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See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/228578451

Integrating physical and empirical landslidesusceptibility models using generalizedadditive models. Geomorphology, 129(3-

4):376-386

Article in Geomorphology · April 2011

Impact Factor: 2.79 · DOI: 10.1016/j.geomorph.2011.03.001

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Jason Goetz

Friedrich Schiller University Jena

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Alexander Brenning

Friedrich Schiller University Jena

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Available from: Jason Goetz

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https://www.researchgate.net/profile/Jason_Goetz?enrichId=rgreq-b13a5fb5-271a-4115-a040-945f199d938b&enrichSource=Y292ZXJQYWdlOzIyODU3ODQ1MTtBUzoxMDQ1NzY2MDI2MDc2MjBAMTQwMTk0NDQxMzM5MQ%3D%3D&el=1_x_4https://www.researchgate.net/?enrichId=rgreq-b13a5fb5-271a-4115-a040-945f199d938b&enrichSource=Y292ZXJQYWdlOzIyODU3ODQ1MTtBUzoxMDQ1NzY2MDI2MDc2MjBAMTQwMTk0NDQxMzM5MQ%3D%3D&el=1_x_1https://www.researchgate.net/profile/Alexander_Brenning?enrichId=rgreq-b13a5fb5-271a-4115-a040-945f199d938b&enrichSource=Y292ZXJQYWdlOzIyODU3ODQ1MTtBUzoxMDQ1NzY2MDI2MDc2MjBAMTQwMTk0NDQxMzM5MQ%3D%3D&el=1_x_7https://www.researchgate.net/institution/Friedrich_Schiller_University_Jena?enrichId=rgreq-b13a5fb5-271a-4115-a040-945f199d938b&enrichSource=Y292ZXJQYWdlOzIyODU3ODQ1MTtBUzoxMDQ1NzY2MDI2MDc2MjBAMTQwMTk0NDQxMzM5MQ%3D%3D&el=1_x_6https://www.researchgate.net/profile/Alexander_Brenning?enrichId=rgreq-b13a5fb5-271a-4115-a040-945f199d938b&enrichSource=Y292ZXJQYWdlOzIyODU3ODQ1MTtBUzoxMDQ1NzY2MDI2MDc2MjBAMTQwMTk0NDQxMzM5MQ%3D%3D&el=1_x_5https://www.researchgate.net/profile/Alexander_Brenning?enrichId=rgreq-b13a5fb5-271a-4115-a040-945f199d938b&enrichSource=Y292ZXJQYWdlOzIyODU3ODQ1MTtBUzoxMDQ1NzY2MDI2MDc2MjBAMTQwMTk0NDQxMzM5MQ%3D%3D&el=1_x_4https://www.researchgate.net/profile/Jason_Goetz?enrichId=rgreq-b13a5fb5-271a-4115-a040-945f199d938b&enrichSource=Y292ZXJQYWdlOzIyODU3ODQ1MTtBUzoxMDQ1NzY2MDI2MDc2MjBAMTQwMTk0NDQxMzM5MQ%3D%3D&el=1_x_7https://www.researchgate.net/institution/Friedrich_Schiller_University_Jena?enrichId=rgreq-b13a5fb5-271a-4115-a040-945f199d938b&enrichSource=Y292ZXJQYWdlOzIyODU3ODQ1MTtBUzoxMDQ1NzY2MDI2MDc2MjBAMTQwMTk0NDQxMzM5MQ%3D%3D&el=1_x_6https://www.researchgate.net/profile/Jason_Goetz?enrichId=rgreq-b13a5fb5-271a-4115-a040-945f199d938b&enrichSource=Y292ZXJQYWdlOzIyODU3ODQ1MTtBUzoxMDQ1NzY2MDI2MDc2MjBAMTQwMTk0NDQxMzM5MQ%3D%3D&el=1_x_5https://www.researchgate.net/profile/Jason_Goetz?enrichId=rgreq-b13a5fb5-271a-4115-a040-945f199d938b&enrichSource=Y292ZXJQYWdlOzIyODU3ODQ1MTtBUzoxMDQ1NzY2MDI2MDc2MjBAMTQwMTk0NDQxMzM5MQ%3D%3D&el=1_x_4https://www.researchgate.net/?enrichId=rgreq-b13a5fb5-271a-4115-a040-945f199d938b&enrichSource=Y292ZXJQYWdlOzIyODU3ODQ1MTtBUzoxMDQ1NzY2MDI2MDc2MjBAMTQwMTk0NDQxMzM5MQ%3D%3D&el=1_x_1https://www.researchgate.net/publication/228578451_Integrating_physical_and_empirical_landslide_susceptibility_models_using_generalized_additive_models_Geomorphology_1293-4376-386?enrichId=rgreq-b13a5fb5-271a-4115-a040-945f199d938b&enrichSource=Y292ZXJQYWdlOzIyODU3ODQ1MTtBUzoxMDQ1NzY2MDI2MDc2MjBAMTQwMTk0NDQxMzM5MQ%3D%3D&el=1_x_3https://www.researchgate.net/publication/228578451_Integrating_physical_and_empirical_landslide_susceptibility_models_using_generalized_additive_models_Geomorphology_1293-4376-386?enrichId=rgreq-b13a5fb5-271a-4115-a040-945f199d938b&enrichSource=Y292ZXJQYWdlOzIyODU3ODQ1MTtBUzoxMDQ1NzY2MDI2MDc2MjBAMTQwMTk0NDQxMzM5MQ%3D%3D&el=1_x_2


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in an empirical–physical model for landslide susceptibility, however

without assessing performance improvements in comparison with

purely empirical models (Chang and Chiang, 2009). The present study

systematically investigates improvements in model performance that

can be attributed to model integration and the use of exible

modeling techniques.

Landslide susceptibility is the predisposition of an area to failure

under the inuence of gravity. Specically it can be described as the

probability of spatial occurrence of slope failure given a range of destabilizing factors (Glade et al., 2005;Guzzetti et al., 2006). Since

landsliding is linked to other geomorphological processes and land-

forms, many methods of susceptibility assessment are based on the

identication of causative factors (Guzzetti et al., 1999; Glade et al.,

2005). Stable and unstable slope conditions can be mapped out by

studying these factors.

Physically-based models utilize the physical properties that

control geomorphological processes spatially and/or temporally.

Empirically-based models generally function under the principle

that landslides are more likely to occur under similar ground

conditions to previous events. Thus, a range of environmental

attributes is typically examined to determine factors related to

landslide initiation (Sidle and Ochiai, 2006). Empirical models of

susceptibility do not usually take into account triggering factors, such

as earthquakes and precipitation. Instead, they rely on factors that

predispose locations to landslide failure (Dai et al., 2002; Sidle and

Ochiai, 2006).

Since many of the regions that are most highly susceptible to

landslides are in developing countries, it is important to develop

methods that are affordable and can perform well with little data

(Sidle and Ochiai, 2006). Even in mountain areas in developed

countries, there is often a lack of adequate geological information. The

proposed empirical–physical modeling approach, which estimates

physical model parameters using an internal optimization, is

implemented in and exemplies the application of free open-source

Geographical Information Systems (GIS) and statistical software in

this context.

2. Study area

Our study area is located in the Klanawa River watershed on the

southwestern coast of Vancouver Island, British Columbia, Canada

(Fig. 1). This site encompasses a total area of 610 km2 with 960 m of

relief. The lithology is composed of grano-dioritic rocks and calc-

alkaline volcanic rocks. Climate effects coupled with its rugged terrain

formed by Pleistocene glaciations makes the study area generally

prone to landsliding. The Klanawa River is located in a temperate

maritime climate with annual precipitation typically greater than

3000 mm (Guthrie et al., 2008). The forest cover is generally

comprised of western hemlock and western redcedar trees. There

have been extensive human activities in this area related to the forest

industry and clear-cutting practices. As of 2001 approximately 46% of

the study area has been logged (Guthrie et al., 2008). Landslides in

this area have been noticed to frequently occur in deforested areas,

which are commonly adjacent to logging roads. In general, landslides

occurring on Vancouver Island have been observed to occur in greater

spatial densities when adjacent to roads. In addition, there has been a

considerable increase in the number of landslides after three decades

of forestry activities (Guthrie, 2002).To exclude the low-lying valley

oor that is not susceptible to landsliding, we only consider terrain

above 150 m elevation, which is an area of 394 km2, in model

construction and assessment.

Fig. 1. Map of the study area with landslide initiation points.

