A new method for determination of most likely landslide initiation

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A new method for determination of most likely landslideinitiation points and the evaluation of digital terrain

model scale in terrain stability mappingP. Tarolli, D. G. Tarboton

To cite this version:P. Tarolli, D. G. Tarboton. A new method for determination of most likely landslide initiation pointsand the evaluation of digital terrain model scale in terrain stability mapping. Hydrology and EarthSystem Sciences Discussions, European Geosciences Union, 2006, 10 (5), pp.663-677. <hal-00305017>

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Hydrol. Earth Syst. Sci., 10, 663–677, 2006www.hydrol-earth-syst-sci.net/10/663/2006/© Author(s) 2006. This work is licensedunder a Creative Commons License.

Hydrology andEarth System

Sciences

A new method for determination of most likely landslide initiationpoints and the evaluation of digital terrain model scale in terrainstability mapping

P. Tarolli 1 and D. G. Tarboton2

1Department of Land and Agroforest Environments, AGRIPOLIS, University of Padova, 35020 Legnaro, Padova, Italy2Department of Civil and Environmental Engineering, Utah State University, Logan, Utah, USA

Received: 10 January 2006 – Published in Hydrol. Earth Syst. Sci. Discuss.: 6 April 2006Revised: 5 July 2006 – Accepted: 21 September 2006 – Published: 27 September 2006

Abstract. This paper introduces a new approach for deter-mining the most likely initiation points for landslides frompotential instability mapped using a terrain stability model.This approach identifies the location with critical stability in-dex from a terrain stability model on each downslope pathfrom ridge to valley. Any measure of terrain stability maybe used with this approach, which here is illustrated usingresults from SINMAP, and from simply taking slope as anindex of potential instability. The relative density of mostlikely landslide initiation points within and outside mappedlandslide scars provides a way to evaluate the effectivenessof a terrain stability measure, even when mapped landslidescars include run out zones, rather than just initiation loca-tions. This relative density was used to evaluate the utilityof high resolution terrain data derived from airborne laseraltimetry (LIDAR) for a small basin located in the North-eastern Region of Italy. Digital Terrain Models were derivedfrom the LIDAR data for a range of grid cell sizes (from 2 to50 m). We found appreciable differences between the densityof most likely landslide initiation points within and outsidemapped landslides with ratios as large as three or more withthe highest ratios for a digital terrain model grid cell size of10 m. This leads to two conclusions: (1) The relative den-sity from a most likely landslide initiation point approach isuseful for quantifying the effectiveness of a terrain stabilitymap when mapped landslides do not or can not differentiatebetween initiation, runout, and depositional areas; and (2)in this study area, where landslides occurred in complexesthat were sometimes more than 100 m wide, a digital terrainmodel scale of 10 m is optimal. Digital terrain model scaleslarger than 10 m result in loss of resolution that degrades theresults, while for digital terrain model scales smaller than 10

Correspondence to:P. Tarolli([email protected])

m the physical processes responsible for triggering landslidesare obscured by smaller scale terrain variability.

1 Introduction

Landsliding associated with rainstorms is a major processof landscape evolution on steep hillslopes. Shallow lands-liding in steep, soil-mantled landscapes can generate debrisflows which scour low-order channels, deposit large quan-tities of sediment in higher order channels and pose a sig-nificant hazard. The hazard occurs where development hasencroached on debris flow source and run-out areas. A vari-ety of approaches are available to assess landslide hazard andproduce maps portraying its spatial distribution (landslidehazard mapping). In the last decade, process-based theoriesand models have been developed that represent the essentialprocesses controlling shallow landsliding, yet remain simpleenough that they can be calibrated and validated using ob-served landslides inventories. Many of these Terrain StabilityModels are based upon the infinite slope stability model (e.g.Hammond et al., 1992; Montgomery and Dietrich, 1994; Wuand Sidle, 1995). Dietrich et al. (1992) and Montgomery andDietrich (1994) developed a simple physically based model,SHALSTAB, based on digital terrain data, which couples ashallow steady state saturated subsurface flow model with aninfinite slope stability model. SHALSTAB is based on theassumptions that shallow subsurface flow dictates the porepressure field and that steady state flow mimics the spatialpattern of soil pore pressures during transient storms and canbe used to map the relative potential for shallow landslidingacross a landscape. Pack et al. (1998) introduced a stabil-ity index approach (SINMAP) to terrain stability mapping, amethodology based upon the same concepts as Montgomery

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664 P. Tarolli and D. G. Tarboton: Most likely landslide initiation points

and Dietrich (1994) in that it combines steady-state hydro-logic concepts with the infinite slope stability model. SIN-MAP differs however in that parameter uncertainty is incor-porated through the use of uniform probability distributionsfor uncertain parameters and that rather than critical rainfall,the measure of stability used is the probability that factor ofsafety is greater than 1.

The steady state subsurface flow assumptions used byMontgomery and Dietrich (1994) and incorporated into SIN-MAP (Pack et al., 1998) have been criticized for beingrestrictive (Iverson, 2000). Iverson’s analysis, based onRichards equation for unsaturated subsurface flow, suggestedthat the time scale necessary for establishment of steady stateconditions was significantly larger than most rainstorms.Consequently, he questioned the use of models based onsteady state assumptions. Hillslope flow processes that leadto the build up of pore pressures that trigger landslides arecomplex and sometimes involve preferential pathways notalways amenable to description using the Richards equationthat was the basis for Iverson’s criticism. Nevertheless, fol-lowing Beven et al. (1995) we feel that the general tendencyof water to flow downhill is amenable to macroscale concep-tualization and that the approach of SINMAP (Pack et al.,1998) and SHALSTAB (Montgomery and Dietrich, 1994)that relate the relative wetness at a location to the upslopecontributing area captures these topographic effects in a sim-ple way. Basically these models represent relative wetness asRa, wherea is the specific catchment area (contributing areaper unit contour width) andR is a constant that can be inter-preted as steady state infiltration. ButR can also more gen-erally be interpreted as a proportionality constant reflectingthe likelihood of greater wetness and higher pore pressuresin convergent areas with largera. Barling et al. (1994) de-veloped a quasi-dynamic wetness index that addresses someof the shortcomings of a steady state wetness index, but re-quires more detailed information on storm duration and soilproperties. Borga et al. (2002) use a quasi-dynamic wetnessindex in response to a rainfall of a specific duration and fre-quency to develop a more general terrain stability model. Wuand Sidle (1995) simulate pore pressure build up in responseto a specific time series of rainfall inputs using an explicitspatially distributed model. While these more detailed ap-proaches clearly represent significant advances, they demandmore information about landslide triggering rainstorms thanis typically available when the purpose is identification of po-tential instability for screening or planning purposes. Theyalso require more detailed information on soil properties.

