate (FPR). The TPR is also called the sensitivity and the FPR is also known as the probability of false alarm, and it can be calculated as (1 − specificity). Thus, the ROC curve represents the sensitivity as a function of FPR. ROC analysis is used as a tool to select optimal models and to discard suboptimal ones. The area under the curve (AUC) is the same as the probability that a classifier will grade a randomly chosen positive case higher than a randomly chosen negative case. The AUC is similar to the Mann–Whitney U, which tests whether positive cases are graded higher than negative cases.

  2. 2.

    Coefficient of variation is also known as relative standard deviation. It is a standardized value of dispersion of a probability distribution. It is calculated by the ratio of the standard deviation to the mean. In this study, it is used for quantifying uncertainty of modeling results.

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Funding

This work was supported by Korea Ministry of Environment (MOE, Project No. 2016000210004) as “Public Technology Program based on Environmental Policy” and the BK 21 Plus Project in 2015 (Seoul National University Interdisciplinary Program in Landscape Architecture, Global Leadership Program toward Innovative Green Infrastructure).

Author information

Correspondence to Dong Kun Lee.

Appendices

Appendix 1: Key features of the 10 SDMs (Franklin 2009)

Model Full name of model Category Occurrence data required Response function Features of the model
GLM Generalized linear model Statistically based model Occurrence/No occurrence Parametric linear, polynomial, piecewise, interaction terms GLMs are a representative model among SDMs. GLMs are a generalization of the multiple regression model that uses the link function to accommodate response variables that are distributed normally, namely, the response distributions
GAM Generalized additive model Statistically based model Occurrence/No occurrence Smoothing function, estimated using local regression, splines or other methods GAMs in SDMs are suggested as a powerful methodology to detect and describe non-linear response functions. The results of GAMs can be used to build a parametric model
MARS Multivariate adaptive regression splines Statistically based model Occurrence/No occurrence Adaptive piecewise linear regression combines splines and binary recursive partitioning MARS can give a type of a generalization of a stepwise linear regression. MARS are suited to analyses with large numbers of variables or a modification of the regression tree method
GBM Generalized boosted regression model Machine learning based model Occurrence/No occurrence Weighted and unweighted model averaging applied to decision trees GBMs are similar to weighting variables that consider higher probabilities of selection, instead of weighting equal probabilities for subsequent variables
CTA Classification tree analysis Machine learning based model Occurrence/No occurrence Divisive, monothetic decision rules (thresholds) from binary recursive partitioning The goal of CTA is to divide data into homogeneous subgroups. The subgroups consist of variables that have similar values or are in the same class in regard to the ranges of values for the variables
ANN Artificial neural network Machine learning based model Occurrence/No occurrence Non-linear decision boundaries in covariate space ANN can be described as a two-stage classification or regression model. A hidden layer of ANN comprises features that are linear combinations of input variables. The output variable is a weighted combination of features in the hidden layer
SRE Rectilinear envelope similar to BIOCLIM Machine learning based model Occurrence only Fuzzy classification approach SRE is a boxcar or parallelepiped classifier that uses BIOCLIM. SRE assesses the potential distribution of the dependent variable by using the multi-dimensional environmental space bounded by the values for all dependent variables
MDA Mixture discriminant analysis Machine learning based model Occurrence/No occurrence Linear MDA is a type of linear discriminant analysis that models the multivariate density of variables by using a mixture of multivariate normal distributions
RF Random forest Machine learning based model Occurrence/No occurrence Weighted and unweighted model averaging applied to decision trees Random forests is a type of bootstrap aggregating method that builds de-correlated trees and averages the trees. Many trees are constructed with subsets of input data. Furthermore, each division of the tree model is also constructed with a random subset of input variables
MAXENT Maximum entropy algorithm Machine learning based model Occurrence only Non-linear response functions can be described Maximum entropy is based on statistical mechanics and information theory. MAXENT can analyze the best approximation of an unknown distribution by using the maximum entropy method, which considers the most spread out and closest to uniform values

Appendix 2: Maps of variables for landslide susceptibility model

figurea
figureb

Appendix 3: Landslide projections of the 10 models for present conditions

1. MAXENT

figurec

2. CTA

figured

3. SRE

figuree

4. FDA

figuref

5. MARS

figureg

6. RF

figureh

7. GLM

figurei

8. GBM

figurej

9. GAM

figurek

10. ANN

figurel

Appendix 4: ROC plots for each model

Axis Value Scope
X Value of each variable The scope of value varies on variables. Please see the Table 1
Y Probability of landslide occurrence 0–1

1. MAXENT

figurem

2. CTA

figuren

3. SRE

figureo

4. FDA

figurep

5. MARS

figureq

6. RF

figurer

7. GLM

figures

8. GBM

figuret

9. GAM

figureu

10. ANN

figurev

Appendix 5: Results of ensemble models for the present conditions

1. PM

figurew

2. PCI lower

figurex

3. PCI upper

figurey

4. PME

figurez

5. CA

figureaa

6. PMW

figureab

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Kim, H.G., Lee, D.K., Park, C. et al. Estimating landslide susceptibility areas considering the uncertainty inherent in modeling methods. Stoch Environ Res Risk Assess 32, 2987–3019 (2018). https://doi.org/10.1007/s00477-018-1609-y

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Keywords

  • Spatial distribution model
  • Ensemble model
  • Coefficient of variation
  • Adaptation plans