SHETRAN-landslide (Burton and Bathurst, 1998)

8/9/2019 SHETRAN-landslide (Burton and Bathurst, 1998)

1/11

Environmental Geology 35 (23) August 1998 7 Q Springer-Verlag 89

Received: 30 October 1996 7 Accepted: 25 June 1997

A. Burton (Y) 7 J. C. BathurstWater Resource Systems Research Laboratory,Department of Civil Engineering, University of Newcastle,

Newcastle upon Tyne, NE1 7RU, UK

Physically based modelling ofshallow landslide sediment yieldat a catchment scaleA. Burton

7

J. C. Bathurst

Abstract A shallow landslide erosion and sedimentyield component, applicable at the basin scale, hasbeen incorporated into the physically based, spa-tially distributed, hydrological and sediment trans-port modelling system, SHETRAN. The componentdetermines when and where landslides occur in abasin in response to time-varying rainfall and

snowmelt, the volume of material eroded and re-leased for onward transport, and the impact on ba-sin sediment yield. Derived relationships are usedto link the SHETRAN grid resolution (up to 1 km),at which the basin hydrology and final sedimentyield is modelled, to a subgrid resolution (typicallyaround 10100 m) at which landslide occurrenceand erosion is modelled. The subgrid discretization,landslide susceptibility and potential landslide im-pact are determined in advance using a geographicinformation system (GIS), with SHETRAN thenproviding information on temporal variation in thefactors controlling landsliding. The ability to simu-

late landslide sediment yield is demonstrated by ahypothetical application based on a catchment inScotland.

Key words Catchment model 7 GIS analysis 7Landslide model 7 Model resolution 7 Sedimentyield

Introduction

Landsliding, as a form of mass movement, is one of theprincipal processes of hillslope erosion and it can there-fore play an important role in determining river-basin se-diment yield. The incidence of landsliding, and thus themagnitude of the erosion and sediment yield, can be

greatly increased by human activities (for example,through land use change) often with detrimental conse-quences downstream, such as reservoir siltation, channelaggradation and instability, and loss of aquatic habitat.Consequently, as the upland areas prone to landslidingbecome increasingly developed, the need increases formethodologies which can predict, at the basin scale, theeffects of development on landslide incidence and the re-

sulting sediment yield. Basin management strategies canthen be identified which minimize unwanted develop-ment impacts, in advance of any development being im-plemented.Such aims are increasingly achieved with the support ofmathematical models which incorporate the available un-derstanding of erosion and sediment yield processes andthe degree to which they are affected by human activities.Because of the need to predict the impacts of change inadvance of the change taking place, only the physicallybased, spatially distributed approach to modelling can beused (for example, Abbott and others 1986a). Until veryrecently, our ability to model basin erosion and sediment

yield on a physical and a spatially distributed basis hasbeen limited to the effects of raindrop impact and over-land flow (for example, Park and others 1982; Wicks andBathurst 1996). Similar progress has not been achievedfor landslide erosion and sediment yield modelling. In-deed it is only very recently that any kind of model ofthe relationship between landslide erosion and basin se-diment yield has been attempted (James 1985; Ziemerand others 1991a, 1991b). This paper therefore presents aphysically based, spatially distributed model for simulat-ing the basin-scale erosion and subsequent sedimentyield arising from landsliding. The paper reviews theprocesses which need to be incorporated in the model,presents the model detail and structure, and illustratesthe capabilities of the model through a hypothetical ap-plication to a landslide active catchment in Scotland. Apartially completed version of the model was described inBurton and Bathurst (1994).The model considers only rain- and snowmelt-triggeredshallow landslides, that is, those that fail in a translation-al rather than a rotational manner. Individually thesemay involve areas of a few hundred square metres anddepths of 12 m; however, large numbers of such slidesmay occur during a single major rainfall event such as acyclone. In this paper, landslide refers to a shallow hills-

lope or soil mass failure at a localized site, landslide ero-


2/11

90 Environmental Geology 35 (23) August 1998 7 Q Springer-Verlag

sion refers to the consequent loss or release of materialfrom landslide sites, and landslide sediment yield refersto that part of the material which, through onward trans-port from the landslide sites, arrives at the outlet from aspecified area (for example a hillslope or a river basin).

Modelling framework

A past obstacle to the development of a landslide erosionand sediment yield model has been the lack of a suitablemodelling framework representing the geotechnical, hy-drological and hydraulic principles involved. However,physically based, spatially distributed, hydrological mod-elling systems are now available which incorporate notonly the overland and channel flow routing needed forsediment transport modelling but the simulation of soilmoisture conditions, essential in determining the poten-tial for rain- and snowmelt-triggered landsliding. This ca-

pability has been achieved through an integrated surfaceand subsurface approach to basin modelling, of which theSystme Hydrologique Europen (SHE) (Abbott and oth-ers 1986a, 1986b; Bathurst and others 1995) is perhapsthe most advanced example intended for practical appli-cation. SHE is a grid-based, finite-difference modellingsystem which represents the major processes of the landphase of the hydrological cycle. At the Water ResourceSystems Research Laboratory, University of Newcastleupon Tyne, it has been further developed into SHETRAN,a water flow, sediment transport and contaminant migra-tion modelling system (Ewen 1995), and it is as a compo-nent of SHETRAN that the landslide erosion and sedi-

ment yield model is being built.It is emphasized that the overall aim of the new compo-nent is simulation of sediment yield at the basin scale; itis not the intention to simulate detailed changes in chan-nel geometry or hillslope geomorphology, except in as faras is required for determining sediment yield. It is alsostressed that the new component is not intended to be anadvanced geotechnical research model or to simulate thefine geotechnical detail of individual hillslope failures. Itsinnovative nature lies in its integration of generally ac-cepted geotechnical techniques in a hydrological and se-diment yield modelling framework, to give a capabilityfor determining the sediment yield from multiple hills-lope failures occurring over periods of time ranging fromsingle rainstorms to several years.