Methods to spatially evaluate slope stability models lagthe development of models themselves. Dietrich et al. (2001)evaluated the SHALSTAB model using landslide density andcumulative percent of landslides and area in each stability in-dex class. Borga et al. (2002) extended the cumulative per-cent idea to cumulative frequency plots of stability index atmapped landslide initiation locations in comparison to thecumulative frequency over the entire domain to quantify the

discriminating capability of a terrain stability map. Chin-nayakanahalli (2004) used a similar approach but extendedthis to construct a threshold independent integral comparisonmeasure from the integral of cumulative frequency plots thatcould be used with a generalized likelihood uncertainty esti-mation approach to optimize model parameters and quantifyuncertainty. Increasingly statistical methods involving splitsampling techniques, either in time or space are also beingused with measures of a terrain stability model’s discriminat-ing capability to evaluate terrain stability models (e.g. Chungand Fabbri, 2003, 2005; Brenning, 2005). Begueria (2006)discusses the difficulties associated with validating naturalhazard models due to the different proportion of positive andnegative cases in typical data. He uses a threshold indepen-dent receiver operating characteristic plot and its integral asa global accuracy statistic.

The accuracy of procedures relying on process-based the-ories depends on the quality of topographic data and is lim-ited by the underlying assumptions used in the models, whichcannot account for many factors which are known to in-fluence landslide hazard, such as mechanically weak rocks,springs, locally high or low root strength and soil thickness,to name a few. With respect to the quality, and resolutionof topographic data the accuracy of base point survey dataand the method used to interpolate the Digital Terrain Modelfrom point survey data can influence the results of terrainstability models. New survey techniques have been intro-duced in the last few years; an example of these is the use oflaser sensors on aircraft (Akermann, 1999; Kraus and Pfeifer,2001; Briese, 2004). This technology, named LIDAR (LIghtDetection And Ranging), provides high quality digital terraindata, and provides more information about land cover thanwas previously available. The application of airborne laseraltimetry technology to slope stability modeling has the po-tential to improve model performance and benefit land man-agement.

There may be some limitations to the improvement oflandslide modeling which can be achieved by using very fineresolution topographic data. Regardless of the algorithms ortype of digital terrain model used, all digital terrain modelanalyses depend crucially on the assumption that the flowpathways will be predominantly controlled by the surface to-pography of the catchment. Even in shallow systems, thebedrock topography may have a greater control on downs-lope saturated flow than the surface topography (Freer etal., 2002). It is likely that differences between surface andbedrock topography is relatively greater at very fine digi-tal terrain model resolution; therefore, very fine topographicdata may lose representativeness for the modeling of subsur-face flow. At very fine resolution slopes from the DTM mayalso lose their representativeness as the slope of the failuresurface in the infinite slope stability model. There are thusphysical and modeling limits on the utility of fine resolutionterrain data.

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P. Tarolli and D. G. Tarboton: Most likely landslide initiation points 665

Practical limits on LIDAR accuracy are still being defined(McKean and Roering, 2004). Data errors can be describedas those originating from the hardware/software componentsof the LIDAR system, those related to the mission designand conduct, and those associated with the laser target char-acteristics (e.g. topography and vegetation contamination inthe distribution of lidar elevation data points) (McKean andRoering, 2004).

In this paper we present a new method for determining themost likely landslide initiation points. This method is re-ferred to as MLIP. The method introduced identifies the gridcell with critical (lowest) stability index on each downslopepath from ridge to valley. If a stability index threshold isspecified the MLIP are a subset of the points with stability in-dex less than the threshold with the special property that theyare flow path specific minima. This makes MLIP points bet-ter points to use in the evaluation of a terrain stability modelwhen the observations being used to evaluate the model arenot limited to initiation locations, but include run out anddeposition areas. A stability index attempts to quantify thepotential for landslide initiation. Evaluation of the effective-ness of a stability index is inhibited when observations do notseparate initiation from run out and deposition areas. The useof MLIP avoids these problems and tabulation of the densityof MLIP points inside and outside such mapped areas pro-vides a quantification of the effectiveness of a terrain stabil-ity model in terms of the density of points within the mappedlandslide scar where landslides are most likely to have ini-tiated. The use of a threshold avoids identification of stablelocations as MLIP on flow paths that do not contain any un-stable locations. We evaluate the benefits of this method andthe sensitivity to varying the grid size resolution of the digi-tal terrain model used for mapping landslide areas with thismethod. The most likely landslide initiation point approachcan be applied with any spatial index of terrain stability, em-pirically or physically derived. Here the most likely landslideinitiation approach was applied using terrain slope as a sim-ple empirical measure of terrain stability. The most likelylandslide initiation point approach was then also applied toa Stability Index field obtained from SINMAP using the de-fault parameters suggested by Pack et al. (1998). The SIN-MAP stability index is used as a convenient example for thedevelopment and evaluation of this method. Comparisons ofthe most likely landslide initiation point approach applied toSINMAP SI and to slope demonstrates how the most likelylandslide initiation points can be used to compare two differ-ent terrain stability models.