377 J.N. Goetz et al. / Geomorphology 129 (2011) 376 – 386

https://www.researchgate.net/publication/222340566_An_integrated_model_for_predicting_rainfall_induced_Landslides?el=1_x_8&enrichId=rgreq-b13a5fb5-271a-4115-a040-945f199d938b&enrichSource=Y292ZXJQYWdlOzIyODU3ODQ1MTtBUzoxMDQ1NzY2MDI2MDc2MjBAMTQwMTk0NDQxMzM5MQ==https://www.researchgate.net/publication/222340566_An_integrated_model_for_predicting_rainfall_induced_Landslides?el=1_x_8&enrichId=rgreq-b13a5fb5-271a-4115-a040-945f199d938b&enrichSource=Y292ZXJQYWdlOzIyODU3ODQ1MTtBUzoxMDQ1NzY2MDI2MDc2MjBAMTQwMTk0NDQxMzM5MQ==https://www.researchgate.net/publication/222340566_An_integrated_model_for_predicting_rainfall_induced_Landslides?el=1_x_8&enrichId=rgreq-b13a5fb5-271a-4115-a040-945f199d938b&enrichSource=Y292ZXJQYWdlOzIyODU3ODQ1MTtBUzoxMDQ1NzY2MDI2MDc2MjBAMTQwMTk0NDQxMzM5MQ==https://www.researchgate.net/publication/223477608_Estimating_the_quality_of_landslide_susceptibility_models_Geomorphology?el=1_x_8&enrichId=rgreq-b13a5fb5-271a-4115-a040-945f199d938b&enrichSource=Y292ZXJQYWdlOzIyODU3ODQ1MTtBUzoxMDQ1NzY2MDI2MDc2MjBAMTQwMTk0NDQxMzM5MQ==https://www.researchgate.net/publication/223477608_Estimating_the_quality_of_landslide_susceptibility_models_Geomorphology?el=1_x_8&enrichId=rgreq-b13a5fb5-271a-4115-a040-945f199d938b&enrichSource=Y292ZXJQYWdlOzIyODU3ODQ1MTtBUzoxMDQ1NzY2MDI2MDc2MjBAMTQwMTk0NDQxMzM5MQ==https://www.researchgate.net/publication/223477608_Estimating_the_quality_of_landslide_susceptibility_models_Geomorphology?el=1_x_8&enrichId=rgreq-b13a5fb5-271a-4115-a040-945f199d938b&enrichSource=Y292ZXJQYWdlOzIyODU3ODQ1MTtBUzoxMDQ1NzY2MDI2MDc2MjBAMTQwMTk0NDQxMzM5MQ==http://-/?-http://-/?-http://-/?-https://www.researchgate.net/publication/222573267_Landslide_risk_assessment_and_management_An_overview_Engineering_Geology_641_65-87?el=1_x_8&enrichId=rgreq-b13a5fb5-271a-4115-a040-945f199d938b&enrichSource=Y292ZXJQYWdlOzIyODU3ODQ1MTtBUzoxMDQ1NzY2MDI2MDc2MjBAMTQwMTk0NDQxMzM5MQ==https://www.researchgate.net/publication/222573267_Landslide_risk_assessment_and_management_An_overview_Engineering_Geology_641_65-87?el=1_x_8&enrichId=rgreq-b13a5fb5-271a-4115-a040-945f199d938b&enrichSource=Y292ZXJQYWdlOzIyODU3ODQ1MTtBUzoxMDQ1NzY2MDI2MDc2MjBAMTQwMTk0NDQxMzM5MQ==http://-/?-http://-/?-http://-/?-http://-/?-https://www.researchgate.net/publication/225482272_Exploring_the_magnitude-frequency_distribution_A_cellular_automata_model_for_landslides?el=1_x_8&enrichId=rgreq-b13a5fb5-271a-4115-a040-945f199d938b&enrichSource=Y292ZXJQYWdlOzIyODU3ODQ1MTtBUzoxMDQ1NzY2MDI2MDc2MjBAMTQwMTk0NDQxMzM5MQ==https://www.researchgate.net/publication/225482272_Exploring_the_magnitude-frequency_distribution_A_cellular_automata_model_for_landslides?el=1_x_8&enrichId=rgreq-b13a5fb5-271a-4115-a040-945f199d938b&enrichSource=Y292ZXJQYWdlOzIyODU3ODQ1MTtBUzoxMDQ1NzY2MDI2MDc2MjBAMTQwMTk0NDQxMzM5MQ==https://www.researchgate.net/publication/225482272_Exploring_the_magnitude-frequency_distribution_A_cellular_automata_model_for_landslides?el=1_x_8&enrichId=rgreq-b13a5fb5-271a-4115-a040-945f199d938b&enrichSource=Y292ZXJQYWdlOzIyODU3ODQ1MTtBUzoxMDQ1NzY2MDI2MDc2MjBAMTQwMTk0NDQxMzM5MQ==https://www.researchgate.net/publication/225482272_Exploring_the_magnitude-frequency_distribution_A_cellular_automata_model_for_landslides?el=1_x_8&enrichId=rgreq-b13a5fb5-271a-4115-a040-945f199d938b&enrichSource=Y292ZXJQYWdlOzIyODU3ODQ1MTtBUzoxMDQ1NzY2MDI2MDc2MjBAMTQwMTk0NDQxMzM5MQ==https://www.researchgate.net/publication/225482272_Exploring_the_magnitude-frequency_distribution_A_cellular_automata_model_for_landslides?el=1_x_8&enrichId=rgreq-b13a5fb5-271a-4115-a040-945f199d938b&enrichSource=Y292ZXJQYWdlOzIyODU3ODQ1MTtBUzoxMDQ1NzY2MDI2MDc2MjBAMTQwMTk0NDQxMzM5MQ==https://www.researchgate.net/publication/225482272_Exploring_the_magnitude-frequency_distribution_A_cellular_automata_model_for_landslides?el=1_x_8&enrichId=rgreq-b13a5fb5-271a-4115-a040-945f199d938b&enrichSource=Y292ZXJQYWdlOzIyODU3ODQ1MTtBUzoxMDQ1NzY2MDI2MDc2MjBAMTQwMTk0NDQxMzM5MQ==https://www.researchgate.net/publication/222571728_The_effects_of_logging_on_frequency_and_distribution_of_landslides_in_three_watersheds_on_Vancouver_Island_British_Columbia?el=1_x_8&enrichId=rgreq-b13a5fb5-271a-4115-a040-945f199d938b&enrichSource=Y292ZXJQYWdlOzIyODU3ODQ1MTtBUzoxMDQ1NzY2MDI2MDc2MjBAMTQwMTk0NDQxMzM5MQ==https://www.researchgate.net/publication/222571728_The_effects_of_logging_on_frequency_and_distribution_of_landslides_in_three_watersheds_on_Vancouver_Island_British_Columbia?el=1_x_8&enrichId=rgreq-b13a5fb5-271a-4115-a040-945f199d938b&enrichSource=Y292ZXJQYWdlOzIyODU3ODQ1MTtBUzoxMDQ1NzY2MDI2MDc2MjBAMTQwMTk0NDQxMzM5MQ==https://www.researchgate.net/publication/222571728_The_effects_of_logging_on_frequency_and_distribution_of_landslides_in_three_watersheds_on_Vancouver_Island_British_Columbia?el=1_x_8&enrichId=rgreq-b13a5fb5-271a-4115-a040-945f199d938b&enrichSource=Y292ZXJQYWdlOzIyODU3ODQ1MTtBUzoxMDQ1NzY2MDI2MDc2MjBAMTQwMTk0NDQxMzM5MQ==https://www.researchgate.net/publication/222571728_The_effects_of_logging_on_frequency_and_distribution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Two hundred and eighty-seven initiation points were extracted

from a landslide inventory using historical medium-scale aerial

photographs dated from 1994 to 2003. The landslides in the sample

typically begin as shallow translational failures, break up and lose

cohesion down-slope, and ultimately behave as ows (Fig. 2).These

shallow landslides are triggered by heavy rainfall occurring on the

coast of British Columbia. The heavy precipitation increases pore

pressure along soil–bedrock interfaces or within the soil prole at

interfaces of lower permeability (Guthrie and Evans, 2004).

