BulletinofGlaciologicalResearch21（2004）2プL29

まヲ⑥JapaneseSocietyofSnowandIce

An estimateofspatialratiosforpreferentialwaterf［owin a meltingsnowpack
ShiqiaoZHOUl，HidekiNARITA2，KeisukeSUZUKl3and MasayoshiNAKAWO2
1InstituteoftheQinghai−TibetPlateau，ChineseAcademyofScience，BeiiinglOOO85China

2ResearchInstituteforHumanityandNature，Kyoto602LO878Japan
3DepartmentofEnvironmentalSciences，ShinshuUniversity，Matsumoto390L8621Japan（ReceivedAugust26，2003；RevisedmanuscriptreceivedNovember21，2003）

Abstract

Observationsweremadeonthediurnalvariationsofdischargesoluteconcentrationsofamelting

SnOWpaCk．Theelutedsoluteamount，fromthepackinonedayinthelatemeltseason，aCCOuntSfor

lessthan23％ofthetotalamountinthewatersheldinthepackbeforedischargeincreasinginthe

day．Based on the preferentialflow model，this ratio canbeinterpretedinto spatialratios of thepreferentialflow．Itisestimatedthatthespatialratioofthepreferentialflowchannelstothewhole

porevolumeofthesnowpackisbelow32％，Whichincludes13％forthemainchannelsand19％for

the non−mainchannels．

1．1ntroduction

Snowis one of theimportant components ofenvironmentathigh1atitudesandaltitudes．Itexerts

flow develops heterogeneous distribution of solute
COnCentrationsintheprofileofasnowpack，Whichhasalsobeenconfirmedbybothexperiment（Harrington
et alリ1996）and field work（Ishikawa et al．，1997）．

greatimpactontheenvironmentinitsdeposit，meta−morphosisandmelt．Forexample，Whenasnowpack

Following models for other porous media and withadaptationsforprocessesuniquetosnow，Harrington

in the first melt water，andits magnitudeis not

Of the mobile phaseis described by an advection−
dispersion equation，and the mobile andimmobile
WaterS eXChangeis described with a fixed rate con−beginstomeltinthespring，SOluteswithinthepack

andBales（1998b）developedanionicsolutetransport
arereleasedinawaywhatscientistscallasfractiona・ model．Themodelconsideredmetamorphicprocessestion process and preferentialelution（Goto−Azuma，
invoIving melt−freeze episodes，aS Wellas the dual−
1998）．Thesetwoprocessesleadtoaveryhighacidity Velocitynatureofthesnowpack．Thesolutebehavior
affectedbysnowdepth（HarringtonandBales，1998a）．

Theacidflushmaycauseseverephysiologicalstresstoaquatic organisms，fishkill（LeivestadandMuniz，
Stant．Fengetal．（2001）appliedasimilarmodelusing
1976）andmanyotherenvironmentalproblems．There− aseries ofartificialrain−OnTSnOW eXperiments．Rarefore，itis veryimportant to explore the physical，
earthelements，Sprayedontothesnowpacksurfaceat
ChemicalandhydrologicalprocessesinvoIvedin theintervals，Were uSed as chemicaltracers．Itis found
SnOW metamOrphism，eSpeCiallyinthe melting snow
thatthemodel，Withafixedexchangerateconstant，

metamorphism．
Similar to water flowin other porous media，
When a snowpack melts，meltwateris considered toflowonlyinpartialpores，Whichistermedthe prefer−entialflow ．Thispart ofthewateris calledmobile

Water，andanotherpartistheimmobilewaterwhich

includes waterin dead−end pores，thinliquid films
aroundsolid particles，andimmobileintra−aggregate

can produce frequently observed decreases in soluteconcentrations with increasing discharges but does
notexplaintheconcentrationincreaseswithincreas−
ingwater flux seenintheir experiments．Hence themobile−immobileexchangeratecoefficientisassumed

to increase exponentially with the effective water
Saturation，and then the solute concentration varia−

tions of the discharge are successfu11y simulated．
These observations suggest that solute transport isunsaturated conditions（Kutilek and Nielsen，1994）． largelydominatedbyfastflowchannels．Thispaperis
The formation of preferential flow paths has been
toexplorethespatialratioofpreferentialflowchan−
Observedin both arctic（Marsh and Woo，1984）andnels via analyzing the diurnal solute concentration
temperate（Kattlemann，1985）snowpacks．Preferential Variationsofdischargeofameltingsnowpack．
Water Or Waterinisolated regions associated with