The flow paths used to evaluate most likely landslide initi-ation locations were determined from theD∞ algorithm in-troduced by Tarboton (1997) and available as part of the opensource TauDEM software (http://www.engineering.usu.edu/dtarb/taudem). A range of stability index threshold valueswere used to define most likely landslide initiation points.The ratio of the density of most likely landslide initiationpoints inside and outside mapped landslide areas was used to

quantify the ability of the terrain stability map to discrimi-nate terrain instability. High values of the most likely land-slide initiation point density ratio indicate good model per-formance. This approach was applied to a study area locatedin Northern Region of Italy where landslide runout areas hadbeen mapped from high resolution aerial photographs. Thebroad question that we address is: What is the influence ofhigh resolution LIDAR derived digital terrain model on ter-rain stability mapping? Specifically we examined what addi-tional information is obtained from the most likely landslideinitiation point method with respect to the standard approachfor mapping landslides based on a stability index, and howsensitive is the most likely landslide initiation point methodto the digital terrain model grid resolution?

The paper is divided into six sections. In Sect. 2 we de-fine most likely landslide initiation points. Section 3 de-scribes the field area in Northern Italy where the approachwas tested. Section 4 describes the method used to calculatethe density of most likely landslide initiation points withinmapped landslide runout zones used to evaluate the model.Sections 5 and 6 present and discuss the results. In Sect. 7we conclude with a summary of our findings.

2 Most likely landslide initiation point definition

A most likely landslide initiation point (MLIP) is defined asthe point along each flow path that has critical value of astability index corresponding to the most unstable locationalong the flow path. This is illustrated in Fig. 1 using a ter-rain stability index map obtained from SINMAP. Figure 1ashows four flow paths from ridge top to valley and alongeach path the grid cell with lowest SINMAP stability indexis identified. In Fig. 1b the most likely landslide initiationpoints along all flow lines are identified. Physically, mostlikely landslide initiation points are the most unstable pointsalong a downslope path from ridge to valley according to theterrain stability model being used. Conceptually they canbe identified by tracing down from each grid cell until oneexits the region and marking the point where stability indexis critical. Depending on the stability index being used, themost critical stability index may be the lowest index value,as in the case of SINMAP, or the highest index value, as inthe case of slope. The actual algorithm for identifying mostlikely landslide initiation points works somewhat differentlyto take advantage of the efficiency of recursive geographicinformation system calculations.

3 Study area

3.1 Setting

The study area is the Miozza catchment, located in Car-nia, a tectonically active alpine region of north-eastern Italy

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http://www.engineering.usu.edu/dtarb/taudem


(a) (b)

Fig. 1. Illustration of most likely landslide initiation points (MLIP).(a) SINMAP Stability Index (SI) map with the locations of the loweststability index value along four example flow paths identified.(b) most likely landslide initiation points identified for all flow paths.

Fig. 2. Miozza basin location map.

(Fig. 2). The area of the Miozza basin is 10.7 km2. Eleva-tion ranges from 471 to 2075 m a.s.l. with an average valueof 1244 m a.s.l. The slope angle has an average value of33◦ with a maximum value of 77◦. The only significant hu-man activity in the basin is forestry. The area has a typicalNorth Eastern Alpine climate with short dry periods and amean annual precipitation of about 2200 mm. Recorded an-nual precipitation ranges from 1300 to 2500 mm. Precipi-tation occurs mainly as snowfall from November to April;runoff is usually dominated by snowmelt in May and June.During summer, flash floods with heavy solid transport arecommon. Vegetation covers 94% of the area and consists offorest stands (74%), shrubs (10%) and mountain grassland(10%); the remaining 6% of the area is unvegetated land-slide scars and deposits. The geomorphologic setting of thebasin is typical of the eastern alpine region, with deeply in-cised valleys. Soil thickness varies between 0.2 m and 0.5 mon topographic spurs to depths of up 1.5 m in topographic

hollows. Part of the soil of Miozza basin is characterizedby morain formations with vegetated talus deposits. Thesecover the 40% of total area. Other soils are calcareous,calcareous-marly, and arenaceous formations that cover the35% of total area. The Miozza basin was chosen as a studyarea because it is representative of the lithological and phys-iographical conditions frequently observed in the Carnia re-gion where mapping landslide impacts is of interest, and be-cause detailed topographic, land use and geomorphologic in-formation from various sources (including LIDAR) is avail-able. Meteorological data are also available from the regionalweather service. Within the study area landslides have beenmapped and the area of erosion and shallow landslide scarsamounts to 0.5 km2, i.e. about 4.7% of the total catchmentarea. The average slope of the landslide scar area is 39◦.Most of these areas, in particular the largest single landslidearea (0.22 km2), are located at the head of the basin and oc-cur in complexes (Fig. 3) that result from the aggregation ofmany shallow landslides. Some of the landslides occurredat the bedrock interface while others occurred in the upperpart of soil (∼0.5 m deep). We do not have data on the spe-cific rainfall that triggered the landslides. The occurrence oflandslides in complexes is not the result of a specific rain-storm event, but a combined effect of different events includ-ing both extreme short rainfalls, low intensity long durationrainfalls, and snow melt. All the landslides mapped in thisstudy are believed to be shallow translational landslides.

3.2 Data

Aerial photography, at a resolution of 0.5 m, and field map-ping was used to develop a detailed inventory of sediment



Fig. 3. Miozza basin landslide scars identified from aerial photog-raphy: illustration of a landslide complex.

source, erosion and landslide scars within the study area asillustrated in Figs. 2 and 3. The mapped landslides comprisedthe entire landslide scar, including runout zone, not limited tothe locations where the landslides initiated. The most recentaerial photographs obtained in Autumn 2004 were used toidentify recent landslides not present in earlier surveys. Thelandslides identified in the aerial photographs were checkedin the field.

LIDAR data was collected during snow free conditionsin November 2003. The LIDAR data was acquired from ahelicopter using an ALTM 3033 OPTECH instrument fly-ing along strips at a height of 1000 m above ground level.The flying speed was 80 knots, scan angle 20 degrees andscan rate 33 KHz. The mean point density was specifiedto be greater than 1 point per m2 with first and last returnsrecorded. LIDAR returns were filtered into returns from veg-etation, and bare ground resulting in an irregular density ofground returns that after filtering had an average point den-sity of 0.26 points per m2 (3.8 m2 per point). Figure 4 illus-trates the distribution of bare ground LIDAR elevation pointswhich contains occasional coverage gaps, 5–7 m in extent, inregions of dense vegetation. In our study the areas with themost regular density of ground returns are the grassland andlandslide scar areas where only some shrubs are present.