Component specification

The new component is required to simulate the effects oflandslide erosion on the basin sediment yield regime. Itmust therefore determine:1. When and where landslides occur, accounting for the

integrated effects of the relevant controls, especially

the changing soil saturated zone thickness as a trigger.

2. The volume of material eroded and released for on-ward transport, and the spatial extent of landslidingacross the basin.

3. The impact on sediment yield at the basin outlet, ac-counting for transport of material from the landslidesite and areas of sediment deposition within the basin.

The relevant physical processes are now briefly reviewed

so that the equations and rules which form the basis ofthe new component can be identified.

Shallow landslide occurrence

Factor of safetyTypically a shallow landslide consists of a slip along aninterface dividing a shallow upper soil layer from an un-derlying stronger and often less permeable lower soillayer or bedrock. The soil is subject to two major oppos-ing influences: the downslope component of soil weight,

which acts to shear the soil along a potential failure planeparallel to the hillslope; and the resistance of the soil toshearing (known as its shear strength). The relationshipbetween the two influences is expressed as a factor of sa-fety, FS, where

FSpResistance of soil to shearing

Downslope component of soil weight(1)

If the downslope weight exceeds the resistance to shear-ing (FS~1), the hillslope is expected to fail. Factor of sa-fety analysis therefore forms the basis for simulatinglandslide occurrence in the new component.

Controls on landslide occurrenceVarious factors influence slope stability and thus land-slide occurrence. Usually they act in combination andslope stability should not therefore be considered interms of just one individual control.Shear strength is controlled by such factors as the cohe-sive forces between soil particles, the binding action oftree roots, and the frictional forces resulting from surfacefriction and interlocking between grains of soil or blocksof rock. In soils or rocks containing water, the frictionalforces are strongly affected by the water pressure in thevoids or pores between the grains or blocks. Typically thehigher the pore-water pressure, the lower are the friction-al resistance and the shear strength; increased soil watercontent also increases the bulk weight of the soil. Hills-lope stability is thus strongly dependent on soil watercontent and, in particular, the thickness of the saturatedsoil zone relative to the soil depth. Important controls onlandslide occurrence are therefore the input of moisturefrom rain and snowmelt (for example, Caine 1980), inter-ception and transpiration of moisture by vegetation (forexample, Greenway 1987) and the concentration ofgroundwater by topographic and geological features suchas topographic depressions or hollows (for example, Sidle

and others 1985; Reneau and Dietrich 1987a).


3/11


The downslope component of soil weight is a function ofhillslope gradient. Field surveys and theory (for example,Sidle and others 1985) suggest that there is a lower slopelimit of about 257 (about 50%) for shallow landslides insaturated soils with typical angles of friction, not rein-forced by root binding. Vegetation is of particular impor-tance in determining hillslope stability. Root binding pro-

vides the main natural mechanism by which the stabilityof a given slope can be increased, while interception andtranspiration have a direct influence on soil moisturecontent (Greenway 1987). Changes in vegetation asso-ciated with land use change are one of the principalmeans by which human activities affect hillslope stability.

Integration of geotechnical and hydrologicalmodels

For the factor of safety stability analysis to be applied todetermine landslide occurrence across a basin, a frame-work is needed to provide the relevant parameters andvariables. From above, these include the basin character-

istics (topographic, soil, geological and vegetation proper-ties), rainfall and snowmelt input, and basin hydrologicalresponse in terms of the soil moisture conditions, all spa-tially and temporally distributed. The framework is pro-vided by an appropriate hydrological modelling system(in this case SHETRAN). The geotechnical stability analy-sis then forms an overlay to the hydrological model, ena-bling the occurrence of landslides in time and space to bedetermined as a function of soil moisture content, vary-ing in response to rainfall and snowmelt.The feasibility of modelling landslide occurrence by ap-plying geotechnical stability analysis to a spatially discre-tized representation of a basin has been demonstrated byWard and others (1981, 1982), Okimura and Kawatani(1987), Mizuyama (1991), Montgomery and Dietrich(1994) and Wu and Sidle (1995). Topographic variation isallowed between discretization elements and the factor ofsafety analysis is applied to each element to give the po-tential for failure. It may be noted, though, that thequoted models are limited to small basins of a few squarekilometres or less, while the SHETRAN component is in-tended to apply at scales ranging from less than a squarekilometre to around 500 km2.

Landslide dimensions and volumeof eroded material

Two contributions to the total amount of material re-leased as a result of landsliding can be identified: materi-al from the landslide itself at the initial point of failure,and material derived from subsequently triggered upslopeand downslope failures.

Characteristic landslide dimensionsAs indicated by their scars, landslides tend to have typ-

ical dimensions in any region (see Table 2 Burton and

others 1998). The range of dimensions can span two orthree orders of magnitude but typically there is a cluster-ing of sizes towards the lower end of the range (for ex-ample, Reneau and Dietrich 1987b; Wieczorek 1987).Reneau and Dietrich (1987b), for example, note that thescars in their study are typically 1020-m long, 710-mwide, 0.71.1-m deep and less than 200 m3 in volume.

The location of the failure plane may lie: within the soil,below the depth of major rooting; at an interface betweensoils of different packing densities; at the bedrock inter-face; or at an interface corresponding to a decrease in hy-draulic conductivity from the overlying soil to the lowerlayer.

