Bulletin ofGlaciologicalResearch22（2005）3949∫タ◎JapaneseSocietyofSnowandIce

Characterisationol＝liquidwatercontentandsnowdensityinacross−COuntry
race＄kitrack

DagAnder＄MOLDESTADllAutoSockAS，MariaDehlisvei57，N−10840slo，Norway（Received August31，2004；Revised manuscriptreceivedNovember4，2004）

Abstract
VarioussnowparametershavebeenregisteredduringmeasurementcampalgnSincrossTCOuntry

race skitracksin Norway（1995−98），Hakuba／Japan（1996−98）and Sundance／USA（1999）．Specificattention has been paid to snow hardness，LWC（liquid water content），SnOW density，SnOW grain
StruCtureandelectrolyticconductivity．ThepresentpaperfocusesonLWC，SnOWdensityandtosome

extentsnowgrainstructure．

Themeandensityoftheupper5cminskitracks（0．50gcm3）isconsiderablyhigherthantypicaldensitiesofseasonalsnowcovers（0．26−0．38gcm3）and higherfortransformedsnowtypes（0．51−0．59gcm3）than new snow types（0．39−0．43gcm3）．The LWC oftheupper5cminaskitracktypicallyranges between O and12．5％per volume．Itis typicallyless than2％for snow temperatures（2cmdepth）below−2℃andless thanl％forsnow temperaturesbelow−70c．LWCexceeding4％have
Onlybeenregisteredatairtemperaturesabove＋lOc．Thetypicalgrainsizeofthesnowsurfaceinaski
trackrangesfromO．26tol．89mmfortransformedsnowtypesandfromO．08toO．38mmfornewsnow
types．In−SitumicroscopeimaglngOfskitracksisverydifBcultfornewsnowtypeswithsnowsurface
grainsbelowO．2mm．

1．lntroduction
Characterisation of the sliding surface，i．e．the
SnOW Surface ofthe cross−COuntry Skitrack，isneces−
Saryln Order to understand skibase sliding friction
and results from skibase sliding friction tests．Itis
thereforeimportant to register essentialsnow pa−
rameters when performing accurate ski base sliding
friction testsin−Situ．In our research we have reglS−
tered and characterised the following snow parame−ters：
・Snowtemperatureatdepths5，−2andOcm rela−tive to the snow surface
・Snow hardness of the snow surface

・LWC（1iquidwatercontent）andsnowdensityofthe

upper5cm of theskitrack．

・Snow type and snow grain structure of the snow
Surface・Electrolytic conductivity and water chemistry ofmelted snow samples from the upper5cm oftheski
track．
In addition the following weather parameters havebeen registered：・Airtemperature（0．5m above thesnowsurface）

・Relativeairhumidity（0．5m）
・Netradiation（0．5m）

Thepresentpaper，Whichfocusesonmeasurementsof
LWC，SnOW density and to some extent snow grain

StruCture，isextractedfromthedr．thesisofMoldestad（1999）．
Several measurement methods can be used for

determiningtheLWCinasnowpack：・Melting（hot）calorimetry，See e．g Yosida（1940；1960），andHansenandJellenik（1957）．
・Freezing（cold）calorimetry，See e．g．Jones etal．

（1983）．

・AIcohoIcalorimetry，Seee．g．Fisk（1986）．
・Dilution measurements，Seee．g．Davisetal．（1985）．
・Centrifugalmeasurements，See e．g．Kuroda andHurukawa（1954），and Kuroiwa（1954）．
・Dielectric measurements，See e．g．Ambach andDenoth（1975），Aebischerand Matzler（1983），Denothetal．（1984），Sihvola and Tiuri（1986），Bergman（1986；
1987），Kendraetal．（1994），Denoth（1997）andSteinetal．
（1997）．

Calorimetry，dilution and centrifugalmeasureT
mentsare destructivemethods．Freezingcalorimetryis accepted as astandardfield measurement method
andis used to calibrate non−destructive methods

Bulletin ofGlaciologlCalResearch

4β（Steinetal．，1997）．Dielectric measurements are fasterto perform than the other measurement methods（Boyne and Fisk，1987）and suitable forin−Situ non−destructivemeasurements．TheSnowForkinstrument（SihvolaandTiuri，1986）hasbeenusedformeasuring

LWCanddensityin thiswork．
Measurements of the LWC have not been madeSyStematically to agreatextentinin−Situskistudies．
Spring（1988）presentedkineticfrictioncoefncientsfor

skisglidingwithspeeds up tolOmslon oldgrainy

SnOW With O and 20％ per volume LWC．Slotfeldt−
Ellingsen and Torgersen（1983）publishedlaboratory

friction tests on crushedice with various LWC，butthese tests were performed with toolow sliderspeed（0．3msl）tobeofgreatrelevancefortypicalskibase
Sliding friction situations．Non−destructivein−Situ

