A NEW METHOD FOR DETERMINATION OF MOST LIKELY A NEW METHOD FOR DETERMINATION OF MOST LIKELY INITIATION POINTS AND EVALUATION OF DIGITAL TERRAIN INITIATION POINTS AND EVALUATION OF DIGITAL TERRAIN

MODEL SCALE IN TERRAIN STABILITY MAPPINGMODEL SCALE IN TERRAIN STABILITY MAPPING

Paolo TarolliPaolo Tarolli11 and David G. Tarbotonand David G. Tarboton22

11University of Padova, Land and Agroforest Environments DepartmenUniversity of Padova, Land and Agroforest Environments Department, Padova, ITALY (t, Padova, ITALY (paolo.tarolli@unipd.it) ) 22Utah State University, Civil & Environmental Engineering DepartmUtah State University, Civil & Environmental Engineering Department, Logan, UT ent, Logan, UT (dtarb@cc.usu.edu)

PhysicallyPhysically--based models have been used previously to model and map the spatbased models have been used previously to model and map the spatial distribution of shallow debris slides, and areas of potentiaial distribution of shallow debris slides, and areas of potential instability. Here we l instability. Here we use the SINMAP stability index (SI) defined as the probability tuse the SINMAP stability index (SI) defined as the probability that the factor of safety is greater than 1. We introduce a new ahat the factor of safety is greater than 1. We introduce a new approach for determining the pproach for determining the Most Most Likely Initiation Point (MLIP)Likely Initiation Point (MLIP) by identifying the grid cell with critical (lowest) stability iby identifying the grid cell with critical (lowest) stability index on each downslope path from ridge to valley. Only potentialndex on each downslope path from ridge to valley. Only potential initiation initiation points less than a threshold are considered to avoid identificatpoints less than a threshold are considered to avoid identification of stable locations on downslope paths that do not contain aion of stable locations on downslope paths that do not contain any unstable locations. Mapped or ny unstable locations. Mapped or observed landslides are often used to evaluate the effectivenessobserved landslides are often used to evaluate the effectiveness of model derived terrain stability maps. The accuracy of modelsof model derived terrain stability maps. The accuracy of models depends on the quality of input depends on the quality of input variables, in particular the digital terrain model (DTM) from whvariables, in particular the digital terrain model (DTM) from which many of the input variables for terrain stability models areich many of the input variables for terrain stability models are derived. In this paper we use airborne derived. In this paper we use airborne laser altimetry (LIDAR) derived elevation data for testing the elaser altimetry (LIDAR) derived elevation data for testing the effect of different DTM grid cell size resolution on the modelingffect of different DTM grid cell size resolution on the modeling of shallow landslides in a small basin of shallow landslides in a small basin located in the Northeastern Region of Italy. Physically based molocated in the Northeastern Region of Italy. Physically based models quantify the potential instability at each location. Becausdels quantify the potential instability at each location. Because in our study area the mapped e in our study area the mapped landslides included landslide runout zones we found that the dirlandslides included landslide runout zones we found that the direct comparison of SI within and outside of mapped landslides wasect comparison of SI within and outside of mapped landslides was not effective. However when not effective. However when MLIP was used we found appreciable differences between the densiMLIP was used we found appreciable differences between the density of MLIP points within and outside mapped landslides with ratity of MLIP points within and outside mapped landslides with ratios as large as three or more, os as large as three or more, demonstrating the utility of MLIP for evaluating terrain stabilidemonstrating the utility of MLIP for evaluating terrain stability maps. ty maps.

ABSTRACTABSTRACT

The MLIP method is based on the DThe MLIP method is based on the D∞∞ algorithm (Tarboton, 1997) for the algorithm (Tarboton, 1997) for the representation and calculation of flow direction and on the stabrepresentation and calculation of flow direction and on the stability index (SI) ility index (SI) from the SINMAP model. The stability index (SI) is defined as thfrom the SINMAP model. The stability index (SI) is defined as the probability e probability that a location is stable (FS > 1) assuming uniform probability that a location is stable (FS > 1) assuming uniform probability distributions of distributions of the uncertain geophysical parameters (Pack et al., 1998). the uncertain geophysical parameters (Pack et al., 1998).