Additional slope failureSubsequent upslope failure may be triggered as theground slope of the upslope soil mass is effectively in-creased by the removal of the support provided by theinitially failed material. Subsequent downslope failuremay occur as the initially failed material is mobilized as a

debris flow and rides over the soil in its path (for exam-ple, Reneau and Dietrich 1987b). Additional soil erosionis then caused either by scour along the flow path or bythe sudden loading (and failure) of the downslope mate-rial by the debris flow.

Transport of failed material

The impact of landslide erosion on basin sediment yielddepends on whether the eroded material is transported tothe channel network. If the material deposits immediately

downslope from the landslide scar, it can enter the chan-nel network only if the landslide is adjacent to the chan-nel or if it can be carried there by overland flow. If thematerial breaks up and, through mixing with water,evolves into a debris flow (for example, Johnson 1984;Takahashi 1991), it can travel a considerable distance andso increase its potential for discharging directly into thechannel network. A method is then required for calculat-ing the percentage of the landslide material which is de-livered to the channel, that is, the percentage delivery.

Effect of vegetationLandslides triggered on forested slopes (planar or gully)release such energy and mass that a debris flow nearly al-ways develops. This usually both scours all the materialin its path and continues to move downslope until thegradient falls below that needed to maintain flow. Someexamples are shown in Eschner and Patric (1982) andDeGraff and others (see Fig. 20 1989). For grass cover theroot-binding effect is weak and failure occurs at condi-tions only slightly exceeding soil strength. If the failureoccurs in a gully or ephemeral channel (which acts toconcentrate a supply of water), there is still a high likeli-hood that the material will move downslope as a debrisflow. If the failure occurs on a planar slope, though, there

is a much lower likelihood of debris flow generation; the


4/11


material is more likely to drain and stiffen, forming a tailto the landslide scar.

Debris flow runout distanceIf a debris flow moves onto a slope too gentle to supportcontinued transport, its ability to reach the channel net-work depends on the distance over which it comes to a

halt the runout distance. No generally satisfactory for-mula for runout distance has yet been devised. Theoreti-cally based relationships (for example, Takahashi 1991)are generally inappropriate for the relatively simple levelof modelling envisaged here but several empirical ap-proaches can be identified in the literature. Four suchformulae were tested using hypothetical and measuredhillslope data by Bathurst and others (1997). The formu-lae are simple relationships which enable runout distanceto be estimated from hillslope geometry. The fraction ofthe landslide material which is delivered to the river sys-tem is then calculated as:

FDELp (WPD

z)

W (2)

where W is the runout distance and Dz is the distancebetween the point at which debris flow deposition beginsand the nearest reach of channel in the downslope direc-tion. Bathurst and others (1997) also tested a fifth, statis-tically based, methodology developed by Ward (1994) toestimate percentage delivery directly. None of the ap-proaches was accurate over the full range of deliveriesand parallel use of two models was recommended to pro-vide uncertainty bounds on the estimated percentage de-livery. However, the best compromise between simplicityand reliability was a model based on a study by Vandre(1985) in which runout distance is given as:

WpaDy (3)

where Dy is the elevation difference between the head ofthe slide and the point at which deposition begins; and ais an empirically derived fraction (set at 0.4 in this case).In general, deposition from debris flows tends to beginonce the slope falls to around 6107, at least in steepchannel networks. The lowest gradient at which debrisflow occurs is around 357 (for example, Ikeya 1981;Johnson 1984; Benda 1985; Vandre 1985).

Model development

Background to the methodologyThe preceding review provides the equations, rules andprocess descriptions which form the basis of the SHE-TRAN landslide erosion and sediment yield component.In the component, the occurrence of shallow landslides isdetermined as a function of the time- and space-varyingsoil saturation conditions simulated by SHETRAN. Thevolume of eroded material is determined and the propor-tion of this material reaching the channel network is then

calculated and fed to the SHETRAN sediment transport

Fig. 1

The dual resolution approach to landslide modelling

component for routing to the basin outlet. Because oflimitations in either current knowledge or computingpower, simplifications are necessary to ensure that all theprocesses are incorporated into the component and thatthe component satisfies its specification requirements.These simplifications provide fertile ground for furtherresearch.

Dual resolutionThe simulation time and memory requirements of SHE-TRAN are proportional to the number of grid squares (orrectangles) used in representing spatial distribution in abasin. For river basins of interest for landslide modelling,which may typically vary in size up to 500 km2, the gridresolution is limited to 0.51 km. However, the precedingreview indicates that landslides and the topographic fea-tures which relate to their occurrence typically have plandimensions of 1020 m. If SHETRAN were to be usedwith a grid resolution of this size, simulations would belimited to basins smaller than 1 km2. To overcome this

problem, a dual resolution approach has been adopted inwhich the basin hydrology is modelled at the SHETRANgrid (coarse) resolution while landslide erosion is mod-elled at a subgrid (fine) resolution. This involves splittingthe process of landslide modelling into two parts, repre-sented by the subcomponents GISLIP and SHESLIP(Fig. 1).GISLIP is a geographical information system (GIS) analy-sis which is applied separately from SHETRAN and priorto the time-varying simulation. It identifies regions of thebasin that are at risk from landslides and the soil satura-tion conditions critical for triggering a landslide at a giv-en point. The failure criteria are determined using factor

of safety analysis. GISLIP also determines the potentialsediment yield consequences of a landslide at each point,including: the initial volume of failed material, the vol-ume of any material subsequently scoured downslope,deposition of eroded material on the ground surface, thetrajectory of any debris flow and, should the trajectoryintercept the channel network, the volume of sedimentdelivered for onward channel routing. The analysis isbased on terrain data (in the form of digital terrain mod-els) that are assumed to be time invariant during the si-mulation. GISLIP is designed for use with a fine-resolu-