4 Methods

Figure 5 illustrates the steps taken in processing the data tomap terrain stability index, and most likely landslide initia-tion points. The numbers in the description that follow corre-spond to elements on the flowchart. The bare ground LIDARdata (1) consists of a set of elevation data points (2). These

Fig. 4. Illustration of the irregular distribution of filtered LIDARbare ground elevation points.

are used as input to the ArcGIS TOPOGRID (3) functionto interpolate a digital terrain model (4) with specified gridcell size. The interpolation of digital terrain models frompoint data can result in artificial pits. Pits are regions of thedigital terrain model surrounded by higher elevations that donot drain anywhere. The TOPOGRID algorithm is a splinetechnique that uses slope rather than curvature as the splinepenalty function. This approach has been shown (Hutchin-son, 1988; Hutchinson, 1989) to limit the occurrence of pitsand produce digital terrain models that are hydrologicallycorrect in the sense that there are fewer pits which resultin internal drainage and incomplete contributing area values.The digital terrain model grids are used as input to the Tau-DEM D∞ function (5) that calculates the terrain flow direc-tion (6) and slope (7) grids. The TauDEM AreaD∞ func-tion (8) is then used to calculate the specific catchment area(9). Specific catchment area and slope are the terrain inputsto SINMAP (11). SINMAP also takes as input geotechnicaland hydrologic parameters (10) characterizing the physicalproperties of the study area. SINMAP produces a map ofthe terrain stability index,SI (12). The stability index maptogether with flow direction grid serve as the inputs to thePath Minimum function (13) that evaluates the minimum sta-bility index value upslope of (14) and downslope from (15)each grid cell. The minimum upslope and downslope grids,in combination with the stability index grid are used to de-termine the most likely landslide initiation point grid (16).Details of SINMAP and the algorithm for evaluation of mostlikely landslide initiation point are given below. This proce-dure was presented for most likely landslide initiation pointsdetermined from SINMAP. If slope, or another index of ter-rain stability is to be used the SINMAP output (12) needs to



Fig. 5. Most likely landslide initiation model flow diagram.

be replaced by the other index. For SINMAP the critical sta-bility index is the minimumSI value, but for other indices,such as slope, the critical stability index may be the maxi-mum value. In these cases the path maximum is evaluatedusing the maximum upslope and maximum downslope at el-ements (13) to (15) to determine the most likely initiationpoints for an index where maximum is critical.

Once stability index and most likely landslide initiationpoints have been derived they were evaluated by comparisonto the observed landslide areas using density ratios. Five dig-ital terrain models were interpolated for the study area withprogressively finer grid cell resolutions of 50, 20, 10, 5 and2 m. For each of these digital terrain models slope and stabil-ity index SI from SINMAP were used as measures of terraininstability. Slope provides a simple empirical measure of ter-rain instability. Most likely landslide initiation points werethen mapped for each digital terrain model grid and a rangeof stability index threshold values. For each stability indexmap corresponding to each digital terrain model grid resolu-tion and a range of stability index thresholds we counted thenumber of grid cells within and outside the mapped landslidearea with stability index less than the threshold value. Thiswas used to determine the stability index density ratio usingthe following equation

density ratio ofSI=(SIlds/landslide area)

(SIbas/basin area)(1)

whereSIlds is the number of stability index cells less than thethreshold that fall within the landslide area andSIbas is thetotal number of grid cells with stability index less than thethreshold within the basin. For the most likely landslide ini-tiation point map corresponding to each digital terrain modelresolution and stability index threshold we counted the num-ber of grid cells within and outside the mapped landslide

area. This was used to determine the most likely landslideinitiation point density ratio using the following equation

density ratio of MLIP=(Plds/landslide area)

(Pbas/basin area)(2)

where Plds and Pbas are respectively the number of mostlikely landslide initiation point grid cells within the landslidearea and within the basin as a whole. The density ratios cal-culated using this procedure were used to compare stabilityindex and most likely landslide initiation point maps devel-oped using different digital terrain model resolutions and sta-bility index threshold,Sthr. High values of the density ratiocorrespond to better performance of the model in discrimi-nating areas where landslides have been observed.

4.1 Stability index

SINMAP (Pack et al., 1998) is based upon the infinite slopestability model (e.g. Hammond et al., 1992; Montgomery andDietrich, 1994) that balances the destabilizing components ofgravity and the restoring components of friction and cohesionon a failure plane parallel to the ground surface with edgeeffects neglected (Fig. 6). The infinite slope stability modelfactor of safety (ratio of stabilizing to destabilizing forces)used in SINMAP is given by the following equation

FS =C + cosθ

[1 − min

(RT

asinθ

, 1)r]

tanφ

sinθ(3)

whereC is dimensionless cohesion,r is the ratio of the den-sity of water to the density of soil (ρw/ρs), θ is slope angle,φthe internal friction angle and min

(RT

asinθ

, 1)

is an estimateof the relative wetness derived following TOPMODEL as-sumptions (Beven and Kirkby, 1979) of steady state drainagedriven by a topographic gradient. Dimensionless cohesion,C, is defined as (Cr+Cs)/(hρsg), whereCr andCs are root



strength and soil cohesion terms,h is the thickness of thesoil (Fig. 6) andg the gravitational constant. In the expres-sion for relative wetness,a (m) is the specific catchment areaderived from the DTM (Tarboton, 1997),T is soil transmis-sivity (m2/hr). R (m/hr) is a proportionality factor that relatesrelative wetness to the specific catchment area which can beinterpreted as recharge under steady state assumptions.

