A BETWEEN-STORM INDICATOR OF AVALANCHE ACTIVITY

Robert E. Davis1

US Army Engineer Research and Development CenterCold Regions Research and Engineering Laboratory

Hanover, New Hampshire

Kelly ElderRocky Mountain Research Station

USDA Forest ServiceFort Collins, Colorado

ABSTRACT: Earlier studies examining relationships between weather factors and avalanche activityshowed that the important between-storm factors include an index related to the minimum and maximumdaily air temperatures. The index helped explain the differences in avalanche activity with similar storms,but with different circumstances affecting the snow between storms. This study used the results of theprevious investigation to guide case studies taking a closer look at the temperature index, which has thename vapor gradient index (VGI). The VGI accumulates each day between storms by adding the currentday's value VGI' with the accumulated value from the previous day. During storms the value remainsconstant, and is reset to zero when the snow stops falling. To calculate the VGI' for the current day, onerequires two temperatures, the daily minimum temperature and the value midway between the dailyminimum and maximum. For each temperature the one then uses Clausius-Clapeyron equation tocalculate the saturation vapor pressure at each temperature. The difference between the two vaporpressures becomes the VGI', the value of the current day. We used the SNTHERM model of snowprocesses to calculate grain growth during a 17-day period between storms in the early winter,1994, atMammoth Mountain, California. During this period the VGI showed a high correlation to grain growth.

KEYWORDS: Snow, metamorphism, avalanche activity

1. INTRODUCTION

The avalanche community has known forsome time the conditions related to release of dryslab avalanches. Among these include factorsthat affect the strength of the old underlying layerand/or the relative degree of sintering between theslab and the old layer (Schweizer, 1999).Metamorphism in near-surface layers prior tosnowfall may affect the degree of involvement ofold snow in slab avalanches and/or the rate ofbonding between the slab and old snow surface.

In analyzing avalanche activity in long-t~rm ~atasets, one frequently finds circumstanceswith different avalanche response to similarstorms, in terms of the number of releases and/orthe ~aximum size (e.g., Davis et aI., 1999). Inparticular, the longer duration between storms, thelarger the avalanche response in many situations.

Some of this difference can be attributed toprocesses near the snow surface during thebetween storm period.

Faceted crystals growing on the surfaceof a snow cover form during conditions of extremetemperature gradients (Colbeck, 1988). Onceburied, these layers can cause persistentweakness contributing to avalanche release(Jamieson and Johnson, 1992).

Recent research has demonstrated thatfaceted crystals near the surface of a snow covercan affect avalanche release and size (Birkelandet aI., 1998a). Faceted crystals in near-surfacelayers can grow in the presence of large gradientsof vapor pressure, driven by 1) differing radiationregimes from solar and longwave radiation havingan approximate balance, 2) presence of a meltedlayer beneath new snow, and 3) large diurnaltemperature gradients (Birkeland et aI., 1998b).

1 Co .646;espondmg author address: Bert Davis, US Army CRREL, 72 Lyme Road, Hanover NH 03755-1290, tel: 603-

219, fax: 603-646-4397, e-mail: bert@crrel.usace.army.mil

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The grain size of the old snow surface canaffect the rate at which new snow becomesbonded to the old. While the processes controllingbonding are not well understood (Colbeck, 1997),it seems clear that the rate of bond formation isinversely proportional to grain size, so that finegrains bond more slowly to coarse grains than toother fine grains (Colbeck, submitted).Accordingly, new snow will bond more slowly to anold snow surface, other factors being the same, ifthe grains of the old surface are large.

The main factors controlling dry snowmetamorphism include temperature, vapor fluxand initial size of the grains (Colbeck, 1982). Atemperature gradient gives rise to a gradient invapor pressure, and the warmer the averagetemperature, the steeper the gradient in vaporpressure. In turn, grains grow in dry snow at arate determined by the vapor flux, which iscontrolled by the gradient of water vapor and thegeometry of the pore space.