5/11


tion grid containing on the order of one million squares;it can therefore represent basins of up to 500 km2 with aspatial resolution appropriate for landslide simulation.SHESLIP carries out the time-varying simulation of land-slide occurrence in conjunction with the SHETRAN simu-lation of basin hydrology and at the SHETRAN grid(coarse) resolution. At each time step the coarse-grid soil

saturation conditions are compared with the critical con-ditions required for failure of subgrid (that is, GISLIPgrid) elements (already determined by GISLIP). For thiscomparison to be made it is necessary to determine thesubgrid saturated zone thickness as a function of theSHETRAN grid saturated zone thickness and to this enda disaggregation technique involving a wetness index isused. If a subgrid element is then simulated as failing,the relevant debris flow trajectory and sediment deliveryalready defined by GISLIP are applied to the SHETRANsimulation to provide the sediment yield at the basinscale. In this way GISLIP provides predetermined infor-mation on a look-up basis for the time-varying SHES-

LIP/SHETRAN simulation.

GIS analysis (GISLIP)

Obtaining a hydrologically sound DEMThe first requirement of GISLIP is a fine-resolution digi-tal elevation model (DEM) that is hydrologically sound.That is, a clearly defined drainage direction exists for ev-ery grid square in the DEM. Commonly DEMs sufferfrom two faults which prevent this requirement from be-ing satisfied without treatment: 1) spurious pits and

dams; and 2) flat regions. Pits are local elevation minimaconsisting of a number of connected squares, all adjacentsquares to which are at a higher elevation. Dams are spu-rious obstructions that block an otherwise well-drainedvalley. Flat regions are connected areas of two or moresquares in which all the squares have the same elevationand at least one square has no clearly defined drainagedirection. The first step in GISLIP is therefore to removethese faults. The dams problem is overcome by artificiallyraising the elevation of the surface behind the dam, thusrestoring the original downhill form of the region. Flatregions are treated by defining an artificial drainage net-work for the region.

Fine-grid failure conditionsThe critical soil saturation conditions for landslide occur-rence across the basin are determined through an inver-sion of the standard factor of safety analysis (Eq. 1). Foran infinite slope (the assumption of which is generallyaccepted as the basis for modelling shallow landslides)the factor of safety is calculated as (for example, Wardand others 1981):

FSp1 2(CscCr)gwdsin(2b)c

(LPm) tanf

tanb 2L

(4)

where

Lpq0gwdcm

gsat

gwc(1Pm)

gm

gw(5)

and FS is the factor of safety (FS~1 unsafe, FS61 safe);Cs is the effective soil cohesion; Cr is the root cohesion; fis the effective angle of internal friction of soil on im-

permeable layer; d is the soil depth above failure plane; bis the slope angle; q0 is the vegetative surcharge per unitplan area; gsat is the weight density of saturated soil; gmis the weight density of soil at field moisture content; gwis the weight density of water; m is the relative saturateddepth (thickness of saturated zone divided by soil depth,above the failure plane). Van Westen and Terlien (1996)note that this is the only model which calculates slope in-stability on a pixel basis and that it is therefore very suit-able for use in a raster-based GIS.Of these terms, most are spatially variable but it is as-sumed that only m is time-varying, that is, the factor ofsafety is a function of m, FS{FS(m). Providing that at

least one of Cs, Cr or tanf is positive, then it can beshown that FS1 is well defined.Assuming that the value of every term, except for m, isknown or can be estimated for each fine-grid square, acritical relative saturated depth, mi

c, can be determinedfor each fine-grid square, i, where mi

cpFSi

1(1). The crit-ical relative saturated depth, for square i, is the value ofm that puts the square on the borderline between safeand unsafe. Consequently, the failure condition for eachgrid square can be written in terms of the time-varyingrelative saturated depth: for mi^mi

c, the slope is safe;and for mi1mi

c, the slope is unsafe. In addition, if mic11

then a square is assumed unconditionally safe; and ifmi

c^0 then a square is assumed unconditionally unsafe.

To obtain these conditions, GISLIP determines mic over

the whole catchment.

Wetness indexIn the time-varying simulation, soil saturation conditionsare modelled at the coarse-grid resolution of SHETRAN;in particular, each SHETRAN grid element is character-ised by a single value of saturated zone thickness at eachtime step. Within the area represented by each coarse-grid element, however, there is likely, in reality, to beconsiderable spatial variability as a function of topogra-phy, soil characteristics and vegetation effects. A wetnessindex is therefore being used to link the coarse-scale sa-turated zone thickness with a subgrid distribution, pro-viding appropriate variability in saturated zone thicknessat the fine-grid resolution. At present the effect of onlytopography is considered, using the index of Beven andKirkby (1979) which takes into account slope and accu-mulated upslope area. This is defined for each fine-gridsquare as:

Iipln 3 aitanbi4 (6)


6/11


and is related to soil moisture deficit in a specified re-gion by:

(zbiPzb)p(IPIi)

f(7)

where Ii is the topographic index for square i; ai is theaccumulated runoff area per unit contour length forsquare i; bi is the slope of square i; zbi is the soil mois-ture deficit of square i; zb and Iare the the mean valuesof zb and I respectively over fine-resolution squares inthe specified region; and f is a basin constant that relatestransmissivity to depth. The prime on the z indicates thatno account is taken of the possibility that unrealistic val-ues of z may result from the use of Eq. 7. For this stageof the analysis, GISLIP uses the multiflow direction algo-rithm, as described in Quinn and others (1991), to deter-mine the topographic index for each fine-grid square inthe catchment.

