STORM AND WEATHER FACTORS RELATED TO DRY SLAB AVALANCHE ACTIVITY

Robert E. Davis *U.S. Army Engineer Research and Development Center

Cold Regions Research and Engineering LaboratoryHanover, New Hampshire USA

Kelly ElderDepartment of Earth Resources

Colorado State UniversityFort Collins, Colorado USA

Daniel HowlettAlta Ski Lift Company

Alta, Utah USA

Eddy BouzaglouMammoth Mountain Ski Area

Mammoth Lakes, California USA

ABSTRACT: Storm cycle factors affect slab avalanche response primarily in terms of loading in starting zones.Wind velocity and supply of transportable snow, relative to terrain, control redistribution and thus potentialloading of avalanche slopes. Snow metamorphism in near-surface layers may affect the degree ofinvolvement of old snow in slab avalanches and the rate of bonding between the slab and old snow surface.Early season snow conditions and general loading rate during the season may also affect avalancheresponse. We evaluated empirical factors that combine wind velocity with new snow amount, describe thepotential for near-surface grain growth and provide indices of between-storm snow condition. The importanceof different factors was rated in terms of explaining deviance in avalanche activity indices. Avalanche activityindices included maximum size, number of releases and sum of sizes of released avalanches. Ranking andscores for the different factors resulted from classification and regression tree analyses carried out onavalanche observations from Alta, Utah and Mammoth Mountain, Califomia. Time lagged conventional factorsdescribing snowfall and derived wind-drift parameters ranked highest in all tests. Snow drift factorssegregated into prominent wind directions showed moderate importance. Among the non-storm factors, thestarting snow depth of a particular year ranked highest showing the importance of interannual variability. Thiswas followed by the accumulated vapor pressure difference, which we formulated to describe the potentialfor near-surface grain growth. The average snow depth increase and other factors followed in importance.

Key Words: avalanche, avalanche forecasting, snow accumulation, snow cover stability

1. INTRODUCTION

Records of weather and storm variables andavalanche observations contain interrelationshipsbetween variables that can be discovered and thatcan lead to improved indices relating to differentlevels and types of avalanche activity. Whiletraditionally this process has been largely based onknOWledge, experience and intuition (LaChapelle,1980), recent progress has been made in applyingadvanced analytical techniques

* Corresponding author address: R.E. Davis,CRREL, 72 Lyme Rd. Hanover NH 03755 USA

to improve forecasts of avalanche hazard (e.g.,Buser et aI., 1987; McClung and Tweedy, 1994;Schweizer and Fohn, 1996).

Since Atwater's (1954) article listing criticalfactors leading to avalanches, much effort hasfocused on determining a limited set of indexparameters, derived from weather observations andmeasurements from snow plots, which reduce thecomplexity of information considered by theforecaster. This development has led primarily tostatistical, expert and hybrid models for assessingavalanche hazard over large regions. A major

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problem in achieving any sort of progress has beenthe development of data sets with verifiableresponse variables describing actual hazard oravalanche activity. Avalanches are recorded leastfrequently when and where the greatest number ofnaturally triggered releases occur: during stormsdeep in the backcountry of large mountain ranges.Addressing this issue, avalanche observations, snowcover tests and other records have been used tohindcast avalanche hazard levels for developing datato test models of regional hazard (Fohn andSchweizer, 1995 as cited in Schweizer and Fohn,1996).

Ski resorts and other organizations in theU.S responsible for controlling public access and useof avalanche prone areas face similar tasks atsmaller spatial scales. However, in this case the jobis to forecast locally specific probabilities foravalanche activity. Many operations of this sort haveneither the resources, nor the records to motivatedevelopment of complex relational models to aidforecasters. Rather, in this era of slim profit marginsand decreasing government resources in the U.S.there have been trends to incrementally develop andincorporate analytical tools that function more to helpinput, output and communications, in relation to ahuman forecaster (Ueland, 1996; Tremper et ai,1996, e.g.). Moreover, day-to-day exposure to localavalanche terrain and long term experience in itsresponse to storms will likely never be replaced byavalanche forecasting models. Still there ismotivation to develop to new ideas that simplifyanalysis of snow conditions, or make more efficientthe recognition of unusual situations.