MINIMUM DOWNSLOPE FUNCTIONMINIMUM DOWNSLOPE FUNCTION

Most Likely Initiation Points (MLIP) are where Most Likely Initiation Points (MLIP) are where SISIupsups = SI = SI downdown = SI < threshold= SI < threshold

C = (Cr + Cs)/(hρsg) r = ρw/ρs

Grid cell with lowest value at or upslope of each grid cellGrid cell with lowest value at or upslope of each grid cell

sinθ

tanr,1sinθ

aTR

min1cosθC

FS

forcesingDestabilizforcessistiveRe

FSsafety, of Factor

φ

−+=

=

SINMAP, SI = probability (FS>1)SINMAP, SI = probability (FS>1)

Failure plane

θ = atan S

Ground surface

Water table hw

Dw

Dh

Resisting forces

Resisting forcesDestabilizing forces

Destabilizing forces

T = soil transmissivity (m2/hr)

R = steady state recharge (m/hr)

SISI

Flow DirectionFlow Direction

min SI downslopemin SI downslope

min SI upslopemin SI upslope

MLIPMLIP

MINIMUM UPSLOPE FUNCTIONMINIMUM UPSLOPE FUNCTION

ALGORITHM FOR CALCULATION MLIPALGORITHM FOR CALCULATION MLIP

TERRAIN STABILITY MODELTERRAIN STABILITY MODEL

THEORY OF MLIPTHEORY OF MLIP

Points with Points with minimum minimum value of SI value of SI along flow along flow pathpath

MLIP for all flow pathsMLIP for all flow paths

MLIP MODELMLIP MODEL

DD∞∞ Algorithm, Tarboton (1997)Algorithm, Tarboton (1997) SINMAP SI MapSINMAP SI Map

Grid cell with lowest value at or downslope of each grid cellGrid cell with lowest value at or downslope of each grid cell ++

Steepest directiondownslope

α1α2

1

234

5

67

8

Proportion flowing toneighboring grid cell 3is α2/(α1+α2)

Proportionflowing toneighboringgrid cell 4 isα1/(α1+α2)

Steepest directiondownslope

α1α2

1

234

5

67

8

Proportion flowing toneighboring grid cell 3is α2/(α1+α2)

Proportionflowing toneighboringgrid cell 4 isα1/(α1+α2)

Flow direction measured ascounter-clockwise anglefrom east

0.8

0.5

0.10.1

0.1

0.1

0.8

0.5

0.10.1

0.1

0.1

0.1

0.1

0.10.1

0.7

0.8

0.1

0.1

0.10.1

0.7

0.8

0.90.80.70.40.3

0.80.50.20.40.5

0.40.20.10.80.9

0.10.30.30.70.7

0.80.40.70.50.8

0.90.80.70.40.3

0.80.50.20.40.5

0.40.20.10.80.9

0.10.30.30.70.7

0.80.40.70.50.8

0.90.80.70.40.3

0.80.50.20.40.5

0.40.20.10.80.9

0.10.30.30.70.7

0.80.40.70.50.8

0.90.80.70.40.3

0.80.50.20.40.5

0.40.20.10.80.9

0.10.30.30.70.7

0.80.40.70.50.8

0.90.80.70.40.3

0.80.50.20.40.5

0.40.20.10.80.9

0.10.30.30.70.7

0.80.40.70.50.8

0.90.80.70.40.3

0.80.50.20.40.5

0.40.20.10.80.9

0.10.30.30.70.7

0.80.40.70.50.8

0.80.80.70.40.3

0.80.50.20.20.4

0.40.20.10.10.1

0.10.10.10.10.1

0.10.10.10.10.1

0.80.80.70.40.3

0.80.50.20.20.4

0.40.20.10.10.1

0.10.10.10.10.1

0.10.10.10.10.1

0.30.3

0.20.2

0.20.20.10.1

0.10.1

0.30.3

0.20.2

0.20.20.10.1

0.10.1

0.80.10.20.30.3

0.80.10.20.40.5

0.10.20.10.80.9

0.10.30.50.70.7

0.80.40.70.50.8

0.80.10.20.30.3

0.80.10.20.40.5

0.10.20.10.80.9

0.10.30.50.70.7

0.80.40.70.50.8

Flow PathFlow Path MLIP along all flow pathsMLIP along all flow pathsFlow PathFlow Path Minimum SI value along flow pathMinimum SI value along flow path

