Engineering Geology 102 (2008) 214–226

Contents lists available at ScienceDirect

Engineering Geology

j ourna l homepage: www.e lsev ie r.com/ locate /enggeo

Transient deterministic shallow landslide modeling: Requirements for susceptibilityand hazard assessments in a GIS framework

J.W. Godt a,⁎, R.L. Baum a, W.Z. Savage a, D. Salciarini b, W.H. Schulz a, E.L. Harp a

a U.S. Geological Survey, Box 25046, MS 966, Denver, CO 80225, United Statesb Department of Civil and Environmental Engineering, University of Perugia, Perugia, Italy

⁎ Corresponding author. Tel./fax: +1 303 273 8626.E-mail address: jgodt@usgs.gov (J.W. Godt).

0013-7952/$ – see front matter. Published by Elsevier Bdoi:10.1016/j.enggeo.2008.03.019

a b s t r a c t

a r t i c l e i n f o

Article history:

Application of transient dete Accepted 4 March 2008Available online 31 July 2008

Keywords:LandslideSusceptibilityInfiltrationRainfallGIS

rministic shallow landslide models over broad regions for hazard and susceptibilityassessments requires information on rainfall, topographyand thedistribution andproperties of hillsidematerials.We survey techniques for generating the spatial and temporal input data for suchmodels and present an exampleusing a transient deterministic model that combines an analytic solution to assess the pore-pressure response torainfall infiltration with an infinite-slope stability calculation. Pore-pressures and factors of safety are computedon a cell-by-cell basis and can be displayed or manipulated in a grid-based GIS. Input data are high-resolution(1.8 m) topographic information derived from LiDAR data and simple descriptions of initial pore-pressuredistribution and boundary conditions for a study area north of Seattle, Washington. Rainfall information is takenfrom a previously defined empirical rainfall intensity–duration threshold and material strength and hydraulicproperties were measured both in the field and laboratory. Results are tested by comparison with a shallowlandslide inventory. Comparison of results with those from static infinite-slope stability analyses assuming fixedwater-table heights shows that the spatial prediction of shallow landslide susceptibility is improved using thetransient analyses; moreover, results can be depicted in terms of the rainfall intensity and duration known totrigger shallow landslides in the study area.

Published by Elsevier B.V.

1. Introduction

Managing hazards associated with shallow landslides requires anunderstanding of where and when such landslides may occur, andhow widespread a potential shallow landslide event might be. Thewide availability of Geographic Information Systems (GIS) and digitaltopographic data has led to the development of various analyticmethods for estimating potential hazards from shallow, rainfall-triggered, landslides over large geographic areas. These includeempirical probabilistic methods based on historical records anddeterministic methods. Empirically based probabilistic methods (e.g.Coe et al., 2004) use historical records of landslide occurrence topredict the temporal and spatial probability of future landslides. Theempirically based statistical approach (e.g. Guzzetti et al., 1999;Carrara et al., 1999; Cannon et al., 2004) relies on multivariatestatistical correlation between locations of failures on steep slopes andfactors such as slope angle, slope curvature, bedrock lithology, soiltype, and basin morphology. The results of the empirically basedanalyses are typically portrayed using GIS.

Deterministicmethods typically rely on applicationof simplemodelsof groundwater flow combined with infinite-slope stability analyses toestimate the potential or relative instability of slopes over a broad

.V.

region. They may involve one, two or three-dimensional steady ortransient groundwater flow models and analytical, numerical, andhybrid mathematical schemes and, usually, an infinite-slope factor ofsafety equation. Some early attempts to develop and apply “physicallybased” shallow landslide initiation models over large areas combinedsteady or quasi-steady groundwater flow models with the assumptionthat flow is exclusively parallel to the slope and flux at the groundsurface (i.e. rainfall) only acts to modify steady or quasi-steady pore-pressure distributions (e.g. Montgomery and Dietrich, 1994; Wu andSidle, 1995). However, slope parallel seepage can only be in equilibriumwith rainfall under a restrictive andunrealistic set of conditions inwhich1) the rainfall is of very low intensity and 2) long duration, 3) the depthto the failure surface is small with respect to the square root of thecontributing area, and 4) the saturated hydraulic conductivity of the soilis strongly anisotropic with the slope-parallel component greatlyexceeding that in the vertical direction (Iverson, 2000). Such conditionsare rarely met in nature. Because the steady and quasi-steady ground-water models do not account for the transient pore-water responseresulting from infiltration, results cannot be used to examine changingrainfall and groundwater conditions that cause shallow landslides todevelop during a rainfall event.

To assess the effects of infiltration on near-surface pore-pressuredistributions and consequent slope stability over broad regionsrequires transient solutions for groundwater flow. Both numerical(e.g. Simoni et al., 2008) and analytical (Morrissey et al., 2001; Crosta

Fig. 1. Sketch showing the coordinate system and groundwater conditions in hillslopesabove an impermeable lower boundary at dlb below the ground surface. The depth ofthe water table is dwt, and the slope angle is β. The vertical, Z, and slope-normal, z,coordinates are also shown.

215J.W. Godt et al. / Engineering Geology 102 (2008) 214–226

and Frattini, 2003; Savage et al., 2003; Morrissey et al., 2004;D'Odorico et al., 2005; Salciarini et al., 2006; Godt et al., 2008)techniques have been appliedwith GIS-based slope stability models tomap areas that are potentially unstable during rainstorms. This paperwill use the model TRIGRS (Transient Rainfall Infiltration and Grid-based Regional Slope-stability analysis) which was developed toaccount for the transient effects of rainfall on shallow landslideinitiation and combines an analytical solution for groundwater flow inone vertical dimension with an infinite-slope stability calculation(Baum et al., 2002; Savage et al., 2003).

Application of models such as TRIGRS in a GIS context for landslidehazard assessment requires digital spatial topographic, geologic, andhydrologic information. In addition, inventories of previous rainfall-induced landslide events are required to test the model results. Digitaltopography (i.e. Digital ElevationModels—DEMs) of appropriate scaleand resolution, areal distribution and depth of susceptible surficialmaterials and their hydrologic and strength properties, near-surfacegroundwater conditions, and spatial and temporal distributions ofrainfall are required. Finally, these methods for estimating potentialhazards from shallow, rainfall-triggered landslides require skilledusers with an understanding of landslide mechanics and triggeringprocesses. We consider each of these subjects in this order and ingreater detail below and using an example application to a study areaof landslide-prone coastal bluffs north of Seattle, Washington. Wethen concludewith a summary and discussion of the requirements forintegrating deterministic shallow landslide models with GIS forhazard and susceptibility assessments.

2. Stability of infinite slopes

Deterministic modeling of slope stability over broad regionstypically relies on one-dimensional infinite-slope stability analysesapplied over digital topography (Montgomery and Dietrich, 1994;Terlien et al., 1995; Wu and Sidle, 1995; Borga et al., 1998; Baum et al.,2002; Casadei et al., 2003; Savage et al., 2003; Salciarini et al., 2006,Harp et al., 2006, Godt et al., 2008). Infinite-slope stability analysisassumes that landslides are infinitely long and is most appropriate foranalysis of landslides with planar failure surfaces that have a smalllandslide depth compared to their length and width, and aredestabilized by widespread areas of positive pore-water pressure(Iverson et al., 1997) or loss of soil suction (Anderson and Howes,1985;Collins and Znidarcic, 2004). Generalized for hillslope materials withcohesion, c′ under the Mohr–Coulomb failure criteria (Das, 2000), andto account for the influence of groundwater, the factor of safety for aninfinite slope is

FS ¼ tan/Vtanβ

þ cV−ψγw tan/Vγsdlbsinβ cosβ

ð1Þ

where ψ is the groundwater pressure head, γw, is the unit weight ofwater, γs, the unit weight of soil, and dlb is the depth of the failuresurface (Fig. 1). The primes next to the cohesion, c′, and friction angle,ϕ′ indicate that thesematerial strength parameters are determined foreffective stress (Terzaghi, 1943), which accounts for the influence ofpore-water on the stress field in thematerial and is defined as the totalnormal stress minus the pore-water pressure. This analysis assumesthat hillside materials are saturated at the time of failure and neglectsthe influence of suction on the shear strength of soils (Fredlund et al.,1978). For shallow landslides triggered by rainfall and over shorttimescales such as that of a rainstorm, the pressure head, ψ, is the onlytime-dependent quantity in Eq. (1).

Although vertical pore-pressure gradients in the saturated zone ininfinite slopes vary as a function of the flux at the ground surface andthe anisotropy of the hydraulic conductivity (Iverson, 1990) assump-tions of spatially invariant failure depth (e.g. Montgomery andDietrich, 1994; Jibson et al., 2000) steady slope parallel flow (e.g.

Pack et al., 1998) and constant relative water-table position (e.g. Harpet al., 2006) are often made in application of Eq. (1) to map shallowlandslide susceptibility over broad regions.

3. Transient vertical groundwater flow

The characteristic time scales for lateral and slope-normal pore-pressure transmission are A /D0, and H2 /D0, respectively, where D0 isthe saturated hydraulic diffusivity, H is the depth of the failure surfacein the slope-normal direction, and A is the upslope contributing areaabove a given location. (Iverson, 2000). Areas of the landscape wherethe vertical component of pore-pressure response to rainfall dom-inates over lateral transmission can be identified by considering aratio, ε, of the two characteristic length scales,

e ¼ HffiffiffiA

p:

ð2Þ

For areas of the landscape where ε≪1 long and short-termpressure-head responses to rainfall is 1) dominated by vertical flowand 2) these areas are typical of shallow landslide locations (Iverson,2000). This implies that pore-pressure variation in response to rainfallin initially wet materials can be adequately described by simplified,one-dimensional forms of the Richards equation.