The main objective of this study was to rankand score weather and snow cover parameters interms of their value in explaining deviance inavalanche activity at two ski areas in the westernU.S.. Stated another way, we sought toquantitatively evaluate weather and snow coverfactors that could affect snow stability and lead toavalanches. This study derived some newparameters in an attempt to evaluate the effects ofstorm direction, snow processes between stormsand differences of snow loading between years.These were tested along with conventional factorsand parameters used previously.

2. METHODS

We used basic weather observations, snowmeasurements and avalanche records from studyplots at Alta, Utah and Mammoth Mountain,

26

California. Alta ski area lies in the WasatchMountains, which experiences intermountain climate.Snow climate conditions leading to avalanching can

vary from deep alpine to moderate / shallow alpinewith one or the other usually dominant in a givenwinter (LaChapelle, 1965). Hence the role of depthhoar can vary from season to season. MammothMountain lies along the crest of the Sierra Nevada inCalifornia, which experiences a strong maritimeeffect with deep stable snow and surfaceavalanching (LaChapelle, 1965). The two ski areashave active and rigorous avalanche controlprograms, so avalanche observers have recordedthe vast majority of significant avalanches. Allreported avalanches were considered in our study,whether triggered by storm activity, explosives or skicutting. Often a delay occurred between whenunstable slabs formed and when instability wasdetected by explosive release or ski cutting. Thiswas simply due to the expediencies of avalanchecontrol work. Processing of the records attemptedto mitigate the delay, or lag, between weatherforming the unstable snow slabs and the artificialavalanche by time shifting some of those occurrencerecords back into the storm cycle.

2.1 Weather Data Processing

Weather and snow measurements included anelementary set measured at most snow plots onceper day in the western U.S.: total snow depth from astake, new snow depth and precipitation (waterequivalent) from snow boards, average wind speedand direction, and maximum and minimum airtemperatures. We tested set of short-term, or stormvariables, in addition to the daily measurements. Aswith previous studies (Judson and Erickson, 1973;Bois et aI., 1975; Bovis, 1977; Obled and Good,1980; and others) we compiled sums of snowfalldepth and water equivalent for 1, two and three dayperiods. Wind speed was averaged over one tothree day periods as well.

Previous studies have used a snow driftparameter, derived as the product of wind speed andeither snowfall depth or precipitation (Judson andErikson, 1973; Fohn et aI., 1977; Davis et aI., 1996,e.g.). Tabler et al. (1990) showed that the mass fluxof snow drifting with an unlimited snow supply wasapproximately proportional to the forth power of thewind speed, confirming an expression derived byPomeroy (1988). We derived factors for snoWdrifting during storms based on the product of 24hrsnowfall, which we assumed to be an index of thesnow supply, and wind speed to the forth power.

Two factors were derived; one using snowfall depthand the other using water equivalent (precipitation).We tested these factors summed over one day, twodays and three days. Previous studies have usedsums of new snow depth over two and more days.One aim in testing these variables was to find out

whether new snow depth and water equivalent areinterchangeable. Also included in the analyses weresnowdrift factors related to wind direction, wheredirection was divided into eight categories of 45°'centered on the directions north, northeast, east, andso forth. Perla (1970) discussed the importance ofwind direction to avalanche release in LittleCottonwood Canyon and Judson and Erikson (1973)tested various combinations of wind and snow,finding that precipitation intensity modified by windspeed and sum of wind speeds resolved to anoptimum direction were important. Obled and Good(1980) considered wind direction segregated intodirection class and accumulated over three days.Here we test a snowdrift parameter, combined asabove using 24hr values of snowfall depth andaverage wind speed, was mapped directly into oneof the direction-related bins. Adjacent direction binswere assigned half the value and the rest set to zero.