3. Materials and methods

3.1. Terrain analysis and exploratory data analysis

Terrain attributes are important components of quantitative

landslide analyses because they simplify complex geomorphological

relationships and serve as surrogates for surface processes and

geophysical site conditions (Pachauri and Pant, 1992; Guzzetti et al.,

1999; Gritzner et al., 2001). Montgomery and Dietrich (1994)

demonstrated how local surface topography could summarize

destabilizing factors such as subsurface ow convergence, increased

soil saturation, and shear strength reduction. This study relies on

seven terrain attributes from a digital elevation model (DEM)

provided by British Columbia Terrain Resources Information Man-

agement (TRIM) with 25-m grid resolution to estimate landslide

susceptibility. These attributes are local slope, catchment area,

catchment slope, elevation, prole and plan curvature, and a

topographic wetness index (TWI ; Beven and Kirkby, 1979).The

province acquired the TRIM data in 1987.

Guthrie (2002) illustrated the inuence of forest-harvesting

activities to increase landslide densities. Thus, data on logged areas

and roads are included as further variables to explore in our empirical

susceptibility models. The road data is from the British Columbia

Digital Road Atlas (BCDRA). This variable is included in the model as

distance from roads up to 100-m, which is the maximum distance we

assume for the roads to have inuence on landslides. The logging

areas are mapped from interpretation of Landsat 5 TM and Landsat

7 ETM+for a timeperiod of1995to 2002 toroughly coincidewiththe

dates of landslides occurring in our inventory (Fig. 3).

The univariate relationships of each terrain attribute to landslide

occurrence are examined by calculating individual area under the

receiver operating characteristic curve values (see below).

3.2. Model assessment

Two decisions have to be made in assessing the performance of

landslide susceptibility models: (1) Which error measure should be

used and (2) how should this quantity be estimated (Brenning, 2005).

In this study, we use the area under the receiver operating

characteristic (ROC) curve ( AUROC ) to assess a model's general ability

to discriminate landslide and non-landslide locations, and its

sensitivity at a xed specicity of 90% and 80% as a performance

measure for landslide detection. These quantities are estimated using

the bootstrap, a non-parametric computational estimation technique

(Efron and Tibshirani, 1993).

The ROC curve of a ‘soft’ classier plots all possible combinationsof

sensitivities (percentage of correctly classied landslide points)

against the corresponding specicities (percentage of correctly

classied non-landslide points) that can be achieved with a given

classier. AUROC is therefore a measure of the ability to discriminate

the two classes that is independent of a specic decision threshold on

the model output. It is normally above 50% (random discrimination)

and not higher than 100% (perfect separation of the two classes).

Previous literature in landslide and hazard susceptibilitymodeling has

mentioned the value of applying ROC curves for model assessment

(Brenning, 2005; Beguería, 2006; Frattini et al., 2010). This method is

particularly useful for application to our study because we use a soft

classication approach for discriminating hazard susceptibility. Suc-

cess and prediction rate curves (Chung and Fabbri, 2003) are related

to theROC curve but dependon thespatial density of landslides. Other

Fig. 2. Typical landslides on Vancouver Island, British Columbia. (A) Stereopair of landslides in a natural setting. Landslides usually begin as shallow translational failures and break

up, losing cohesion, as they move down-slope. (B) Landslides initiating from a concave slope into a gullysystem. (C) Landslides in a forested setting. (D) Landslide showing both the

distinct planar failure surface, and the complete disintegration of material downslope.