24

BulletinofGlaciologicalResearch

2．Observations
︵
U
O
︶
．
d
∈
む
ト
J
叫
く

The field work was conducted at the Snow

MeltingResearchStationofInstituteofLowTemperT

atureScience，HokkaidoUniversity，Moshiri（44023′N，142017′E），in the northern part of Hokkaido，Japan0

fromMarchlO，Whenthesnowpackbegantomeltand

itsdepthwas150cm，tOtheend ofApril1989，When
the snowpack disappeared（Suzuki，1991），The data

used in the present analysis were obtained between
Apri120andApri126．Dischargewaterwascollectedusinga3．6×3．6m21ysimeterplacedatthebottomof

thesnowpack．Dischargewasmeasuredbyatipping−bucket gauge and a pulse counter．Meltwater was
Sampledhourlyoreverytwohoursusinganautomatic
Water Sampler．Meltwater percolatingin the
SnOWpaCk wasalso collectedbyaporouscup and avacuumsyringe．Atrenchwasdugandaplastictube
With the porous cup wasinstalledin the snowpackhorizontally．Percolating water surrounding the
porous cup was sucked upinto the vacuum syrlnge．
Air temperature was recorded by an automatic sta−

†
︼
b
小
三
喜
こ
昌
宏
︒
喜
U

tion．Precipitationwascollectedandsampled．

Thesesampleswerefilteredandthensubjectedto
Chemicalanalysis forion concentrations by anion

Chromatography（Dionex−2020i／SP）．

3，DiurnalVarjations of Discharge andits So］ute
Concentration

Inameltingseason，thesnowpacksurfacegener−

allyundergoesdiurnalmelt−freezecyclesandthusthe
discharge also shows daily variations．It has been

Shown（Zhou et al．，2001a）that thereis stillfaintdischargeflowevenifthemeltinghasceasedforone

OrtWO days．Sincemeltwaterisproducedin thesur−
facelayer within severalcentimeters（Zhou et al．，
2001a；Ohno and Nakawo，1998）the discharge of

SnOWpaCk can be partitioned into two parts：themeltwaterfromthesurfaceproducedintheday，andthe water heldinthe pack since before．Thus the
SOluteconcentrationsofthedischargedependonthe
COnCentrationcontrast，mixlngandexchangingofthe
two parts．Figurelshows some data obtainedinaround Apri121．Itincludes variations of the airtemperature，dischargeanditsCl−andSO42￣concen−
trations．It can been seen，from Fig．1，that highdischargesare associatedwithlowsolute concentra−
tions as a whole，Whichindicates that solute concen−

trationsin surface meltwater arelower thanin theinterstitialwater since before．From O：00to6：000n

Apri121，the Cl￣concentrationincreasedin a small
range，anddecreasedslightlyafter6：00．Then，from7：
00tolO：00，it remained a concentration ofabout156
JLeql十AfterlO：00，theconcentrationdecreasedasthe

flow rateincreasing dramatically，then reached thelowestvalue of80．9FLeqlrlat13：00and keptit con−

︵
丁
■
−
∪
︶
品
J
ヱ
U
S
岩

12 00 18 00 0 00 6 00 12 00 18 00 0〔10 6 00 12 00
Apr．20Åpr・21

Apr．22

Fig．1．Variations of discharge，its solute concentrations
and airtemperaturearoundApri121，

Stant（actually variedin aboutlFEeql−1）till15：00．
Afterthat，the concentrationincreased again．In the

Variations，ifthelowest concentrationstands for the
Value for the surface meltwater，aS SuggeSted by
Suzuki（1993）and Suzukiet al．（1994）then we canfurtherexploresomesolutetransportmechanisms．
Since the measured snow thickness was only 45

CmOnApri121，theshapeofthedischargecurve（Fig．
1）indicatesthatthesurfacemeltcurveisanapproxi−
mateparabola（Zhouetal．，2001b）whichcanbepartly
Seen from the air temperature variations（Fig．1）．

