Avalanche Dynamics

ESTIMATING AVALANCHE RUNOUT ON THE MILFORD ROAD, NEW ZEALAND

H. Conway*, W. Carran and A. CarranUniversity of Washington, USA and Transit New Zealand Milford Road Avalanche Programme

ABSTRACT: For operational purposes it is of interest to determine when and whether anavalanche will affect the road. The size and runout of an avalanche depends on the initial depthof failure and subsequent entrainment/deposition of snow as it travels down the path. Here weinvestigate a mass balance approach in which avalanches gain mass above the snowline andlose mass below it; the size by the time it reaches the road depends on conditions along the pathas well as the depth of the initial fracture. We do not capture all details of the flow, but results areencouraging and indicate the importance of entrainment/deposition processes when predictingavalanche runout distances. We caution that the model is not perfect; even a small under­prediction of runout could have major consequences for a traveler on the road.

KEYWORDS: Snow, avalanches, runout distances

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1. INTRODUCTIONThe Milford Road (SH-94) links TeAnau toMilford Sound on the southwest coast of NewZealand. The road, which follows the valleyfloor, is in the runout zone of avalanches thatstart more than 1000m higher (Fig. 1). Mostpotentially hazardous avalanches are "direct­action" avalanches· that release as slabsduring or soon after storms that deposit up to3m of snow in the start zones. The avalanchesgain speed and often become airborne (Fig. 2)as they travel over the cliff bands in mid-path(Fig. 1). The avalanches of the Milford regionare well known for their magnitude, speed andimpact pressures (Smith, 1947; Fitzharris andOwens, 1984).

Previously we have applied a simple force­balance model that has proven useful forforecasting the timing of direct-actionavalanches (Conway et aI., 2000). Howeverfor operational purposes it is also of interest todetermine whether an avalanche that hasreleased will reach the road.

Snow in motion is complex; approaches tomodeling flow-characteristics range fromstatistical (e.g. McClung and Lied, 1987), tosimple dynamic models (e.g. Perla et aI.,1980; Savage and Hutter, 1991; Bartelt et aI.,2000), to fully-physical three-dimensionalmodels (eg. Hutter, 1996). Statistical modelsare easily applied and have been usedsuccessfully in many regions to estimaterunout. However their success is limited, partlybecause the dynamic behavior of avalanchesis not governed by topography alone. On theother hand, physical models are more realisticbut application requires knowledge of themass, friction and drag of the flow and howthese properties vary spatially and with time.

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Figure 1: Aerial view of the East Homer slide path.The road traverses up the Hollyford valley, passesthrough the Homer tunnel (bottom center) into theCleddau valley, which it follows to Milford Sound.Avalanches start about 1100m above the road andoften become airborne as they travel over the cliffband.

* Corresponding author address: Howard Conway,Earth and Space Sciences, University ofWashington, Seattle, WA 98195, USA; tel: 206-685­8085; email: conway@ess.washington.edu

International Snow Science Workshop (2002: Penticton, B.C.)

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2000

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Figure 3: Profiles of the Raspberry, East Homerand Moir avalanche paths (adapted from Fitzharrisand Owens, 1980). The Raspberry path is steeperthan East Homer but the highway is farther from theend of the track (250m compared to 90m at EastHomer). The elevation of the highway beneath Moiron the west side (700m) is about 200m lower thanthat on the east side.

Figure 2: Airborne avalanche crossing the Milfordroad .

2. CONCEPTUAL MODELRelatively few authors have attempted tomodel entrainment/deposition processes inavalanches (e.g. Issler, 1998), but we suspectthat these processes have a crucial role indetermining runout distances. Here weassume that a "direct-action" avalanche willentrain snow above the snowline and depositsnow when it runs below the snowline. Wetrack the mass of snow moving down a one­dimensional flow line of a particular path; therun-out position is defined to be where themass of the flow becomes zero. Implicit inthese assumptions is that avalanches willalways reach the road when the snowline is atroad level.