Snow stability is also related to the conditions ofthe old surface snow underlying the new slab. Forexample, recent research has demonstrated thatfaceted crystals near the surface of a snow covercan affect avalanche release and size (Birkeland etaI., 1998a). Faceted crystals can grow in thepresence of large gradients of vapor pressure, drivenby large diurnal temperature gradients (Birkeland etaI., 1998b). The grain size of the old snow surfacecan affect the rate at which new snow becomesbonded to the old. While the processes controllingbonding are not well understood (Colbeck, 1997), itseems clear that the rate of bond formation is

~ inversely proportional to the grain size. Accordingly,new snow will bond more slowly to an old snowsurface, other factors being the same, if the grains ofthe old surface are large. We derived an index todescribe grain growth. The main factors controllinggrain growth are the temperature, the vapor flux andthe initial size of the grains (Colbeck, 1982). Atemperature gradient gives rise to a gradient in vaporpressure, and the warmer the average temperature,the steeper the gradient. To formulate an index wecalculated the difference between the saturationvapor pressure at the daily minimum temperatureand at the average of the daily maximum andminimum air temperatures. This value was summedevery day between avalanche days. Duringavalanche days the value was held constant, andafter the avalanche cycle the sum was reset to the

value of that day.

Three parameters were derived from the dailytotal snow depth. Attempting to account for snowstrengthening during periods between avalanches,we summed the daily settlement, provided that thesnow pack did settle, between avalanche days.Obled and Good (1980) also used this parameter.The settlement value remained constant when snowwas accumulating, or avalanching. The factor wasreset after avalanche days and the value wasrestarted at zero. Previous work with the Alta dataset (Davis et aI., 1996) showed that the accuracy ofclassifying different levels of avalanche activity couldbe improved by dividing the seasonal records intoyears with thin snow at the beginning of avalanchecontrol work from years starting with a substantialsnow pack. The former were characterized bygreater avalanche activity, given certain stormcharacteristics, and sometimes called "depth hoaryears" (Perla, 1970). Attempting to account forinterannual differences, we included the depth at thestart of the snow season, a parameter held constantfor the year. Blattenberger and Fowles (1994)evaluated a factor something like this; they usedsnow depth over some low threshold. The seasonalrate of snow loading was computed by the leastsquares method as the slope of depth increase fromthe beginning of the season the day in question.This factor changes most in the early part of theyear.

Table 1 summarizes the weather and snowrelated factors tested.

Table 1. List of weather and snow factors.

1. total snow depth2. 24hr new snow depth3. 48hr new snow depth4. 72hr new snow depth5. 24hr total precipitation6. 48hr total precipitation7. 72hr total precipitation8. 24hr average wind speed9. 48hr average wind speed10. 72hr average wind speed11. (24hr snowfall depth)x(24hr wind speed)412. (48hr snowfall depth)x(48hr wind speed)413. (72hr snowfall depth)x(72hr wind speed)414. (24hr total precip.)x(24hr wind speed)415. (48hr total precip.)x(48hr wind speed)416. (72hr total precip. )x(72hr wind speed)417. west: (24hr snowfall depth)x(24hr wind speed)4

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18. northwest: (24hr snowfall depth)x(24hr windspeed)4

19. north: (24hr snowfall depth)x(24hr windspeed)4

20. northeast: (24hr snowfall depth)x(24hr windspeed)4

21. east: (24hr snowfall depth)x(24hr wind speed)422. southeast: (24hr snowfall depth)x(24hr wind

speed)423. south: (24hr snowfall depth)x(24hr wind

speed)424. southwest: (24hr snowfall depth)x(24hr wind

speed)425. maximum air temperature26. minimum air temperature27. degree days28. cumulative vapor pressure difference29. cumulative settlement30. starting snow depth of year31. average snow depth increase from beginning

of year

2.2 Avalanche Data Processing

We compiled and processed avalancherecords to build a matrix consisting of daily values ofthe 31 parameters listed above, the sum ofavalanche sizes, the maximum size class, and thespecification of avalanche day or not (1 and 0respectively). Visually inspected plots of weatherand avalanche variables guided further processing ofthe combined avalanche and weather data. Weselectively eliminated long periods with no new snowor avalanches, reducing the number of "no action"days until days with avalanche days composed about20 to 30 percent of the data. Effectively thiseliminated about 13 percent of the record from Altaand 18 percent of the record from Mammoth, mostly

~> - during springtime. Cumulative variables were~

adjusted accordingly.

