02 mountainrisks intensivecourse barcelona 08 vanwesten susceptibility

ISL 2004

International Institute for Geo-Information Science and Earth Observation (ITC)

Landslide susceptibility assessmentLandslide susceptibility assessment

Cees van WestenUnited Nations University ITC School for Disaster Geo-Information Management

International Institute for Geo-Information Science and Earth Observation (ITC)Enschede, The Netherlands

E-mail: [email protected]

Associated Institute of the

ISL 2004


SuceptibilitySuceptibility: contents of lecture: contents of lecture What is susceptibility What controls it:

Landslide type Scale Objectives

Which data are required? Which techniques can be used to assess it?

Heuristic, statistical, deterministic Validation From susceptibility to hazards Discussion part..Which method to use when?

Landslides Susceptibility

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What is susceptibility?What is susceptibility?Landslide susceptibility is: The relative spatial likelihood for the occurrence of

landslides of a particular type and volumeLandslide hazard is: The probability of occurrence of a particular landslide

type (initiation and run-out, volume, speed) within a specified period of time and in a given area.

Landslide risk is: The expected losses (monetary, or in number of buildings

/ people) due to specific landslide type type (initiation and run-out, volume, speed) within a specified period of time and in a given area.

Where?

Spatial probability

When?

Temporal probability

Hazard = Susceptibility * Triggering factors

ISL 2004


Population, building, industry, agriculture,Infrastructure, services

Landslides Inventory

Spatial landslide risk assessment frameworkSpatial landslide risk assessment framework

OccurrenceEnvironmentalParameters Triggering Factors Elements at Risk

Susceptibility

Natural HazardSpecific Risk

Total Risk

Vulnerability

Geology, Soil,Landuse,Slope, HeightInternal relief

Earthquakesand

Rainfall

Susceptible areas for the initiation of landslide.

Probability of occurrence within a specified period of time and within a given area of a landslide.

Expected degree of loss due to landslide.

Degrees of loss to a given element(s) at risk resulting from the occurrence of a landslide of a given magnitude. [0, no loss.. 1, total loss]

Expected number of lives lost, persons injured, damage to property, or disruption of economic activity due to landslide.

type, magnitude,time, activity

values, classes time, magnitude,intensity

object and attributes

FrequencyAnalysis

(type, magnitude)/ time

Run-outValue

%- (probability) /(type, magnitude)

% / (type, magnitude) / time

FrequencyAnalysis

(intensity, magnitude)/ time

$ / object[0..1] / (type,magnitude, distance)

% / [0..1] / (type, magnitude) / time

% / $ / (type, magnitude) / time

Number of occurrence in a given time.

Number of occurrence in a given time.

Landslide hazard methods

Heuristic analysis

Statistical analysis

Inventory analysis

Deterministic analysis

Consequence

$ / (type, magnitude)

Loss outcome from the occurrence a landslide of certain type or magnitude.

Risk evaluation

Acceptable risk

Tolerable risk

m - (distance) /(type, magnitude)

Costs of building, engineering works, infrastructure, environmental features, and economic activities in the area affected by landslides.

Potential path covered by the landslide occurrence.

E. C

astellanos,, 2008

ISL 2004


What is required for expressingWhat is required for expressing

RealRealYesYes

AbsoluteAbsoluteYesYes

RelativeAt best relativeYesRelative

Landslide initiationSpatial probabilityTemporal probabilityLandslide typeVolume

YesYesYesYesYes

YesYesYesYesYes

NoNoNoNoNo

Landslide runoutSpatial probabilityTemporal probabilityLandslide typeVolumeSpeed

YesYesYes

NoNoNo

NoNoNo

Landslide consequencesBuilding damageInfrastrusture damagePopulation damage

Component RiskHazardSusceptibility

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What controls landslide susceptibility?What controls landslide susceptibility? Landslide distribution

Landslide types Failure mechanisms Age & activity Area covered by landslides Controlling factors Type

Homogeneity Triggering factors

Earthquakes Rainfall Human interventions Others

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All landslides knownAll landslides known??

Red : landslide initiation on cut slope Pink : Landslide run out Dark green : landslide initiation on natural

slope Light green : Landslide run out Triangles : Rain gauge location

Type of study area? Watershed Line Point

Basically all landslides are known from the past 30-40 years based on registers

Pankaj Jaiswal, 2008

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An example of rapid change in land cover in the Nilgiri hills. Marapallam debris slide as seen in different years.