Coarse-grid failure conditionsA failure criterion for each fine-grid square is required interms of the soil saturation conditions over the parentSHETRAN grid rectangle, for comparison with the time-varying simulated conditions. This is achieved by com-bining the soil saturation failure criteria for each fine-grid square, with the distribution of soil moisture withinthe SHETRAN grid rectangle provided by the topographicindex, Eqs. 6 and 7. Equation 7 describes the subgrid dis-tribution of moisture conditions relative to the meancondition for a region, in this case a coarse-grid rectan-gle. It therefore provides a method by which, given a sa-turated zone thickness at one fine-grid square, it is possi-

ble for the saturated zone thicknesses at all the otherfine-grid squares in the parent coarse-grid rectangle to becalculated. Consequently, knowing the critical saturatedzone thickness for a fine-grid square, the correspondingvalues of saturated zone thickness can be found for allthe other fine squares. Aggregated together these give thecritical saturated zone thickness at the coarse-grid scalewhich corresponds to the critical condition for the parti-cular fine-grid square. This is a fixed time-invariant val-ue. GISLIP carries out this calculation for each fine-gridsquare before the time-varying simulation and stores theresults in the look-up table. During the time-varyingSHESLIP/SHETRAN simulation, all that is then necessary

to determine whether a fine-grid square is at its criticalcondition at any time step, is to compare the correspond-ing critical saturated zone thickness for the parentcoarse-grid rectangle with the actual (time-varying) thick-ness determined by SHETRAN at that time step.Although Eq. 7 provides a means to distribute moisturewithin a SHETRAN rectangle, it takes no account of thepossibility that, given a set of the other three variables,both zbi and Zb can be calculated to have an unrealisticvalue in the sense that they might exceed the soil depthor be negative. In order to use this approach within themodel, zbi is considered to be a potential value, such thatzbi outside the valid range is considered to be the value

that would be attained if possible, and that it actuallycorresponds to a soil moisture deficit zi which is trun-cated to either 0 or di as appropriate. The value of zb isconsidered to be the effective mean soil moisture deficitwithin the SHETRAN rectangle, thus relating the poten-tial soil moisture deficits between the contained finesquares by Eq. 7. The following procedure is then used to

account for this problem in order to relate the fine-square failure criterion to the average relative saturateddepth of the SHETRAN rectangle.For a fine square, i, that is conditionally unsafe,0^mci^1, the soil moisture deficit, zb

ci will lie in the

valid range. Therefore:

zbcipzcipdi (1Pm

ci) (8)

From Eq. 7,

zbcipdi (1Pmci)P

(IPIi)

f(9)

is the effective mean soil moisture deficit in the SHE-TRAN (coarse) rectangle to be critical for the fine squarei. However, in this formulation, the deficit is calculatedwithout considering whether the corresponding moisturecontents implied for the other fine-grid squares are real-istic. A further adjustment is therefore required. Giventhe effective mean soil moisture deficit at the coarse-gridscale, the potential soil moisture deficit can be obtainedfrom Eq. 7 for the other fine squaresj for the conditionsat which fine square i has a critical moisture deficit:

zbcijpdi (1Pmci)P

(IiPIj)

f(10)

This value is adjusted in the model as follows:

zijbc is negative, corresponds to exfiltration, so zij

c is setto zero.

zijbc is greater than the soil depth, corresponds to nega-

tive moisture, so zijc is set to dj.

Otherwise zijbc is considered to be valid and zij

c is set tothe same value.

That is:

zcijp

50,

dj,zbcij,

zbcij~0

zbcij`dj

otherwise(11)

The actual mean soil moisture deficit across the SHE-TRAN rectangle is then:

zcipmeanj (zcij) (12)

Finally, to account for the possibility that the soil depthrepresentation in a SHETRAN rectangle may not corre-spond exactly to the mean soil depth in the fine-gridsquares which make up the GISLIP representation of therectangle, the total volume of saturated soil in the fine-grid squares is set equal to the volume of saturated soil


7/11


in the parent coarse rectangle, that is for every SHE-TRAN rectangle:

DZpdz (13)

where Z is the soil moisture deficit in a SHETRAN rec-tangle; D is the soil depth in a SHETRAN rectangle; anddand zare the average values of d and z over the fine

squares contained within the rectangle.If M is the relative saturated depth in a SHETRAN rec-tangle, then

Mp1PZ

D(14)

Substituting for critical values in Eqs. 13 and 14 the fol-lowing expression is obtained:

McipdPzci

D(15)

Knowing the critical soil moisture condition in fine-grid

square i, the corresponding critical relative saturateddepth for the coarse-grid rectangle containing square i,Mi

c, can be obtained. This is the value of M that corre-sponds to square i being at its critical relative saturateddepth mipmi

c. Consequently, Mic can be determined for

each fine-grid square in the basin and the failure criteri-on for each fine square can be written entirely in termsof the coarse-grid soil saturation conditions. That is, forM Mi

c, the slope is safe; and for M1Mic, the slope is

unsafe.A hazard map is constructed of only those fine squares inthe catchment that have a potentially unsafe critical rela-tive saturated depth, 0^mi

c~1 and whose Mi

c permits

the possibility of failure. Also, as indicated previously,shallow landslides do not generally occur on slopes lessthan 257. Consequently, an option exists within the modelto exclude all fine squares with slopes less than 25 7.