When air temperatures become above O OCin themorning，thesurfacelayermeltsandthenmeユtwater
begins to percolate downward．Accordingto the the−OryOfpreferentialflow，themeltwaterwouldprefer−entiallyenter the most easily accessible water chan−nels andmiⅩWith the water having existedin the
Channels since before，and thus the snow water con−tentwouldgoup．Asthechannelsconsistofporesand
meanwhile connect around with numerous pores ofWhichsomeareholdingimmobilewater，therisingof
WaterCOntentisnotjustanincreaseinwaterfluxesin

thesechannels；SOmeWaterWOuldenterthesurround−Zhou（2JαJ．

2fi

ingporesandkeeplinkedwiththechannels．Forthe
Waterleavingthechannels，SOmeWOuldstillbemobile

tion．According to Harrington s model（Harrington
and Bales，1998b），the exchange rate coefficientis

andmobilizesomeimmobilewater；SOmeOtherwater
WOuld becomeimmobile water as thinliquid films，

relatedittotheeffectivewatersaturationinapower

Water，and thusincrease channels；SOme WOuld mix COnStant，and equals4×10−6s￣1．Feng et al．（2001）

function．However，themobile−immobilesolutetrans・

Surface meltingintensifies，the water fluxesin thealreadydevelopedchannelsincreaseandnewchannels
aredeveloped．Sincethenewchannelshavenotbeen
elutedyet，SOluteconcentrationsinthesechannelsare

ferisaverycomplicatedproblem．Ifimmobilewater
istruly quiescent even when water fluxis changed，then the transferis only by molecular diffusion．
Nevertheless，the solute transfer coefficient depends
not only on the molecular diffusion coefficient but

water fluxes and concentrationsbetweenthe oldand

Of not only the diffusion rate but also the solute

Waterin dead−end pores orin other forms．As thehigherthanintheoldones．Therefore，SOluteconcen− also on the distance and the cross−SeCtionalarea for
trations of the discharge depend on the contrast of diffusion（SmedtandWierenga，1984）andisafunction

thenewchannels，SuppOSlngthesoluteconcentration
Ofthesurfacemeltwaterisconstantinasamedayand
the solute exchange between snow grains and per−COlating water can beignored．As the water fluxis
related to the effective water saturation in a power

retardationfactor，COlumnlength，andthefluidveloc−ity（YoungandBall，1995）．Manyexperimentsshowa

growthofwaterfluxesismainlyintheoldchannels．

divide the mobile andimmobile phases，and theimT
mobilewaterisnotreallyimmobile．When asudden
increasein water flux occurs at the surface，this
disturbancepropagatesdownthecolumnfasterthan

dependence ofthemasstransferrate on pore water

Velocity（Griffioen et alリ1998）because the water
COntentisgreaterathighporewatervelocities，prOb−
function（Colbeck，1972）andthentheincreasingrate ablyresultinginalargercross−SeCtionalarea（Smedt
fortheformerismuchlargerthanforthelatter，theandWierenga，1984）．Infact，thereisnoclearlineto
Since solute concentrations of the water in the old

Channelsbecomelower andlowerastheelutionpro−
Ceeds，the solute concentration of the discharge
decreasesgraduallybeforethedischargepeak．Afterthewateritself（Fengetal．，2001）．Thismeansthatthe

the peak，an OppOSite process occurs，namely，the flow velocity or the effective water saturation at a

portionofthewaterintheearlydevelopedchannels
getssmallerandsmallerwiththeportioninthelate
developed channels becominglarger，thus the solute
COnCentrationofdischargereturnstothehighvalue

given depth would increase before the water

Variations．It can be seen from the figure that both
CurVeS for Cl and SO42 are consistent with theabove−eXplained modeland each forms a rough1y
Clockwiseloop．Differences are stillshown on theprocesses，their effect onthe concentrationsignalis

introduced at the time of disturbance reaches that

depth，Orin short，theimmobile water can become
movable．Inthemodeling，Whilehydrodynamicdisper・
gradual1y．Figure2showstheconcentration−dischargeSionandinterphasemasstransferaredistinctphysicalflow−fallinglimb of the hydrograph．With the dis−

Charge having droppedin alarge range after the
Outflow peak，thelowest concentration remains for