A major limitation of using such a simplifiedapproach is that we cannot examine theimpact of air blasts that are often associatedwith larger avalanches in the region.

Here we make use of data that are (6.SoCkm-1). We assume that precipitation falls

generally available to a forecaster as snow when the air temperature is <2°C and(precipitation, temperature, topography and rain otherwise; this assumption implies thatavalanche runout) and develop a statistical the snowline (at the elevation where Tz =model that is based on mass continuity. Our +2°C) is -300m below the freezing level. Weplan is to evaluate the limitations of such an have found that a gauge at road level (atapproach; our overarching goal is to develop 900m) yields a reliable estimate oftools that are useful for operational forecasting precipitation in the start zones.along the Milford road. Observations of avalanche occurrence

down specific paths include the time, runoutposition relative to the centerline, and depth ofdeposit on the road.

3. APPLICATION TO MILFORD ROAD3.1 Weather and avalanche databaseHourly weather data, including measurementsof precipitation and air temperature aretelemetered from a network of five remoteweather stations to a base station in TeAnau.The air temperature Tz at an elevation duringtimes of precipitation is estimated from T1600

measured at the Mt Belle weather station (at1600m) and the moist adiabatic lapse rate

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3.2 TerrainMore than 50 avalanche paths threaten theMilford road (Fitzharris and Owens, 1980).Most paths are steep (35-45°) and long (morethan 1km); Fig. 3 shows profiles of three of themost hazardous paths that threaten the road.

3.3 Model developmentAs a first approximation we assume that anavalanche will entrain all of the new snowabove the snowline, and the mass loss perunit area below the snowline is an adjustablemodel parameter. In reality not all of the newsnow will be entrained, and the mass lossbelow the snowline will depend on the pathroughness as well as the dynamics of the flow.

We sub-divide each path into discretelengths LlXi of constant slope ei and calculatethe mass balance iteratively down progressivesegments along the flow line. For segmentsabove the snowline, the mass gain per unitwidth (LlM; in kg/m) above the snowline is:

(1 )

where I.P is the storm accumulation in

kg/m2. That is, all of the storm-snow is

entrained by the avalanche.For segments below the snowline, the

mass loss by deposition is:

Avalanche Dynamics

where values of 0 (kg/m2) are adjusted to

minimize the mismatch between the modeledand observed stopping point. We use themodel to examine case histories anddetermine the range of possible values for D.

4. MODEL RESULTSWe have developed and tested the modelusing measurements from seven storms thatproduced avalanche activity. For each cyclewe compare observations of runout positionfor three paths (Raspberry, East Homer andMoir) with model results obtained for varyingvalues of 0 (mass loss per unit area). Fig. 4shows results for all paths for the case 0 =O.5kg/m2

, which is the value that yields thebest overall fit to the observations.

Results are encouraging, although notperfect, as illustrated by the scatter about thedashed line (the perfect fit) in figA. Modelresults indicate that avalanches down EastHomer have the highest potential for reachingthe road, which is also well known by localavalanche forecasters. The modelsuccessfully predicted five of the sixavalanches that crossed the road. It alsosuccessfully predicted 10 of the 14 avalanchesthat did not cross the road, with false alarms(over-predicting) for the other four avalanchesthat did not reach the road (Fig. 4).