LIDARLIDARPoint Elevation

Data

DTMDTM

Topogrid TauDEMTauDEMD∞

Slope

Flow Direction

TauDEMTauDEMArea D∞

Contributing Area

SINMAPSINMAP

SISI

Path Min

Min Upslope

Min Downslope

MLIPMLIP

Field Survey / Field Survey / Laboratory Laboratory

AnalysisAnalysis

Geotechnical parameters

ReferencesReferencesBorga, M., Dalla Fontana, G., and Cazorzi, F., 2002b: Analysis of topographic and climatic control on rainfall-triggered shallow landsliding using a quasi-dynamic wetness index. J. Hydrol., 268 (1-4), 56-71.Montgomery, D.R., and Dietrich, W.E., 1994. A physically based model for the topographic control on shallow landsliding. Water Resour. Res., 30(4), 1153-1171.Pack, R., et al., 1998. The SINMAP Approach to Terrain Stability Mapping. Submitted to 8th Congress of the International Association of Engineering Geology, Vancouver, British Columbia, Canada. Tarboton, D.G., 1997. A new method for the determination of flow directions and upslope areas in grid digital elevation models. Water Resour. Res. 33, 309–319.

AcknowledgementsAcknowledgementsThe authors are grateful to “Servizio Territorio Montano e Manutenzioni” (Direzione Centrale Risorse Agricole, Naturali, Forestali e Montagna) of Friuli Venezia Giulia Region for the collaboration in field surveys and furniture of lidar, and aerial photographs database. This work has benefit from discussion with Kiran Chinnayakanahalli. We thank Michela Dini and Luca Bincoletto that provided critical support during field work and data collect. Tarolli also acknowledges the contribute of Giancarlo Dalla Fontana and Marco Borga during the prework discussion, and the support of Ing. Aldo Gini Foundation on the scholarship period at Utah State University .

CONCLUSIONSCONCLUSIONS

RESULTSRESULTS

STUDY AREASTUDY AREA METHODOLOGYMETHODOLOGY

(i)(i) Digital Terrain Model (DTM) computed from LIDAR points at multipDigital Terrain Model (DTM) computed from LIDAR points at multiple le resolutions: 50m, 20m, 10m, 5m, and 2m. resolutions: 50m, 20m, 10m, 5m, and 2m.

(ii)(ii) Terrain stability index, SI, computed for each resolution DTM frTerrain stability index, SI, computed for each resolution DTM from SINMAP om SINMAP using default parameters using default parameters

(iii)(iii) MLIP grids evaluated for each DTM resolution SI grid for a rangeMLIP grids evaluated for each DTM resolution SI grid for a range of of threshold SI values.threshold SI values.

(iv)(iv) A range of thresholds applied to SI grid for each DTM resolutionA range of thresholds applied to SI grid for each DTM resolution to to categorize terrain instability. categorize terrain instability.

The quality of the SI map is evaluated by comparing the density The quality of the SI map is evaluated by comparing the density of MLIP points of MLIP points within and outside observed landslide area within and outside observed landslide area

)area basin/P(

)area lanslide/P(tioDensity Ra

bas

lds=

PPldslds, and P, and Pbasbas are the number of cells within the landslide area and within thare the number of cells within the landslide area and within the e basin as a whole, mapped by the approach. When used with SI thebasin as a whole, mapped by the approach. When used with SI these are grid se are grid cells less than a SI threshold. When used with MLIP these are gcells less than a SI threshold. When used with MLIP these are grid cells rid cells identified by the MLIP upslope and downslope criteria and less tidentified by the MLIP upslope and downslope criteria and less than a SI han a SI threshold. Threshold ranges are given at the left of the table threshold. Threshold ranges are given at the left of the table below. below.

1111111111SI 0SI 0--infiniteinfinite1.311.311.291.291.291.291.271.271.331.33SI 0SI 0--112.172.172.242.242.232.232.272.272.252.25SI 0SI 0--0.50.52.342.342.352.352.612.612.472.473.413.41SI 0SI 0--0.20.2

2255101020205050Grid resolution (m)Grid resolution (m)

2.562.562.912.913.513.511.381.381.461.46MLIP SI 0MLIP SI 0--infiniteinfinite2.572.572.912.913.533.531.421.421.531.53MLIP SI 0MLIP SI 0--112.572.572.932.933.663.661.911.913.193.19MLIP SI 0MLIP SI 0--0.50.52.572.572.972.973.813.811.831.835.235.23MLIP SI 0MLIP SI 0--0.20.2

2255101020205050Grid resolution (m)Grid resolution (m)