Simi1ar；thereforeitisprobablethatthepairofparam−

etersusedinthecalculationsisnonunique（Harrington

andBales，1998b）．Therefore，itisveryhardtocalcu−

1atethediffusioneffectinvolvedinthelowestconcen−

tration of the discharge．However，the diffusion

Shouldbeverylimitedbecausethesnowthicknessis

about4hours rather thanincreasesinstantly．Con− OnlyOA5mthroughwhich，aCCOrdingtoourobservaTSidering a constant concentration supposed for thetion（Zhou et al．，2001b），the meltwater flux peak
Surface meltwater，the remaining can only be ex−passesinless than50minutes（The molecular diffu−
plainedbysaylngthatconcentrationsforthewaters
SioncoefficientforchlorideisO．054cm2h−1（Griffioen
intherelativelyfastflowchannelshavereachedthe
etal．，1998））．EventhoughHarrington sexchangerate
Samelevelandthewatersfromotherchannelscanbe

ignored．Thislevelmust be the concentration value

COnStantOf4×10￣6s￣1isadopted，andassumingaCl￣

COnCentrationof70〃eql．1forsurfacemeltwater，70
minutes for percolatingtime，alowest water satura・
relatively fast flow channels are eluted out，because tionof7％andlOO％ofboththemobileandimmobile
for the surface meltwater，namely，SOlutesin these

Waterintheearlydevelopedchannelsshould always
havehighervelocities andlower concentrationsthan
in thelate developed channels except that allthe

COnCentrations have reachedthelowestlevel．ThereT

Waterinvolvedintheexchange，thesoluteexchangeamountequalsonlyl．26％。Oftheamountelutedinone
hour at thetime of around discharge peak．Further−more，the concentration does not change for along

fore，thelowestvalue80．9JLeql￣1isregardedasthe time after the discharge peak．Therefore，Weignore
surfacemeltwaterconcentration．

Nevertheless，in the above analysis，the soluteexchange between mobile andimmobile wateris
ignored，andsothelowestconcentrationvaluecould
Stillbehigherthanthesurfacemeltwaterconcentra−

the diffusion and treat the lowest concentration asthat for the surface meltwater．

26

BulletinofGlaciologicalResearch

4．Estimateofthespatialratiosforpreferentialflow
Onthebasis of above analysis and assumptions，
the solute amount eluted from the snowpack in the
daycanbepartitioned．InFig．2，Aisthestartpoint

for dischargeincrease and Fis the point for thedischargefallingtothestartlevel，SuppOSingboththedischargeandconcentrationcurves（Fig，1）arecontin−
uousfunctions，thentheelutedCl▲amount Qlfortheflow−increasingABCsegment（Fig．2）is：

nels．This amount could probably flowin at a time
approachingthedischargepeak，WhichmeansQ2maymainly come from the finally developed channels
becauseonlythesechannelswouldhavelowerwater
saturations andbe far from the main channels．Since

theconcentrationsnearthedischargepeakarelower，
this exchange amountisignoredin the following
calculations．

Figurelshowsthattheflowrateofthedischarge

WaS8．1×10￣8ms￣1（0．293mmhpl）beforeit began toincreaseinthemorning．Accordingtothefieldmea−
SurementSbyZhou et al．（2003）theflowratescorre−
AβC
where uis water flux of discharge，tis time，Cis SpOndtoanaveragedwatersaturationofO．05−0．07forthe snowpack．The averaged snow densityis 470
COnCentration and cbis thelowest concentration．
Similarly，adopting constant cb for CD segment，the kgm￣3withthesnowdepthbeingOA5mintheday．As
thecalculatedmeltthickness ofthedayisO．03m，aeluted C卜amount Q2for the flow−fa11ing DEF seg−

Ql＝∬c（〟湖〟d卜co上C祝（樋，（1）thicknessofOA2misadoptedforthesoluteamountmerltis：Calculations．Based on these data and using the dis−￠2＝∬c（〝，f）血成一Co上E㍑（′）d′・

（2）

ハr．l−

Charge concentration of156JLeqlJAlbefore theUsingthehourlydatashowninFig．1，WegOt：Ql＝ increase，thetotalsoluteamountforCl，inthediffer−entpooIsorflowpathsofthepackbeforedischarge
1．51×10▲2FLeqCmM2，and Q2＝7．65×103／JeqCmJ2．It
has been known，from the above conceptualmodel， increasing，iscalculatedtobeO．1688−0．2419／JeqCmZ．
that Qlisthesoluteamountfromthefastflowchan−nels，andthatQisfromtheslowonesaswellasthose
far from the mains．There should be some soluteexchangebetweenthefastandtheslowchannels，and

ontherisinglimb of the hydrograph（Fig．1）the netbalancefortheslowonesshouldbepositive，namely，
Q2Should contain some amount from the fast chan−Thus the ratios of the eluted solutes to the total