The Richards equation describes unsaturated Darcian flow inresponse to infiltration at the ground surface. In one verticaldimension for a sloping surface it can be written as

AψAt

C ψð Þ ¼ A

AZK ψð Þ Aψ

AZ− sinβ

� �� �ð3Þ

where ψ, is pressure head, K(ψ) the pressure-head dependenthydraulic conductivity, C(ψ) is the specific moisture capacity, C(ψ)=∂θ /∂ψ, θ is the volumetric water content, β is the slope angle of theground surface, and Z is the vertical depth (Philip, 1991). Because ofthe nonlinear dependence of hydraulic conductivity and moisturecontent on pressure head, solutions to Eq. (3) generally requirespecialized numerical techniques (Rubin and Steinhardt, 1963; Freeze,1969). Several analytical solutions to one-dimensional forms of theRichards equation are available that make use of discrete assumptionsto simplify the analysis (Philip, 1957; Parlange, 1972; Philip, 1991;Srivastava and Yeh, 1991) and one has been applied to boundaryconditions suitable for slope stability analysis (Savage et al., 2004,Baum et al., 2008).

216 J.W. Godt et al. / Engineering Geology 102 (2008) 214–226

For the study presented here, we rely on solutions to Eq. (3)presented by Iverson (2000) assuming that the zone above the watertable is tension-saturated to the ground surface (Fig. 1). For this end-member case the pressure dependent terms, K(ψ) and C(ψ) becomeconstant values, KZ and C0. Eq. (3) then reduces to a linear diffusionequation

AψAt

¼ D1A2ψ

AZ2 ð4Þ

where D1=D0 /cos2 β, and the hydraulic diffusivity, D0 equals KZ /C0,where C0 is the minimum slope of the soil–water characteristic curve.Iverson's (2000) original solutions for pore-pressure response in aninfinitely deep half-space have been applied in a GIS framework(Morrissey et al., 2001; Crosta and Frattini, 2003). The solution to Eq.(4), given a time-varying specified flux boundary condition (assuggested by Iverson, 2000) at the ground surface and an imperme-able basal boundary at a finite depth dlb, given by Savage et al. (2003)and implemented in TRIGRS (Baum et al., 2002), is:

ψ Z; tð Þ ¼ Z−d½ �λcosβ

þ2 ∑N

n¼1

InZKZ

H t−tnð Þ D1 t−tnð Þ½ �12 ∑∞

m¼1ierfc

2m−1ð Þdlb− dlb−Zð Þ2 D1 t−tnð Þ½ �12

" #þ ierfc

2m−1ð Þdlb þ dlb−Zð Þ2 D1 t−tnð Þ½ �12

" #( )

−2 ∑N

n¼1

InZKZ

H t−tnþ1ð Þ D1 t−tnþ1ð Þ½ �12 ∑∞

m¼1ierfc

2m−1ð Þdlb− dlb−Zð Þ2 D1 t−tnþ1ð Þ½ �12

" #þ ierfc

2m−1ð Þdlb þ dlb−Zð Þ2 D1 t−tnþ1ð Þ½ �12

" #( )

ð5Þ

where ψ is pressure head, t is time, d is the depth of the steady-statewater table measured in the z-direction, and where λ=cosβ− (IZ /KZ).Here IZ is the long-term (steady-state) rainfall flux at the groundsurface in the Z-direction, KZ is the hydraulic conductivity in the Z-direction, InZ is the surface flux for the nth time interval, and dlb is thevertical depth to the lower boundary, N, is the total number of timeintervals, and H(t− tn+1) is the Heavyside step function. The functionierfc(η) is equivalent to 1/√π exp(−η2)−ηerfc(η), where erfc(η) is thecomplementary error function. The first term on the right-hand side ofEq. (5) describes a steady-state pressure-head distribution in the Z-direction for a homogeneous soil in response to long-term rainfall, IZ.The other terms on the right-hand side describes the transient pore-pressure distribution in response to a time-varying flux at the groundsurface in a layer with a finite depth, dlb, in the Z-direction. The firstfew terms of the infinite series converge to an acceptable degree ofaccuracy so that the computation of Eq. (5) is very efficient and can beapplied over broad areas on a cell-by-cell basis in a GIS frameworkyielding a time-varying pore-pressure and factor of safety for each gridcell as a function of depth in response to rainfall (Baum et al., 2002).

The TRIGRSmodel imposes an additional physical limitation that atany depth Z the maximum pressure head under downward gravity-driven flow cannot exceed that which would result from having thewater table at the ground surface and maintaining the original flowdirection and hydraulic gradient (Iverson, 2000; Baum et al., 2002)given by

ψ Z; tð ÞV Zλcosβ: ð6Þ

4. Input and test data requirements

4.1. Landslide inventories

Landslide inventories should include information on where andwhen the landslides occurred, the type, size and the regional extent ofthe landslides, as well as information on triggering conditions if theyare to be used to test results from deterministic models. Landslide

inventories are typically compiled from aerial photography (e.g.Bucknam et al., 2001) using photogrammetric techniques (e.g. Godtand Coe, 2003) or eye-hand transfer of landslide features totopographic maps (e.g. Harp and Jibson, 1995). Triggering conditionsare not easily determined from aerial photographs and their definitionrequires nearby measurement of rainfall and observations of soil-moisture conditions. Landslide inventory maps are typically eitherscanned or digitized manually to create a digital dataset compatiblewith GIS. The accuracy of the landslide inventory is a function of theoriginal image quality, the scale and quality of the topographic base,and the skill of the geologist. The increasing availability of high-resolution digital imagery and soft-copy photogrammetry promises toreduce the error introduced in the digital conversion of maps byallowing the geologist to compile the inventory digitally (e.g. Stocket al., 2006). For testing shallow landslide initiation models such asTRIGRS, landslide sources, tracks, and deposits should be mappedseparately, but photograph quality and scale or resolution, landslidesize, and the scale of the topographic base make this impossible inmany cases.

4.2. Digital topography

Digital Elevation Models (DEMs) are regularly-spaced arrays ofelevation values that have become essential for regional landslidehazard analysis. Other digital data structures exist to representtopography (e.g. Triangular Irregular Networks — TINs), however, werestrict our discussion here to DEMs because of their wide availabilityand use. The spatial resolution of a DEM is typically described by thedistance on the ground represented by the array spacing. The accuracyof the DEM is a function of the accuracy and spacing of the originalsource data and the accuracy of the interpolation of those data to aregularly-spaced grid.

DEMs are generated from a variety of original topographic datasources including: photogrammetrically generated contour maps,ground-based surveys, and remotely-sensed data. At this time, DEMsinterpolated from topographic contour data are probably the mostcommonly used for landslide hazard mapping mainly because large-scale topographic maps are widely available for many localities.However, elevation data from both airborne and spaceborne sensorsare increasingly available and have been used in a variety of landslideapplications. Of the remote-sensing technologies, Light Detection andRanging (LiDAR) has arguably had the most impact on landslidehazard mapping and modeling (e.g. McKean and Roering, 2004;Schulz, 2007). LiDAR-derived DEMs are typically of very high spatialresolution (1 to 5 m) with low elevation (Z) errors (typically b20 cm inunvegetated, low-slope landscapes). In vegetated steeplands, LiDARerrors are typically much greater (e.g. Haneberg, 2008). Because tensor hundreds of thousands of laser pulses per second aremade during aLiDAR survey, data processing algorithms have been designed todiscriminate between returns from vegetation and those from theground surface (e.g. Haugerud et al., 2003). Thus, LiDAR canpotentially provide DEMs with a much more accurate depiction ofthe topographic surface than DEMs derived from photogrammetri-cally mapped contours, even in heavily vegetated areas.

Deterministic shallow landslide susceptibility modeling requiresDEMs of adequate resolution to capture landslide features in a givenstudy area. Since most of these study areas are likely to be in highlydissected terrain with high relief, high-resolution data (5–10 m) aretypically required (Zhang and Montgomery, 1994). Slope anglecalculations and other elevation derivatives such as curvature andcontributing area are dependent on the scale of the source elevationdata and the grid-cell spacing of the DEM (Garbrecht and Martz, 1994;Zhang and Montgomery, 1994; Thieken et al., 1999; Claessens et al.,2005). Finer grid spacing typically produces steeper slope angles andat very fine spacing (e.g. b5 m) large local variability of curvatureresults from small-scale topographic features such as animal burrows

217J.W. Godt et al. / Engineering Geology 102 (2008) 214–226

and mounds surrounding vegetation (Heimsath et al., 1999). Elevationerrors in DEMs also have an effect on the calculation of topographicderivatives such as slope and contributing area (e.g. Holmes et al.,2000). Haneberg (2006, 2008) shows that elevation errors in a 1-mLiDAR and 10-m USGS DEMs lead to errors in the calculation oftopographic slope that may be as large as ±3°. The effect of the errorson the slope stability calculations is mitigated somewhat because theabsolute error tends to decrease with increasing slope angle for slopesless than about 45°. Haneberg (2006) estimates that the net effect ofthe elevation error is uncertainty in the final results that is comparableto the uncertainty introduced by the spatial variability of the strengthparameters of the hillslope materials.