http://-/?-http://-/?-http://-/?-http://-/?-https://www.researchgate.net/publication/252510607_A_Physically_Based_Model_for_the_Topographic_Control_on_Shallow_Landsliding?el=1_x_8&enrichId=rgreq-b13a5fb5-271a-4115-a040-945f199d938b&enrichSource=Y292ZXJQYWdlOzIyODU3ODQ1MTtBUzoxMDQ1NzY2MDI2MDc2MjBAMTQwMTk0NDQxMzM5MQ==https://www.researchgate.net/publication/200472220_A_Physically_Based_Variable_Contributing_Area_Model_of_Basin_Hydrology?el=1_x_8&enrichId=rgreq-b13a5fb5-271a-4115-a040-945f199d938b&enrichSource=Y292ZXJQYWdlOzIyODU3ODQ1MTtBUzoxMDQ1NzY2MDI2MDc2MjBAMTQwMTk0NDQxMzM5MQ==https://www.researchgate.net/publication/200472220_A_Physically_Based_Variable_Contributing_Area_Model_of_Basin_Hydrology?el=1_x_8&enrichId=rgreq-b13a5fb5-271a-4115-a040-945f199d938b&enrichSource=Y292ZXJQYWdlOzIyODU3ODQ1MTtBUzoxMDQ1NzY2MDI2MDc2MjBAMTQwMTk0NDQxMzM5MQ==https://www.researchgate.net/publication/222571728_The_effects_of_logging_on_frequency_and_distribution_of_landslides_in_three_watersheds_on_Vancouver_Island_British_Columbia?el=1_x_8&enrichId=rgreq-b13a5fb5-271a-4115-a040-945f199d938b&enrichSource=Y292ZXJQYWdlOzIyODU3ODQ1MTtBUzoxMDQ1NzY2MDI2MDc2MjBAMTQwMTk0NDQxMzM5MQ==http://-/?-https://www.researchgate.net/publication/29629981_Spatial_prediction_models_for_landslide_hazards_review_comparison_and_evaluation_Nat_Hazard_Earth_Syst_Sci_5853-862?el=1_x_8&enrichId=rgreq-b13a5fb5-271a-4115-a040-945f199d938b&enrichSource=Y292ZXJQYWdlOzIyODU3ODQ1MTtBUzoxMDQ1NzY2MDI2MDc2MjBAMTQwMTk0NDQxMzM5MQ==https://www.researchgate.net/publication/29629981_Spatial_prediction_models_for_landslide_hazards_review_comparison_and_evaluation_Nat_Hazard_Earth_Syst_Sci_5853-862?el=1_x_8&enrichId=rgreq-b13a5fb5-271a-4115-a040-945f199d938b&enrichSource=Y292ZXJQYWdlOzIyODU3ODQ1MTtBUzoxMDQ1NzY2MDI2MDc2MjBAMTQwMTk0NDQxMzM5MQ==https://www.researchgate.net/publication/29629981_Spatial_prediction_models_for_landslide_hazards_review_comparison_and_evaluation_Nat_Hazard_Earth_Syst_Sci_5853-862?el=1_x_8&enrichId=rgreq-b13a5fb5-271a-4115-a040-945f199d938b&enrichSource=Y292ZXJQYWdlOzIyODU3ODQ1MTtBUzoxMDQ1NzY2MDI2MDc2MjBAMTQwMTk0NDQxMzM5MQ==https://www.researchgate.net/publication/224839810_An_Introduction_to_the_Boot-Strap?el=1_x_8&enrichId=rgreq-b13a5fb5-271a-4115-a040-945f199d938b&enrichSource=Y292ZXJQYWdlOzIyODU3ODQ1MTtBUzoxMDQ1NzY2MDI2MDc2MjBAMTQwMTk0NDQxMzM5MQ==https://www.researchgate.net/publication/224839810_An_Introduction_to_the_Boot-Strap?el=1_x_8&enrichId=rgreq-b13a5fb5-271a-4115-a040-945f199d938b&enrichSource=Y292ZXJQYWdlOzIyODU3ODQ1MTtBUzoxMDQ1NzY2MDI2MDc2MjBAMTQwMTk0NDQxMzM5MQ==https://www.researchgate.net/publication/224839810_An_Introduction_to_the_Boot-Strap?el=1_x_8&enrichId=rgreq-b13a5fb5-271a-4115-a040-945f199d938b&enrichSource=Y292ZXJQYWdlOzIyODU3ODQ1MTtBUzoxMDQ1NzY2MDI2MDc2MjBAMTQwMTk0NDQxMzM5MQ==https://www.researchgate.net/publication/29629981_Spatial_prediction_models_for_landslide_hazards_review_comparison_and_evaluation_Nat_Hazard_Earth_Syst_Sci_5853-862?el=1_x_8&enrichId=rgreq-b13a5fb5-271a-4115-a040-945f199d938b&enrichSource=Y292ZXJQYWdlOzIyODU3ODQ1MTtBUzoxMDQ1NzY2MDI2MDc2MjBAMTQwMTk0NDQxMzM5MQ==https://www.researchgate.net/publication/29629981_Spatial_prediction_models_for_landslide_hazards_review_comparison_and_evaluation_Nat_Hazard_Earth_Syst_Sci_5853-862?el=1_x_8&enrichId=rgreq-b13a5fb5-271a-4115-a040-945f199d938b&enrichSource=Y292ZXJQYWdlOzIyODU3ODQ1MTtBUzoxMDQ1NzY2MDI2MDc2MjBAMTQwMTk0NDQxMzM5MQ==https://www.researchgate.net/publication/29629981_Spatial_prediction_models_for_landslide_hazards_review_comparison_and_evaluation_Nat_Hazard_Earth_Syst_Sci_5853-862?el=1_x_8&enrichId=rgreq-b13a5fb5-271a-4115-a040-945f199d938b&enrichSource=Y292ZXJQYWdlOzIyODU3ODQ1MTtBUzoxMDQ1NzY2MDI2MDc2MjBAMTQwMTk0NDQxMzM5MQ==https://www.researchgate.net/publication/226802573_Validation_of_Spatial_Prediction_Models_for_Landslide_Hazard_Mapping?el=1_x_8&enrichId=rgreq-b13a5fb5-271a-4115-a040-945f199d938b&enrichSource=Y292ZXJQYWdlOzIyODU3ODQ1MTtBUzoxMDQ1NzY2MDI2MDc2MjBAMTQwMTk0NDQxMzM5MQ==https://www.researchgate.net/publication/226802573_Validation_of_Spatial_Prediction_Models_for_Landslide_Hazard_Mapping?el=1_x_8&enrichId=rgreq-b13a5fb5-271a-4115-a040-945f199d938b&enrichSource=Y292ZXJQYWdlOzIyODU3ODQ1MTtBUzoxMDQ1NzY2MDI2MDc2MjBAMTQwMTk0NDQxMzM5MQ==https://www.researchgate.net/publication/226802573_Validation_of_Spatial_Prediction_Models_for_Landslide_Hazard_Mapping?el=1_x_8&enrichId=rgreq-b13a5fb5-271a-4115-a040-945f199d938b&enrichSource=Y292ZXJQYWdlOzIyODU3ODQ1MTtBUzoxMDQ1NzY2MDI2MDc2MjBAMTQwMTk0NDQxMzM5MQ==https://www.researchgate.net/publication/29629981_Spatial_prediction_models_for_landslide_hazards_review_comparison_and_evaluation_Nat_Hazard_Earth_Syst_Sci_5853-862?el=1_x_8&enrichId=rgreq-b13a5fb5-271a-4115-a040-945f199d938b&enrichSource=Y292ZXJQYWdlOzIyODU3ODQ1MTtBUzoxMDQ1NzY2MDI2MDc2MjBAMTQwMTk0NDQxMzM5MQ==https://www.researchgate.net/publication/29629981_Spatial_prediction_models_for_landslide_hazards_review_comparison_and_evaluation_Nat_Hazard_Earth_Syst_Sci_5853-862?el=1_x_8&enrichId=rgreq-b13a5fb5-271a-4115-a040-945f199d938b&enrichSource=Y292ZXJQYWdlOzIyODU3ODQ1MTtBUzoxMDQ1NzY2MDI2MDc2MjBAMTQwMTk0NDQxMzM5MQ==https://www.researchgate.net/publication/222571728_The_effects_of_logging_on_frequency_and_distribution_of_landslides_in_three_watersheds_on_Vancouver_Island_British_Columbia?el=1_x_8&enrichId=rgreq-b13a5fb5-271a-4115-a040-945f199d938b&enrichSource=Y292ZXJQYWdlOzIyODU3ODQ1MTtBUzoxMDQ1NzY2MDI2MDc2MjBAMTQwMTk0NDQxMzM5MQ==https://www.researchgate.net/publication/252510607_A_Physically_Based_Model_for_the_Topographic_Control_on_Shallow_Landsliding?el=1_x_8&enrichId=rgreq-b13a5fb5-271a-4115-a040-945f199d938b&enrichSource=Y292ZXJQYWdlOzIyODU3ODQ1MTtBUzoxMDQ1NzY2MDI2MDc2MjBAMTQwMTk0NDQxMzM5MQ==https://www.researchgate.net/publication/223671096_Techniques_for_evaluating_the_performance_of_landslide_susceptibility_models?el=1_x_8&enrichId=rgreq-b13a5fb5-271a-4115-a040-945f199d938b&enrichSource=Y292ZXJQYWdlOzIyODU3ODQ1MTtBUzoxMDQ1NzY2MDI2MDc2MjBAMTQwMTk0NDQxMzM5MQ==https://www.researchgate.net/publication/224839810_An_Introduction_to_the_Boot-Strap?el=1_x_8&enrichId=rgreq-b13a5fb5-271a-4115-a040-945f199d938b&enrichSource=Y292ZXJQYWdlOzIyODU3ODQ1MTtBUzoxMDQ1NzY2MDI2MDc2MjBAMTQwMTk0NDQxMzM5MQ==https://www.researchgate.net/publication/226802573_Validation_of_Spatial_Prediction_Models_for_Landslide_Hazard_Mapping?el=1_x_8&enrichId=rgreq-b13a5fb5-271a-4115-a040-945f199d938b&enrichSource=Y292ZXJQYWdlOzIyODU3ODQ1MTtBUzoxMDQ1NzY2MDI2MDc2MjBAMTQwMTk0NDQxMzM5MQ==https://www.researchgate.net/publication/200472220_A_Physically_Based_Variable_Contributing_Area_Model_of_Basin_Hydrology?el=1_x_8&enrichId=rgreq-b13a5fb5-271a-4115-a040-945f199d938b&enrichSource=Y292ZXJQYWdlOzIyODU3ODQ1MTtBUzoxMDQ1NzY2MDI2MDc2MjBAMTQwMTk0NDQxMzM5MQ==https://www.researchgate.net/publication/225919953_Validation_and_Evaluation_of_Predictive_Models_in_Hazard_Assessment_and_Risk_Management?el=1_x_8&enrichId=rgreq-b13a5fb5-271a-4115-a040-945f199d938b&enrichSource=Y292ZXJQYWdlOzIyODU3ODQ1MTtBUzoxMDQ1NzY2MDI2MDc2MjBAMTQwMTk0NDQxMzM5MQ==http://localhost/var/www/apps/conversion/tmp/scratch_5/image%20of%20Fig.%E0%B2%80http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-


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performance measures, such as a confusion matrix, require a hard

classier or cut-off values representing different levels of susceptibil-

ity to evaluate model performance.

In practice, the area delineated as unsafe or unstable by a landslide

susceptibility model must be small in order to reect the typically lowdensity of landslides and not restrict land use more than necessary.

Such a focused prediction is only possible when a high specicity is

achieved. As a second performance measure, we therefore estimate

the sensitivity of each model at a high specicity level of at least 90%,

and at the 80% level.

In the landslide literature, such model performance measures are

often measured on the training set of the classication rule or on a

separate test area; the latter is often, not quite correctly, referred to as

cross-validation. Brenning (2005) emphasizes that the training-set

estimation is over-optimistic and therefore biased, and that the test-

set approach may suffer from population drift, or spatially varying

distributional properties, and he therefore proposes a spatial cross-

validation approach for situations where complete gridded landslide

inventories are used for training a model. In our study we use lessdense random point samples for training and testing (on average 1.5

training and test samples per square kilometer) and therefore use

non-spatial error estimation techniques.

In addition to the training-set estimation of AUROC and sensitivity,

we apply the bootstrap estimation technique for model evaluation.

The bootstrap draws independent samples (with replacement) from

the available data in order to simulate the underlying data-generating

distribution. This distribution is thus approximated by the data them-

selves without making any parametric distributional assumption. The

bootstrap is a computationally intensive resampling-based statistical

estimation technique. We use 100 independently drawn bootstrap

replications of training and test sets in order to estimate the AUROC

and sensitivity for 100 independently trained models. Training and

test samples are each generated by drawing, with replacement, 287

landslide initiation points and 287 non-landslide points from the

available inventory.

3.3. Physically-based models

Our analysis considers two physically-based model components,

the SHALSTAB model and the FS model of the innite-slope stability

model introduced in this section. Both models and derived approaches

such as SINMAP are widely applied to landslide susceptibility map-

ping(Tarolli and Tarboton, 2006; Meisina and Scarabelli, 2007;Gomes

et al., 2008).