Next, we subjectively shifted the records ofexplosive avalanche release from the period of nonew snow, immediately after storm cycles, back intothe period of the storm. Previous results (Davis etaI., 1995) showed that the majority of severe errorsoccurred due to avalanches released by control workdays after storms cleared. The great majority of theshifts were one day backwards. For a few we feltcomfortable with a 2-day shift. Where we shiftedavalanche records to days with their ownavalanches, we summed the records. Otherwise theshift replaced a day with no avalanche observations.The Alta data set totaled 1895 days, spanning theperiod of winters from 1983 through 1994. There

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were 532 days with avalanches (unshifted). Weshifted 137 daily avalanche records. The Mammothdata set totaled 890 days,-spanning the period 1989to 1998, with two years missing. There were 160days with avalanches, of which we shifted 47.

2.3 Classification and Regression Trees

We presumed that a set of tests using arobust method for determining relationships betweenavalanche activity and the index parameters shouldprovide a useful way to rank and score the indexparameters. Binary tree models provide a pragmaticand effective altemative to multiple linear regressionmodels, classification algorithms and hybridtechniques. We selected classification andregression trees to perform these analyses primarilybecause the methodology is essentially non­parametric (Breiman et aI., 1993). This test is not a"black box"; the theory is well documented and themethod has seen a wide variety of applications in thephysical and biological sciences. The tree modelsare particularly effective where the data containhierarchical or nonlinear relationships. These modelsare pragmatic because the results are easilyinterpretable by people with a wide range ofstatistical understanding.

Not only can these models be used forprediction where appropriate, but they are also veryeffective tools for uncovering, interpreting anddescribing structure within a data set. Thisinterpretation may be extended to the process levelwhere physical relationships exist. Althoughinferential statistics are not yet well developed for therelatively new tree based models, there are somesimple metrics for assessing model performance.One of the strengths of the method is the ability tooverfit a given model for exploratory purposes, whileretaining a more conservative model for predictiveapplications. The conservative model is obtained bypruning an over-fit tree back to a statisticallydefensible size though cross-validation or cost­complexity measures. Over-fitting the model allowsone to uncover odd or rarely observed relationshipsin the data. In this mode the decision trees are reallyan exploratory tool for data analysis. This is theapplication for which we have used the trees in thisstudy.

In using classification trees, the relationsbetween predictors and responses are notparticularly sensitive to statistical distributions ofeither the dependent or independent variables, sotransformations of the data into new scalar, arbitrary,

or "experienced-based", class intervals are notrequired. The construction of regression treesrequires the assumption of Gaussian distribution inscalar data, but this is loosely enforced due to theobservation that the final tree structure is"surprisingly insensitive" to the splitting rule andhence the distributions of variables (Breiman et aI.,1993).

In general, the algorithm uses a data set togrow a decision tree by recursively partitioning thedata into increasingly homogeneous subsets untileach subset contains a small number of cases. Thealgorithm then selectively prunes (recombines)decision branches of the tree until a stopping rule, ordesired level of complexity, is satisfied (Breiman etaI., 1993). Another way of describing this process isthat first the algorithm finds out how almost everycase is different from the rest. Then by pruning itfinds the similarities in the differences. The methodcan be applied where one has a set of independent(predictor) variables (x) and a single dependent(response) variable (y). Classification trees must beused where the response is a discrete member of afinite set, class or category. In this set of analyseswe used the Gini index of diversity to define subsetimpurity, defining the splitting rule, and we limited thedepth of the final trees to 100 or less layers.Regression trees are used where the responsevariable is numeric or continuous. We again limitedthe depth of the final trees to 100 and used ahierarchical least squares rule to split nodes.