Fig．1．Setup forsnow surface measurements withthe
S氾0膵Fりγ々．

measurements of LWC in snow have been presented

bye．g．SihvolaandTiuri（1986），Toikka（1992），Kendra
etal．（1994），Denoth（1997）and Steinetal．（1997）．

ing LWC between O andlO％withan accuracyof±
0．3％（Toikka，1996）．Themeasurementofsnowdensity
has an accuracy of±0．005gcm3．The SnowForkis

2．Measurement methodsand procedures

O．6gcm3，butis also possible to use for measuring

まノ．5乃0比，Jβ∽♪eγαJ祝γeSnow temperature has been measured using aSTAR HD 8901Hygrometer−Thermometer with a
SnOWPrObewithasmalltemperaturesensorinthetip．

Theinstrument has an accuracy of±0．1％of regis−
tered value±0．20c（STAR，1995）．Snow temperature
measurements have been taken at three differentlev−

elsin the race skitrack：5cm below the surface of the

track，2cm below the surface of the track，andin thesurface of the track．

It can be difficult to perform qualitatively goodmeasurements of snow surface temperature due topotentialinfluencefromairtemperature，PreCIPitationand solar radiation on the snow temperature sensor．
Direct sunlight on the sensor has been avoided byusing the body oftheperson that holdsthe probe，tO
Shadeforthesun whennecessary．
Differentmeasurementlevelshavebeenchosenin
Order to get consistent snow temperature measure−ments andobtaininformation aboutthe temperature
gradientinthesnow．Throughoutthispaperthesnow
temperature2cm below the surface of the trackis
referred toasthesnow temperature Ts．
ヱヱ」L‖1／け（川／（J甘〃左り▲（、0〃付〃ナノ（川（′∫〃りけ（′l）旧〃l・

LWC（1iquid water content）and snow density

have been measured with the Snow Forkinstrument（SihvolaandTiuri，1986）．TheSnowForkisasteelfork

used as microwave resonator which operates in thefrequency range500to1000MHz and measures theprlmarilydesignedformeasuringsnowdensitybelow

highersnow densities．
Normally when measuring the LWC and snow
density，theSnowForkispushedhorizontallyintothe
SnOW paCk．In order to measure the LWC and snow
density as close as possible to the snow surface，the
SnowForkhasbeenputintothesnowsurfacewithan
angle ofapproximately300relativetothesnowsur−
face．This corresponds to measuring the LWC andSnOWdensityoftheupper5cmoftheskitrack．Figure
lshowsthemeasurementsetup．WhentheSnowFork
measurementsareperformedatanangleof300tothe
SnOWSurface，aSmallpartofthemeasurementvolume
Willcontain airinstead of snow．Itisimportant toadjusttheLWCanddensityresultsaccordingly．This
Canbeperformedquitesimplybyusingthefactthat
the spikes of the SnowFork are75mmlong，and theWidthis20mm．Assuming that theSnou）Fork meas−

urement volume consists of a75mmlong cylinder

WithlOmm radius，it can be found that6％of themeasurementvolumeisairwhentheSnowForkisput
into the snow at a300 angle relative to the snow
Surface．The calculated density and snow humidity
musttherefore bemultiplied by thefactor：
75＝1．0612726：こ1．06．

（75票）

If a450 angle to the snow surfaceis usedin themeasurementsinstead ofa30O angle，the multiplica−tion factor wi11be approximatelyl．034．Half−SpaCe
measurements（Sihvola and Tiuri，1986）where theresonancefrequency，attenuationand3−dBbandwidth Snow Forklies at the snow surface have also beentestedin my research．This setup has not glVen reli−

Of a snow volume．From these electricalparameters
thecomplexdielectricpermittivityofthesnowcanbe
CalculatedaswellasthedensityandLWCofthesnow（Toikka，1998）．TheSnowForkisdesignedformeasur−ableresults，prObablyduetomeasurementnoisefrom
the air above the snow surface，SOlar radiation andprecIPitation．

Moldestad

Tablel．Classification of LWC of snow according toColbecketal．（1990）．
Term

4J

Table2．Classification of d according to the clas−
SificationofgrainsizegiveninColbecketal，（1990）．

Termlγ、rt】1．，％（％）

Dry
Moist
Wet

Verywet
Slush

0

＜3
38

815
＞15

d（mm）

Very負ne

＜0．2

Fine

0，20．5

MediumCoarseVerycoarse
Extreme0．51．01．02．02．0−5．0＞5，0Table3．Classification of the grain shape of the snow
accordingtoColbecketal．（1990）．
Basicclassification

Graphic
SymbolPreclpitationparticles
Decomposingandfragmentedprecipitationparticles
Roundedgrains（monocrystals）