SHALSTAB combines an innite slope stability model and a

hydrological model to predict the steady-state rainfall that can

cause slope failure related to shallow landslides (Montgomery and

Dietrich, 1994; Guimarães et al., 2003). The model assumes that local

surface topography is the dominant control of landslide occurrence

(Montgomery and Dietrich, 1994), which makes it appealingfor DEM-

based landslide analyses and clearly calls for a quantitative compar-

ison with empirical models. SHALSTAB distinguishes between threeslope stability classes: unconditionally stable, conditionally stable,

and unconditionally unstable. Conditionally stable locations can be

characterized by their critical ratio of steady-state rainfall to soil

transmissivity (Q /T ; compare, e.g., Montgomery and Dietrich, 1994;

Guimarães et al., 2003),

Q = T = r 1

a sinθ

1−

tanθ

tanϕ

ð1Þ

where Q represents a given steady-state rainfall (m s−1), T is the soil

transmissivity (m2 h−1), a is the specic catchment area (m), which is

the catchment area (m2) divided by the contour length or width of a

grid cell (m), θ is the local slope (°), ϕ is the friction angle (°) dening

instability, and r is the ratio of the saturated bulk density of soil to the

Fig. 3. Map of forest-harvesting related land use. The logged areas represent a mosaic of forest cuts from the years 1995 to 2002.


https://www.researchgate.net/publication/29629981_Spatial_prediction_models_for_landslide_hazards_review_comparison_and_evaluation_Nat_Hazard_Earth_Syst_Sci_5853-862?el=1_x_8&enrichId=rgreq-b13a5fb5-271a-4115-a040-945f199d938b&enrichSource=Y292ZXJQYWdlOzIyODU3ODQ1MTtBUzoxMDQ1NzY2MDI2MDc2MjBAMTQwMTk0NDQxMzM5MQ==http://-/?-http://-/?-http://-/?-http://-/?-https://www.researchgate.net/publication/252510607_A_Physically_Based_Model_for_the_Topographic_Control_on_Shallow_Landsliding?el=1_x_8&enrichId=rgreq-b13a5fb5-271a-4115-a040-945f199d938b&enrichSource=Y292ZXJQYWdlOzIyODU3ODQ1MTtBUzoxMDQ1NzY2MDI2MDc2MjBAMTQwMTk0NDQxMzM5MQ==https://www.researchgate.net/publication/252510607_A_Physically_Based_Model_for_the_Topographic_Control_on_Shallow_Landsliding?el=1_x_8&enrichId=rgreq-b13a5fb5-271a-4115-a040-945f199d938b&enrichSource=Y292ZXJQYWdlOzIyODU3ODQ1MTtBUzoxMDQ1NzY2MDI2MDc2MjBAMTQwMTk0NDQxMzM5MQ==https://www.researchgate.net/publication/252510607_A_Physically_Based_Model_for_the_Topographic_Control_on_Shallow_Landsliding?el=1_x_8&enrichId=rgreq-b13a5fb5-271a-4115-a040-945f199d938b&enrichSource=Y292ZXJQYWdlOzIyODU3ODQ1MTtBUzoxMDQ1NzY2MDI2MDc2MjBAMTQwMTk0NDQxMzM5MQ==http://-/?-http://-/?-https://www.researchgate.net/publication/29629981_Spatial_prediction_models_for_landslide_hazards_review_comparison_and_evaluation_Nat_Hazard_Earth_Syst_Sci_5853-862?el=1_x_8&enrichId=rgreq-b13a5fb5-271a-4115-a040-945f199d938b&enrichSource=Y292ZXJQYWdlOzIyODU3ODQ1MTtBUzoxMDQ1NzY2MDI2MDc2MjBAMTQwMTk0NDQxMzM5MQ==https://www.researchgate.net/publication/252510607_A_Physically_Based_Model_for_the_Topographic_Control_on_Shallow_Landsliding?el=1_x_8&enrichId=rgreq-b13a5fb5-271a-4115-a040-945f199d938b&enrichSource=Y292ZXJQYWdlOzIyODU3ODQ1MTtBUzoxMDQ1NzY2MDI2MDc2MjBAMTQwMTk0NDQxMzM5MQ==http://localhost/var/www/apps/conversion/tmp/scratch_5/image%20of%20Fig.%E0%B3%80http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-


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density of water ( ρs/ ρw). Essentially, the lower theQ /T value,the more

susceptible to landsliding a location is.

Unconditionally unstable slopes are dened as the slope gradient

being equal to or greater than the friction angle:

tanθ ≥ tanϕ ð2Þ

Unconditionally stable areas are dened as locations that are

stable when saturated. Hence, as soil conditions become saturated,the friction angle causing landslide failure decreases:

tanθ b tanϕ 1−1 = r ð Þ ð3Þ

Due to a lack of knowledge of critical slope angles (ϕ) and

saturated bulk density (r ) for many landslideproneareas, we estimate

optimal ϕ and r values for our study area from the training data set.

We perform a complete grid search of ϕ and r values based on a

discretization of both variables.

An AUROC criterion on the training data set is used to evaluate the

model performance and to identify the optimal ϕ and r values that

maximize this performance measure. Specically a modied AUROC

(mAUROC ) is applied, which uses the ‘minimal path’ curve in thesense

of Zweig and Campbell (1993) to represent tied data, instead of the

usual straight diagonal path which was adopted for calculating our

AUROC values. The mAUROC penalizes for extreme parameter

combinations that would produce strongly tied data and this helps

with the convergence of the optimization within a physically mean-

ingful domain.

We examine a range of twenty ϕ values from 25° to 45° and the

same number of r values from 1 to 3. The bootstrap distribution of

parameter estimates of ϕ and r obtained on each bootstrap sample

provides an assessment of parameter uncertainty. We apply the

SHALSTAB model to a study area that is inuenced by soil cohesion as

shown by the vegetation cover in Fig. 2. SHALSTAB can be applied to

areas where cohesion is an important factor by increasing the friction

angle appropriately, although this does not fully capture the effects of

cohesion (Montgomery and Dietrich, 1994).In our case, the ‘opti-

mized’ version of SHALSTAB will compensate the effect of cohesion inthe friction angle. Thus, the empirically optimal friction angle can be

expected to be greater than the actual one.

The innite slope model of FS is another common method for

quantifying the susceptibility of landslide occurrence. It can be

expressed as the ratio of stabilizing forces (cohesion and restoring

components of friction) to destabilizing forces (components of

gravity) on a failure plane parallel to the ground surface (Meisina

and Scarabelli, 2007). The formula of FS used in this study is given by

FS = C + cosθ⌊1− min

RT

asinθ ;1

= r ⌋ tanϕ

sinθ ð4Þ

where C is dimensionless cohesion, R (m h−1) is steady state recharge

and T (m2 h−

1) is soil transmissivity. The measure (T /R)sinθ can beconsidered as the length (m) of a planar hillslope required to reach

saturation; we use the ratio of T /R (m) to represent R and T as a single

parameter in the FS model (Pack et al., 1998; Meisina and Scarabelli,

2007).

We consider FS as a function of C, ϕ, T /R, and r, and use a similar

method to numerically optimize these unknown parameters as in the

SHALSTAB model. Initial attempts to simultaneously optimize all four

parameters did not result in physically meaningful estimates of ϕ or r .

We therefore decided to plug SHALSTAB's more reasonable estimates

of ϕ and r into FS to reduce the dimension of the optimization space.

We also assume cohesionless ground conditions (C =0); this worst-

case scenario is widely used in the literature (Meisina and Scarabelli,

2007) and was the consistent result of initial modeling attempts with

only very little inuence of C on mAUROC . Therefore, only a one-

dimensional optimization of the remaining T /R parameter is required

for FS . We examine a logarithmic-scale discretization of T /R values

from 50 to 500 m; the T /R value that maximizes the mAUROC on

the training set is deemed to be optimal. In model assessment,

independent optimizations are carried out on each bootstrap training

sample.

3.4. Generalized additive model (GAM)

We use the generalized additive model (GAM) and the generalized

linear model (GLM) for empirical and combined empirical–physical

modeling of landslide susceptibility. The GAM is a semi-parametric

extension of the GLM (or logistic regression in the case of a binary

response variable) that combines linear and nonlinear relationships

between predictor and response variables (Hastieand Tibshirani,1990).

Nonlinear terms utilize smoothers to transform predictor variables. The

most widely used statistical approach for landslide susceptibility

mapping is the GLM (Ayalew and Yamagishi, 2005; Brenning, 2005).

The GAM has only recently been applied to landslide susceptibility

(Brenning, 2008; Jia et al., 2008; Park and Chi, 2008) and geomorpho-

logical distribution modeling in complex terrain (Brenning et al., 2007;

Brenning, 2009), showing stronger predictive performance than the

more widely used GLM (Park and Chi, 2008; Brenning, 2009).