Transport trajectories, erosion and depositionFor this step of the analysis, GISLIP considers a landslideoccurring independently at each fine square in the hazardmap. Through simulation of debris flow transport,eroded material is partitioned between direct delivery tothe stream system and deposition along the hillslope.As previously noted, landslide scars tend to have typicaldimensions in any region and the failure plane can lie ata variety of locations below the surface. As a first esti-mate GISLIP bases the width of the initial failure uponthe width of typical landslides in the area or in regions ofsimilar geographical properties; the depth of the initialfailure is set to the soil depth. These dimensions enablethe volume of material released by the landslide to be de-termined.As described above, there is the potential for onwardtransport of eroded material by debris flow to be stronglydependent on vegetation cover and whether the initialfailure occurs on a planar slope or in a gully. In accor-dance with this, GISLIP applies a rule-based transport

model:

1. On a planar grass-covered slope, there is no onwardtransport. Eroded material forms a tail to the landslidescar, with a length typical of the region.

2. On a planar forested slope, and for landslides occur-ring in gullies, the landslide evolves into a debris flow.

The rules applied to govern debris flow transport and se-diment deposition are as follows:

1. For slopes greater than 107, the debris flow continuesunconditionally; all soil along the track is scoured andadded to the eroded material from the initial landslidesite.

2. For slopes between 47 and 107 the debris flow comesto a halt either over the runout distance or on reach-ing the 47 slope, whichever condition is first satisfied.Deposition occurs at a rate such that all the debrisflow material would be spread uniformly over the fullrunout distance (even if the debris flow reaches the 47slope first).

3. For slopes less than 47 the debris flow halts uncondi-tionally and deposits all remaining material.

The runout criterion is based empirically on Eq. 3. A de-bris flow halts once

1Distance travelled on slopesbetween 47 and 107 2`0.41Elevation lost

on slopes`1072 (16)where the travel distances are measured along the slope.The potential trajectory of the debris flow is simulated bystarting at the originating fine square and progressingfrom square to square down the maximum gradient. Theslope and runout distance are calculated using the slopedistance between the centres of squares in the trajectory.Deposition and erosion occurring between two squares

are distributed equally between them.Within GISLIP, a representation of the channel networkwithin the basin relates the SHETRAN channel links tolocations within the fine-grid. If the debris flow is inter-cepted by one of these locations then it stops immediate-ly and all remaining material is deposited in the corre-sponding channel, according to Eq. 2. Equation 16 can becalibrated for a particular region, in terms of the slopeangles and the decimal fraction. It can also easily be re-placed by alternative formulae (for example, from thesurvey of Bathurst and others 1997) if these are consid-ered more appropriate for a given application.

Combination for SHESLIPFor each fine square in the hazard map, the details relat-ing to its potential landslide are expressed in terms oftheir relevance to the time-varying simulation of thecatchment by SHETRAN at the coarse resolution. It isnot necessary for SHETRAN to know details about thefine square that is failing, only details of the coarse rec-tangle containing the potential failure, the critical coarse-grid saturation necessary for failure and the supply andremoval of sediment to each coarse-grid square andchannel element. The failure criterion for each finesquare in the hazard map is already defined in terms of

the relative saturated depth of the parent SHETRAN rec-


8/11


Fig. 2Distribution of topographic index for the test area. See text for

explanation

Fig. 3Map of critical relative saturated depth for the test area. Scale isexplained in the text

tangle. Consequently, the final step in the GISLIP analysisis to express for each fine square in the hazard map, thefine-resolution erosion, deposition and supply to chan-nels of sediment, in terms of sediment removal andsupply to affected coarse-resolution rectangles and chan-nel links.

Demonstration application

A hypothetical application to the topography of a 20-km2

area containing the Kirkton research catchment at Balqu-hidder in Scotland (managed for scientific purposes bythe UK Institute of Hydrology) is used to illustrate thesteps in the modelling. The catchment itself is approxi-mately 7 km2 in area and lies in a steep-sided glaciatedvalley with elevations ranging from about 240 m to850 m. A number of landslides have been documented inthe catchment.

The GIS analysis is based on a fine-grid DEM with a re-solution of 20 m within a SHETRAN grid composed of200-m squares. Figure 2 shows the distribution of the to-pographic index (Eq. 6) across the catchment; darkershades indicate greater potential for soil saturation. Fig-ure 3 is a map of critical relative saturated depth ob-tained from the factor of safety analysis using estimatedterrain data. The scale on this map is such that values inexcess of 1000 indicate squares which are unconditionallysafe and values less than 1000 indicate squares that havethe potential for failure. The map of critical relative satu-rated depth is then combined with the topographic indexdistribution to obtain for each fine square the corre-

sponding critical saturated depth for the SHETRAN par-

ent square. This enables a map of potential landslide sitesto be determined, for each of which the debris flow tra-

jectories are calculated and regions of erosion and depo-sition are determined. The potential trajectories areshown in Fig. 4, in which black areas indicate depositionwhile the light grey shading indicates erosion.These results were processed to determine their conse-quences for the coarse-resolution simulation of hydrology

and sediment transport for the 7-km2 Kirkton catchment.Figure 5 shows the grid and channel network representa-tion of the catchment for the SHETRAN time-varying si-mulations. To test the combined SHETRAN and landslidecomponent model, a single landslide was selected fromthe list of potential landslides and its effect upon the se-diment regime of the catchment was investigated in isola-tion. To reduce the number of factors in the simulation,the main SHETRAN soil erosion component was parame-terised so that erosion by raindrop impact, overland flowand bank erosion was eliminated and only a single sedi-ment type was used in the catchment. Once soil is simu-lated as eroded by a landslide failure, then any sedimentdeposited on the hillslope is available for transport byoverland flow; thus in the simulation the only supply ofsediment in the catchment was from the landslide failureand the model could demonstrate the subsequent trans-port of the sediment by debris flow, overland flow andchannel flow.For test conditions an initial soil saturation of 50% wasset across the whole catchment. Rainfall was then appliedat the rate of 2 mm h1 for a period in excess of 150 h.Figure 6a, the hydrograph at the catchment outlet, showsa flow of less than 0.5 m3 s1 for about the first 25 h, aft-er which the lower regions of the catchment are saturated

and the outflow rises in response to the overland flow.