Classification trees with nominal response dataresults in decision structure similar to:

if(wind speed < 12 m s·') & (wind direction E

_* {N, NW})then

maximum avalanche size class =2

where wind speed and wind direction are membersof x, and the maximum avalanche size class is thedependent variable y. Regression trees with ratioscale response variables take the form:

if(new snow depth < 200 mm) & (air

temperature < -5C)& (wind direction E {SW, W})

thensum of avalanche sizes = 63 (± some

deViance)

where new snow depth, air temperature and wind

direction are members of x, and the sum ofavalanche sizes is the dependent variable y.

Accuracy of classification trees can beexpressed as the probability of correct classificationfor a particular category, which for over-fit and verylarge trees is higher than is reasonable if theapplication is to predict outcomes, but notunreasonable if the application is to explorestructures in the data. Average accuracy of responseclasses comprises one of our metrics in this study.The accuracy of regression trees is expressed asthe coefficient of determination (R2

), using therelationship between tree deviance and total setdeviance. The coefficient of nondetermination for agiven tree is the sum of squared differences of allmembers of each terminal node from the predictednodal value, summed for all terminal nodes, andthen divided by the sum of squared differences ofthe entire data set from the grand mean of theresponse variable. The R2 is simply one minus thecoefficient of nondetermination.

We used successive tests to assess therelative merits of the derived factors in comparisonto each other and to the conventional parameters. Atest was assumed valid if a reasonable degree ofexplanation of the deviance in avalanche activitycould be achieved. Importance of independentvariables, expressed as scores, depends on howeffectively a variable can a split cases. This is basednot only on whether a variable gives the best split fora node, but also whether it gives the second or thirdbest, and so forth. The values of importance resultfrom comparison of the relative misclassification costthat the use of each variable brings. All of theparameters in Table 1 were used to growclassification trees on maximum avalanche size andavalanche day, and regression trees wereconstructed for sum of avalanche sizes. Weselectively eliminated various classes ofconventional and derived parameters to see bothhow the ranking and scoring of the remainingvariables changed and to assess the change inclassification accuracy. We removed variables thatseemed to duplicate the information, such as newsnow water equivalent or new snow depth. Weeliminated parameters that described multi-dayaverages or sums. Finally we added back thederived parameters one at a time to assess theirrelative value in explaining deviance in avalancheday or not, maximum size class and sum of sizes.

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3. RESULTS

3.1 Classification and Regression Tree Accuracy

Table 2. Binary tree accuracy - maximum sizeclass. Values show the probability or correctclassification.

2 0.94 0.93 0.9.~ 3 0.87 0.82 0.81

4 0.70 0.68 0.645 0.73 0.73 0.55

Factors based on snowfall water equivalent hadslightly higher scores than those based on snowfalldepth at both Alta and Mammoth. Table 2 alsoshows the effects of removing factors based onsnowfall depth from the test on classificationaccuracy at both areas. We saw an improvement inprobability of correct classification of the maximumsize class 5 of about 0.09 at Alta and 0.57 atMammoth, The averaged classification accuracy forall sizes decreased 0.02 for Alta but increased 0.12for Mammoth. This result indicates that use of manycorrelated variables as predictors can sometimesincrease the ambiguity in determining the best splits.Table 2 shows results of analyses with only thederived factors (14-27 and 30-34 in Table 1); theaccuracy decreased somewhat for most of theavalanche size classes, with the exception of class5 avalanches at Mammoth. The averageclassification accuracy using only the derivedvariables was comparable with the analyses using allfactors.

Factors describing conditions between storms andbetween years showed some value in explainingdeviance in the avalanche observations. Thesederived factors were most important to explainingdeviance in maximum avalanche size, relative tothe other two avalanche activity indices. Rankingswere somewhat similar between the two data sets.