We use the GAM and GLM with a combined backward-and-

forward stepwise variable selection based on the Akaike Information

Criterion ( AIC ), a measure of goodness-of-t that penalizes for model

complexity, starting from the null model. Each variable in a GAM can

be entered as linear (untransformed), nonlinear (transformed by

smoothing splines of two equivalent degrees of freedom), or not

included in the model. In this study the following GAM and GLM

models for predicting landslides are explored; empirical models using

only the above-mentioned seven terrain attributes as explanatory

variables (referred to as T-GAM and T-GLM); combined empirical–

physical models using the (log-transformed) outputs of the SHALSTAB

(log(Q /T )) model and FS of the innite-slope model (log FS ) described

above (PT-GAM and PT-GLM); empirical models using land use data,

logged areas and distance from road, and terrain attributes (LT-GAM

and LT-GLM); and combined empirical–physical models using landuse data (LPT-GAM and LPT-GLM).We furthermore assess the relative

importance of each predictor variable in empirical and combined

models by determining their variable selection frequencies in GAMs

and GLMs built on bootstrap training samples.

3.5. Geocomputing software

Statistical geocomputing, the practical statistical analysis of geodata,

hasstrongly benettedin recentyearsfrom an increasing trend towards

an integration of statistical data analysis, especially the open-source

statistical software R, with geographic information system (GIS) soft-

ware (Bivand, 2000; Brenning, 2008). We use a tight coupling of SAGA

GIS, an open-source GIS with strong terrain analysis capabilities, with R

for ouranalysis(R version 2.8.1;R Development Core Team, 2008; SAGAGIS 2.0.3;Conrad, 2006;Brenning,2008), andapply theimplementation

of the GAM in the R package ‘gam’.

4. Results

4.1. Physically-based model parameter optimization

In the SHALSTAB model, the median optimal parameters are

ϕ=40.6° (bootstrap standard deviation 3.1°) and r =1.78 (std. dev.

0.17) based on 100bootstrap replications. In the FS model, the median

optimal T /R value is 91.65 m (std. dev. 54 m). Figs. 4 and 5A illustrate

the parameter optimization of SHALSTAB and FS when applied to the

entire study area, respectively. In this particular situation, the two-

dimensional parameter optimization for SHALSTAB reaches a unique


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maximum at ϕ=40.5° and r =1.67. Small changes in ϕ (±3°

deviation from the optimum) and r have little inuence on the

mAUROC . The FS parameter optimization (using the plug-in estimates

of ϕ and r from SHALSTAB) peaks at T /R =214 m.

4.2. Exploratory data analysis

Using AUROC to assess the discriminatory power of individual

variables outside a statistical model, the strongest predictors are log

FS (with physical parameters determined by optimization on the

entire study area) and slope ( AUROC N70%), followed by SHALSTAB's

log(Q /T ), catchment slope, elevation, TWI , and distance to road

( AUROC N60%; Table 1). Although prole and plan curvature and the

catchment area are weakly related to landslide occurrence

( AUROC b60%), they may be still important in multiple-variable

models. For logging as a binary variable, the odds of landslide

occurrence are 3.5 times higher in logged areas than in deforested

areas, the odds being de

ned as the probability ratio of landslideoccurrence to non-occurrence in the respective area. All differences in

values of the predictor variables between landslide and non-landslide

points are statistically signicant at the 5% level based on Wilcoxon

rank sum tests (for continuous variables) and aχ 2 test (for logged

areas),all nominal p-values being b0.001.

Spearman's rank correlation coef cient ( ρSp) was used to examine

correlations between predictor variables. A strong inter-correlation

exists between log FS , slope and log(Q /T ) (− ρSp|N0.82). Most notably,

log FS and slope have a very strong negative correlation for this

particular set of estimated parameters, although not in general for

different physical parameters that may result from the optimization

( ρSp=−0.90; compare Fig. 5B). TWI and log catchment area share a

strong correlation ( ρSp=0.85). Catchment slope has a moderate

correlation with log FS , log(Q /T ) and slope (0.68≤ | ρSp|≤0.73). All

other correlations between variables are less strong with | ρSp|b0.50.

4.3. Predictive performance

The performance results of the bootstrap estimation show that all

empirical and combined models ( AUROC between 73.7% and 80.8%)

outperform the physical models, FS (71.9%) and SHALSTAB (68.9%;

Table 2). The models containing land use data, LT-GAM and LPT-GAM

( AUROC =80.8%) followed by LT-GLM and LPT-GLM (80.3%), are the

strongest at predicting landslide susceptibility. The performance of

the remaining models is lead by PT-GAM and T-GAM (74.9%),

followed by PT-GLM and T-GLM (73.7%). GAMs achieved only

marginal improvements in bootstrapped AUROC compared to the

corresponding GLMs, and only two of the four comparisons showed

statistically signicant differences ( p-valuesb0.001).Adding the landuse characteristics lead to larger performance improvements com-

pared to addingterrain attributes to a model.Adding physically-based

variables had negligible effects on model performance.

An argument can be made that a good model is contingent on its

ability to detect landslide initiation points without classifying large

areas as “unsafe”, which leads to consider the bootstrap-estimated

sensitivity at 90% specicity as a more focused criterion than AUROC .

Differences between the models were more pronounced but also

more scatteredin this situationcompared to thecomparison of AUROC

values. In particular, the GAMs performed consistently and signi-

cantly 2.1–2.8% points more sensitive than the corresponding GLMs

using the same variables. The results for sensitivity at 80% specicity

are between ones for AUROC and the sensitivities at 90% specicity

and therefore lead to the same interpretations as these two criteria(Table 2). For each of the performance measures, the Kruskal–Wallis

rank sum test indicates an overall signicant difference in bootstrap

performance between the models. However, the Wilcoxon signed

rank sum tests did not always indicate statistically signicant

differences in the pairwise model comparisons (Fig. 6).

Landslide susceptibility maps using training data for the entire

study area were created for LPT-GAM, PT-GAM and FS and are shown

in Fig. 7. These three models represent the better-performing models

from within each model group (empirical with and without land use

variables, and physically-based models). Qualitatively, the empirical

models (LPT-GAM and PT-GAM) illustrated in Fig. 7 show more detail

in selection of very high landslide susceptibility than the physically-

based model (FS ). The areas most susceptible to landslides in the FS

model tend to be generally associated with steep convergent hillslopes.

Fig. 4. Parameter optimization of r and ϕ in the SHALSTAB model using the entire study

areafor illustration. The median optimal values, basedon the 100 bootstrapreplications

are ϕ=40.6° (std. dev. 3.1°) and r =1.78 (std. dev. 0.17).

Fig. 5. Parameter optimization of T /R using the entire study area for illustration. (A) An

illustrationof theeffects of a rangeof T /R values on model performanceof FS andPT-GAM

at different cohesions. Theoptimal T /R value, based on theentirestudy area, is 214 m with

an FS performance of 73.6% AUROC . The median optimal T/R value, based on the 100

bootstrap replication, is 92 m with a median FS performance of 71.6% AUROC . (B) An

illustrationof theeffects of a range of T /R values on thecorrelations betweenslope andlog

catchment area to log FS at different cohesions.


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In contrast, the empirical models classify highly susceptibly areas based

on more specic slope angles, upwardly concave prole and convergent

plan curvature conditions. The inuence of incorporating deforested

areas for land use data in the LTP-GAM model can be observed in the

lower southwest corner of the map, which is an area of very highlandslide susceptibility that was not captured by the physically-based

models or the empirical models without land use data.

4.4. Variable importance and nonlinearity

In terms of their variable-selection frequencies in the GAMs, the

most important variables for the terrain-attribute-based models were

plan andprole curvatureand slope variables, which were included in

more than 90 of the 100 bootstrap replications. The land use models

had a similar selectionas the terrain-attribute-based models, however

with the addition of the variables for distance from road and logged

areas, which were selected in 100% of the bootstrap replications.

Nonlinear in

uences of these variables were found very frequently(44–100% of the replications), based on the AIC criterion. Including

nonlinear versions of variables can inuence their relative impor-

tance. For example, slope in T-GAM is more frequent in the GAM

(99%), where it is in most cases nonlinearly smoothed (86%), than in

the GLM (90%).

For PT-GAM, the relative importance of terrain attributes is similar

to the terrain-based models, except from slope being selected only in

32% of the cases, certainly because of its very strong correlation with

log FS , which is selected in 98% of the bootstrap replications. Its most

important variables are plan and prole curvature and log FS . Linear

and nonlinear representations of log FS are nearly balanced, while

nonlinear representations are dominant in the case of the curvature

variables.