4.3. Soil thickness and shallow landslide depth

4.3.1. Field observationsMaps of the soil depth on steep hillsides are required for

deterministic shallow landslide models that include the effects ofinfiltration or soil cohesion (Dietrich et al., 1995; Baum et al., 2002).However, since collecting sufficient measurements to map soilthickness compatible with the scale of high-resolution DEMs is apractical impossibility, deterministic modeling efforts have typicallyrelied on empirical or theoretical models to create soil depth maps(e.g. Dietrich et al., 1995; DeRose et al., 1996; Casadei et al., 2003;Salciarini et al., 2006; Godt et al., 2008). Field observations of soildepth in landslide-prone areas indicate that colluvium tends to collectin areas of topographic convergence (hollows) and is periodicallyremoved by shallow landsliding during heavy rainfall (Dietrich andDunne, 1978; Dietrich et al., 1986; Reneau and Dietrich, 1987; Denglerand Montgomery, 1989; Reneau et al., 1990; DeRose, 1991). Attemptsto correlate field measurements of soil depth with topographicattributes such as total topographic curvature and topographic slopehave met with varying success and provide somewhat contradictoryresults. Topographic curvature was shown to be positively correlatedwith the thickness of colluvial soils in areas of topographic divergence(noses) on low gradient (0–25°) slopes in both Marin County,California (Heimsath et al., 1999) and the eastern Australian escarp-ment (Heimsath et al., 2000); however, little or no correlation withcurvature or other topographic attributes was identified on divergenttopography in the generally steeper terrain of the Oregon Coast Range(Roering et al., 1999; Heimsath et al., 2001). In convergent, steep(generally greater than about 20°) landslide source areas in the centralCalifornia Coast Ranges, Reneau et al. (1990) reported data indicatingthat colluvial depth is poorly correlated with topographic slope.However, in the eastern Taranaki hill country of New Zealand whereshallow landslides and debris flows dominate erosion processes onsteep hillslopes (Trustrum and DeRose, 1988), DeRose et al. (1991)showed that at the scale of shallow landslides typical of the area, soilthickness in hollows steeper than 20° decreases exponentially withslope. Subsequent study of this area showed that topographic slopeexplains about 50% of the variation in mean soil depth for bothconvergent and divergent hillsides with slopes ranging from 5 toabout 60° (DeRose, 1996).

4.3.2. Soil mantle evolution theoryDietrich et al. (1995) proposed a model, later developed by

Heimsath et al. (1997, 1999), for vertical soil depth in temperate, soil-mantled landscapes with well-developed dendritic drainage patternsassuming that 1) biogenic activity and moisture content variation isresponsible for the production of colluvial soils on hillsides, 2) anymass loss due to solution processes is negligible, and 3) that the netdownslope transport of colluvium is proportional to the local slope ofthe ground. For low-slope environments the net downslope flux of soilis often assumed to be a linear function of slope (e.g. Culling, 1960;McKean et al., 1993) and analogous to a diffusion process. However, forsteep hillsides where shallow landslides are more likely to occur, the

net downslope flux of colluvial material has been shown to be anonlinear function of topographic slope (Andrews and Bucknam,1987;Roering et al., 2001a,b). The nonlinear model does not explicitlyaccount for sediment transport by landslides and debris flows butexperimental results indicate that it may be adequate for areas wheresediment flux is dominated by shallow landslides (Roering et al.,2001a). The rate of soil production is calibrated empirically and hasbeen shown to decline exponentially with depth. Numerical solutionsto producemaps of soil thickness (Dietrich et al., 1995; Heimsath et al.,1999; Casadei et al., 2003) require estimates of soil production ratesfrom cosmogenic nuclide or other dating techniques (e.g. Heimsath etal., 1999). Assuming soil thickness ultimately achieves a local steady-state, numerical results agree well with field observations on noseswith slopes less than about 25°. Similar models have been used toestimate the spatial variability of soil thickness for models of regionallandslide susceptibility in temperate, unglaciated environments (e.g.Dietrich et al., 1995; Casadei et al., 2003).

4.3.3. Empirical modelsTo estimate colluvial thickness in the southwestern part of Seattle

for an assessment of rainfall-induced landslide susceptibility, Godtet al. (2008) relied on a set of site-specific correlations betweencolluvial depth and hillside morphology developed by Schulz et al.(2008). A systematic variation of colluvium thickness among threehillslope landforms (escarpment, midslopes, and footslope) wasidentified. These landforms were mapped using shaded-relief imagesof a LiDAR DEM and the height and topographic slope of eachlandform was calculated. A GIS database of borehole locations wascreated based on the compilation of geotechnical exploration logs(Troost and Booth, 2008). Ground-surface elevation and subsurfaceattributes (depth of colluvium, depth of water table, date of water-level measurement) for each borehole location were determinedbased on the geological and geotechnical properties provided in thelogs, findings at nearby exploration locations, and the geologic andtopographic setting. Empirical relations to fit a surface to the base ofthe colluvium were developed using the geotechnical boreholedatabase locations. Four topographic parameters were used as inputdata in the model: 1) topographic slope angle of the ground surface,2) slope angle of the escarpment, 3) height of the escarpment, and4) distance downslope from the escarpment (Godt et al., 2008; Schulzet al., 2008). Topographic slope angle was used by DeRose (1996) in anexponential relation with soil thickness described previously toproduce map depicting shallow landslide susceptibility. Salciariniet al. (2006) also used an exponential function of topographic slope tomap the lower boundary depth for a parametric study of shallowlandslide susceptibility in central Italy.

The selection of an approach to model soil thickness for GIS-basedhazard assessment will likely be driven by the available data. For well-dissected landscapes in temperate environments where soil produc-tion rates can be estimated, numerical soil diffusion models may yieldaccurate estimates of soil thickness. However, site-specific empiricalrelations between soil thickness and topography may be moreappropriate for formerly glaciated landscapes (e.g. Alpine environ-ments) where non-diffusive processes such as rock fall dominatecolluvial transport and deposition.

4.4. Initial and boundary conditions

4.4.1. Initial groundwater conditionsGroundwater flow models are generally very sensitive to initial

conditions and applications to simulate actual landslide events requiresome knowledge of initial water-table depths and the moistureconditions of the unsaturated zone. Godt et al. (2008) relied on adatabase of geotechnical borings and regression techniques similar tothose described for colluvial thickness in the previous section to mapaverage winter-season water-table depths for a TRIGRS application in

Fig. 2. Map showing the location of the study area and Edmonds field site north ofSeattle, Washington.

218 J.W. Godt et al. / Engineering Geology 102 (2008) 214–226

Seattle (Schulz et al., 2008). Where detailed information on ground-water conditions is unavailable, parametric studies assuming a rangeof initial conditions may provide insights into the conditions that havecaused shallow landslides in the past (Crosta and Frattini, 2003;Salciarini et al., 2006). Additional research is needed to establishefficient and reliable methods to define initial conditions for transient,deterministic, shallow slope stability models.

4.4.2. Rainfall fluxThe spatial and temporal scales of rainfall data required for

transient modeling of infiltration and shallow slope stability isdictated by the purpose of the study. Attempts to recreate conditionsfor past landslide events will likely benefit from rainfall datawith highspatial (kilometer scale) and temporal (hourly) resolution. Rainfallestimates from weather radars have been shown to improve modelcomparisons with landslide inventories both spatially and temporally(Crosta and Frattini, 2003). However, most studies will be likely forcedto rely on available rainfall information from gauge networks (Godt etal., 2008). Empirical rainfall intensity–duration thresholds can be usedin applications designed to estimate the likelihood of landslideoccurrence for a given set of initial and rainfall conditions.

4.5. Hydraulic and strength properties of hillside materials

The strength and hydraulic properties of hillside materials and anestimate of their spatial distribution are required for models such asTRIGRS. Coulomb strength parameters (angle of internal friction andcohesion) can be obtained from standard geotechnical tests (e.g. Das,2000; Savage and Baum, 2005). Plant roots are thought to impartsignificant strength to hillside soils (e.g. Wu et al., 1979; Schmidt et al.,2001; Sidle and Ochiai, 2006); however, the resisting forces impartedby plant roots are typically dependent on failure depth and do notnecessarily parallel the ground surface. Lumping this contributionwith cohesion in infinite-slope stability analysis (Eq. (1)) is physicallyincorrect. Three-dimensional solutions are needed (e.g. Burroughs,1985; Dietrich et al., 2006) to accurately represent lateral resistingforces typically associated with vegetation roots.

Hydraulic properties of hillside materials that are typicallyrequired for analyses include the saturated hydraulic conductivityand saturated hydraulic diffusivity. Unlike material strength proper-ties, the saturated hydraulic conductivity of soils with similar texturesderived from the same parent material can vary over several orders ofmagnitude (Freeze and Cherry, 1979). Laboratory tests using eitherconstant or falling head instruments are typically used for measuringsaturated conductivity. Because diffusion solutions to groundwaterinfiltration are sensitive to the diffusivity term, some understanding ofthe unsaturated hydraulic characteristics of hillside materials isneeded to accurately estimate this parameter and to define therange of soil-moisture conditions for which the approximate solution(e.g. Eq. (5)) can be applied. Loose, coarse-grained colluvial soilstypically involved in shallow landslides exhibit pronounced hysteresisamong the relations between moisture content, pressure head andhydraulic conductivity (Freeze and Cherry, 1979). Laboratory tests todetermine the moisture content–pressure-head relation or soil–watercharacteristic curve (SWCC) and hydraulic conductivity function (HCF)should be obtained using a wetting process to simulate rainfallinfiltration. Examples include the so-called Bruce and Klute experi-ments for measuring soil–water diffusivity in which the water isallowed to imbibe into a horizontal column (Bruce and Klute, 1956;Clothier and Scotter, 2002). These tests are typically performed onrepacked materials and because bulk density has a significantinfluence on soil hydraulic properties, care should be taken toreplicate field densities or account for variation. Other laboratorytests include those using constant-flow permeameters that can beused to determine the SWCC and HCF for either the wetting or dryingprocess (Wildenschild et al., 1997; Lu et al., 2006).