Facetedcrystals
Cup−Shapedcrystalsanddepthhoar
Wetgrains

＋

●
［コ

∧
（⊃

Featherycrystals
Icemasses

Surfacedepositsandcrusts＞□∀］− SnOWgrainsurfacenumberinamicroscope
Fig．2．Snow microscopy setup without camera

COnneCted to the phototube．The camerais used to
takethesetup picture，Classification of LWC of snow according toColbeck etal．（1990）is shownin Tablel．Snow with
LWCless than O．5％per volume has been approxi−

mated asdryinourmeasurements．

Zヱ S乃0ぴわ少eα乃dざ乃0ぴgγαょれSfγ祝CJ〟γe

To avoid damage ofthe orlglnalstructure ofthe

SnOWSurfacein thetrack，WeChosetouse ameasure−ment procedure that did not involve movement of
SnOWfromthetrack．ALEICAMS5stereomicroscope

imageofasnowsurface
dj−length ofthelargest2Ddiagonalforsnow

grainsurfacenumber］1namicroscopeim−

ageofasnow surface，mmng− numberofsnowgrainswithdistinguishable
boundaries in a microscope image of a snow
Surfaced− meanOfdjforthengsnowgrainswithdistin−

guishableboundariesinamicroscopeimage
Ofasnow surface，mm
6d T Standard deviation of dj for the ng snow
grainswithdistinguishableboundariesin a
microscopeimageofasnowsurface，mm

万has also been classified according to the classific−
ation of grain sizegivenin Colbeck etal．（1990），See

Table2．
（max．40×magnification）was used to observe the
Further，the snow typein the track has roughly
SnOWSurfacedirectlyin−Situinthetrack．Microscope been classified according to the following snow typeimages of the snow surface were captured with aCategOries：
Nikkon F70D camera connected to the microscope
1． Fa11ing new snow
through a phototube．Figure2shows thesetupwith−

2．New snow

Out Camera COnneCted to the phototube．At alater

3．Combination of new snow and transformed

digitalformbyascanner，andanalysedandcharacterL
iseddigitallyusingthegeneralimageprocessingpro−

4．Combination of new snow and transformed

Stage（indoor）thecapturedimageswereconverted togram AdobePhotoshop5．0（Adobe，1998）．

The2Dsnowgrainsurfacesinmicroscopeimages
have been characterised using the following defin−

itions：

SnOW，mainly newsnow

SnOW，mainly transformed snow

5．Transformed snow
6．Artificialsnow

The grain shape of the snow has furthermore been

ClassifiedaccordingtoColbecketal．（1990），SeeTable3．

Bulletin ofGlaciologicalResearch

42urementresultsarebasedonmeasurementcampaigns

2．4．Aよγfe∽♪emわJ柁Airtemperature，T。，hasbeen measured by using

in Norway，1995−98，Hakuba／Japan，1996L98and Sun−an air probe on the STAR HD 8901Hygrometer−
Thermometer．The measurement of air temperature
hasthesameprecisionasthesnowtemperaturemeas−

dance／USA，1999．

Thesnow temperatureinthecampalgnShasran−urements（STAR，1995）．Themeasurementshavebeen
performedO．5m abovethesnowsurface．

gedfromOto−22．10c（Granasen，26．01．1996），Whilethe
air temperature has ranged from ＋14．2（Hakuba，
14．02．1996）to14．60c（Gran且sen，26．01．1996）．The rela−

tivehumidityofairhasvariedfrom18％indrysunny

Sundance（03．03．1999）tolOO％duringsnow eventsinヱユ 斤（一山〟＝・汀汀／川川′（J〃l・

Relativeair humidity has been registered O．5m
abovethesnowsurfacewiththesameairprobeasintheairtemperaturemeasurements．Themeasurement

Trondheim（winter1996）．Amaximumnetradiationof

816Wm2 has been registeredin Hakuba at360N（27．01．1998）．

Figure3showshistogramsforsnowdensitymeaT
SurementS Of different snow typesin cross−COuntry
raceskitracks，WhileTable4givessnowdensitystaL

Of relative air humidity has a precision of±2％forrelative air humidities between5and90％and十4／
2．5％forrelativeairhumiditiesbetween90and98％．
The relative air humidity，Rh，is defined as the ratio

tistics．ThefollowingdefinitionsareusedinTable4：

between the amount of vapour present in the air
considered and the amount that air at the same tem−

Perature COuld containifit was saturated．Airis de−fined as saturated whenitin these determined condi−

tions of temperature，air and pressure，has absorbed

thegreatestpossibleamountofvapour．
2．丘．Ⅳefγαdgαfわ乃αれd cわ〟dg乃eSS

戸 meansnowdensityforasnowtype，gCm3
6。 Standarddeviationof戸，gCm3
pm。X maXimumsnowdensityforasnowtype，gCm3
Pm．n minimumsnowdensityforasnowtype，gCm3

p50 mediansnowdensityforasnowtype，gCm3
np number of density measurements for a glVen