DENSITY RATIODENSITY RATIO

A.A. THE THE MOST LIKELY INITIATION POINTMOST LIKELY INITIATION POINT (MLIP) METHOD IS SUGGESTED AS A NEW (MLIP) METHOD IS SUGGESTED AS A NEW WAY TO EVALUATE TERRAIN STABILITY MODELS WHEN MAPPED LANDSLIDE WAY TO EVALUATE TERRAIN STABILITY MODELS WHEN MAPPED LANDSLIDE AREA INCLUDES RUNOUT ZONESAREA INCLUDES RUNOUT ZONES

B.B. THE HIGHER DENSITY RATIO FOR THE MLIP APPROACH THAN FROM THE HIGHER DENSITY RATIO FOR THE MLIP APPROACH THAN FROM CATEGORIES DEVELOPED FROM THE SI GRID ALONE, VALIDATES THE CATEGORIES DEVELOPED FROM THE SI GRID ALONE, VALIDATES THE POTENTIAL OF THE MLIP METHODPOTENTIAL OF THE MLIP METHOD

A.A. MAP LANDSLIDE RUNOUT AREA FROM MLIP TRIGGER POINTS MAP LANDSLIDE RUNOUT AREA FROM MLIP TRIGGER POINTS

B.B. INVESTIGATE INVESTIGATE ““SCALE EFFECTSCALE EFFECT”” WITH INCREASING RESOLUTION OF DTMWITH INCREASING RESOLUTION OF DTM

C.C. A DTM RESOLUTION OF 10m GIVES THE HIGHEST MLIP DENSITY RATIOS A DTM RESOLUTION OF 10m GIVES THE HIGHEST MLIP DENSITY RATIOS SUGGESTING THAT FOR THIS DATA THE 10m RESOLUION IS OPTIMAL. (THSUGGESTING THAT FOR THIS DATA THE 10m RESOLUION IS OPTIMAL. (THE ONE E ONE EXCEPTION FOR A 50m DTM IS SPURIOUS DUE TO SMALL NUMBER OF PIXELEXCEPTION FOR A 50m DTM IS SPURIOUS DUE TO SMALL NUMBER OF PIXELS)S)

D.D. THE MLIP APPROACH PROVED USEFUL FOR EVALUATING THE QUALITY OF A THE MLIP APPROACH PROVED USEFUL FOR EVALUATING THE QUALITY OF A SI SI MAP WHERE MAPPED LANDSLIDES INCLUDED RUNOUT ZONES AND PROVED MAP WHERE MAPPED LANDSLIDES INCLUDED RUNOUT ZONES AND PROVED USEFUL FOR TESTING THE PERFORMANCE OF SI DERIVED FROM DIFFERENT USEFUL FOR TESTING THE PERFORMANCE OF SI DERIVED FROM DIFFERENT RESOLUTION DTMRESOLUTION DTMSS

FUTURE WORKFUTURE WORKC.C. TEST THE MLIP APPROACH WITH OTHER TERRAIN STABILTY MODELS LIKE TEST THE MLIP APPROACH WITH OTHER TERRAIN STABILTY MODELS LIKE SHALSTAB (Montgomery and Dietrich, 1994) AND QUASI DYNAMIC (BorgSHALSTAB (Montgomery and Dietrich, 1994) AND QUASI DYNAMIC (Borga et al., 2002).a et al., 2002).

D.D. ANALYZE EFFECTS OF A VERY HIGH RESOLUTION DTM OBTAINED BY LIDARANALYZE EFFECTS OF A VERY HIGH RESOLUTION DTM OBTAINED BY LIDARSURVEY IN A REGION WITHOUT HIGH TREE FORESTSURVEY IN A REGION WITHOUT HIGH TREE FOREST

SLOPE SLOPE ““ SCALE EFFECTSCALE EFFECT”” PROBLEMPROBLEM

Computed slope is more variable with higher values for a smallerComputed slope is more variable with higher values for a smaller DTM grid resolution. DTM grid resolution.

2075Maximum elevation (m.a.s.l.)

470Minimum elevation (m.a.s.l.)

1244Average elevation (m.a.s.l.)

10.7Catchment area (km2)

0.5 (4.7% of basin)Area of Landslides (km2)

2200Mean annual precipitation (mm)

77Maximum slope gradient (°)

33Mean slope gradient (°)

LANDSLIDE AREALANDSLIDE AREA

10 m10 m

1 m1 m

LOW SLOPELOW SLOPE

HIGH SLOPEHIGH SLOPE

MLIPMLIP