When the predictive models are built on the training set for

the study area, the PT-GAM includes four variables: log FS (linear),

log(Q /T ) (linear), prole curvature (nonlinear) and plan curvature(nonlinear). T-GAM and T-GLM include the same three variables:

slope, prole curvature and plan curvature; in T-GAM, all are non-

linearly transformed. The nonlinear variable transformations used in

PT-GAM and T-GAM are illustrated in Fig. 8. For comparison, the

SHALSTAB and FS models both incorporate two terrain attributes

(slope and specic catchment area) and two (FS : three, excluding

cohesion) additional parameters to be tuned.

5. Discussion

5.1. Model interpretation

Landslides are typically more prone to occur in steep convergentareas (Montgomery and Dietrich, 1994). These curvature conditions

force soil water to converge at the soil –bedrock contact or where the

soil meets an underlying impermeable layer (Wilson and Dietrich,

1987).After heavy rainstorms or long periods of rain, upwardly

concave slopes can hold more water for a longer period of time ( Lee

and Min, 2001). A combination of antecedent rainfall conditions and

rainstorm or rapid snowmelt can result in an increase of pore water

pressure, which can lead to hillslopes becoming more susceptible to

failure (Talebi et al., 2008).

The empirical model results indicate that hillslopes with concave

prole and convergent plan curvature tend to have increased

Table 1

Descriptive statistics of the morphometric and physical model predictor variables used for modeling landslide susceptibility.

Predictor v ariable Non-l andslide points:

Median (std. dev)

Landslide points:

Median (std. dev)

AUROC (%)

Study area

AUROC (%)

Bootstrap test set (std. dev)

log FS a −0.06 (0.31) −0.22 (0.15) 73.6 71.9 (2.2)

Slope (degrees) 23.0 (10.3) 31.5 (7.3) 73.0 72.1 (2.1)

log(Q /T )a −2.5 (0.8) −3.0 (1.0) 71.1 68.9 (2.6)

Catchment slope 23.9 (7.7) 27.7 (5.5) 67.0 65.0 (2.4)

Elevation (m) 371 (183) 472 (152) 61.7 62.9 (2.2)

Distance to road (m) 354 (840) 112 (346) 62.7 61.9 (2.0)TWI 6.0 (1.5) 5.7 (0.9) 58.5 60.1 (2.3)

Plan curvature 0.001 (0.006) 0.000 (0.011) 57.6 57.4 (2.4)

Prole curvature 0.000 (0.007) 0.001 (0.008) 54.6 52.4 (3.6)

log catchment area 3.6 (0.5) 3.7 (0.4) 52.7 50.2 (2.4)

Logging (land use) No n-lan ds lid e p oin ts ( %) La nds li de p oi nt s ( %)

Logged 16.4 40.4

Forested 83.6 59.6

a After parameter optimization of SHALSTAB and FS .

Table 2Model performance of GAM, GLM, and physically-based models (SHALSTAB and FS ) estimated using the bootstrap and the training set (median value and standard deviation). The

median variable frequency represents the average number of variables included in each model for the bootstrap.

Model Bootstrap Study area

AUROC

(%)

Sensitivity (%) at

90% specicity

Sensitivity (%) at

80% specicity

Mean variable

frequency

AUROC

(%)

Sensitivity (%) at

90% specicity

Sensitivity (%) at

80% specicity

LPT-GAM 80.8 (2.0) 47.7 (5.4) 63.4 (4.6) 6.1 (0.9) 83.4 56.4 69.7

LPT-GLM 80.3 (2.1) 45.6 (5.8) 62.7 (5.1) 6.0 (0.9) 83.3 54.4 69.7

LT-GAM 80.8 (2.0) 48.4 (5.4) 63.8 (4.5) 5.9 (1.0) 83.8 56.4 70.4

LT-GLM 80.3 (2.0) 46.2 (5.7) 62.4 (5.0) 5.8 (1.1) 83.2 56.8 67.2

PT-GAM 74.9 (2.2) 31.6 (5.4) 48.3 (5.4) 4.3 (1.0) 77.7 35.8 54.4

PT-GLM 73.7 (2.2) 29.1 (5.5) 45.6 (5.1) 4.4 (1.1) 77.1 35.8 51.2

T-GAM 74.9 (2.2) 31.0 (5.0) 47.7 (5.5) 3.9 (1.1) 77.4 36.7 54.0

T-GLM 73.7 (2.2) 28.2 (5.4) 46.7 (5.3) 4.1 (1.2) 76.6 34.5 51.2

FS 71.9 (2.2) 19.5 (5.0) 41.8 (6.7) – 73.6 24.0 47.0

SHALSTAB 68.9 (2.6) 19.0 (10.7) 38.1 (6.9) – 71.1 24.4 42.2


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landslide susceptibility (Fig. 8). The terrain attributes for curvature

are interpreted as representing the topographic inuence of local

morphology on slope hydrology (Lee and Min, 2001) and soil erosion

or deposition. Prole curvature characterizes the subsurface acceler-

ation or deceleration of ow down a slope, which in turn is related

to potential erosion or deposition rates and consequently spatially

Fig. 6. Diagram of model performance andsignicance. The performance ofeach empirical model has been mapped in a diagram wherethe arrow points to a modelthat had a lesser

performance; a solid line indicates that there is no difference, statistical or otherwise, between model performance. The numbers adjacent to the arrows indicate the percent

difference in performance between comparing models. Additionally, the statistical signicance of model differences are indicated using signicance codes following the percent

difference.

Fig. 7. Landslide susceptibility maps for physically-based (FS ),and combined models (LPT-GAM and PT-GAM) applied to the subarea shown in Fig. 1. The models are trained on the

entire study area. The area designated as ‘

Not applicable’ is a portion of the study area below the models' 150 m threshold.


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varying soil depth. Plan curvature characterizes the convergence and

divergence of topography and near-surface water ow. Together, the

empirical representation of curvaturemay represent subsurface water

conditions and substrate properties that have an important inuence

on landslide occurrence.

By contrast, the physically-based models SHALSTAB and FS

represent slope shape through the incorporation of a(sinθ)−1.

According to these models, less precipitation is required for instability

when a larger contributing area is providing drainage across specicwidth (Dietrich et al., 2001). SHALSTAB and FS do account for the

inuence of acceleration of ow through prole curvature but only

characterize ow down a straight prole.

A key advantage of integrating empirical models with physically-

based models is the ability to compliment the latter with ancillary

process-related variables, such as terrain attributes, geology, and land

use, and to calibrate this combined model at a regional scale. Intensive

and expensive eldwork is required to estimate values for spatially

varying physical model parameters that may only be applicable at a

local scale. Our empirical approach allows us to estimate these values

at a regional scale by parameter optimization, which can be used to

produce models representing a larger area (Lacroix et al., 2002;

Barnett et al. 2004). In our study area soil conditions generally differ

depending on the land use. In general, forest harvesting practices canchange the physical structure of a soil, causing an increase in bulk

density and compaction as well as a decrease in organic matter

(Huang et al., 1996; Merino et al., 1998). In addition, landslides occur

in higher densities in logged areas and areas adjacent to logging roads

(Guthrie, 2002; Guthrie et al., 2010).Therefore, land use data is

incorporated into our model as a proxy for unknown soil conditions,

and proved to be an important factor associated with differences in

landslide density in this study.

5.2. Relationship between FS and terrain attributes

The correlation between slope and log FS varies with physical

parameters and is strongest near the optimized physical parameter

values (Fig. 5B). This requires further interpretation. Slope angle θ

will have the strongest inuence on FS when

R

T

a

sinθ

≥1 ð5Þ

In this case, T /R and a will have no inuence on FS , and only

constants such as C , r and θ and the spatially variable slope angle will,

resulting in a monotonically decreasing nonlinear function of θ.

The reverse situation occurs when the specic catchment area (or,

on planar slopes, slope length) is smaller than some threshold

T

R sinθ ð6Þ

which decreases towards at areas and is substantially smaller than T /

R. In this case, the monotonic decrease of FS with increasing slope

angle is further modied depending on the specic catchment area,

which could statistically be represented in a GAM by a bivariate

interaction term. In our study, however, the optimal bootstrap T /R

values were oftenb100 m, which implied that specic catchment areainuenced FS only near the ridges, resulting in an extremely strong

correlation with slope.