In Eq. (3)a andθ are derived from the DTM. SINMAPtakes the geophysical parametersC, R/T and tanφ as un-certain and assumes that each has a uniform probability dis-tribution. The stability index (SI) is defined with respect tothese probability distributions as the probability that a loca-tion is stable, i.e. hasFS>1 (Pack et al., 1998).

SI = prob(FS > 1) (4)

In the special case thatFS is greater than 1 for all values ofC, R/T and tanφ within their uniform distribution rangesSIis reported as theFSvalue for the most conservative param-eter values, namely the minimumC and tanφ and maximumR/T .

With the physical parameters being taken as uncertain,the parameters input to SINMAP become the minimum andmaximum values of the ranges that define the uniform prob-ability distributions. In SINMAPT/R is used as an inputparameter rather thanR/T because it has a physical inter-pretation as the hillslope length required for saturation underparallel flow conditions.

4.2 Calculation of most likely landslide initiation points

The numerical evaluation of most likely landslide initiationpoints is achieved in three steps. Inputs are a grid of stabilityindex values and a grid of flow directions determined fromthe digital elevation model. First, based on the flow direc-tions, the minimum stability index value downslope of eachgrid cell is computed and saved as the minimum downslopegrid. Then, also based on the flow directions, the minimumstability index upslope from each grid cell is computed andsaved as the minimum upslope grid. Most likely landslideinitiation points are then identified as those points where theminimum downslope, minimum upslope and original stabil-ity index grid values are all equal. This procedure was fol-lowed so as to take advantage of the efficiency provided bya recursive evaluation of minimum downslope and minimumupslope values adapted from the recursive evaluation of con-tributing area used by Tarboton (1997) with theD∞ multipleflow direction model for representation of flow over a terrainsurface.

Figure 7 illustrates the minimum upslope and minimumdownslope functions. Figure 7a is an example of a stabilityindex grid. Figure 7b gives a flow path through this grid.The values of the minimum upslope function along this flowpath are given in Fig. 7c. Numerically the minimum ups-lope value is computed recursively as the minimum of thecell value itself and the result from the minimum upslope

Fig. 6. Infinite slope stability model schematic.

function applied at grid cells immediately upslope. On theillustrated path the top left grid cell has no grid cells upslopeso when the procedure is called the minimum upslope valueis set equal to the cell value itself (in this case 0.8). Whenthe procedure is called at the next grid cell down the mini-mum upslope value is the minimum of the cell immediatelyupslope (0.8) and the grid cell itself (0.7) resulting in a min-imum upslope value of 0.7 in this case. Similarly at the thirdcell the minimum is 0.1. At the fourth cell the evaluationis the minimum of the cell value of 0.5 and the minimumupslope of the third grid cell, 0.1, resulting in a minimumupslope value of 0.1 for the fourth grid cell, and similarly forthe fifth grid cell. In general there may be multiple grid cellsimmediately upslope of any specific grid cell, because flowpaths merge. TheD∞ approach proportions flow betweendownslope grid cells. Grid cells that contribute 20% or moreof their flow to a grid cell were counted as being upslope of agrid cell for the purposes of evaluating the minimum upslopegrid value. The procedure was implemented in a C++ com-puter program. Figure 7d illustrates the minimum downslopefunction, the computation of which is similar to the minimumupslope function except that instead of looking at each gridcell upslope from a specific grid cell it looks at each grid celldownslope from a specific grid cell.

The minimum upslope and minimum downslope grids areevaluated separately because recursion can not function inthe upslope and downslope directions simultaneously. How-ever once the minimum upslope and downslope grids havebeen evaluated the minimum value along a flow path can beidentified by the condition that the minimum upslope value isequal to the minimum downslope value and the value at thegrid cell itself. This is illustrated in Fig. 8. The most likelylandslide initiation point method can be used without anycondition on the values of stability index at the most likelylandslide initiation locations. However, some flow paths thatnever go through an unstable location will still be identifiedas most likely landslide initiation points because they havethe lowest stability index value along the flow path, but the



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Figure 7. Illustration of the minimum upslope and downslope functions. a) Example stability

index grid. b) Example flow path. c) Example values of the minimum upslope function along

the flow path in (b). d) Example values of the minimum downslope function along the flow

path in (b).

1

Fig. 7. Illustration of the minimum upslope and downslope func-tions. (a) Example stability index grid.(b) Example flow path.(c)Example values of the minimum upslope function along the flowpath in (b). (d) Example values of the minimum downslope func-tion along the flow path in (b).

stability index value may be large and unlikely to be a land-slide initiation point. Therefore we use a threshold with theidentification of most likely landslide initiation points, onlyidentifying most likely landslide initiation locations whosestability index value is less than the input thresholdSIthr .In the illustration in Fig. 8,SIthr=0.2 results in identificationof only the dark grid cells as most likely landslide initiationlocations.

5 Results

For each of the five digital terrain models interpolated forthe study area with progressively finer grid cell resolutionsof 50, 20, 10, 5 and 2 m, slope and stability index,SI, fromSINMAP were used as measures of terrain instability. De-fault SINMAP parameters were used so as to be objectivewithout attempting calibration. These parameters were: 0–0.25 for the range of dimensionless cohesion,C, 30◦–45◦ forthe range of internal frictional angle,φ, and 2000–3000 mfor the range of the ratioT/R. Slope thresholds of 1.05, 0.9,0.52 and 0, and SINMAP stability index thresholds of 0.2,0.5, 1 and 10 were specified and the number of grid cells inthe domain meeting each threshold was tabulated (Table 1).The slope thresholds were chosen so that the percentage ofarea meeting each threshold are roughly equivalent to the

percentages of area meeting theSI thresholds so that later re-sults are comparable. The percentages of area meeting eachthreshold can not be made the same for all grid cell resolu-tions while keeping the thresholds the same, so we chose tomatch the percentages for the highest resolution DTM grids.The slope threshold of 0 and SINMAPSI threshold of 10 arenon-limiting thresholds that serve to select the entire domain.