1993 1998 2007

All landslides known?All landslides known?

Pankaj Jaiswal, 2008

Mapping landslides from images without prior knowledge is a tricky business many old landslides are not properly known

The use of (as many as possible) sets of older images (airphotos and satellite images improves the interpretability.

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Who needs a susceptibility map if you know all slides

CEO Hong Kong: Enhanced Natural Terrain Landslide Inventory (ENTLI) : ~15,800 recentlandslide features have been identified based on airphoto interpretation. For each terrain unit the temporal and spatial probability is known.

Ken Ho, CEO, HongKong, 2007

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Scale of analysisScale of analysis National scale

(< 1:1.000.000) Mainly inventory. Public awareness & policy support

Regional scale(1:100.000 - 1:1.000.000) For reconnaissance phases for planning projects for the construction of infrastructural works, or agricultural development projects.

Medium scale(1:25.000 - 1:100.000). For land use planning and construction of infrastructural works, environmental impact assessment and municipal planning.

Large scale(1:2.000 - 1:25.000). For risk assessment and detailed planning.

Site investigation(>1: 2.000). Detailed risk assessment, and design of slope stabilization works

Geological Periode.g. Middle Eocene: Aleutorite, marl, limestone, chert, conglomerate, olitostrome.

Geological formationse.g. Yateras formation: limestones, marls and clays

Lithological unite.g. karstic limestones

Geotechnical parameterse.g. Internal friction 5, bulk unit weight 16.5 kPa/m, viscosity 2.5 kPa.s

GEOLOGY

National level1:1,000,000 scale

Provincial Level1:100,000 scale

Municipal level1:50,000 scale

Local level1:25,000 scale

Np

Nmh

Nb

Ha

Hazard example

Castellanos and Van Westen, 2008

Each scale has its own objectives, and has its own possibilities for data

collection


1 : 2,750,000

Landslide Susceptibility in GermanyLandslide Susceptibility in Germany

93,8

5,4

0,6

0,2

Very lowLowModerateHigh

Building destruction likely, people endangeredHigh

Building damage possible, people probably endangeredModerate

Building damage and directly affected people unlikelyLow

At human discretion no dangerVery low

DescriptionClass

Glade, Dikau and Bell

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Example: CubaExample: Cuba

Local disaster risk reduction plan Identifying elements at risk affected by different scenarios and implementing mitigation actions

Local and municipal government and civil defence

QuantitativeRunout modelling based on geotechnical parameters(adaptation needed for generalization)

Local(1:25,000)

Municipal disaster risk reduction planEstimating losses and delimitating areas for mitigation actions

Municipal government and civil defence

QuantitativeTMU and expert judgment(adaptation needed for generalization)

Municipal(1:50,000)

Provincial disaster risk reduction planLocating landslides and priority areas for investigating causes and consequences

Provincial government and civil defence

Semi-quantitative with SMCESpatial model viaStatistical method and weighting

Provincial(1:100,000)

Locating priority areas for regional studies and guide national policyPeriodic assessment to monitor local improvement

National Civil Defence

Semi-quantitative with SMCERisk index by ranking and weighting

National(1:1,000,000)

UseOrganizationMethodLevel (scale)


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Geotechnical parametersHydrological parameters

Geotechnical parametersHydrological parameters

Hydrological parameters

Slope hydrology

R

Scale

M LUse

RS

H

DEM Slope / Aspect etcElevation

Building footprintsPopulation data

Infrastructure

Land use

Catalogs & strong motion

Hazard maps

Rainfall / Temperature

Flow accumulation

Detailed mapping units

Main units

Soil depth

Soil types

Faults

Structure

Lithology

Occurrence/Inventory

Elements at risk

Seismic data

Meteo data

Geomorphology

Hydrology

Soils

Geology

Landslides

ModelsUpdate Frequency

>10 DPSday0.8110

High

Moderate

Low

Input dataInput dataRegional Medium Large

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Which data to collect?Which data to collect?Objectives of the study

Availability of existing dataAvailable resources

Complexity of the area

Selection of susceptibility analysis technique

Selection Collection spatial and non spatial data

Type of landslidesSize of study area

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Main methodsMain methodsKnowledge driven: Boolean Logic Fuzzy logic Multiclass overlay Spatial multicriteria

evaluationData driven: Bivariate statistics Weights of evidence Information value Frequency ratio Multi-variate statistics Logistic regression Discriminant analysis Cluster analysis Artificial Neural Networks