Recent snow models have reached astage of sophistication where one can estimategeneral changes to grain size and density withinsnow layers (Brun et aI., 1989; Davis et aI., 1993,2001; Fierz et aI., 1997; Fierz and Gauer, 1998;Fierz and Lehning, 2000; Jordan, 1991; Jordan etaI., 1999; Gubler, 1998). The variables listed inTable 1 show the inputs generally required atfrequent time intervals by snow models of thistype (Davis et aI., 2001).

Table 1. Variables required by models fullycharacterizing snow processes and properties.

1. Incoming (reflected*) solar radiation2. Incoming longwave radiation (surface

temperature*) .3. Air temperature4. Humidity5. Wind speed6. Precipitation and type

* alternate variables used by Swiss SNOWPACKmodel.

On the other hand, ski areas, departmentsof transportation and other organizations in theUS typically measure the variables listed in Table2 on a daily basis.

Table 2. Typical weather measurements byavalanche practitioners in the US.

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1. Total snow depth2. New snow depth3. New snow water equivalent4. Minimum and maximum air temperature5. Average wind speed.

We derived an index to roughly descrigrain growth in the near surface of the old snowbased only on the minimum and maximum air.temperatures.

2. METHODS

This section describes the formulation ofindex, which describes the potential for snowmetamorphism at the snow surface and in near-

.surface layers during periods between storms.This section also describes a case stUdy in whithe SNTHERM model (Jordan, 1991) simulatedgrain growth to compare with the index.

2.1 The Vapor Gradient Index

We propose that the minimum daily airtemperature forms a reasonable surrogate forminimum surface temperature of dry snow nearthe site of the air temperature measurement.Further, we assume that the temperature midwabetween the minimum and the maximum daily aitemperatures represents a crude apprOXimationdry snow temperature near the diurnal dampingdepth, several centimeters below the surface.

The Vapor Gradient Index (VGI) presents acumulative expression of temperature gradienteffects on the potential vapor gradient duringperiods with no significant snowfall. To formulathe VGI we calculated an individual daily interivalue VGI', based on the difference in saturativapor pressure between the two temperatures.Buck (1981) formulated modified expressions ofthe Clausius-Clapeyron relation to estimate thesaturation vapor pressure Pv,sat (mb) based ontemperature T (0C):

Pv,sat = 6.138 exp(22.452 T/(272.55 + T»)

The current-day value of the interim vaporpressure gradient VGI' comes from the differenbetween Pv,sat at the two temperatures:

VG I' = Pv,sat (Tmin) - Pv,sat ((Tmin - Tmax)/2)

For between-storm periods

3. RESULTS

SNTHERM showed grain growth on sunnyslopes as slow at first, then increasing at a steadyrate until the next storm started. Figure 1 showsthe trend in mean grain size from the threeaspects under sunny conditions.

near-surface facets seemed likely; high pressuredominated the synoptic weather withpredominantly clear skies and low winds.

This study compared the VGI for thissame 17-day test period, normalized to themaximum reached, with the grain growth fromSMTHERM.

20

•••

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:5 0.4 •~ 0.3 ••

••0.2 •0.1 •••••••O'---'"'-=-'----'-------'---..........L---

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VGI'VG1today ::: VGlyesterdaY +

. storms VGI ::: constant at the last valueDun~; snowfall. The first day after snowfall VGI :::~f. for the day. That is, the VGI comes from theV lative sum of the daily values VGI' every daycumu n avalanche/storm days. Functionally,betwee .' t' t' fVGI has simllanty to the es Ima Ion 0 near-th~ ce gradients of vapor density proposed by~u~er (1998), except that Gubler's methodrequires much more meas~rement support andprovides more frequent estimates of near-surface

processes.