Based on the stability index maps for each digital terrainmodel grid resolution, most likely landslide initiation loca-tions were identified using the procedure described above.Slope thresholds of 0, 0.52, 0.9, and 1.05, and stability in-dex thresholds,SIthr of 0.2, 0.5, 1, and 10 were again used.Table 2 gives the number of most likely landslide initiationpoints identified for each DTM resolution and for each sta-bility threshold. Table 2 also gives the percentage of the do-main that these most likely landslide initiation points rep-resent. Notice that these percentages are small because themost likely landslide initiation point procedure only identi-fies one point on each flow path. Notice also that these per-centages are only weakly dependent on the stability criterionthreshold, because in the majority of cases the most likelylandslide initiation point selected meets all stability criteria.

The observed landslides were overlaid on the slope andSImaps for each grid resolution and the percentage of the areaexceeding the stability index criterion that occurs within themapped landslide area was calculated. The results are givenin Table 3 for slope and in Table 4 for SINMAPSI. Hereexceeding the stability index criterion means slope greaterthan the threshold, or SINMAPSI less than the threshold.Based on the stability index maps for each digital terrainmodel grid resolution most likely landslide initiation loca-tions were identified using the procedure described above,for slope thresholds of 0, 0.52, 0.9, and 1.05, and for stabil-ity index thresholds,SIthr of 0.2, 0.5, 1, and 10 again. Foreach of these most likely landslide initiation point maps thepercentage of most likely landslide initiation locations oc-curring within the mapped landslide area was calculated andalso tabulated in Tables 3 and 4. Specifically for a grid res-olution of 2 m there are 248 379 grid cells with slope greaterthan or equal to 1.05 (Table 1). Of these 24 753 occur withinthe mapped landslide area, representing a percentage of 10%as reported in Table 3. Similarly there are 245 309 grid cellswith SI<0.2 for a grid resolution of 2 m (Table 1). 27 496 ofthese occur within the mapped landslide area representing apercentage of 11.2%. For the MLIP percentages reported inTable 3 there are a total of 5828 MLIP grid cells identifiedusing a slope threshold of 1.05 for a grid resolution of 2 m(Table 1). Of these 724, representing 12.4% occur within themapped landslide area.

The density ratio of stability index meeting each thresh-old criterion was calculated using Eq. (1) and presented inTable 5 for slope and Table 6 for SINMAPSI under thecolumns labeled slope andSI respectively. The density ra-tio of most likely landslide initiation locations identified wascalculated using Eq. (2) and presented in Table 5 for slope



Fig. 8. Illustration of the combination of minimum upslope and minimum downslope functions to identify most likely landslide initiationpoints (MLIP). The shaded grid cells are identified as most likely landslide initiation points in all cases. The dark shaded grid cells are mostlikely landslide initiation points determined forSI≤SIthr=0.2.

Table 1. Number of grid cells and percentage of the domain meeting each stability index threshold for each DTM grid resolution.

Grid Resolution (m) 50 20 10 5 2

Thresholds n % n % n % n % n %

Slope≥1.05 4 0.1 612 2.3 5402 5.1 31672 7.4 248379 9.3Slope≥0.9 178 4.2 2495 9.3 14908 14.0 72568 17.0 519394 19.4Slope≥0.52 2746 64.4 18542 69.4 75986 71.1 306918 71.8 1922810 72.0All Slopes 4265 100.0 26712 100.0 106864 100.0 427407 100.0 2671290 100.0SI <0.2 92 2.2 1218 4.6 6731 6.3 33996 8.0 245309 9.2SI <0.5 447 10.5 3507 13.1 17065 16.0 75712 17.7 501811 18.8SI <1 3132 73.4 19920 74.6 79359 74.3 313497 73.3 1920411 71.9SI <10 4265 100.0 26712 100.0 106864 100.0 427407 100.0 2671288 100.0

Table 2. Number of most likely landslide initiation point grid cells and percentage of the domain that these comprise derived from eachstability index threshold for each DTM grid resolution.


Thresholds n % n % n % n % n %

Slope≥1.05 3 0.07 182 0.68 845 0.79 2439 0.57 5828 0.22Slope≥0.9 60 1.41 389 1.46 1245 1.17 3076 0.72 6315 0.24Slope≥0.52 260 6.10 742 2.78 1628 1.52 3516 0.82 6630 0.25All Slopes 272 6.38 773 2.89 1733 1.62 3671 0.86 6887 0.26SI <0.2 20 0.47 206 0.77 1147 1.07 7186 1.68 65927 2.47SI <0.5 59 1.38 284 1.06 1332 1.25 7296 1.71 65967 2.47SI <1 150 3.52 472 1.77 1451 1.36 7340 1.72 65975 2.47SI <10 157 3.68 484 1.81 1461 1.37 7344 1.72 65994 2.47



Table 3. Percentage of area with slope greater than threshold, and percentage of identified most likely landslide initiation points, MLIP,occurring within mapped landslide area.


Slope Thresholds Slope MLIP Slope MLIP Slope MLIP Slope MLIP Slope MLIP

Slope≥1.05 0.0 0.0 7.8 3.8 9.4 9.2 9.5 11.8 10.0 12.4Slope≥0.9 6.7 6.7 6.9 5.7 8.9 10.8 9.5 11.0 9.3 11.6Slope≥0.52 6.5 4.2 6.2 6.2 6.2 10.0 6.2 10.0 6.2 11.1All Slopes 4.7 4.0 4.7 6.0 4.7 9.3 4.7 9.6 4.7 10.7

Table 4. Percentage of area with stability index,SI, less than threshold, and percentage of identified most likely landslide initiation points,MLIP, occurring within mapped landslide area.


SI thresholds SI MLIP SI MLIP SI MLIP SI MLIP SI MLIP

SI <0.2 16.3 25.0 11.8 8.7 12.5 18.2 11.2 14.2 11.2 12.28SI <0.5 10.7 15.3 10.9 9.2 10.7 17.5 10.7 14.0 10.4 12.27SI <1 6.4 7.3 6.1 6.8 6.2 16.9 6.2 13.9 6.3 12.27SI <10 4.7 7.0 4.7 6.6 4.7 16.8 4.7 13.9 4.7 12.26

and Table 6 for SINMAPSI under the columns labeledMLIP.