Net radiation，qnet，is the difference betweenin−

COming and outgoing radiation at the surface of theearth．Modelling of net short wave andlong wave
radiation has been performed by e．g Male and Gray

35

−All
＋Snowtypel
一★−Snowtype2＋Snowtype3

30（1981），and Loset（1992）．

Netradiation hasbeenregisteredO．5m abovethe・・・♯−Snowtype4
・・◎−Snowtype5

25

SnOWSurfacewiththeAnderaaInstrumentsnetradia−∈

tion sensor 2811instrument．This sensor measuresboth sunlight andinfrared radiation．The measure−mentrangeoftheinstrumentis±2000Wm2，andthe
accuracy±1％offullscale．
Cloudiness，C，has roughly been characterisedin
OCtOpartS（0＜C＜8）．A complete cloud coveris ex−pressedasC＝8，WhileC＝Oindicatesaclearsky．

巴 20
くっ〉
○

蔓15
＝

10
5

0・川2・0・80・91

3．Results
ThissectionpresentsmaJOrreSultsfrommeasure−mentsofLWCandsnowdensityofthe upper5cmin

Fig．3．Histograms for snow density measurements ofdifferent snow typesin cross−COuntry raCe Ski
tracks．

l17cross−COuntryraCeSkitracks．Thepresentedmeas−

Table4．Snow density statistics for different snow typesin cross−COuntry

race skitracks．

Snowtype （gcm3）
／）

A
l
1
2
3
4
5

0
0
0
0
0
0

5
3
■
4
5
5
5

0
9
3
1
7
9

㌔

（g3）（g3）（g＝う）（g3）
0
0
0
0
0
0

3
1

6

0

8

0

3

0

2

1

2

1

0
0
0
0
0
0

2

9

6
9

0
0

．6
4

0

6

0

5
7
9

9
2

0
0

2
2
3
4
4
4

2
2

0
0
0
0

0
5
7
1

0
0

乃p
9

4
3

9
3
2

．6
4 6
5
5
5

Moldestad

J． ？

SnOW type

Thesnowdensityvaluesinthel17measurementschaverangedbetweenO．22andO．92gcm3，i．e，uptOthe ・∈density ofice．The minimum density was registeredfor Snow typelin GranÅsen，27．03．1996．The highest 0？
measured density value was obtained for wet snow
言u（Wv。1，％＝5A％）inSundance，27．02．1999．Theaccuracyof
名
this value can be questioned since the Snow Fork，喜ualthoughusablealsoformeasuring highersnow den−S
Sities，isprlmarily designedformeasuring snowden−
SitybelowO．6gcm3．Thehighestmeasuredsnowden−
Sity for new groomed snow types，0．69gcm3，WaS
registeredonawarmday（T。＝＋5．1℃）inLillehammer

inApril1998．ThelowestsnowdensityvaluefortransT

Fig．4．Snow density plotted as a function of LWC for
differentsnow typesinskitracks．

formed snow types，0．41gcm3，WaS Obtainedin
Granasen24．02．1997，immediatelyafterthelOkmclassic

raceformenintheNordicWorldSkiChamplOnShips
97．

12

It can be seen from both Table4and the histo−

gramsin Figure3that the mean snow densityis
higher for transformed snow types than new snow
types．While Snow typesland2have mean snow

10

densitiesofO・39andO．43gcm3respectively，themean
辞
SnOW densitiesof Snow types3，4and5areO．51，0．57
andO．59gcm3．

Figure4showssnowdensityplottedasafunction
OfLWCfordifferentsnowtypesinl16skitracks．We
CanSeethatthesnowdensityincreaseswithincreased

LWC，atleastforLWCupto6％pervolume．
The LWC has ranged from O to12．5％in thel17
measurementsin skitracks．No LWC（Wv。］．％＝0．0％）

hasbeenfoundatsnowtemperaturesbelowapproxi−

mately−60c．The highestvaluewasmeasuredon21

April1998atLillehammeronawarm，Sunnydaywith
high net radiation．At this day the LWCincreased

fromO．6％at9：40（T。＝＋3．lOcandqn。t＝431Wm2）to12．5％atll：59（T。＝＋5．80candq。et＝753Wm2）．Large

variations in LWC have also been measured during

Skicompetitionsin winter．During the Nordic Com−

binedcompetitionintheNordicWorldSkiChampion−

8

6

」
4

2

月2

−10

−8

−6

−4

Snowtemperature，OC−20

Fig．5．LWCversussnowtemperature（2cmdepth）fordifferent snow typesin skitracks．LWC values
lower than O．5％ are regarded as dryin thesemeasurements．