Time-based, or lagged, parameters derivedfrom snowfall depth or new snow water equivalentdominated the rankings and scores. The results withindividual lagged factors of the conventional type,such as 2-d and 3-d snowfall depth, were similar toprevious results by many other researchers. Snowfalldepth and water equivalent tended to rank in the topfive parameters, with wind lower in the middle of therankings, and temperatures generally even lower. Ofthe derived factors, snow and wind measurementscombined in the snowdrift parameters for two andthree days scored the highest for all three of theavalanche activity indices. These factors ranked inthe top five in every test using them, and hadshowed scores only slightly lower than the two and3-day snowfall water equivalent and depth. In testsusing only derived factors (Table 2) the snow driftparameters ranked above the rest. Table 3 showsthe list of independent variables and their ranking inanalyses for maximum size class, avalanche day ornot, and sum of sizes for Alta. Table 4 shows thesame for Mammoth Mountain.

3.2 Ranks and Scores of and Time-Lagged andDerived Factors

0.820.950.670.29

0.900.860.710.71

0.850.950.790.14

All No DerivedFactors Snowfall Factors

Depth Only

SizeClass

2345

Mammoth

SizeClass

Alta

The analyses using all factors from Table 1showed probabilities for correct classification fortrees with maximum depth 100 (rather over-fit)ranging from 0.14 to 0.98 depending on avalancheactivity variable. The probability of correctclassification for maximum size class ranged from0.70 to 0.94 at Alta and 0.14 to 0.95 at MammothMountain. The average classification accuracy formaximum size at Alta was 0.81 and at Mammoth0.68. The average classification accuracy foravalanche size classes 2, 3 and 4 was 0.84 for Altaand 0.86 for Mammoth. Table 2 summarizes theresults for classification accuracy of maximum sizeclass and avalanche day for Alta and MammothMountain. The probability for correct classification ofan avalanche day at Alta using all factors was 0.97,and at Mammoth 0.98. The probability of correctclassification of non-avalanche days was higher. Thecoefficient of determination, W, in predicting the sumof avalanche sizes using all factors was 0.84 for theAlta data and 0.88 for the Mammoth data. Thesetests formed the baseline accuracy against which allsubsequent tests were compared.

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Table 3. Classification-tree scores for derived factors from tests with Alta data. Values describe scores ofimportance in terms of reduced misclassification accuracy due using the parameter for either primary orsurrogate splitting decisions.

Derived Factor

(48hr total precip.)x(48hr wind speed)(48hr snowfall depth)x(48hr wind speed)4(72hr total precip. )x(72hr wind speed)4(24hr total precip.)x(24hr wind speed)4(72hr snowfall depth)x(72hr wind speed)4(24hr snowfall depth)x(24hr wind speed)4starting snow depth of yearcumulative vapor pressure differenceaverage snow depth increase from beginning of yeardegree dayswest: (24hr snowfall depth)x(24hr wind speed)4cumulative settlementsouthwest: (24hr snowfall depth)x(24hr wind speed)4

-Total

The starting depth of snow for the year rankedhighest of this group of factors, showing moderateimportance to the coefficient of determination of sumof sizes at Alta, and showing moderate importanceto probability of correct classification of maximumavalanche size at Mammoth Mountain. Theaccumulated vapor pressure difference was nextdown in the rankings of this group (Tables 3 and 4)and was most important to classification ofmaximum avalanche size in both data sets.Proceeding downward in the rankings, the averagesnow depth increase from the beginning of the yearwas next, followed by degree days and cumulativesettlement between storms. In tests where time­lagged factors were eliminated, the between-stormderived factors ranked in the top five of every test,with similar relative ranking in their scores asdescribed above. The snow drift parameters relatedto direction showed moderate importance comparedto the other factors. At both Alta and MammothMountain the west (270o±22.5°) component of snowdrift ranked highest, with the southwest (225°±22.5°)somewhat lower (Tables 3 and 4).