In-situ tests on hillside materials in field areas probably providethemost representative estimates ofmaterial properties at the scale ofshallow landslides. Data from well and ring permeameter tests ofunsaturated materials can be used to estimate the field saturatedhydraulic conductivity (Reynolds et al., 2002). The term field saturatedis often used for these types of tests because air is usually entrapped inthe soil by infiltrating water, which is typically the case during naturalrainfall. Permeameter data can also be reduced to estimate unsatu-rated-zone parameters as well. Disc permeameters provide measure-ments of hydraulic conductivity at small negative pressures and datacan be reduced to estimate soil–water characteristic curves anddiffusivity (Clothier and Scotter, 2002).

Prediction of SWCCs from more easily measured soil parameterssuch as particle-size distributions has been performed using bothempirical and theoretical approaches (Brakensiek et al., 1981;Haverkamp and Parlange, 1986). The theoretical or physically-basedmodels (e.g. Arya and Paris, 1981) typically link the cumulativeparticle-size distribution and other properties such as bulk densitywith the SWCC. Empirical pedotransfer functions (PTFs) are used topredict soil hydraulic properties from readily available soil informa-tion such as bulk density and soil texture using regression or neuralnetwork techniques (Leij et al., 2002). Where soils mapping isavailable, this approach, combined with field and laboratory analysismay yield reasonable estimates of the spatial variability of materialparameters for model input. However, it is important to note thatwhile empirical models are available to account for hysteresis (e.g.Kool and Parker, 1987) most predictive models and PTFs are designedfor drying curves; empirical data for wetting curves are virtually non-existent (Leij et al., 2002).

More detailed information on empirical, field, and laboratorytechniques to determine soil hydraulic properties can be found in therelevant chapters of Dane and Topp (2002) and Lu and Likos (2004). Inthe following section we describe an example application of atransient infiltration slope stability model to a landslide-prone studyarea north of Seattle, Washington and compare results with those

Fig. 4. Rainfall (A), volumetric water content (B), and pressure head (C) measured atvarious depths at the Edmonds field site during the winter wet season. Arrows indicatethe timing of landslides near the monitoring site.

Fig. 3.Map showing landslides that occurred in the study area during the winter seasonof 1996–1997 (modified from Baum et al., 2000).

219J.W. Godt et al. / Engineering Geology 102 (2008) 214–226

from a static infinite-slope stability analysis assuming fixed water-table positions.

5. Example application

5.1. Physiographic and geologic setting of the study area

The 3 km2 study area is in the Puget Lowland about 15 km north ofSeattle,Washington (Fig. 2). The Puget Lowland is a broad basin locatedbetween theOlympicMountains to thewest and the active volcanic arcof the Cascade Range to the east. The topography of the Puget Lowlandconsists of rolling north–south oriented ridges and valleys left by theretreat of glacial ice about 16,400 years ago (Booth, 1987; Booth et al.,2005). Steep coastal bluffs line the shores of Puget Sound and otherbodies of surface water in the area and were formed by deposition ofmaterials prior to and during glacial advance, and their subsequenterosion byfluvial andhillslope processes andwave erosion of bluff toesfollowing glacial retreat (Booth,1987; Shipman, 2004). Glacial isostaticrebound and glacial tectonic uplift are responsible for the relativeelevation of the coastal bluff uplands above sea level. Since glacialretreat, the coastal bluffs have retreated by an estimated 150 to 900m,primarily by landslide processes andwave action (Galster and Laprade,1991; Shipman, 2004; Schulz, 2007). Many of the bluffs (including

those of the study area) are now protected from wave attack byshoreline protection structures and engineered fill.

The climate of the Seattle area is characterized by a pronouncedseasonal precipitation regime with a wintertime maximum; 75% ofthe annual precipitation total of 963 mm falls between November andApril (Church, 1974). Storms that trigger shallow landslides in Seattleare generally of long duration (more than 24 h) and of relatively lowintensity compared to landslide-causing rainfall in other parts ofNorth America (Godt et al., 2006).

During the winter season of 1997–1998 heavy rainfall and themelting of a deep snowpack triggered numerous shallow landslides onthe bluffs along Puget Sound that periodically disrupted rail service onthe Seattle to Everett corridor (Baum et al., 2000). Fig. 3 shows part ofa landslide inventory for an area along the Puget Sound north ofSeattle, Washington, compiled primarily from the interpretation of1:12,000 color aerial photography taken in May of 1998 (Baum et al.,2000). The inventory shows the outlines of shallow landslide scars anddeposits in the study area.

Shallow landslides in the Seattle area commonly involve the thin(less than 3 m thick) colluvium that mantles the steep hillslopes(Tubbs,1974; Galster and Laprade,1991; Baumet al., 2000; Schulz et al.,2008). The colluvium is largely the product of mechanical weatheringof the underlying glacial and non-glacial parent sediments, land-sliding, and other mass-movement processes. The particle-sizedistribution of the colluvium is generally dominated by sand, but

220 J.W. Godt et al. / Engineering Geology 102 (2008) 214–226

ranges from boulders to silt and clay (Galster and Laprade, 1991; Godtand McKenna, 2008). Gravel and cobble-sized material is generallysupplied by the Vashon till (Qvt), a highly-variable, basal-lodgementtill that discontinuously caps many of the uplands in the Seattle area.An extensive water-bearing unit, the Vashon advance outwash sand(Qva) supplies mainly sand-sized material. Finer-grained material issupplied by the generally well-consolidated sediments of Pleistoceneand older Quaternary age that underlie Qva and in the study area aremapped as transition beds (Qtb) by Minard (1982).

5.2. Field monitoring site

A system to monitor the shallow groundwater response to rainfallinfiltration operated for 4 winter seasons on an area of steep (N40°)landslide-prone coastal bluffs (Baum et al., 2000) about 3 km southof the study area near Edmonds, Washington (Fig. 2) and was part of aU.S. Geological Survey near-real-time landslide-monitoring projectalong the Seattle — Everett, Washington rail corridor (Baum et al.,2005: Godt and McKenna, 2008). The 50-m-high bluff is capped byVashon-age glacial till (Qvt) and is underlain by subhorizontallybedded glacial advance outwash sand overlying glaciolacustrine siltdeposits (Minard,1982). Themonitoring instruments were installed inthe dense, uniform, medium outwash sand about 30m above sea levelin Puget Sound. A thin (10 to 20 cm), loose, sandy colluvium producedby mechanical weathering of the outwash sand covers much of thehillside in the area where the instruments were installed. Downslopefrom the instrument installations, the colluvium is thicker (1 m). InJanuary of 2006 a shallow landslide destroyed most of the instrumentarray. Details on the instruments and monitoring data are available inBaum et al. (2005) and in Godt and McKenna (2008).

Monitoring data (Fig. 4) collected in a landslide-prone hillside nearSeattle show that soil moisture is strongly seasonal (Baum et al.,2005). Soil moisture begins to increase near the ground surface with

Fig. 5.Maps showing topographic slope (A), depth to the lower boundary (B), and simplified ginclude: Qtb = transition beds including the Lawton Clay, Qva = Advance outwash sand, Qvt

the onset of rainy weather in the late fall and early winter. At depthsgreater than 1m the soil moisture begins to increase after the first fewrainstorms and typically stays elevated until later March or early Aprilwith the cessation of consistently wet weather. At the timescale ofindividual storms, the pore-water response to rainfall varies as afunction of the water content of the soil; when soils are initially wet,infiltrating rainfall causes wetting fronts to rapidly propagate throughthe upper 2 m of hillside materials, however, the magnitude of theresponse is attenuated with depth and rainfall of high intensity andshort duration has a limited effect at depth. Monitoring observationsprior to shallow landslides occurring near the field sites indicate thatpressure heads in hillside materials were near zero (Fig. 4).

5.3. Input data

For the application presented here, slope angles (Fig. 5A) werecalculated from a 1.83-m (6 ft) DEM derived from remotely-sensedLiDAR elevation data (Haugerud et al., 2003). These data have beenprocessed to provide a detailed depiction of the ground surfacebeneath vegetation. We follow DeRose (1996) and Salciarini et al.(2006) and estimate the depth to the lower boundary, dlb, (Fig. 5B) asan exponential function of slope, β, where dlb=7.72 e−0.04β so that dlbis at a minimum of about 0.5 m on the steepest slopes, about 1.4 m on40° slopes, and about 2.0 m on 30° slopes consistent with fieldobservations of shallow landslide failure depths in the study area (e.g.Baum et al., 2000; Baum et al., 2006). The assumption of tension-saturated materials in the infiltration model of TRIGRS (Baum et al.,2002) is consistent with field monitoring observations describedabove and for this applicationwe assume that the initial water table iscoincident with the lower boundary. Three property zones (Fig. 5C)were defined based on geologic mapping of the area (Minard, 1982)with an assumption that the fine-grained fraction of the colluviumincreases with decreasing elevation (Godt et al., 2008). The saturated

eology (C) for the study area. Geologymodified fromMinard (1982). Geologic map units= till.