9/11


10/11


1. Landslide incidence as a function of precipitation andcatchment properties, on a spatially distributed basis;

2. Debris flow transport and sediment delivery to thechannel system, allowing also for deposition of sedi-ment along the debris flow track and the subsequenttransport of that sediment by overland flow;

3. Transport of sediment along the river system from the

point of injection.Overall the component constitutes an innovative ap-proach to modelling shallow landslide erosion and sedi-ment yield at the basin scale. Its dual resolution basis,whereby basin hydrology is modelled at the SHETRANgrid scale while landslide erosion is modelled at a sub-grid scale, enables the impact of landslide erosion to bestudied for basins of up to 500 km 2 or so. Its use of aGIS analysis to determine the consequences of potentiallandslides prior to carrying out the time-varying simula-tions (storing the information in look up tables) sup-ports a relatively fast computation procedure. Neverthe-less, for this first development the simplest realistic ap-

proach to modelling has been adopted and improvementsmay be envisaged in the future, especially once practicalexperience in applying the model is accumulated. Themodular approach of the GIS part of the model providesexceptional flexibility which can readily incorporate fu-ture modifications.Validation of the model requires data sets linking multi-ple landslide occurrences in a basin with the rainfall orsnowmelt conditions triggering the occurrences and withthe resulting sediment yield out of the basin. This is ademanding requirement, likely to be satisfied only insmall research basins. Even then, and much more so forlarger basins, it is unlikely that satisfactory data sets will

be available for all the physical parameters required bythe component and a degree of parameter estimationmay be required (for example, using data in the litera-ture). There may therefore be considerable uncertaintyattached to parameter evaluation. Further, the use of asingle value for a parameter for a fine-grid square maynot correctly represent the spatial variability within thatsquare. However, quantification of the uncertainty and amore accurate representation of the within-grid spatialvariability may be possible if the statistical properties ofthe parameters are known. A programme of field studiesat the plot scale in a landslide prone area is currently at-tempting to address this particular issue (Burton andothers 1998). Similarly, representation of the initial land-slide dimensions might be improved by using distribu-tions instead of single values. These considerations formpart of the long-term research programme for the newcomponent.

Acknowledgements The research for this paper was carried outas part of the MEDALUS II (Mediterranean Desertification andLand Use) collaborative research project. MEDALUS II wasfunded by the European Commission under its EnvironmentProgramme, contract numbers EV5V-CT92-0128/0164/0165 and0166, and this support is gratefully acknowledged. The authors

thank the reviewers for their helpful comments.

References

Abbott MB, Bathurst JC, Cunge JA, OConnell PE, Ras-mussen J (1986a) An introduction to the European Hydrolog-ical System Systme Hydrologique Europen, SHE, 1: his-tory and philosophy of a physically-based, distributed modell-ing system. J Hydrol 87:4559

Abbott MB, Bathurst JC, Cunge JA, OConnell PE, Ras-mussen J (1986b) An introduction to the European Hydro-logical System Systme Hydrologique Europen, SHE,2:structure of a physically-based, distributed modelling sys-tem. J Hydrol 87:6177

Bathurst JC, Wicks JM, OConnell PE (1995) The SHE/SHESED basin scale water flow and sediment transport mod-elling system. In: Singh VP (ed) Computer models of water-shed hydrology. Water Resources Publications, HighlandsRanch, Colo., pp 563594

Bathurst JC, Burton A, Ward TJ (1997) Debris flow run-outand landslide sediment delivery model tests. Proc Am Soc CivEng, J Hydraul Eng 123 : 410419

Benda LE (1985) Behavior and effect of debris flows on streamsin the Oregon Coast Range. In: Bowles DS (ed) Delineation of

landslide, flash flood, and debris flow hazards in Utah. Gen-eral Series Rep. UWRL/G-85/03, Utah Water Research Labora-tory, Utah State University, Logan, Utah, pp 153162

Beven KJ, Kirkby MJ (1979) A physically based, variable con-tributing area model of basin hydrology. Hydrol Sci Bull24:4369

Burton A, Bathurst JC (1994) Modelling shallow landslideerosion and sediment yield at the basin scale. In: ArmaniniA, Di Silvio G (eds) Proceedings International AssociationHydraulic Research International Workshop on Floods andinundations related to large earth movements, University ofPadua, Padua, Italy, pp B7.1B7.13

Burton A, Arkell TJ, Bathurst JC (1998) Field variability oflandslide model parameters. Environ Geol 35 : 100114

Caine N (1980) The rainfall intensity-duration control of shal-low landslides and debris flows. Geogr Ann 62A:2337

DeGraff JV, Bryce R, Jibson RW, Mora S, Rogers CT(1989) Landslides: their extent and significance in the Carib-bean. In: Brabb EE, Harrod BL (eds) Landslides: extent andeconomic significance. Balkema, Rotterdam, p 68

Eschner AR, Patric JH (1982) Debris avalanches in easternupland forests. J For 80: 343347

Ewen J (1995) Contaminant transport component of the catch-ment modelling system (SHETRAN). In: Trudgill ST (ed) So-lute modelling in catchment systems. Wiley, Chichester, UK,pp 417441

Greenway DR (1987) Vegetation and slope stability. In: Ander-son MG, Richards KS (eds) Slope stability. Wiley, Chichester,UK, pp 187230