3.3 Tree Structure and Terminal Nodes

The trees were over fit to the extent thatten:ninal nodes containing rare events resulted fromsplits between only a few cases. This was thesituation with avalanches of the class 4 and class 5sizes, for example. At Alta there were 47

Max. Size Aval. Day Sum of TotalClass Sizes

91 77 33 20177 78 36 19179 64 31 17472 57 38 16784 27 25 13634 59 33 12621 19 38 7829 26 21 7620 25 24 6928 21 15 6418 15 19 5220 16 14 5016 8 11 35

589 492 338

avalanches described in the size class 4 categoryand 11 in size class 5 during the period of record. AtMammoth Mountain there were 24 avalanches withsize class 4 and 7 with size class 5. We found thatthe derived factors played a more important role inthe splits for maximum size class for both test sites(Table 3 and 4). By derived we mean factors otherthan the conventional daily variables and laggedconventional variables (Le. 14-27 and 30-34 fromTable 1). We also found that derived factors playadecidedly more important role in the splits of rareevents. At Alta, about half of all splits determiningclassification of class 4 or class 5 avalanches usedderived factors as the primary decision, of as high­ranking surrogates. The majority of splits classifyingavalanches with sizes 4 and 5 at Mammoth Mountainwere determined by derived factors. In both datasets the most important derived factors were one ofthe snow drift parameters. The most important non­storm factor was the accumulated vapor pressuredifference.

4. DISCUSSION

These results represent several years of carefulanalysis and reanalysis of two comprehensive datasets. We have refined the techniques of exposingdata structure and correlation betweenmeteorologically based independent variables andindices of avalanche activity using binary decisiontrees. We have also refined the data setsthemselves to present a set of logical dependent

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Table 4. Classification-tree scores for derived factors from tests with Mammoth Mountain data. Valuesdescribe scores of importance in terms of reduced misclassification accuracy du~ using the parameter foreither primary or surrogate splitting decisions.

Derived Factor Max. Size Aval. Day Sum of TotalClass Sizes

(24hr total precip.)x(24hr wind speed) 90 86 63 239(48hr snowfall depth)x(48hr wind speed)4 98 77 46 221(24hr snowfall depth)x(24hr wind speed)4 81 70 61 212(48hr total precip.)x(48hr wind speed)4 97 92 21 210(72hr total precip. )x(72hr wind speed)4 76 66 29 171(72hr snowfall depth)x(72hr wind speed)4 44 23 27 94west: (24hr snowfall depth)x(24hr wind speed)4 30 13 50 93starting snow depth of year 41 22 20 83southwest: (24hr snowfall depth)x(24hr wind speed)4 16 11 54 81cumulative vapor pressure difference 29 26 21 76average snow depth increase from beginning of year 26 25 24 75degree days 28 21 15 64cumulative settlement 20 16 14 50

-Total 676 548 445

variables that are coherent in time with observedstorm characteristics. One should keep in mind thatthe results are critically linked to three main factors:1) the avalanche activity we are modeling applies tonatural and artificial release; 2) all observations areat ski areas where skiing and control activityconsiderably alters the local snow stability comparedto surrounding "natural" conditions; 3) the study sitesrepresent best-case scenarios where a full suite ofindependent variables are collected on a regularbasis.

It should be noted that the objective of the studywas to evaluate the relationship between

,""', meteorologically based independent variables andavalanche activity, not to produce a forecastingmethod applicable either to a ski area or itssurroundings. The results should be interpreted as"here are the factors that appear to be linked toavalanche activity at these ski areas and this is themanner in which they interact". This statement isreally the root of the study and it should beemphasized. Artificial release provides aconservative estimate of potential activity. Natural orskier releases will likely be much lower even in thesame terrain in the absence of artificial control. Thisrelationship means that results from ski areas can beused in local or even regional forecasting outside ofthe ski area bounds only if forecasters and usersrealize the obvious nature and problems associatedwith this type of extrapolation. Indeed, many localand regional forecasts in mountainous areas of the

32

United States are critically linked to results of nearbyski area control activity. The fact that ski areaactivity often reduces deep slab instability andmagnitude of individual events also confoundsforecasting for local and regional activity, but theerror this time may be that greater instability in the"natural" snowpack is undetected at the ski area. Itmay be that these two factors are compensating, butthe information necessary to assess the fullrelationship is not available due to limitedbackcountry observations.