C＝3andq。。t＝114Wm2．
・Airtemperaturesabovethemeltingpointoficei．e．

Ships 97in Granasen（23．02．1997），the LWC changed T。＞OOc（15measurements），e．g．inGranasen20．02．97atfrom2．4％atll：40（Ta＝＋2．6℃andqnet＝131Wm2）to10：41：Wv。1，％＝1．5％，Snow type 4，Ts＝T2．40C，T。＝＝6．8％at14：17（T。＝＋6．70candqn。t＝103Wm2）dueto＋2．2Oc，Rh＝67％，C＝8andq。et＝OWm2．

rapidincreaseinairtemperature．

Figure 5 shows LWC plotted as a function ofsnow temperature for different snow types in ski
tracks．Inthepresentexperimentsitisfoundthatthe
LWCisless than2％for snow temperatures below

・ Fa11ing newsnoworrecentlyfallennewsnowand

relative air humidity above75％，i．e．Snow typel2

andRh＞75％（9measurements），e．g．inHakuba29．01．97
at15：41：Wv。1，％＝1．4％，Snow typel，Ts＝−1．7℃，Ta＝一2．40c，Rh＝88％，C＝8andq。。t＝OWm2．

−20c andlessthanl％forsnowtemperaturesbelow
・Air temperatures below but close to the melting−70c．Furthermore，theLWCisfoundtobelessthanpointofice and relativeair humidityabove70％，i．e．
2％fornewsnowtypesandbelowzerosnowtempera− T。＝Ll．500candRh＞70％（4measurements），e．gintures．LWC−Values above O．5％ at below zero snow
Granasen19．02．97atlO：33：Wv。1，％＝1．3％，Snowtype3，
Ts＝4．40c，T。＝−0．7℃，Rh＝83％，C＝8andqnet＝37W
temperaturescanbeexplained by：・Solar radiationi．e．qn。t＞50Wm2and T。＜0℃（22measurements），e．g．inHakuba3l．01．97at13：20：W，。），％
Figure6depictsLWCversusairtemperaturefor＝1．1％，Snowtype2，Ts＝一4．90c，7t＝−1．20c，Rh＝57％， Varioussnow typesinskitracks．Itcanbeseenfrom

■J・J

Bu11etin ofGlaciologlCalResearchthefigure that the LWCisless thanl％forairtem−
peratures below p40c andless than2％forairtem−
peraturesbelow−20c．LWCexceeding4％haveonly
beenregisteredatairtemperaturesabove＋1Oc．

Figure7shows a contour plot of the measured
LWCinskitracksasafunctionofrelativeair humid−

ity and air temperature．A C／Eline（Condensation／
Evaporationline）basedonPetterssen（1956）hasbeen

added to the plot．Thislineindicates thelimiting

辞
■
U
宴
﹂

8
6

4

Value of relative air humidity．If the relative air hu−

midityln the airabove the snowis higherthan thatindicated by theline，WaterVapOurCOndensesonthe2

SnOW，Otherwiseitevaporates．Itcanbeseenfromthe

figure that the highest LWC are registered on clear，Warm days with relative humidities between40and

560％and air temperatures above十5Oc．The LWCis

−10

−5

0

Airtemperature，OC

5 10 15

Fig．6．LWC plotted as a function of air temperaturefordifferentsnowtypesinskitracks．

relativelyloweratrelativehumiditiesbetween60and

80％，prObably due toless efhcient solar radiation

COmpared tolower relative humidities．At relative
humidities above80％the LWCshowsanincreasing
tendencyagalnWhencondensationprocessesstartto

LV〉C（†Jlし・erSしiS3‖t丹11Pe「封侶e即再圧再l汀己細り1し…（叫be efncient．For relative humidities exceeding65％，
the LWCis highest to the right of the C／Eline，i．e．
when condensation on the snow dominates over eva−

poration from thesnow．

Figures8−11depictLWCofsnowsurfaces．Exam−
plesofverywet，Wet，mOistanddrysnowsurfacesarepresentedin Figures8，9，10andll，reSPeCtively．Fig−

ures12and13show examples of snow surfaces of
Snow type5with highandlowdensities．
Themean snowgrain diameterand thestandard
deviationofsnowgraindiameterswerecalculatedfor
34snow surface microscopeimages of skitracksin