2.2 Grain Growth Simulation with SNTHERM

The simulation of grain growth usedSNTHERM (Jordan, 1991; Jordan et al., 1999), aphysically-based 1-dimensional mass and energybalance model that simulates details in changingsnow cover properties over time in response tometeorological forcing (Table 1).

Primary meteorological measurementscame from the Mammoth Mountain cooperativesnow study plot (Painter et aI., 2000). This sitelies in the Sierra Nevada at about 2926 melevation (37Q 39'N, 119Q 02'W). We adjusted themeteorological measurements to account for avariety of notional starting zones with propertieslisted in Table 3.

Table 3. Conditions used for simulating graingrowth using SNTHERM.

1. mean elevation 3200 m: air temperaturesand humidity adjusted for a normal lapserate;

2. three aspects: north, northeast andnorthwest;

3. mean slope: 35Q ;4. solar illumination: two cases - 75% sunny

and 75% shaded (periods during day)5. length of simulation: 17 days6. snow profile: themally semi-infinite with

isothermal temperature set at the meanair temperature over the 5 precedingdays;

7. model spin up period: 48 hours;8. initial grain radius: 0.025 mm;9. initial snow density: 125 kgm-3

Further . ., we selected the 17-day penod from the

Weather record during which the formation of

Figure 1. Grain growth simulated by SNTHERMon sunny slopes under conditions specified inTable 3.

The simulated grain growth showed minorvariations across the different aspects, with themajor difference between sunny and shadedslopes. Figure 2 shows that the grains on thesunny slopes grew at about twice the rate as thegrains on the shaded slopes.

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4. DISCUSSION AND FUTURE DEVELOPMENT

7. REFERENCES

Birkeland, K. W., 1998b: Terminology andpredominant processes associated with theformation of weak layers of near-surfacefaceted crystals in the mountain snow pack.

5. CONCLUSIONS

6. ACKNOWLEDGMENT

Birkeland, K. W., R. F. Johnson and D. S. Sch1998a: Near-surface faceted crystals formdiurnal recrystallization: A case study oflayer formation in the mountain snowpackcontribution to snow avalanches. ArcticRes., 30(2), 200-204.

specific rates and values reached by the VGI,related to actual grain growth and potentialformation of faceted crystals, will clearly provespecific. However, this simple index offersanother piece in the puzzle of avalanche reIcharacteristics. One can calculate the VGI uSia simple spreadsheet application and theequations presented above.

The VGI does not distinguish betweentypes of surface or near-surface crystal forma·in snow. Further development might incorpowind speed as an additional factor, which mayallow site-specific separation between casesrounded grain growth, surface hOar growth anthe formation of near-surface facets within thesnow cover.

The U.S. Army Project 4A762784AT42helped fund the analytical work to evaluate thesnow modeling using data from the MammothMountain study plot. We thank the ERDC-CRREL technical and research staff for designiand building sensor mounts and other specialtyequipment. We also gratefully acknowledgeMammoth Mountain Ski Area and the Valentine!Eastern Sierra Reserve for their support inacquiring field data.

This study described the Vapor GradiIndex, a simple parameter that may proVideimportant clues to the conditioning of old snowprior to storm cycles. Using a limited case stuwe showed that the VGI can have a highcorrelation to grain growth, at least as simulatby the SNTHERM model under conditionsdescribed in Table 3.

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y =0.5393xR2 =0.9851

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We consider this limited case stUdy asoffering reasonable evidence that the VGI canprovide a simple surrogate to conditionscontrolling metamorphism. Though the VGI usedair temperature measurements from the study plot,we still found good correlation to conditions in thenotional avalanche starting zones and paths. The

The normalized VGI showed a highcorrelation with the mean grain growth from allmodel simulations, as shown in Figure 3.

Figure 3. Comparison between the mean graingrowth across all conditions list in Table 3 and thenormalized VGI during the test period.

Figure 2. Comparison between simulated graingrowth on sunny and shaded slopes.

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