Fig. 7. Example contingency table (also known as a confusion matrix) for a two classproblem and performance metrics calculated from it. Each output grid cell from thethree models can be mapped to one of the four elements of the matrix. See text for anexplanation of criteria for membership in each of the elements and performancemetrics (modified from Fawcett, 2006).

Table 1Material strength and hydraulic properties for the three geologic units in Fig. 5C

Unit IZa KS

b D0c ϕ′d c′e

(m/s) (m/s) (m2/s) (°) (kPa)

Qtbf 1.5×10−7 1.0×10−5 5.0×10−5 33.6 4.6Qvag 1.5×10−7 5.0×10−5 1.0×10−4 33.6 4.6Qvth 1.5×10−7 1.0×10−6 1.0×10−5 33.6 6.0

a IZ = long-term rainfall flux.b KS = saturated hydraulic conductivity.c D0 = hydraulic diffusivity.d ϕ′ = minimum angle of internal friction for effective stress.e c′ = cohesion for effective stress.f Qtb = transition beds including the Lawton Clay.g Qva = advance outwash sand.h Qvt = till.

221J.W. Godt et al. / Engineering Geology 102 (2008) 214–226

hydraulic conductivity (Table 1) was estimated for the three unitsbased on slug tests performed at the field monitoring site and well-permeameter tests performed in the study area and elsewhere in theSeattle area in similar geologic formations and hillside deposits.Hydraulic diffusivity (Table 1) was estimated using results from open-tube capillary rise tests performed to determine the SWCC for thewetting process of colluvial soils in the study area and comparison ofTRIGRS results with fieldmonitoring data and 1-D numerical solutionsfor vertical flow in the unsaturated zone (Godt et al., 2008; Godt andMcKenna, 2008). Material strength parameters were taken from directshear tests on colluvial soil (Godt and McKenna, in press). We apply aconstant rainfall flux of 1.5 mm/h for 36 h, which just exceeds theempirical threshold (Fig. 6) defined for the Seattle area (Godt et al.,2006).

5.4. Interpretation and testing of model results

Pore-pressures and factors of safety, FS, are calculated at everytimestep for each 1.8 m grid cell over the approximately 5×105 cells.Because thesegrid cells aremuchsmaller than typical shallow landslidesin the study area, we aggregate the FS results to a 9×9 m grid. Ninemeters is approximately the lateral dimension of the smallest landslidemapped in the study area. To create the aggregated grid each small(1.83 m) grid cell is assigned either a 1 or 0 to indicate that it is eitherstable (FSN1.0) or unstable (FS=1.0), respectively. The value thenassigned to the large (9 m) grid is based on the value of the majorityof the 25 small grid cells. If 13 ormore of the small grid cells have FS=1.0

Fig. 6. Rainfall intensity–duration threshold above which the occurrence of widespreadshallow landslides can be expected in the Seattle area. Threshold can be represented byI=82.73D−1.13 where I is the mean rainfall intensity (in mm/h) and D is the stormduration (in h) (modified from Godt et al., 2006).

then the aggregated cell is unstable. The operation is not performed in amoving-window fashion, but bymovinganon-overlapping9×9mblockacross the digital landscape. The aggregated stability grid can then becompared to the landslide inventory at roughly similar scales.

The success of regional landslide susceptibility models has beentypically evaluated by comparing the location of known landslideswith model results (e.g. Montgomery et al., 1998, 2001; Godt et al.,2008). The least critical test is to count a success when a single gridcell with a FS=1.0 falls within a mapped landslide polygon. Morecritical tests involve some assessment 1) the model's ability tocorrectly identify mapped landslides (true positive), 2) the error whenmapped landslides are not correctly identified (false negative), and 3)over prediction (false positive). An ideal landslide susceptibility mapsimultaneously maximizes the agreement between known andpredicted landslide locations and minimizes the area outside theknown landslides predicted to be unstable (over prediction).

Originally developed for use in signal detection theory and appliedin diverse fields such as epidemiology, weather forecasting, machinelearning, and landslide susceptibility mapping, receiver operatingcharacteristics (ROC) graphs are a technique to assess the performanceof models for which results can be assigned to one of two classes orstates (Swets, 1988; Fawcett, 2006; Van Den Eeckhaut et al., 2006). Forlimit-equilibrium slope stability models, the states are stable or un-stable, and for comparison of grid-based predictions of slope stabilitywith a landslide inventory, four outcomes are possible for each grid

Fig. 8. Pore-pressure response (dashed line) and resultant factor of safety (solid line)simulatedwith TRIGRS for a single cell with a depth of 1.0 m an initial water-table depthof 1.0 m, and a slope angle of 40° for a constant rainfall of 1.5 mm/h.

222 J.W. Godt et al. / Engineering Geology 102 (2008) 214–226

cell. If the grid cell is modeled to be unstable and is coincident with amapped landslide in the inventory it is counted as a true positive; if itfalls outside a mapped landslide it is counted as a false positive. If thegrid cell is modeled to be stable and it falls outside a mapped slide it iscounted as a true negative; if it falls within a mapped slide it is countedas a false negative. The outcome counts can be entered in a 2×2contingency table (so-called confusion matrix, Fig. 7) from whichseveral measures of model performance can be calculated (Fawcett,2006). The true positive rate is the ratio of the number of true positivesto the total number of positives (landslide cells). The false positive rateis ratio of the number of false positives to the to the total number ofnegatives (non-landslide cells). Areas with slopes ≤15° were excludedfrom the analysis because: 1) the mapped landslides include shallowlandslide sources as well as deposits and the deposits tend to be on flatslopes and the models do not account for travel or deposition, and 2)for the material strengths (Table 1) and soil depths (Fig. 5B) used inthis study, slopes less than about 17° are stable under any hydrologiccondition resulting from infiltration.

6. Results

Fig. 8 shows the pore-pressure response and resultant factor ofsafety at the lower boundary for an example grid cell with a 40° slopeand outwash sand material properties (Table 1). The depth to thelower boundary and initial water-table depth were both 1.0 m.Pressure head increases linearly after the first hour in response toconstant rainfall of 1.5 mm/h, which results in a linear decrease in thefactor of safety with time. Failure is predicted after about 35 h ofrainfall. Pressure head and factors of safety are calculated in the samemanner for about 5×105 cells in the study area.

After 36 h of rainfall, pressure heads have increased at the base ofeach cell from the initial condition of zero to greater than 0.4 m; thespatial variability in the pressure head increase is a function of the

Fig. 9.Modeled pressure head (A), factor of safety (B), and aggregated factor of safety (C) after 3

slope, depth, and hydraulic properties of the hillside materials(Fig. 9A). The resultant factor of safety reflects the pattern of thesesame variables since we assume the material strength properties arethe same throughout the study area (Fig. 9B). Factors of safety equal to1.0 are located in the steepest topography along the bluff crests and atthe toe of the bluffs along the Puget Sound. Fig. 10C shows theaggregated factor of safety; the main effect of aggregation is toeliminate isolated cells with FS=1.0.

6.1. Comparison of TRIGRS results with static factor of safety maps

Fig. 10 compares the results from the TRIGRS model that accountsfor the transient effects of rainfall infiltration on pressure head withresults from a static infinite-slope analysis assuming two water-tableconditions. All other factors are equal or held constant between thethree analyses. The static maps were generated by applying Eq. (1) ona cell-by-cell basis for the material strength properties in Table 1 anddepths shown in Fig. 5B. Pore-pressures, ψ, were calculated with thewater table located at half the depth of the lower boundary (Fig. 10A)and at the ground surface (Fig. 10B) assuming slope parallel flow overan impermeable lower boundary

ψ ¼ mdlb cos2 β ð7Þ

where m is the vertical height of the water table expressed as afraction of the total depth, dlb, and β is the slope angle. Both staticinfinite-slope analyses capturemore of themapped landslide area andpredict more of the study area to be unstable compared to thatpredicted using the transient analysis.

Fig.11 is a ROC graph comparing the results from the static infinite-slope stability calculations (m=0.5 and m=1.0) with those from theTRIGRS model and depicts the relative tradeoff between success (truepositives) and over prediction (false positives). Model results that plot

6 h of rainfall. Pressure heads and factors of safety are not shown for cells with slopes ≤15°.

Fig. 10. Extent of unstable area for static infinite-slope stability calculation assuming the water-table depth is half the depth to the lower boundary (A) (m=0.5), at the ground surface(m=1.0) (B), and for the transient solution in the TRIGRS model after 36 h of rainfall (C).

223J.W. Godt et al. / Engineering Geology 102 (2008) 214–226

towards the upper left of the graph are generally considered superior.The origin of graph (0,0) represents a model result with no falsepositive errors because it predicts no instability. The converse, a modelresult where the entire area is predicted to be unstable would belocated at the upper right (1,1). A perfect prediction would be locatedat the upper left (0,1). A model result that falls along the dashed line isconsidered random in that it predicts instability falling within andoutside the mapped landslides at the same rate (Fawcett, 2006).Comparison of the three models shows that while the TRIGRS model

Fig. 11. ROC graph comparing the results from each of the three models. Grid cells withslopes ≤15° were excluded from the analysis.

tends to under predict the spatial extent of landslides relative to thestatic factor of safety calculations, its over prediction is much lesssevere (Table 2). The lower rate of over prediction of the TRIGRSmodelyields much greater estimates of accuracy and precision compared tothe static models.