Moldestad（1999）and Loset and Moldestad（2000）．It

WaS Shown that the typicalgrain sizein skitracks

Fig．7，Contour plot of the measured LWCin ski

ranged from O．26tol．89mm for transformed snow
types，i．e．Snowtypes4and5，andfromO．08toO．38mm
fornewsnowtypes，i．e．snowtypes2and3．Thein−Situ

measurement procedure has proved to be very efnc−
ient for skitracks with snow surface grainslarger

tracks as a function of r・elative air humidity andair temperature．A C／Elineindicates the borderline between condensation and evaporation on
the assumption of OOc snow surface temperature（Petterssen，1956）．

thanapproximatelyO．10．2mm．Forsmallersnowsur− was commentedin the results section that the accu−
facegrainsithasbeendi庁iculttocapturemicroscope racyofthehighestvaluecanbequestionedsincethe

imageswithsufncientquality．Themeansnowgrainmeasurement equipment，although usable also for

4．Discussion

thedensityoficewasreached．Thistypica11yoccurred
When the snow pi11ar was compressed to approxi−

measuring higher snow densities，is prlmarily de−diameter，d，and the standard deviation of grain di−ameters，6d，forthesnowsurfacemicroscopeimagesof Signed for measuring snow density below O．6gcm3．
Skitracksin Figures813are presentedin Table5
In spite of thisit can not be excluded that snow
together withinformation of time，location，SnOW densityin the proximity of the density ofice（0．92g
type，grainshape，SnOWhumidity Wv。1，％，SnOWdensity cm3）might occurin groomed compressed wet ski
P，SnOW hardnessHandsnowtemperatureTs．Table6 trai1s that havegone throughseveralmelt−freezecyT
presentsdataonairtemperatureTa，relativehumidity
Cles and are approachingice．Yosida（1963）showed
Rh，CloudinessCand netradiationqn。t atthe timeof that a snow pillarwithinitialdensity ofO．35gcm3
COuld bedeformedwithacompressionmachineuntil
SnOWmicroscopeimageregistr・ation．

｝ The snow density has ranged between O．22andO．92■gcm3（i．e．densityofice）inourmeasurements．It

matelyone−hundredthofitsinitialheight．Sommerfeld
and LaChapelle（1970）referred a typicaldensity
range ofO．80toO．83gcm3for firnification inducedMoldestad

Fig．8，Example of a very wet snow surface（Wv。l．㌔＝
12．5％，d＝0．86mm and6。＝0．29mm）．The distance
between the tick marks of the ruler to the right intheimageislmm．

Fig．9．Example ofa wetsnow surface（W、 1．0。＝6．8％，d＝0．72mm and6d＝0．2rnm）．

45

Fig．1l．Example of a dry snow surface（W川1．0。＝0％，d＝1．11mm and6（l＝0．54mm）．The distance between
the tick marksofthe rulerin thelowerpartofthe
imageislmm．

Fig．12．Example of a snow surface with high density
わ＝0．89gcm3，d＝0．95mm and6d＝0．34mm）．The
distance between the tick marks of the rulerin thelowerpartoftheimageislmm．

Fig．10．Example of a moist snow surface（W川1、。。＝

2A％，d＝0，84mm and6．FO．29mm）．

Fig．13．Example of a snow surface withlow density
わ＝0．41gcm3，d＝1．38mm and6（1＝0．44mm）．The
distance between the tick marks of the ruler to therightin theimageislmm．

Bu11etin ofGlaciologlCalResearch

4∂

Table5．Tableofsnow measurementsforthesnowsurfacemicroscopeimagesinFigures813．

Fig・（豊）Location ミ；3ごGrainshape諾 傷）％（g。eln3）（（

Lillehammer 500．86±0．29 12．5

0．61 1．1±1040．O

821．04．98

9

23．02．97

Granasen5（⊃0．72±0．20

6．8

0．8

2．6±104

0．1

10

23．02．97

Granasen

5（⊃0．84±0．29

2．4

O．59

4．1±1040．1

1103．03．99

Sundance

5

0

O．62

3．6±1040．0

1202．03．99

Sundance

5

（⊃

O．89

2．2±104

0．0

13

24．02．97

Granasen

5

0

O．41

2．2±104（11：59）（14：17）（11：40）（10：55）（13：43）（11：45）

Medium Very wet
Medium Wet

Medium Moist

1，11±0．54
Coarse Dry
0．95±0．34
Medium Wet

1．38±0．44 1．5

Table6．Table of weather measurements for the snow
SurfacemicroscopeimagesinFigures8−13．
月ゐ