Deterministic methods Static methods Infinite slope based Profile based Dynamic methods

Inventory based Magnitude-frequency Activity mapping

Probabilistic methods Parameter uncertainty Temporal prediction

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Landslide activity analysis

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Landslide mapping can be difficultLandslide mapping can be difficult

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Direct / Indirect methodsDirect / Indirect methods Direct methods

experience driven applied geomorphological approach, where the earth scientist evaluates the direct relationship between the landslides and the geomorphological and geological setting during the survey at the site of the failure.

Indirect methodsthe mapping of a large amount of parameters and the (statistical or deterministic) analysis of all these possible contributing factors in relation to the occurrence of slope instability phenomena, determining in this way the relation between the terrain conditions and the occurrence of landslides. Based on the results of this analysis statements are made regarding the conditions under which slope failures occur.

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Geomorphological hazard mappingGeomorphological hazard mapping

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Storing Storing GeomorphologicalGeomorphological data in GISdata in GIS Store Geomorpholo-

gical information in several data layers:A: Main UnitsB: Sub unitsC: LandslidesD: Material typesE: Hazard

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Geomorphological hazard mapGeomorphological hazard map

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Rating methodsRating methods Index methods: predefined,

e.g. Mora-Vahrson method

(Central America) BIS method (India) Problem: they are either very

general and cannot be applied in larger scales

Differences between areas are ignored

Sometimes do not even require a landslide inventory

Index methods: experts derived

Index overlay, multi-class overlay

Fuzzy-logic Spatial Multi Critera

Evaluation

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Knowledge driven methodKnowledge driven methodThe expert decides: On which criteria are used On which input maps are selected On the weights of the classes of

the input maps On the weights of the input maps

themselves

Subjective Not reproducible Difficult: how important are the

different factors

Is there a way to improve and make this more objective?

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Spatial MultiSpatial Multi--Criteria EvaluationCriteria Evaluation

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The criteria treeThe criteria tree

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Multi Criteria EvaluationMulti Criteria EvaluationInventory Environmental Parameters

Geomorphometric Ground ConditionsTriggering Factors

National LandslideMitigation PlanNational LandslideMitigation Plan

Data sources: SRTM DEM derivatives maps (90m) National Atlas of Cuba (1:1,000,000 scale) National Statistics Office (ONE) National Organizations

Area: 110,860 km2Analysis unit: pixel based at 90 m.Risk assessment method: semi-quantitative spatial multicriteria.Final map: at 1:1,000,000 scale

Internal relief

Landslides

Slope Angle

Geology

Landuse

Earthquakes

Rainfall

Provinces

Municipalities

SusceptibilityIndex

a. slope angle, b. geology, c. landuse, d. maximum rainfall

expected in 24h and e. maximum peak ground acceleration


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Final output mapFinal output map


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Knowledge driven methodsKnowledge driven methodsAdvantages: Expert knowledge can be properly included Flexible, both in causal factors, as in sub-goals Can be used for both hazard and risk assessmentDisadvantages: Subjectivity (however.) Doesnt give quantitative estimation of hazard Cannot be used for quantitative risk assessment

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Data driven methodsData driven methodsThe expert decides: On which criteria are used On which input maps are selected

Weights are determined: By comparing the inputs maps

with known occurrence of the feature one would like to predict

Basically based on densities Converted into spatial

probabilities Using bivariate or multivariate

methods Results can be validated

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BivariateBivariate statistical methodsstatistical methods Frequency ratio:

Area of landslides in Class / Area of all LandslidesFR =

Area of Class / Entire map

Area of landslides in Class / Area of ClassFR = LN

Area of all landslides in the map / Area of Entire map

Hazard index:

Weights of evidence:i+

ei

iW =

P { B |S}P { B |S }

log

i-

ei

iW =

P { B |S}P { B |S }

log

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Slope angle versus Slope angle versus landslideslandslides

SRTM DEM

1:50000 topomap

1:2000 topomap

Lidar DEM

Influence of input dataInfluence of input data

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BivariateBivariate statisticalstatistical analysisanalysis

(Castellanos & van Westen, 2008)

Soil

Cross tablesFactor maps Weight maps

M

a

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v

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r

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a

y

i

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p

r

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c

e

d

u

r

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Slopes

Landslides

Geology

Susceptibility map

WSoils

WSlopes

WGeology

C

o

m

b

i

n

a

t

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f

w

e

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s

.