Calibration of material strength parameters and water-tabledepths to generate a best fit to the landslide inventory could beperformed and would likely improve the spatial prediction of thestatic susceptibilitymap (Harp et al., 2006). However, our results showthat the transient analysis yields an improved prediction for this studyarea using material strength and hydraulic properties measured in thefield and laboratory and for pore-pressure distributions that arephysically linked with rainfall infiltration.

7. Concluding discussion

Accounting for the transient effects of rainfall infiltration on pore-water response and consequent effects on slope stability improves theeffectiveness of regional shallow landslide hazard maps. Because thetransient model physically links rainfall with pore-water response at

Table 2Comparison of model performance between static infinite-slope stability calculationsfor two water-table positions and results from the transient TRIGRS model after 36 h ofrainfall

Model Truepositiverate

Falsepositiverate

Falsenegativerate

Accuracy Precision

Static factor of safetywith m=1.0

0.95 0.86 0.05 0.22 0.11

Static factor of safetywith m=0.5

0.63 0.33 0.37 0.66 0.18

TRIGRS 36 h 0.42 0.16 0.58 0.80 0.23

Grid cells with slopes≤15° were excluded from the analysis. See text and Fig. 11 forexplanation of performance metrics.

224 J.W. Godt et al. / Engineering Geology 102 (2008) 214–226

depth, results can be depicted in terms of historical, real-time, orforecasted rainfall. This greatly expands the range of landslide hazardissues and questions that can be explored compared to what can beexamined using static analysis. However, transient modeling ofinfiltration and landslide processes over broad regions requiresunderstanding of initial and boundary conditions as well as materialstrength and hydraulic properties and some estimate of their spatialvariability. High-resolution (≤10 m) topographic data are required forthe assessment of shallow landslide susceptibility and the increasingavailability of LiDAR data promises to provide accurate topographicinformation even in heavily vegetated landscapes. In areas whereabundant geotechnical information is available, site-specific, empiri-cal models of soil thickness and water-table depth can be used toprovide initial and boundary conditions such as used in the examplepresented here. Most applications, however, are likely to be in areaswhere such information is lacking and process-based theoreticalmodels may provide away to characterize the spatial variability of soilthickness and groundwater conditions over broad areas. Additionalwork is needed to show that the theoretical soil-thickness models areappropriate for landscapes in which shallow landslides and debrisflows dominate sediment transport. Field and laboratory methodsdeveloped for soil science applications can be adapted to determinethe hydraulic properties of hillside materials; but, appropriatestatistical relations between soil hydraulic properties and more easilymeasured parameters such as grain-size distributions (so-calledPedotransfer Functions) await the collection of adequate field andlaboratory data for the wetting process. Additional research is neededto identify the most effective ways to describe boundary and initialconditions and determine and map hillside material properties beforetransient landslide susceptibility models such as TRIGRS (Baum et al.,2002) can be applied as a hazard management tool.

The example presented here, with simple assumptions of slopedependent boundary and initial conditions and material strength andhydraulic properties for hillside materials measured in the field andlaboratory, yielded an improved spatial prediction of shallow land-slide occurrence compared to static infinite-slope stability analyseswith fixed water-table depths. Results from the static analyses withthe water table located at the ground surface can be interpreted as themost conservative; however such assessments risk being under-utilized because they tend to depict all steep slopes as equallyhazardous. These results from the transient analysis suggest that thespatial and temporal accuracy of the shallow landslide susceptibilitymodel can be further improved with accurate characterization of theinitial and boundary conditions and spatial distribution of materialproperties. Incorporation of the effects of the unsaturated zone oninfiltration (Savage et al., 2004; Baum et al., 2008) and slope stability(Fredlund et al., 1978; Collins and Znidarcic, 2004; Lu and Likos, 2004;Baum et al., 2006) may also improve model results.

Acknowledgements

Brian Collins, Jason Kean, Paolo Frattini, and an anonymousreviewer provided thoughtful and constructive reviews of this paper.Paolo Frattini also suggested the application of the ROC technique forcomparing the static and transient analyses.

References

Anderson, M.G., Howes, S., 1985. Development of a combined soil water-slope stabilitymodel. Quarterly Journal of Engineering Geology 18, 225–236.

Andrews, D.J., Bucknam, R.C., 1987. Fitting degradation of shoreline scarps by anonlinear diffusion model. Journal of Geophysical Research 92, 12,857–12,867.

Arya, L.M., Paris, J.F., 1981. A physico-empirical model to predict the soil moisturecharacteristic from particle size distribution and bulk density data. Soil ScienceSociety of America Journal 45, 1023–1030.

Baum, R.L., Harp, E.L., Hultman, W.A., 2000. Map showing recent and historic landslideactivity on coastal bluffs of Puget Sound between Shilshole Bay and Everett,Washington. U.S. Geological Survey Miscellaneous Field Studies Map MF-2346.

Baum, R.L., Savage, W.Z., Godt, J.W., 2002. TRIGRS: a Fortran program for transientrainfall infiltration and grid-based slope-stability analysis. U.S. Geological SurveyOpen-File Report 2002-424. 38 pp.

Baum, R.L., McKenna, J.P., Godt, J.W., Harp, E.L., McMullen, S.R., 2005. Hydrologicmonitoring of landslide-prone coastal bluffs near Edmonds and Everett, Washing-ton. U.S. Geological Survey Open-File Report. 42 pp.

Baum, R.L., Godt, J.W., Savage, W.Z., 2006. Unsaturated zone effects in predictinglandslide and debris-flow initiation. Eos Transactions of the American GeophysicalUnion 87 (52) H54B-06.

Baum, R.L., Savage, W.Z., Godt, J.W., 2008. TRIGRS — A FORTRAN program for transientrainfall infiltration and grid-based regional slope stability analysis, Version 2.0. U.S.Geological Survey Open-File Report, 2008-1159, 75 pp. http://pubs.er.usgs.gov/usgspubs/ofr/ofr20081159.

Booth, D.B., 1987. Timing and processes of deglaciation along the southernmargin of theCordilleran ice sheet. In: Ruddiman, W.F., WrightJr. Jr., H.E. (Eds.), North Americaand Adjacent Oceans During the Last Deglaciation; The Geology of North America,K-3. Geological Society of America, Boulder, Colorado, pp. 71–90.

Booth, D.B., Troost, K.G., Shimel, S.A., 2005. Geologic map of northwestern Seattle (partof the Seattle north 7.5′×15′ quadrangle), King Count, Washington. U.S. GeologicalSurvey Scientific Investigations Map 2903.

Borga, M., Fontana, G.D., Ros, D.D., Marchi, L., 1998. Shallow landslide hazard assessmentusing a physically based model and digital elevation data. Environmental Geology35 (2–3), 81–88.

Brakensiek, D.L., Engleman, R.L., Rawls, W.J., 1981. Variation in texture classes of soilwater parameters. Transactions of the ASAE 24, 335–339.

Bruce, R.R., Klute, A., 1956. The measurement of soil moisture diffusivity. Soil ScienceSociety of America Proceeings 20, 458–462.

Bucknam, R.C., Coe, J.A., Cavarria,M.M., Godt, J.W., Tarr, A.C., Bradley, L., Rafferty, S.A., Hancock,D., Dart, R.L., Johnson,M.L., 2001. Landslides triggeredbyHurricaneMitch inGuatemala—inventory and discussion. U.S. Geological Survey Open-File Report 2001-443. 38 pp.

Burroughs Jr., E.R.,1985. Landslide hazard rating for the Oregon Coast Range. In: Jones, E.B.,Ward, T.J. (Eds.), Watershed Management in the Eighties: Proceedings of theSymposium Sponsored by the Committee on Watershed Management of theIrrigation and Drainage Division of the American Society of Civil Engineers. ASCE,New York, pp. 132–139.

Cannon, S.H., Gartner, J.E., Rupert, M.G., Michael, J.A., 2004. Emergency assessment ofdebris-flow hazards from basins burned by the Padua fire of 2003, southern,California. U.S. Geological Survey Open-File Report 2004-1072. 14 pp.

Carrara, A., Guzzetti, F., Cardinali, M., Reichenbach, P., 1999. Use of GIS technology in theprediction and monitoring of landslide hazard. Natural Hazards 20 (2–3), 117–135.

Casadei, M., Deitrich, W.E., Miller, N.L., 2003. Testing a model for predicting the timingand location of shallow landslide initiation in soil-mantled landscapes. EarthSurface Processes and Landforms 28, 925–950.

Church, P.E., 1974. Some precipitation characteristics of Seattle. Weatherwise,December, pp. 244–251.

Claessens, L., Heuvelink, G.B.M., Schoorl, J.M., Veldkamp, A., 2005. DEM resolutioneffects on shallow landslide hazard and soil distribution modeling. Earth SurfaceProcesses and Landforms 30, 461–477.

Clothier, B., Scotter, D., 2002. Unsaturated water transmission parameters obtainedfrom infiltration. In: Dane, J.H., Topp, G.C. (Eds.), Methods of Soil Analysis — Part 4Physical Methods. Soil Science Society of America, Madison, WI, pp. 879–898.

Coe, J.A., Michael, J.A., Crovelli, R.A., Savage, W.Z., Laprade, W.T., Nashem, W.D., 2004.Probabilistic assessment of precipitation-triggered landslides using historicalrecords of landslide occurrence, Seattle, Washington. Environmental Engineeringand Geoscience 10 (2), 103–122.