T。

（％）

（Oc）

8

5

8

9

6

7

0

2

6

1

9

6

2

7

0

3

2

3

C

（7．1et（octoparts） （Wm2）

3
5

4

6

7

8

3

2

9

2

1

7
1
1

5
0
3
9
4

6

4

4．6

3
3
1
4
0
0

Coarse Moist

MediumMediumMediumMediumMediumMedium−0．4

COnductionandconvectionfromairwithtemperature
above the melting point ofice，that cause melting atthesnowsurfaceandlocalmeltingln thesnowpack．
Humid precipitation and airintroduce airborneliq−

uid／moistureon thesnowsurface，Whichfurthercanbe transferredinto the snow pack．Furthermore，re−Cent AFM（Atomic Force Microscope）studies by e．g．
D6ppenschmidtetal．（1998）and Bluhm and Salmeron（1999）have shown thatliquid can exist below themeltingpointofice．D6ppenschmidtetal．（1998）foundthe thicknessoftheliquidlikelayeron thesurfaceof

by advanced pressure metamorphismin theirclassi−

icetovarybetweenabout12×109mat−24℃and70
×10▼9m at ro．70c．The relative air humidity deterT

forslalomandgiantslalomracesshouldnotbemuch

1ine solidinto aliquid begins atlower temperatures

Of skitracks．

evolvesinto the successive melting ofatomiclayers，and endsin bulk coexistence．The memory of theprocess remains within a few molecular distances at

fication ofsnow by metamorphicstate．Anyhow，the mined with an electronic thermo−hygrometer was
80％．Bluhm and Salmeron（1999），uSing AFM andmeandensityofsnowintheupper5cmofskitracks
SPFM，found alayer thickness of5±0．5×10￣9m be−（0．50gcm3）isconsiderablyhigherthantypicaldensi−
tween−20and−10OCandatarelativehumidityof〜
ties of seasonalsnow covers．Sturm etal．（1995）re−ferred bulk densities of O．38gcm3for tundra，0．26g 83％forthinlayersoficeonmica．Iongrowthexperi−
cm3fortaigaandO．35gcm3formaritimesnowcov− mentsonionTfreesubstratesshowedtheexistenceofa
liquid waterlayer at temperatures down to−40℃．
ersintheirseasonalsnowcoverclassificationsystem．
Dash（2002）statedthatthetransformationofacrystal−
Yosida（1971）concluded that theidealsnow density
less than O．5gcm3．This corresponds to the mean than the melting point of the bulk．It starts at theedgesofcrystalplanes，prOgreSSeSaCrOSSthesurface，
SnOWdensitylnOurmeaSurementSintheupper5cm

ThesnowdensitylSimportantforthepermeabil−
ityofthesnowandthepotentialdrainageoffrictional

Waterfilm downin the snow during skiing．The re−sults section showed that the mean snow densities

Were higher for transformed snow types than new

SnOWtypeS．Althoughfine−grainedcompactsnowcan

havelowerpermeabilitythancoarse−grainedsnowinthe crystal−meltinterface．Premelting occur atinter−faceswithsolidsubstrates，i．e．interfacialmelting，andat grain boundaries of polycrystalline materials，i．e．

grainboundarymelting．Thisimpliesthatpremelting
at the snow surface andin the snow pack alsois an

Spiteoflowerdensity（Shimizu，1970），thismightindi− explanation forLWC−Valuesabove O％atbelowzero

Catehigherfrictionalwaterfi1m thicknessinaverageduringskiingontransformedsnow．Higherfrictional
waterfilm thickness means that coarser skibase str−

uctures have to be used in order to attain optimum

Slidingproperties．SeeMoldestad（1999）orMoldestad
and Loset（2000）formoredetails．
LWC−ValuesaboveO．5％pervolumeatbelowzero
SnOW temperatureS（2cm depth）can beexplained bypenetrationofsolarradiationintothesnow，andheat

SnOW temperatureS．

TheLWCoftheupperpartoftheskitrackcanbe

viewed as anindicatorof theinitialwaterfi1m thickT
nessin the skitrack and the frictionalwaterfilm

thicknessthatispossibletoattainduringskiing．This
makesit a verylmpOrtant parameter for optimum

Choices of skibase structure，glide wax／powder andkick waxinaskicompetition．Shimbo（1961）hasalso

pointedouttheimportanceofLWConsnowfriction．

47

Moldestad

Table7．Typicalrelations betweenoptimumstructureroughness，LWC and snow typein sliding tests ofcross−COuntry Skisin cross−COuntry raCe Skitracks（from Moldestad，1999）．

LWC Snowtype
OptimumstructureroughnesslVv。1，％（％）

≦56

＝56

＝9

≦0．6

2

≦1．3

2

＝0．3−4 4and5

＝13

＞4

2 and 5The typical distribution of LWC with relative air
humidityandairtemperaturewasshownforthemea−
SurementSin Figure7．Thisfigureindicates underwhich weatherconditions the LWC（and thereby the
initialwaterfilmthickness）issignificantandneedsto
be measured．Forinstanceitis sufncient to perform
LWC measurementsatairtemperaturesabove−30cwhentherelativeairhumidityis40％，Whileithasto

beconsideredfortemperaturesdownto100c when

the relative air humidityis80％．Typicalrelations
betweenoptimumskibasestructureroughness，R。．yWS，

LWC and snow typeinslidingtestsofcross−COuntry
skisin crossTCOuntry raCeSkitracksfrom Moldestad（1999）aresummarisedinTable7．