6 Discussion

6.1 Effectiveness of stability index

The results presented above allow us to assess the effec-tiveness of the slope and the stability index map, and mostlikely landslide initiation procedure at discriminating poten-tial landslide initiation locations in comparison to mappedlandslide locations. Columns labeled slope in Table 3 rep-resent the percentage of terrain within landslide scars that isgreater than the indicated threshold. As the slope thresholdis increased, moving up the column the percentage of ter-rain less than the slope threshold that falls within the mappedlandslide scars generally increases (except for the small sam-ple 50 m resolution case), reflecting the fact that a higherfraction of terrain with high values of slope falls within themapped landslide scar. This increase is a measure of theeffectiveness of the slope approach at discriminating terrainwhere landslide scars have been mapped. Columns labeledSIin Table 4 represent the percentage of terrain within landslidescars that is less than the indicated threshold. Specifically forthe 50 m grid resolution all the terrain hasSI <10 and 4.7%of the terrain is within mapped landslide scars so the per-centage is 4.7. As the stability index threshold is reduced,moving up the column the percentage of terrain less than thestability index threshold that falls within the mapped land-

slide scars increases, reflecting the fact that a higher fractionof terrain with low stability index falls within the mappedlandslide scar. This increase is a measure of the effective-ness of the stability index approach at discriminating terrainwhere landslide scars have been mapped. The trend is essen-tially the same for all grid resolutions.

6.2 MLIP density ratios as a measure of stability index ef-fectiveness

In Tables 5 and 6 the density ratio values provide a rela-tive measure of the effectiveness of the stability index mapto discriminate unstable terrain in comparison to the mappedlandslide scars. We see that generally comparing Table 6 toTable 5 that the density ratios forSI are greater than forslope providing a measure of the added value of contribut-ing area in the SINMAP calculation at discriminating unsta-ble terrain. This can also be seen comparing Tables 3 and 4where area percentages are generally higher in Table 4. Onecan also observe in these tables that for DTM resolutions of10 m and finer the percentages (in Tables 3 and 4) and den-sity ratios (in Tables 5 and 6) are generally higher for mostlikely landslide initiation points than forSI. Specifically theSI density ratios in Table 6 indicate that at the lowest stabil-ity index threshold the ratio of density between points withinand outside landslide scars is around 2.5, a measure of the ef-fectiveness of simple stability index thresholding at discrim-inating landslide scars locations. However, as mentioned be-fore, this comparison is hampered by the fact that mappedlandslides included the entire landslide scar, not only the ini-



Table 5. Density ratio between locations with stability index, slope, less than a threshold, and between most likely landslide initiation points,MLIP, within and outside the observed landslide area.


Slope Thresholds Slope MLIP Slope MLIP Slope MLIP Slope MLIP Slope MLIP

Slope≥1.05 0 0 1.64 0.80 1.97 1.93 1.99 2.48 2.08 2.60Slope≥0.9 1.41 1.39 1.43 1.18 1.86 2.25 1.98 2.30 1.95 2.43Slope≥0.52 1.36 0.88 1.30 1.30 1.31 2.08 1.30 2.10 1.30 2.32All slopes 1 0.85 1 1.24 1 1.95 1 2.01 1 2.24

Table 6. Density ratio between locations with stability index,SI, less than a threshold, and between most likely landslide initiation points,MLIP, within and outside the observed landslide area.


SI thresholds SI MLIP SI MLIP SI MLIP SI MLIP SI MLIP

SI <0.2 3.41 5.23 2.52 1.86 2.68 3.90 2.41 3.06 2.41 2.63SI <0.5 2.25 3.19 2.32 1.95 2.29 3.75 2.30 3.01 2.23 2.63SI <1 1.33 1.53 1.30 1.45 1.32 3.62 1.33 2.99 1.34 2.63SI <10 1 1.46 1.00 1.41 1.00 3.59 1.00 2.99 1.00 2.63

tiation zones. The most likely landslide initiation point re-sults allow us to assess the effectiveness of the most likelylandslide initiation locations identified from the slope andstability index maps. The fact that MLIP density ratios aregenerally higher, with values as high as 3.9, suggests that inthis setting, where mapped landslides include the entire land-slide scar, the most likely landslide initiation point procedureis more effective at quantifying the effectiveness of the stabil-ity index map at discriminating potential landslide initiationlocations.

We also note in Tables 5 and 6 that MLIP density ratios areless sensitive to threshold than slope or stability index. Thisis because MLIP is designed as a threshold independent ap-proach with threshold functioning as a secondary screening.The lack of sensitivity to threshold suggests that MLIP doesnot suffer from some of the sensitivity issues that Begueria(2006) discusses and is a good measure for quantifying theeffectiveness of the stability index map in terms of the dif-ference in density of MLIP locations inside and outside ofmapped landslides.

6.3 Scale effects

It is also of interest to note that the highest most likely land-slide initiation point percentage and density ratios occur for adigital terrain model grid cell resolution of 10 m, with the oneexception of the smallest threshold and largest digital terrainmodel cell size. This is a small sample size effect that wedisregard. With a 50 m cell size and 0.2 threshold there areonly 20 most likely landslide initiation point grid cells, insuf-

ficient to be representative. The peak in most likely landslideinitiation point density ratios for digital terrain model gridcell resolution of 10 m we take as support for the idea that a10 m digital terrain model grid cell resolution is optimal forthe identification of potential instability in terrain stabilitymapping in this setting.

This 10 m scale may be a natural scale associated with thelandslides under consideration. At scales coarser than 10 mthe loss of information appears to result in a drop off in thediscriminating capability of the stability index map as quanti-fied by most likely landslide initiation point density ratio. Atscales finer than 10 m small scale errors in the determinationof slope, for example, may result in increases in the numberof spurious most likely landslide initiation locations reducingthe discriminating capability. Both the physical scale associ-ated with the convergence of subsurface flow and the physi-cal scale of a failure plane in the infinite slope model appearto have scale limits that contribute to a 10 m resolution digi-tal terrain model having optimal discriminating capability inthis study.