Collins, B.D., Znidarcic, D., 2004. Stability analyses of rainfall induced landslides. Journalof Geotechnical and Geoenvironmental Engineering 130, 362–372.

Crosta, G.B., Frattini, R., 2003. Distributed modelling of shallow landslides triggered byintense rainfall. Natural Hazards and Earth System Sciences 3, 81–93.

Culling, W.E.H., 1960. Analytical theory of erosion. Journal of Geology 68, 336–344.Dane, J.H., Topp, G.C. (Eds.), 2002. Methods of Soil Analysis — Part 4 Physical Methods.

Soil Science Society of America, Madison, WI. 1692 pp.Das, B.M., 2000. Fundamentals of Geotechnical Engineering. Brooks/Cole, Pacific Grove,

CA. 593 pp.Dengler, L., Montgomery, D.R., 1989. Estimating the thickness of colluvial fill in

unchanneled valleys from surface topography. Bulletin of the Association ofEngineering Geologists 16 (3), 333–342.

DeRose, R.C., 1991. Geomorphic change implied by regolith–slope relationships onsteepland hillslopes, Taranaki, New Zealand. Catena 18, 489–514.

DeRose, R.C., 1996. Relationships between slope morphology, regolith depth, and theincidence of shallow landslides in eastern Taranaki hill country. Zeitschrift fürGeomorphologie Supplementband 105, 49–60.

Dietrich, W.E., Dunne, T., 1978. Sediment budget for a small catchment in mountainousterrain. Zeitschrift für Geomorphologie Supplementband 29, 191–206.

Dietrich, W.E., Wilson, C.J., Reneau, S.L., 1986. Hollows, colluvium and landslides in soil-mantled landscapes. In: Abrahams, A.D. (Ed.), Hillslope Processes. Allen and Unwin,London, UK, pp. 361–385.

Dietrich, W.E., Reiss, R., Hsu, M., Montgomery, D.R., 1995. A process-based model forcolluvial soil depth and shallow landsliding using digital elevation data. Hydro-logical Processes 9, 383–400.

Dietrich, W.E., McKean, J., Bullugi, D., 2006. The prediction of landslide size using amulti-dimensional stability analysis. Eos Transactions of the American GeophysicalUnion 87 (52) H54B-01.

D'Odorico, P., Fagherazzi, S., Rigon, R., 2005. Potential for landsliding: dependence onhyetograph characteristics. Journal of Geophysical Research 110, F01007.

Fawcett, T., 2006. An introduction to ROC analysis. Pattern Recognition Letters 27, 861–874.

225J.W. Godt et al. / Engineering Geology 102 (2008) 214–226

Fredlund, D.G., Morgenstern, N.R., Widger, R.A., 1978. Shear strength of unsaturatedsoils. Canadian Geotechnical Journal 15, 313–321.

Freeze, R.A., 1969. The mechanism of natural ground-water recharge and discharge 1.One-dimensional, vertical, unsteady, unsaturated flow above a recharging ordischarging ground-water flow system. Water Resources Research 5, 153–171.

Freeze, R.A., Cherry, J.A., 1979. Groundwater. Prentice-Hall Inc., Englewood Cliffs, NewJersey. 604 pp.

Galster, R.W., Laprade, W.T., 1991. Geology of Seattle, Washington, United States ofAmerica. Bulletin of the Association of Engineering Geologistst 18, 235–302.

Garbrecht, J., Martz, L., 1994. Grid size dependency of parameters extracted from digitalelevation models. Computers and Geosciences 20 (1), 85–87.

Godt, J.W., Coe, J.A., 2003. Map showing alpine debris flows triggered by a July 28, 1999thunderstorm in the Central Front Range of Colorado. U.S. Geological Survey Open-File Report 03-0050, scale 1:24,000, 4 pp.

Godt, J.W., Baum, R.L., Chleborad, A.F., 2006. Rainfall characteristics for shallow landslidingin Seattle, Washington, USA. Earth Surface Processes and Landforms 31, 97–110.

Godt, J.W., McKenna, J.P., 2008. Numerical modeling of rainfall thresholds forshallow landsliding in the Seattle, Washington, area. In: Baum, R.L., Godt, J.W., Highland,L.M. (Eds.), LandslidesandEngineeringGeologyof theSeattleWashingtonArea.GeologicalSociety of America Reviews in Engineering Geology, vol. 20. doi:10.1130/2008.4020(07).

Godt, J.W., Schulz, W.H., Baum, R.L., Savage, W.Z., 2008. Modeling rainfall conditions forshallow landsliding in Seattle, Washington. In: Baum, R.L., Godt, J.W., Highland, L.M.(Eds.), Landslides and Engineering Geology of the Seattle Washington Area. GeologicalSocietyof AmericaReviews inEngineeringGeology, vol. 20. doi:10.1130/2008.4020(08).

Guzzetti, F., Carrara, A., Cardinali, M., Reichenbach, P., 1999. Landslide hazardevaluation: a review of current techniques and their application in a multi-scalestudy, Central Italy. Geomorphology 31 (1–4), 181–216.

Haneberg, W.C., 2006. Effects of digital elevation model errors on spatially distributedseismic slope stability calculations: an example from Seattle, Washington.Environmental & Engineering Geoscience 12 (3), 247–260.

Haneberg, W.C., 2008. Elevation errors in a LiDAR Digital Elevation Model of WestSeattle and their effects on slope stability calculations. In: Baum, R.L., Godt, J.W.,Highland, L.M. (Eds.), Landslides and Engineering Geology of the SeattleWashington Area. Geological Society of America Reviews in Engineering Geology,vol. 20. doi:10.1130/2008.4020(03).

Harp, E.L., Jibson, R.W., 1995. Inventory of landslides triggered by the 1994 Northridge,California earthquake. U.S. Geological Survey Open-File Report. 18 pp.

Harp, E.L., Michael, J.A., Laprade, W.T., 2006, Shallow-landslide hazard map of Seattle,Washington. U.S. Geological Survey Open-File Report 2006-1139. Scale: 1:25,000, 2sheets, 20 p.

Haugerud,R.A.,Harding,D.J., Johnson, S.Y.,Harless, J.L.,Weaver, C.S., Sherrod, B.L., 2003.High-resolution Lidar topography of the Puget Lowland, Washington. GSA Today 13, 4–10.

Haverkamp, R., Parlange, J.Y., 1986. Predicting the water retention curve from particle-size distribution: I. Sand soils without organic matter. Soil Science 142, 325–339.

Heimsath, A.M., Dietrich, W.E., Nishiizumi, K., Finkel, R.C., 1997. The soil productionfunction and landscape equilibrium. Nature 388, 358–361.

Heimsath, A.M., Dietrich, W.E., Nishiizumi, K., Finkel, R.C., 1999. Cosmogenic nuclides,topography, and the spatial variation of soil depth. Geomorphology 27, 151–172.

Heimsath,A.M., Chappell, J., Dietrich,W.E.,Nishiizumi,K., Finkel, R.C., 2000. Soil productionon a retreating escarpment in southeastern Australia. Geology 28 (9), 787–790.

Heimsath, A.M., Dietrich, W.E., Nishiizumi, K., Finkel, R.C., 2001. Stochastic processes of soilproduction and transport: erosion rates, topographic variation andcosmogenic nuclidesin the Oregon Coast Range. Earth Surface Processes and Landforms 26, 531–552.

Holmes, K.W., Chadwick, O.A., Kyriakidis, P.C., 2000. Error in a USGS 30-meter digitalelevationmodel and its impacton terrainmodeling. Journal ofHydrology233,154–173.

Iverson,R.M.,1990.Groundwaterflowfields in infinite slopes.Geotechnique40 (1),139–143.Iverson, R.M., 2000. Landslide triggering by rain infiltration. Water Resources Research

36 (7), 1897–1910.Iverson, R.M., Reid, M.E., LaHusen, R.G., 1997. Debris-flow mobilization from landslides.

Annual Review of Earth and Planetary Sciences 25, 85–138.Jibson, R.W., Harp, E.L., Michael, J.A., 2000. A method for producing digital probabilistic

seismic landslide hazard maps. Engineering Geology 58, 271–289.Kool, J.B., Parker, J.C., 1987. Development and evaluation of closed-form expressions for

hysteretic soil hydraulic properties. Water Resources Research 23, 105–114.Leij, P.J., Schaap, M.G., Arya, L.M., 2002. Indirect Methods. In: Dane, J.H., Topp, G.C. (Eds.),

Methods of Soil Analysis— Part 4 Physical Methods. Soil Science Society of America,Madison, WI, pp. 1009–1045.

Lu,N., Likos,W.J., 2004.Unsaturated SoilMechanics. JohnWiley&Sons,Hoboken,NJ. 556pp.Lu, N., Wayllace, A., Carrera, J., Likos, W.J., 2006. Constant flowmethod for concurrently

measuring soil–water characteristic curve and hydraulic conductivity function.Geotechnical Testing Journal 29 (3), 230–241.

McKean, J.A., Dietrich, W.E., Finkel, R.C., Southon, J.R., Caffee, M.W., 1993. Quantificationof soil production and downslope creep rates from cosmogenic 10Be accumulationson a hillslope profile. Geology 21, 343–346.

McKean, J., Roering, J., 2004. Objective landslide detection and surface morphologymapping using high-resolution airborne laser altimetry. Geomorphology 57, 331–351.