Ikeya H (1981) A method of designation for area in danger ofdebris flow. In: Davies TRH, Pearce AJ (eds) Erosion and se-diment transport in Pacific Rim steeplands. International As-sociation Hydrological Science Publ No 132, Institute of Hy-drology, Wallingford, Oxon, UK, pp 576588

James LD (1985) Flood hazard measurement who has a ruler?In: Bowles DS (ed) Delineation of landslide, flash flood, anddebris flow hazard in Utah. General Series Rep UWRL/G-85/03, Utah Water Research Laboratory, Utah State University,Logan, Utah, pp 313335

Johnson AM (with Rodine JR) (1984) Debris flow. In: Brunsd-en D, Prior DB (eds) Slope instability. Wiley, Chichester, UK,pp 257362


11/11


Mizuyama T (1991) Sediment yield and river bed change inmountain rivers. In: Armanini A, Di Silvio G (eds) Fluvial hy-draulics of mountain regions. Lecture Notes in Earth SciencesNo. 37. Springer, Berlin Heidelberg New York, pp 147161

Montgomery DR, Dietrich WE (1994) A physically basedmodel for the topographic control on shallow landsliding.Water Resour Res 30: 11531171

Okimura T, Kawatani T (1987) Mapping of the potential sur-

face-failure sites on granite mountain slopes. In: Gardiner V(ed) International geomorphology 1986, part I. Wiley, Chi-chester, UK, pp 121138

Park SW, Mitchell JK, Scarborough JN (1982) Soil erosionsimulation on small watersheds: a modified ANSWERS mod-el. Trans Am Soc Agric Engrs 25: 15811588

Quinn P, Beven K, Chevallier P, Planchon O (1991) Theprediction of hillslope flow paths for distributed hydrologicalmodelling using digital terrain models. Hydrol Proc 5: 5980

Reneau SL, Dietrich WE (1987a) The importance of hollowsin debris flow studies; examples from Marin County, Califor-nia. In: Costa JE, Wieczorek GF (eds) Debris flows/aval-anches: process, recognition, and mitigation. Geological So-ciety of America Reviews in Engineering Geology vol 7, Geo-logical Society of America, Boulder, Colo., pp 165180

Reneau SL, Dietrich WE (1987b) Size and location of collu-vial landslides in a steep forested landscape. In: Beschta RL,Blinn T, Grant GE, Ice GG, Swanson FJ (eds) Erosion and se-dimentation in the Pacific Rim. International Association Hy-drological Science Publ No 165, Institute of Hydrology, Wal-lingford, Oxon, UK, pp 3948

Ries JB (1994) Soil erosion in the high mountain region, East-ern Central Himalaya: a case study in the Bamti/Bhandar/Sur-ma area, Nepal. PhD thesis, Heft 42, Institut fr PhysischeGeographie der Albert-Ludwigs-Universitt, Freiburg imBreisgau, Germany

Sidle RC, Pearce AJ, OLoughlin CL (1985) Hillslope stabilityand land use. Water Resources Monograph Series 11, Ameri-can Geophysical Union, Washington, DC

Takahashi T (1991) Debris flow. Balkema, RotterdamVandre BC (1985) Rudd Creek debris flow. In: Bowles DS (ed)

Delineation of landslide, flash flood, and debris flow hazardsin Utah. General Series Rep UWRL/G-85/03, Utah Water Re-search Laboratory, Utah State University, Logan, Utah,pp 117131

Van Westen CJ, Terlien MTJ (1996) An approach towardsdeterministic landslide hazard analysis in GIS: a case studyfrom Manizales (Colombia). Earth Surf Processes Landforms21:853868

Ward TJ, Li R-M, Simons DB (1981) Use of a mathematicalmodel for estimating potential landslide sites in steep forest-ed basins. In: Davies TRH, Pearce AJ (eds) Erosion and sedi-ment transport in Pacific Rim steeplands. International Asso-

ciation Hydrological Science Publ No 132, Institute of Hydro-logy, Wallingford, Oxon, UK, pp 2141Ward TJ, Li R-M, Simons DB (1982) Mapping landslide haz-

ards in forest watersheds. Proc Am Soc Civ Eng, J GeotechEng Div 108(GT2):319324

Ward TJ (1994) Modeling delivery of landslide materials tostreams. New Mexico Water Resources Research Institute RepNo 288, New Mexico State University, Las Cruces, N.M.

Wicks JM, Bathurst JC (1996) SHESED: a physically-based,distributed erosion and sediment yield component for theSHE hydrological modelling system. J Hydrol 175:213238

Wieczorek GF (1987) Landslide erosion in central Santa CruzMountains, California, USA. In: Beschta RL, Blinn T, GrantGE, Ice GG, Swanson FJ (eds) Erosion and sedimentation inthe Pacific Rim. International Association Hydrological

Science Publ No 165, Institute of Hydrology, Wallingford,Oxon, UK, pp 489498

Wu W, Sidle RC (1995) A distributed slope stability model forsteep forested basins. Water Resour Res 31:20972110

Ziemer RR, Lewis J, Rice RM, Lisle TE (1991a) Modeling thecumulative watershed effects of forest management strategies.J Environ Qual 20:3642

Ziemer RR, Lewis J, Lisle TE, Rice RM (1991b) Long-term se-dimentation effects of different patterns of timber harvesting.In: Peters NE, Walling DE (eds) Sediment and stream waterquality in a changing environment. International AssociationHydrological Science Publ No 203, Institute of Hydrology,Wallingford, Oxon, UK, pp 143150

Documents

SHETRAN-landslide (Burton and Bathurst, 1998)