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Figure 4: Modeled andmeasured runout distances(relative to the centerline ofthe road) for the Raspberry(squares), East Homer(circles) and Moir(triangles) avalanchepaths. In a/l cases shownhere, 0 = O.5kg/m2

. Thedashed line represents aperfect model fit to theobservations.

s

ObserVlld runoul (lIllIlllrs from cllnlllrllnll)

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International Snow Science Workshop (2002: Penticton, B.C~)

5. DISCUSSION AND CONCLUSIONSWe have examined in more detail thepotentially more serious case (under­prediction of the avalanche that crossed theroad), which occurred on the Raspberry pathon October 6,2000. Storm total was estimatedto be 150mm (water equivalent) and theaverage snowline during the storm was 964m.Calculations indicate that the model would fitthe observations exactly if either: the stormtotal was double (300mm); the averagefreezing level was 100m lower (864m); or themass loss was half (D = 0.25 kg/m\ Howeverduring the same storm, the model over­predicted East Homer (360m compared with20 m observed) and was nearly correct forMoir (20m compared with -50m observed),which suggests that the storm characteristicswere not anomalous. It is possible however,that D was relatively low in the Raspberrypath. In fact in four of the six cases studied,the model under-predicted runout on theRaspberry path, which might imply that D isgenerally lower there.

It is also instructive to examine the case onOctober 7, 1996 where the modeled runout onMoir (340m) was much larger than theobserved runout (-200m). Storm total wasestimated to be 627mm (water equivalent) andthe average freezing level was 1308m. Themodel would fit the observations exactly ifeither: the storm total was half (315mm); theaverage snowline was 150m higher; or D = 1kg/m2

. During this cycle the model over­predicted runout distances on all paths(although not as much as that on Moir), whichsuggests that the estimate of the snowline istoo low. The snowline on the west side of thedivide (which include Moir) is often higher thanthat at Mt 8elle (where temperatures aremeasured) on the east side of the divide.

We are encouraged that such a simplemass continuity model does so well atpredicting runout of direct-action avalanches.The model does not capture all details of thedynamics, for example it does not simulate theair blast, which is often severe in the Milfordregion (McLauchlan, 1995). Nevertheless, theresults emphasize the importance of includingentrainment/deposition processes whenmodeling avalanche flow. We caution that themodel is not perfect; even a small under­prediction of runout can have majorconsequences for a traveler on the road.

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6. ACKNOWLEDGEMENTSThis work was supported by Transit NewZealand and the U.S. National ScienceFoundation. We also thank all the people whohave worked on the Milford highway. Theirdedication and observations made thisresearch possible.

7. REFERENCES8artelt, P., M. Kern and M. Christen, 2000. A

mixed flowing/powder snow avalanchemodel. Proceedings, ISSvv, 2000, BigSky, Montana, 280-289.

Conway, H., W. Carran and A. Carran, 2000.The timing, size and impact of snowavalanches along the Milford Highway,New Zealand. Proceedings, ISSvv, 2000,Big Sky, Montana, 167-172.

Fitzharris, 8.8. and I.F. Owens, 1980.Avalanche atlas of the Milford road and anassessment of the hazard to traffic. NZMountain Safety Council AvalancheCommittee Report NO.4.

Fitzharris, 8.8. and I.F. Owens, 1984.Avalanche tarns. J. Glacial., 30(106), 308­312.

Hutter, K., 1996. Avalanche dynamics. InSingh, V.P., ed. Hydrology of disasters.Kluwer Academic Publishers, 317-394.

Issler, D., 1998. Modeling of snow entarinmentand deposition in powder-snowavalanches. Ann. Glacial., 26, 253-258.

McClung, D.M. and K. Lied, 1987. Statisticaland geometrical definition of snowavalanche runout. Cold Reg. Sci. andTechnol., 13(2), 107-119.

McLauchlan, H.J., 1995. An assessment of thevelocities, impact pressure and otherrelated effects of the avalanches on theMilford road, Fiordland, New Zealand,Unpublished Ms thesis, U. Canterbury,New Zealand.

Perla, R., T.T. Cheng and D.M. McClung,1980. A two-parameter model of snow­avalanche motion. J. Glacial., 26(94), 197­207.

Savage, S.8. and K. Hutter, 1991. Thedynamics of avalanches of granularmaterials from initiation to runout. Part 1:Analysis. Acta Mechanica, 86,201-223.

Smith, H.W., 1947. Avalanches. NZ Eng., 2(5),491-496.