Minard, J.P., 1982, Distribution and description of geologic units in the MukilteoQuadrangle, Washington. U.S. Geological Survey Miscellaneous Field Studies MapMF-1438, scale 1:24,000.

Montgomery, D.R., Dietrich, W.E., 1994. A physically-based model for the topographiccontrol on shallow landsliding. Water Resources Research 30 (4), 1153–1171.

Montgomery, D.R., Greenberg, H.M., Laprade, W.T., Nashem, W.D., 2001. Sliding inSeattle: test of a model of shallow landsliding potential in an urban environment.In: Wigmosta, M.S., Burges, S.J. (Eds.), Land Use and Watersheds: Human Influenceon Hydrology and Geomorphology in Urban and Forest Areas: Water Science andApplication. American Geophyisical Union, Washington D.C., pp. 59–73.

Montgomery, D.R., Sullivan, K., Greenberg, H.M., 1998. Regional test of a model forshallow landsliding. Hydrological Processes 12 (6), 943–955.

Morrissey, M.M., Wieczorek, G.F., Morgan, B.A., 2001. A comparative analysis of hazardmodel for predicting debris flows in Madison County, Virginia. U.S. GeologicalSurvey Open-File. Report 01-0067, http://pubs.usgs.gov/of/2001/ofr-01-0067/.

Morrissey, M.M., Wieczorek, G.F., Morgan, B.A., 2004. Transient hazard model usingradar data for predicting debris flows in Madison County, Virginia. Environmentaland Engineering Geoscience 10 (4), 285–296.

Pack, R.T., Tarboton, D.G., Goodwin, C.N., 1998. The SINMAP approach to terrain stabilitymapping. Proceedings of the 8th Congress of the Association of Engineering ofGeology, vol. 2, pp. 1157–1165.

Parlange, J.Y., 1972. Theory of water movement in soils: 8. One dimensional infiltrationwith constant flux at the surface. Soil Science 114, 1–4.

Philip, J.R., 1957. The theory of infiltration 1. Soil Science 83, 345–357.Philip, J.R.,1991. Hillslope infiltration: planar slopes.WaterResources Research27,109–117.Reneau, S.L., Dietrich, W.E., 1987. The importance of hollows in debris flow studies:

examples fromMarin County, California. In: Costa, J.E., Wieczorek, G.F. (Eds.), DebrisFlows/Avalanches: Process, Recognition, and Mitigation. . Review in EngineeringGeology, vol. 7. Geological Society of America, pp. 165–658.

Reneau, S.L., Dietrich, W.E., Donahue, D.J., Jull, A.J.T., Rubin, M., 1990. Later Quaternaryhistory of colluvial deposition and erosion in hollows, central California CoastRanges. Geological Society of America Bulletin 102, 969–982.

Reynolds, W.D., Elrick, D.E., Youngs, E.G., Amoozegar, A., 2002. Field methods (Vadoseand saturated zone techniques). In: Dane, J.H., Topp, G.C. (Eds.), Methods of SoilAnalysis — Part 4 Physical Methods. Soil Science Society of America, Madison, WI,pp. 817–858.

Roering, J.J., Kirchner, J.W., Dietrich, W.E., 1999. Evidence for nonlinear, diffusivesediment transport on hillslopes and implications for landscape modeling. WaterResources Research 35, 853–870.

Roering, J.J., Kirchner, J.W., Dietrich,W.E., 2001a. Hillslope evolution by nonlinear, slope-dependent transport: steady state morphology and equilibrium adjustmenttimescales. Journal of Geophysical Research 106 (B8), 16,499–16,513.

Roering, J.J., Kirchner, J.W., Sklar, L.S., Dietrich, W.E., 2001b. Hillslope evolution bynonlinear creep and landsliding: an experimental study. Geology 29 (2), 143–146.

Rubin, J., Steinhardt, R., 1963. Soil water relations during rain infiltration: 1. Theory. SoilScience Society of America Proceedings 27, 246–251.

Salciarini, D., Godt, J.W., Savage, W.Z., Conversini, R., Baum, R.L., Michael, J.A., 2006.Modeling regional initiation of rainfall-induced shallow landslides in the easternUmbria Region of central Italy. Landslides 3, 181–194.

Savage, W.Z., Baum, R.L., 2005. Instability of steep slopes. In: Jakob, M., Hungr, O. (Eds.),Debris-Flow Hazards and Related Phenomena. Springer, Berlin, pp. 53–77.

Savage, W.Z., Godt, J.W., Baum, R.L., 2003. A model for spatially and temporallydistributed landslide initiation by rainfall infiltration. In: Rickenmann, D., Chen,Chen-lung (Eds.), Debris Flow Hazards Mitigation: Mechanics, Prediction, andAssessment. Millpress, Rotterdam, The Netherlands, pp. 179–187.

Savage, W.Z., Godt, J.W., Baum, R.L., 2004. Modeling time-dependent areal slopestability. In: Lacerda, W.A., Ehrlich, M., Fontoura, S.A.B., Sayao, A.S.F. (Eds.),Landslides. Taylor and Francis Group, London, pp. 23–36.

Schmidt, K.M., Roering, J.J., Stock, J.D., Dietrich, W.E., Montgomery, D.R., Schaub, T., 2001.The variability of root cohesion as an influence on shallow landslide susceptibilityin the Oregon Coast Range. Canadian Geotechnical Journal 38, 995–1024.

Schulz, W.H., 2007. Landslide susceptibility revealed by LiDAR imagery and historicalrecords, Seattle, Washington. Engineering Geology 89, 67–87.

Schulz, W.H., Lidke, D.J., Godt, J.W., 2008. Modeling the spatial distribution of landslide-prone colluvium and shallow groundwater on hillslopes of Seattle, WA. EarthSurface Processes and Landforms 33, 123–141.

Shipman, H., 2004. Coastal bluffs and sea cliffs on Puget Sound,Washington. In: Hampton,M.A., Griggs, G.B. (Eds.), Formation, Evolution, and Stability of Coastal Cliffs — Statusand Trends. U.S. Geological Survey Professional Paper, vol. 1693, pp. 81–94.

Sidle, R.C., Ochiai, 2006. Landslides Processes, Prediction, and Land Use. AmericanGeophysical Union, Washington D.C., p. 312.

Simoni, S., Zanotti, F., Bertoldi, G., Rigon, R., 2008. Modelling the probability ofoccurrence of shallow landslides and channelized debris flows using GEOtop-FS.Hydrological Processes 22, 532–545.

Srivastava, R., Yeh, T.C.J., 1991. Analytical solutions for one-dimensional, transientinfiltration toward the water table in homogeneous and layered soils. WaterResources Research 27, 753–762.

Stock, J.D., Reid, M.E., Wieczorek, G.F., Godt, J.W., 2006. Landslide processes of theVentura anticline viewed from the field and from 1-m LiDAR. Eos Transactions ofthe American Geophysical Union 87 (52) (H53B-0625).

Swets, J., 1988. Measuring the accuracy of diagnostic systems. Science 240, 1285–1293.Terlien, M.T.J., Van Western, C.J., Van Asch, T.W.J., 1995. Deterministic modeling in a

GIS-based landslide hazard assessment. In: Carrara, A., Guzzetti, F. (Eds.),Geographical Information Systems in Assessing Natural Hazards. Kluwer, Dor-drecht, pp. 57–77.

Terzaghi, K., 1943. Theoretical Soil Mechanics. John Wiley and Sons, New York. 510 pp.Thieken, A.H., Lücke, A., Diekkrüger, B., Richter, O., 1999. Scaling input data by GIS for

hydrological modeling. Hydrological Processes 13, 611–630.Troost, K.G., Booth, D.B., 2008. Geology of Seattle and the Seattle area, Washington. In:

Baum, R.L., Godt, J.W., Highland, L.M. (Eds.), Landslides and Engineering Geology ofthe Seattle Washington Area. Geological Society of America Reviews in EngineeringGeology, vol. 20. doi:10.1130/2008.4020(01).

Trustrum, N.A., DeRose, R.C., 1988. Soil depth–age relationship of landslides ondeforested hillslopes, Taranaki, New Zealand. Geomorphology 1, 143–160.

Tubbs, D.W., 1974. Landslides in Seattle. State of Washington Department of NaturalResources Division of Geology and Earth Sciences Information Circular 52.

226 J.W. Godt et al. / Engineering Geology 102 (2008) 214–226

Van Den Eeckhaut, M., Vanwalleghem, T., Poesen, J., Govers, G., Verstraeten, G., Vandekerc-khove, L., 2006. Prediction of landslide susceptibility using rare events logistic regression:a case-study in the Flemish Ardennes (Belgium). Geomorphology 76, 392–410.

Wildenschild, D., Jense, K.H., Hollenbeck, K.J., Illangasekare, T.H., Znidarcic, D.,Sonnenborg, T., Butts, M.B., 1997. A two-stage procedure for determining theunsaturated hydraulic characteristics using a syringe pump and outflow observa-tions. Soil Science Society of America Journal 61, 347–359.

Wu,W.M., Sidle, R.C., 1995. A distributed slope stability model for steep forested basins.Water Resources Research 31 (8), 2097–2110.

Wu, T.H., McKinnel, W.P., Swanston, D.N., 1979. Strength of tree roots and landslides onPrince of Wales Island, Alaska. Canadian Geotechnical Journal 16, 19–33.

Zhang, R.S., Montgomery, D.R., 1994. Digital elevation model grid size, landscaperepresentation, and hydrologic simulations.Water Resources Research 30,1019–1028.