Figure 9 gives the most likely landslide initiation pointmap for part of the study area withSIthr=1, compared tomapped landslide scars. Note in this figure how most likelylandslide initiation locations cluster at the upslope end oflandslide scars indicating their most likely initiation points.Figure 10 illustrates the mapped most likely landslide initia-tion locations draped on an aerial photograph of part of thestudy area. Figure 11 illustrates the stability index and cor-responding most likely landslide initiation points for a repre-sentative set of the digital terrain model resolutions used for



Fig. 9. Most likely landside initiation point map for 10 m resolutiondigital terrain model grid andSIthr<1.

one landslide complex. This figure shows the effects of DTMscale on terrain stability index and most likely landslide ini-tiation points. At the 50 m resolution the digital terrain modeis too coarse to resolve the detail in the landslide scar. At2 m resolution the most likely landslide initiation locationsspread out as a blur, rather than a line of single most likelylandslide initiation locations. The 10 m resolution DTM ap-pears to offer a good resolution compromise for the identifi-cation of most likely landslide initiation points. At the 10 mscale there is some blurring of grid cells together but most ofthe identified locations are distinct and occur at or around theupper end of the mapped landslide scar.

In interpreting most likely landslide initiation point mapsit is important to bear in mind that the procedure only iden-tifies one most likely landslide initiation point along eachflow path. The possibility exists that landslides may initi-ate at different locations along a unique flow line. Pointsmay be identified as most likely landslide initiation pointsthat haveSI less critical than other cells because the othercells are not the most critical along a specific flow line. Thethreshold used in the procedure for identifying most likelylandslide initiation points should be chosen to preclude iden-tifying very stable non critical points. However one shouldkeep in mind that most likely landslide initiation points donot quantify the potential terrain instability at each and ev-ery location. They are not a substitute for a stability index.Rather they are additional information that complements theinformation in a terrain stability map that were shown to beuseful in this paper for evaluating the discriminating capa-bility of a terrain stability map where comparison is againstentire landslide scars, not only initiation regions. They mayhave other uses, for example as trigger points in dynamic

Fig. 10. 3-D view (same area as Fig. 9) of most likely landslideinitiation locations (10 m digital terrain model resolution).

modelling or simulation of landslides, a potential use that wehave not yet explored.

7 Conclusions

The most likely landslide initiation point (MLIP) method hasbeen introduced as a new way to generate information fromterrain stability maps. Most likely landslide initiation loca-tions are of interest because they identify the most potentiallyunstable location along each flow path. They also provide away to assess the discriminating capability of a terrain sta-bility map in comparison to mapped landslide scars. Thisdiscriminating capability was measured using the ratio of thedensity of most likely landslide initiation locations withinand outside mapped landslide scars. Most likely landslideinitiation locations proved to have a greater discriminatingcapability than simple thresholding of the stability index mapin the study area where this was applied where mapped land-slide scars include runout areas. The most likely landslideinititiation point procedure may be used with any index ofterrain stability. In this work we used both terrain slope andSINMAP stability index as indices of terrain stability. Wemade no effort to calibrate or adjust the SINMAP parame-ters; rather default model parameter were used. This wasdone to keep the evaluation of the most likely landslide ini-tiation point approach general, without being dependent onspecifically calibrated parameters. We found that ratios of thedensity of most likely landslide initiation points within andoutside mapped landslide areas were significantly higher (3.6to 3.9 for a 10 m resolution DTM) from SINMAP than fromslope (1.9 to 2.2 for a 10 m resolution DTM). This allowsus to conclude that the information provided by contribut-ing area that is input to SINMAP results in terrain stabilitymaps that are more discriminating than simply using slopeas an index of terrain stability. We can also conclude thatthe most likely landslide initiation point procedure is effec-tive at quantifying the discriminating capability of a terrain



(a) (b)

(c) (d)

(e) (f)

Fig. 11. Illustration of the stability index, and corresponding most likely landslide initiation locations identified for one landslide complex forrepresentative digital terrain model resolutions used:(a) and(b) 2 m digital terrain model resolution,(c) and(d) 10 m digital terrain modelresolution,(e)and(f) 50 m digital terrain model resolution.



stability map in comparison to mapped landslide scars wherethe runout zone is included and useful for comparing differ-ent terrain stability models. Without calibration or input ofsite specific information, density ratios in excess of 3 of mostlikely landslide initiation point density between within land-slide and outside of landslide area were obtained with theSINMAP terrain stability index. This suggests that SINMAPand the most likely landslide initiation point approach mayhave generality beyond our specific study area, a suggestionthat merits further evaluation at other locations. The compar-isons of most likely landslide initiation point density ratiosfor different resolution digital terrain models showed that forthis data a 10 m resolution digital terrain model is optimal.Future work should test this approach in other settings andwith other terrain stability models, such SHALSTAB (Mont-gomery and Dietrich, 1994) and Borga et al.’s (2002), quasidynamic model.

Acknowledgements.This research was supported by the InterregIIIB Spazioalpino project: CATCHRISK (Mitigation of hydroge-ological risk in alpine catchments). The authors are grateful to“Servizio Territorio Montano e Manutenzioni” (Direzione CentraleRisorse Agricole, Naturali, Forestali e Montagna) of Friuli VeneziaGiulia Region for the collaboration in field surveys and providingaerial photographs data. LIDAR data were collected in the InterregIIIA Italia-Slovenia project: “Ricomposizione della cartografiacatastale e integrazione della cartografia regionale numericaper i sistemi informativi territoriali degli enti locali mediantesperimentazione di nuove tecniche di rilevamento”. This work hasbenefited from discussion with K. Chinnayakanahalli. Tarolli alsoacknowledges the contributions of G. Dalla Fontana and M. Borgaduring the prework discussion, and the support of Ing. Aldo GiniFoundation on the scholarship period at Utah State University.

Edited by: P. Molnar

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A new method for determination of most likely landslide initiation