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....

E. Castellanos, Jun-2008

Validation

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ExampleExampleB B

S

S

npix1 npix2

npix3 npix4

180 20 200

3420

3600 6400 10000

6380 9800

i+

ei

iW =

P { B |S}P { B |S }

log

i-

ei

iW =

P { B |S}P { B |S }

log

i+

e

1

1 2

3

3 4

W = +

+ Npix

log

NpixNpix Npix

NpixNpix

i-

e

2

1 2

4

3 4

W = +

+ Npix

log

NpixNpix Npix

NpixNpix

=

180180 + 20

3420 + 63803420

=0.9

0.349= Ln 2.578 = 0.9474

=

20180 + 20

3420 + 63806380

=0.1

0.651= Ln 0.1536 = -1.87

ISL 2004

International Institute for Geo-Information Science and Earth Observation (ITC)Example of statistical analysis Evidence maps

drain fault roadgeomgeolAspcl slidelanduseslope slide60

Rasterize; distance calculation

Create class, group domain, Reclassify

Class_distroadClass_disrtdrainClass_distfault

Create attribute map, calculate prior probability for all landslides in study area. Then, create a bit map showing only

active landslides

bslide60bslide

Cross operation between factor maps and evidence maps

Waspclw60aspcl

Wgeomw60geom

Wlandusew60landuse

Wslopew60slope

Wfaultw60fault

Wdrainw60drain

Wroadw60road

Wgeolw60geol

To calculate four possible combinations of potential landslideconditioning factor and a landslide inventory map that are npix shows

pixel number. Then calculate weight of evidence can be written in number of pixels as follow equations:

i+

e

1

1 2

3

3 4

W = +

+ Npix

log

NpixNpix Npix

NpixNpix

i-

e

2

1 2

4

3 4

W = +

+Npix

log

NpixNpix Npix

NpixNpix

To create final weight evidence maps for each evidence maps (Use script)To calculate success rate and predict rate then reclassify final weight evidence map.

To compare the result map, which is shows added activity landslide. Also this map can be to check result is how well predicting final weight evidence map.wfinal w60final

Prediction rate Success rate

Prediction map of landslides

Class_wfinal Class_w60finalAdded landslide area

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Combine methods..Combine methods..

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Landslide mappingLandslide mapping

100.0281Total

6.418Topples

76.5215Slides

7.822Rock fall

9.326Debris flow%Frequency

Castellanos, 2008

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Hazard analysis Hazard analysis -- factorsfactorsGeomorphology Geology Landuse

Slope angle Slope aspect Internal relief

Drainage density Soils

Rainfall PGA Road distance

Fault distance

Castellanos, 2008

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MultiMulti--variatevariate modelsmodels Multiple regression Logistic regression Artificial Neural Network Basic units:

Pixels Unique condition polygons DTM slope units

Castellanos, Melchiore and Van Westen, 2008

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Susceptibility maps per causal mechanism Susceptibility maps per causal mechanism Debris hazard

No hazardLow hazardModerate hazardHigh hazard

SlideT hazard

Rockfall hazard Slide hazard

Topples hazard All hazards


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Combine methods..Combine methods..

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Main data types: Soil data

Depth Hydrological properties Geotechnical properties

Digital Elevation Models Slope angle Local drain direction Contributing areas

Groundwater measurements

Physically based modelingPhysically based modeling

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Deterministic Models: No Uncertainty (Single value at a given space& moment of time)

Stochastic Models: Involves Uncertainty (Probability depended)

Static Models: Independent of time. Time Frozen Dynamic Models: Simulates changes through time

Process Driven Models: Models based on general physical laws. Data Driven Models: Models valid under certain conditions defined

by the properties and processes of the study area.Eg: Downward approach to hydrological model development

Physically based modelingPhysically based modeling

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Dynamic modelsDynamic models

IO: Institute of Origin; PE: Programme Environment; TC: Temporal Component; D: Dimension; HC: Hydrological Component; SPC: Spatial Parameterization Capability

IncapableCapable (not recommended)Capable (not

recommended)Fully capableSPC

Wetness Index [Bevenand Kirkby, 1979]