We have quantitatively compared conventionaland derived parameters in terms of determining howindices of avalanche activity were different inresponse to storm and between-storm conditions,and how these differences compare. In doing so wehave also demonstrated how binary decision treescan uncover the relationships and interactionbetween the independent variables and observedavalanche activity. Three derived parametersshowed particular value in identifying structure in thedata. Of these the wind drift parameter was themost important of the storm related factors. Thissimply confirms what is already well known, butprovides a metric that has some basis to physicalprocess. The two other derived parameters relate toconditions of the existing snow cover, not the slabformed by the storm. The starting depth of snow forthe year was useful in separating general avalancheactivity response to a given storm from one year tothe next. Without multiple years of data, this factor

would not show any importance. It seems commonlyunderstood by experienced forecasters that yearsstarting with thin snow tend to produce more, ~ut notnecessarily larger avalanches, than years with anearly thick snow cover.

The accumulated difference in vapor pressuredifference was also important, notably in its value inseparating the maximum avalanche size on differentdays and especially in distinguishing between thelarger events. We believe this also has a basis inphysical process in that it provides an index of graingrowth in the near-surface layers of snow. Originallywe thought this index would work two ways. If theindex accumulated rapidly then maybe this was asignal that the snow was loosing strength. In thiscase we would expect some increased importancein distinguishing maximum sizes. If the indexaccumulated slowly, but over a long time, thenmaybe the grains were growing large and rounded,so the textural mismatch might make for poorbonding between the slab and snow surface. In thiscase we might expect more releases and henceincreased importance in the sum of sizes. If theindex increased at some intermediate rate we mightexpect that both processes were competing, with nonet effect on bonding (Colbeck, personalcommunication). While this index deserves somefuture attention, the results appear to show that thisparameter makes some indication of surfaceweakening.

5. CONCLUSIONS

We have evaluated 31 conventional, timelagged and derived factors of weather and snowconditions as they relate to avalanche activity indicesmaximum size, avalanche day and sum of avalanchesizes. Tests with derived factors by themselves haveslightly lower overall accuracy in explaining deviancein avalanche activity indices than tests using all ormost of the factors, showing that conventional andlagged conventional factors cannot be ignored.

Storm related factors dominated the scored ofall tests, with those factors using snowfall waterequivalent slightly more important than those usingdepth. Snowfall water equivalent and snowfall depthappeared more or less interchangeable, and wefound that elimination of one or the other fromclassification tree analyses increased the probabilityof.correctly classifying larger avalanches. The snowdrift parameter based on snowfall water equivalent~nd wind speed to the forth power was the mostImportant of the derived variables. A similar factor

segregated into predominant directions was muchless important, but identified directions mostassociated with avalanches.

Between-storm factors improved classificationand regression accuracy, primarily the probability tocorrectly classify maximum avalanche size class.Moreover, derived factors in general were importantfactors in decision splits for rare events, such aslarge avalanches. Our tests show that starting snowdepth of the year was surprisingly the most importantof the non-storm derived factors. It appeared mostlyin the splits for moderate size avalanches andmoderate sums of sizes of releases. Theaccumulated vapor pressure difference rankedsecond of this type of factor and scored high indecisions classifying maximum avalanches sizes 4and 5. Other factors showed modest importance.

6. ACKNOWLEDGEMENTS

Our thanks to Ron Perla for stimulatingdiscussions about avalanche forecasting. WalterRosenthal provided many insights about use ofclassification and regression trees and avalanchecontrol work at Mammoth Mountain. Also thanks toAlta Lifts Company and Mammoth Mountain Ski areafor providing the data. Data preparation andanalyses were funded by US Army Project4A762784AT42.

7. REFERENCES

Atwater, M. M., 1954: Snow avalanches. Sci. Amer.,190(1),26-31.

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