In order to further explore the potential predictive value of log FS

and its dependence on slope angle, we determined the relationship of AUROC forPT-GAM and log FS given a range of T /R values(Fig.5A).Our

expectation was that log FS may improve the PT-GAM whenever its

correlation with θ (or the less inuential catchment area) is weakest

(Fig. 5B). Correlation with θ however remains always stronger than−0.80 (weakest for T /R≈900 m), and correlation with catchment

area remains weak. The AUROC for PT-GAM is the greatest given a

small T /R near our optimal parameter estimate, though T /R in general

has little inuence on the AUROC of PT-GAM. This conrms the utility

of our optimization strategy for the construction of integrated

physical–

empirical models of landslide initiation.

Fig. 8. Transformation of predictorvariables in thegeneralized additive models,for PT-GAM(A) andT-GAM (B), that utilize theentire study area as training sample. A splinefunction

for non-parametric smoothing of the variables, s(variable), indicates a nonlinear transformation. The dotted lines represent condence bands. In the plan curvature plot, a negative

value indicatesa convergent surface, a positive value indicatesa divergentsurface,and value of 0 indicatesthe plan is straight.In theprole curvatureplot,a negative value indicates

a convex surface, a positive value indicates a concave surface, and a value of 0 indicates no surface curvature.


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5.3. Model comparison

We found that being able to include nonlinear (transformed)

terms or linear (untransformed) terms in the GAM rather than only

linear ones as in the GLM provided only a marginal enhancement of

the landslide susceptibility model (Fig. 6). The predictive and

analytical advantage of GAM over the GLM may become more

prevalent in areas that exhibit stronger nonlinear relationships to

landsliding.Broadly speaking, the geomorphic processes involved in causing

landslides to occur can in fact be considered to have nonlinearities.

Phillips (2003) discusses that nonlinearity can occur in geomorphic

systems that progress towards a threshold or critical state, a point

where a system changes behaviour. In the case of hillslopes, this can

be observed when it becomes unstable as a consequence of changing

hydrological conditions. Moreover, landslides are a result of multiple

topographic and climatic variables that inuence erosion and

weathering rates, which lead to a progressive transformation and

movement of slope material. Thus, some of the topographic variables

used in our models may be expected to have nonlinear relationships

to the process or conditions they may represent as proxy variables. In

our study, we found that when given the choice to represent the

relationship between hillslope topography (slope and curvature) and

landslide occurrence as nonlinear or linear, the predominant selection

wasto include a nonlinearversion of thevariable(Table 3). Themodel

improvements between a GAM and GLM were small (Fig. 6);

however, the predominant nonlinear selection of topographic vari-

ables provides some empirical evidence for the actual presence of

nonlinearities in these relationships. Therefore, nonlinear regression

techniques, such as theGAM, allow us to capture complex geomorphic

processes that are dif cult to represent in a linear form.

The practical needs to delineate relatively small high-risk areas

that contain a large portion of the potentially unstable hillslopes lead

to the determination of sensitivity at a high specicity (Brenning,

2005). This performance measure is more focused than AUROC . It is

key for being able to interpret the ability of a model to differentiate

between classes where it matters for practical purposes. The

limitations especially of SHALSTAB in predicting at a high specicitycan partly be attributed to its “ hard” classication of unconditionally

unstable slopes, which does not provide a means for further

continuously differentiating among the numerous unconditionally

unstable grid cells. These areas are determined only based on the

friction angle, which was assumed to be spatially constant in our

study and in most other published applications of SHALSTAB. The use

of multiple predictor variables in empirical and combined models

may, by contrast, be interpreted in terms of a spatially varying friction

angle that partly depends on geomorphic proxies of substrate

properties or land cover characteristics. While the FS approach is

not subject to the limitation of classifying certain areas into an

unconditionally unstable category, it does however assume the

friction angle to be known and, in most studies, to be constant in

space.

Although the proposed approach of integrating SHALSTAB and FS

with empirical models did not provide a statistically signicant

advantage over the terrain analysis approach in terms of predictive

capabilities in this study area, the results provide better insights into

site characteristics that inuence landsliding. The predictive useful-

ness of these models may increase in situations where limited

landslide inventory data increases the uncertainties in

exible data-driven models, or where additional information on spatially varying

soil physical properties is available from detailed eld studies. We

were able to use statistical techniques to estimate physical parameters

required for physical models, such asϕ and r , for the entire study area.

The location of landslide initiation points is the only actual training

data required to produce our susceptibility models. Our model

comparison strategy based on resampling-based error estimation

provides a general framework that can be applied to guide model

selection in an unbiased way (Brenning, 2005).

On the other hand, the integration of both model types may also

provide directions for improving physically-based slope stability

models. The PT-GAM indicates that plan and prole curvature contain

signicant information that may be used to improve the FS model in

our study area. Specically, local convergence and local concavity

appear to constitute more important inuences on landslide initiation

than reected by the specic catchment area in the FS model, which

partly reects the average upslope plan curvature, and not primarily

local slope geometry. The actual physical link may be related to

spatially varying soil thickness or sediment types with different

friction angles and densities, which are approximated by curvature

variables as proxies for the underlying processes of erosion and

deposition. This interpretation is supported by previous statistical

analyses in forested mountain areas that found that spatially varying

soil thickness is a function of ow accumulation and acceleration,

which are characterized by prole and plan curvature (Rahman et al.,

1996; Heimsath et al., 1999).

6. Conclusions

The application of novel statistical techniques, such as the GAM

and bootstrap method for bias-reduced error estimation, to combine

physically-based and empirical models for landslide susceptibility

modeling was explored in this study. It is found that this method can

enhance physically-based slope stability models in terms of their

predictive performance, and improve the interpretability of empirical

models.

Nonlinear enhancements of the GLM achieved by applying the

GAM only provided marginal improvements in predictive perfor-

mance, but appear to better reect the often nonlinear response of

slope stability to varying site conditions, whether it is slope angle or

distance from an anthropogenic disturbance.

Incorporating physically-based models, SHALSTAB and FS , into the

empirical modeling and parameter estimation framework providedphysical meaning to the susceptibility models by spatially represent-

ing hillslope processes, but did not achieve a performance improve-

ment compared to purely terrain-based empirical models. Terrain

attribute information was used as a proxy for natural geophysical site

conditions that may increase the predisposition to landslide initiation,

and land use variables provided additional important information on

anthropogenically modied site conditions.

Plan and prole curvature, in addition to slope, were found to be

important modiers of slope stability in our study. Landslide

susceptibility is maximized on steep hillslopes that have an upwardly

concave prole and convergent plan curvature. An advantage of using

terrain attribute information in an empirical model was allowing for

the incorporation of different curvatures (convex, concave or plane)

for prole and plan curvature. In contrast, FS and SHALTAB do account

Table 3

Variable-selection frequencies and percentage of nonlinear occurrence for GAM models

on 100 bootstrap training samples.

Variable LPT-GAM LT-GAM PT-GAM T-GAM

Distance t o road 1 00 (4 4%) 1 00 (4 4% ) – –

Logging 100 100 – –

Plan curvature 99 (56%) 100 (50%) 100 (69%) 99 (66%)

logFS 99 (52%) – 98 (52%) –

Prole curvature 93 (75%) 94 (77%) 81 (100%) 93 (87%)

Elevation 37 (100%) 39 (91%) 27 (100%) 25 (100%)

Slope 22 (32%) 100 (90%) 32 (31%) 99 (87%)

log(Q /T ) 21 (33%) – 26 (38%) –

TWI 19 (32%) 27 (26%) 21 (52%) 38 (37%)

log catchment area 10 (30%) 16 (25%) 23 (22%) 21 (14%)

Catchment slope 9 (33%) 12 (33%) 12 (25%) 17 (29%)


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for different plan curvatures in the upslope contributing area indi-

rectly through the specic catchment factor, however no information

on the slope prole is incorporated into these models. Therefore, the

inclusion of an empirical variable for prole curvature is important to

represent the potential range of ow and inltration characteristics

for different prole curvatures that the physically-based landslides

susceptibility models may not account for.

Overall, the methods implemented in this study, which combine

empirical and physically-based approaches and include bias-reducederror estimation, were presented as a general framework to enhance

the analysis of performance for landslide susceptibility models. In

addition, the use of a nonlinear regression technique, such as the

GAM, demonstrated the importance of representing the nonlinear

relationships of predictor variables of landslide occurrence, which

allows for a more exible and interpretable analysis of landslide

susceptibility.

Acknowledgements

This research was funded through an NSERC Discovery Grant —

Individual awarded to A. Brenning. We acknowledge constructive

comments provided by the anonymous referees.

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