Wetness Index [Beven and Kirkby,

1979]

Infiltration, Runoff,

Pressure head at min FOS

Water Level, Effective Degree of Saturation,

Runoff, Bed Rock StorageHC

1DStatic

ArcView

University of California (Berkeley),

and Stillwater Sciences

SHALSTAB

1DStatic

ArcView

Utah State University

SINMAP

2 D + 1DDynamicFortran

USGS

TRIGRS

2.5 D + 1DDynamicPCRaster

Utrecht University

STARWARS + PROBSTAB

D

TC

PE

IO

Different implementations of the infinite slope model

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STARWARS + PROBSTABSTARWARS + PROBSTAB

STARWARS

DischargeBRStore

WL

DEMSD

CRC BU S

PROBSTAB

ETRF Ksat hA n

PFFOS

RF: Rainfall (time series) (m/d) ET: Evapotranspiration (m/d) Ksat: Saturated Hydraulic

Conductivity (m/d) hA: Air Entry Value (m) : Slope of SWRC (-) N: Porosity (-) RC: Root Cohesion (kPa) C: Soil Cohesion (kPa) : Internal friction angle BD: Bulk Unit Weight (kN/m3) S: Surcharge (kPa) BRStore: Bed rock store (m3) WL: Water level (m) : Volumetric moisture content PF: Probability of Failure FOS: Factor of Safety

Perched Water Level (m)Perched Water Level (m) Factor of Safety (with Factor of Safety (with root cohesion)root cohesion)

Factor of Safety (withFactor of Safety (without root cohesion)out root cohesion)

Sekhar et al., 2008

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NRI: Net Rainfall Intensity (time series) (m/sec)

Ksat: Saturated Hydraulic Conductivity (m/sec)

C: Cohesion (kPa) : Internal friction angle () uwv: Unit Weight of Water (Kgm/s2) uws: Unit Weight of Soil (Kgm/s2) idw: Initial depth of water (m) inf: Initial infiltration rate (m/sec) D: Diffusivity (m2/sec) SD: Soil depth (m) PP: Pressure head at maximum depth FOS: Factor of Safety (-)

uww uws SD DEMinfidw D Ksat C

NRI

TRIGRS

FOSPP

TRIGRSTRIGRS

FOS

Factor of Safety (with Factor of Safety (with root cohesion)root cohesion)

Factor of Safety (withFactor of Safety (without root cohesion)out root cohesion)

Sekhar et al., 2008

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StabilityIndex

Phimax Phimin T/Rmax T/Rmin Cmax Cmin

DEM SINMAP

Scenario actual inputs

Scenario default inputs

SINMAPSINMAP



Sekhar et al., 2008

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StabilityIndex

DEM SHALSTAB

Phi q/t CSden



Scenario default inputs Scenario actual inputs

SHALSTABSHALSTAB

Sekhar et al., 2008

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Model comparisonModel comparison STARWARS+PROBSTAB provided better results than other modelsSTARWARS+PROBSTAB provided better results than other models

99 Area of failure over estimatedArea of failure over estimated99 Temporal failure conditions predicted fairly wellTemporal failure conditions predicted fairly well

SHALSTAB provided better results than SINMAPSHALSTAB provided better results than SINMAP99 Not to over look the capability of SINMAP for distributed Not to over look the capability of SINMAP for distributed

parameterizationparameterization Applicability of TRIGRS is limited in data poor regions because Applicability of TRIGRS is limited in data poor regions because of:of:

99 Lack of rainfall intensity data in most landslide hazard prone aLack of rainfall intensity data in most landslide hazard prone areas of reas of the developing worldthe developing world

99 Lack of knowledge of initial conditionsLack of knowledge of initial conditions

8

2.8

SHALSTAB(limited to stability index

-2.5)

13

3.7

SINMAP(limited to lower

threshold)

1518Known landslide locations

predicted failed during the critical season (FOS

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ValidationValidation

Best validation is to wait and see Very few publications on checking landslide

hazard maps (or risk maps) some time later. Now it is based on historical data. Dynamic deterministic modeling allows to

validate when and where Other methods only where.

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ValidationValidation Several studies have been done on comparing

method Very few studies have been done on checking old

landslide maps.