Throughoutthispaperasimpleclassificationsys−
temforsnowtypesonsnowsurfaceshasbeenapplied．
Thissystem hasbeenusedquiteextensivelyinprac−
ticebyskitechniciansduetoitseasetousewhenno

SnOWSurfacegrainsareessentialforthecontactcon−
figuration between the ski base structure and the
SnOW Surface，and the design of optimum skibase
structures for different snow conditions．

5．Conclusions
During measurement campalgnSin skitracksin

Norway（1995−98），Hakuba／Japan（1996−98）and Sun−dance／USA（1999），the following parameters havebeen registered：air temperature，relative air humidT
ity，net radiation，SnOW temperature，SnOW hardness，
LWC（1iquidwatercontent），SnOWdensity，SnOWtyPe，

SnOW grain structure，electrolytic conductivity andioniccontentofmeltedsnow samples．Specificatten−

tion has been paid to LWC and snow density and to
SOmeeXtentSnOW grainstructurein thispaper．
Themeasurementsofsnowdensityintheupper5
cm of skitracks have shown that：

・ThesnowdensitytyplCallyrangesbetweenO．2andO．9gcm3．
・Themeandensityofsnowinskitracks（0．50gcm：i）

is considerably higher than typlCaldensities of sea−sonalsnowcovers（0．260．38gcm3）．
・The mean snow densities are higher for trans−
formed snow types（0．5l−0．59gcm3）than new snow
types（0．39−0．43gcm3）．

The measurementsofLWCin the upper5cm ofSkitrackshaveresultedinthefollowing丘ndings：
・TheLWCtypicallyrangesbetweenOand12．5％permeasurement equlpmentis accessible．Itis forin− volume．It hasbeen measured anincreasein the LWCfrom O．6％ to12．5％ during two hours on a warm，
StanCeeaSytOinterpretSnowtype5inthissystemas
sunny dayin Aprilat Lillehammer（T。＝＋5．80c and
SnOW Where klister wax ought to be applied as kick
qnct＝753Wm2）．TheLWCoftheupperpartoftheski
wax，andSnowtype2assnowwherehardwaxshould
trackcanbeviewedasanindicatoroftheinitialwater
be applied．The grain shape and grain size classiB−
fi1mthicknessin theskitrackand thefrictionalwater
CationsystempresentedbyColbecketal．（1990）should

beusedinadditionwhenamicroscopeorhandlensis
accessibleforinspectionofthesnowsurface．
The typICalgrain size ofsnow surfacesincross−fi1mthicknessthatispossibletoattainduringskiing．
Itis thus a veryimportant parameter for optimum

Observed at the surface of the earth rangein maxi−

forsnowtemperaturesbelow L70c．

Choices ofskibase struCture，glide wax／powderandkick waxinaskicompetition．
COuntry raCe Skitracks has ranged from O．08tol．89
mm．This corresponds wellwith Schemenauer etal． ・The LWCis typicallyless than2％for snow tem−
peratures（2cm depth）below−20C andlessthanl％（1981）who havestated thatindividualsnow crystals
mumdimensionfromapproximatelyO．05mmto5mm．
Wiesmannetal．（1998）foundthatgrainsizesinsnow
COVerS ranged fromlessthanO．1mm to3mm．In our

fewanalysedmicroscopeimagesofnewsnowtypesin

・LWCexceeding4％haveonlybeenregisteredatair
temperaturesabove＋1℃．
・The highest LWC has been registered on clear，Warm days with relative humidities between40and

Skitracks grain sizes have ranged from O．08to O．38

60％，andanairtemperatureabove十50c．Duetocon−

SnOW microscopeimages of new snow types．In−Situ

above80％and air temperatures between＋1and＋
6℃compared to relative humidities between60andmm．Smaller grain sizes would probably also havebeen obtained if we had been able to register more

microscopeimaging ofskitracksisverydifncultfor
new snow types with snow surface grains below O．2
111111．

Moremicroscopeimagesofskitracksneedtobe
registeredin order tofind typlCaldistributions ofgrain sizesfordifferentsnow types．Thesizesofthedensationprocessesbeingmoreefhcient，theLWChas
shown an increasing tendency at relative humidities

80％．

Themeansnowgraindiameterandthestandard
deviation of snow grain diameters were calculated
andshownfor34snowsurfacemicroscopeimagesof

Skitracksin Moldestad（1999）and L（うSet and・措

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746．
Loset，S．and Moldestad，D．A，（2000）：Characterisation oftypeswithsnowsurfacegrainsbelowO．2mm．
SnOW StruCturein a cross−COuntry raCe Skitrack．In
Hjorth−Hansen，E．，Holand，Ⅰ．，L8Set，S．andNorem，H，，eds
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