Partition of the data setEstimation Group and Validation Group

Methods of Crossvalidation

- random validation

- spatial validation (moving window)

- temporal validation

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Success & Prediction rateSuccess & Prediction rateP

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Percentage of weight map ordered from high to low

70 percent of all new landslides is located in 30 % of the map with highest prediction scores

Success rate: How well the model performs.Prediction rate: How well the model predicts

(Chung & Fabbri, 1999)

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Success rateSuccess rate

ANN with continuous variables

ANN with classes variables

Weight of evidence all variables

Weight of evidence combining variables

Topples

Slides

Large rockslides

Rockfalls

Debrisflows

Castellanos, Melchiore and Van Westen, 2008

If you use heuristic analysis, the success rate could be very high

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Results..Results..

91.7 %1 %

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From susceptibility to hazardFrom susceptibility to hazard

4426 buildings

9645buildings

22019buildings

Risk = Hazard * Vulnerability * Amount

How much percentage of the high, moderate and low hazard classes may be affected by landsides?

In which period will these landslides occur? What is the vulnerability to landslides?

Results using mapping unitsHigh Moderate Low

Known nowStill to doOnly susceptibility

Hazard = Spatial probability * Temporal probability

The temporal probability that landslides may occur due to a triggering event. Here we will link the return period of the triggering event with the landslides that are caused by it. We have differentiated return periods of: 50, 100, 200, 300 and 400 years.

The spatial probability that a particular area would be affected by landslides of the given temporal probability. This is calculated as the landslide density within the landslide susceptibility class.

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From susceptibility to hazardFrom susceptibility to hazardMillion dollar information!!!

Landslide related to different return periods

Landslide_ID map If the indication of the high, moderate and low areas susceptibility is correct, different landslide events with different return periods will give different distributions of landslides in these classes.

The probability can be estimated by multiplying the temporal probability (1/return/period for annual probability) with the spatial probability (= what is the chance that 1 pixel is affected)

Susceptibility

Cross

Density in high

Density inmoderate

Density inlow

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Calculating hazardCalculating hazardAssumption is that events with a larger return period

will also trigger those landslides that would be triggered by events from smaller return periods

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Return periods

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From susceptibility to hazardsFrom susceptibility to hazards


ConclusionsConclusions

No

No

Yes

Process-basedAnalysis

Quantitative methodsQualitative methods

NoYes/NoYesYes> 1:100,000

YesYesYesYes1:25,000 1:50,000

YesNoYesYes< 1:10,000

Neural networkAnalysis

StatisticalAnalysis

HeuristicAnalysisInventoryScale

based on Soeters & van Westen (1996) and Aleotti & Chowdhury (1999)

Relation between scale and landslide susceptibility models

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ConclusionsConclusions Separate landslide susceptibility models

are needed: For different landslide types For different failure mechanisms

Sometimes it is better to skip susceptibility assessment. If you already know the landslide initiation areas If landslides are caused by reactivation of old ones

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Conclusions: methods..Conclusions: methods..

There are many papers that compare methods for susceptibility assessment

Susceptibility research is much more model driven, than data driven.

Much more emphasis should be given on the analysis of appropriate input data, and of the inclusion of expert opinion in the analysis.

Most methods report that around 75% of the landslides were predicted. What about the 25%?

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Conclusions: dataConclusions: data The availability of data greatly determines the

possibility of using particular susceptibility methods

Physical based models require detailed soil/rock characteristics

Depends on the homogeneity of the area Dont simple use the factors everyone is using:

GIS-based factor derived from DEMs are easy to make but are they also useful?

Strong relation between failure mechanism and factors to collect.

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ConclusionsConclusions Validation.

A susceptibility map is useless unless it is validated. Spatial validation Temporal validation

Validation of statistically derived results are often more difficult

How long is a susceptibility map valid? As soon as any of the (intrinsic or triggering) factors

changes, e.g.: Road construction Climate change

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RiskCityRiskCityTraining package on landslide Training package on landslide

susceptibility, hazard and risk assessmentsusceptibility, hazard and risk assessment

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Discussion:Discussion:

What would be the best methods to use in the Mountain risk study areas? Valtellina? Firenze? Dolomites? Andorra? Barcelonette? Swiss areas?

= landslide = susceptibility

02 mountainrisks intensivecourse barcelona 08 vanwesten susceptibility

Documents

landslide of certain

probability type

given magnitude

initiation of landslide

particular type

given time

geoinformation science

probability of occurrence