amountare6．24％to8．95％forG，3．16％to4．53％for
Q，and9．40％to13．48％for the whole．Suppose a

uniformdistributionofthewatersinthepackbefore
the outflowincrease andthedifferencesofthesoluteexchange between grain melting and water freezlng
Canbeneglected，thesoluteamountratioforQICanberegardedasthespatialratioofthemainchannels（thefastflow channels）to the whole pore volume ofthe
SnOWpaCk，buttheratioforQ2Can

r
−
b
む
ヨ
≡
こ
巴
；
U
呂
︒
U

7

tbeinterpretedso

Simplybecause theslow andfarTreaChingflowchan−nelsarejustpartiallyeluted．Accordingtotheabove
model，the farther the channels from the main ones

0

0

■
．0
⊃

are，thelessthe solutesinthem are eluted，andvice

versa．Thusweassumethattheelutedratiodecreases︵
VlinearlyfromlOO％inthemainchannelstoO％inthe
farthestchannels，then the spatialratios of the non−mainchannels（the slow and far−reaChing flow chan−

︑O
J

−
−

nels）tototalporesaretwotimesaslargeastheratios

forthesoluteamount，being6．32−9．06％．Asumofthetworatiorangesyieldsarangeof12．5618．01％which

9Standsfortheratiooftheporesforwaterpercolation
r
；
−
ミ
︒
︒
こ
呈
亡
3
︒
︒
U

tothetotalporespaceofthesnowpack（P）．
As shownin Fig．2，the shape of the
COnCentration−dischargeplotforSO。2isthesameas
theloopforCIT．Followingtheabovecalculations，WeO

Obtained：Ql（SO。21＝8．75％〜12．53％，（込（SO．2）＝3．

05％〜4．37％，anda P value of14．85％〜21．27％．The
Ol（SO42￣）ratios arehigher，but the Q（SO。2￣）ratios

arealmostthesameascomparedwiththoseforCl▼，

0 0

0．5

10

l．う

2 0

ヱ．5

Di5Cbarge（。血，￣1）
Fig．2．ConcentrationvsdischargeforApri121，

Whichmightcomefromthedistributiondifferencesof
thetwokindsofsolutesinthesnowpack．
Figure3presents a data set similar to the one

Shownin Fig．1，for Apri124．Figure 4is the
COnCentration−dischargerelationsoftheday．Compar−

27

Zhou（Z′αJ．

︵
U
O
︶
．
h
∈
り
↑
︼
完

ニ
．
；
u
ユ
︶
u
︒
こ
雲
∈
む
︒
u
︒
U

0

7
く
J0
l
一0
−
9
′

0

ニ
．

■
b
U
ユ
︶
u
O

0

▲U

ニ
．
■
b
；
︶
喜
こ
雲
U
︒
︒
冒
U

巴
︶
已
り
U
∈
O
U

︵
T
一
！
∪
︶
旨
d
宅
S
石

▲
U

0

0

0．0

0．5

1．0

1，5

2．0

2．5

Discharge（mmll・1）

Fig．4．ConcentrationvsdischargeforApri124．

】2．00

ほ（X〉

Apr・230，00

6，00

1二≧ 00 18：〔r O OO

Apr．24（〉 00

1二Z OO

Apr．25

Fig．3．Variations of discharge，its solute concentrations
andairtemperaturearoundApri124．

ingwasslowerintheearlyperiod．Thedifferencesof
restoration in concentration may be related to theelutionofthedaybefore．Ifthedischargewaslarger
andtheelutionwasstrongerina firstdaythanina
SeCOndday，thenthespatialrangeofflowchannelsin

theseconddaywouldbesmaller，andthustheconcen−
edwithFig．2，Fig．4isdifferentinthreeaspects：first， trationcanreturnbacktotheoriginallevelwhenor
Ontheflow−rlSlnglimbofthegraphs，theconcentra・ evenbeforethe幻owraterestores；andviceversa．This
tiondecreasesalmostlinearlywithdischargeincreas−
agreeswellwiththesituationsinthetwodays（Fig．1
ing，yetthedropinFig．2isinitiallyslowandfinally andFig．3）．Thedischargeon21stwaslargerthanon
fast．Second，OnCethedischargepeakpasses，unlikea 20th，butthat on24thwassmallerthanon23rd．
COnStant Value kept for four hoursin Fig．2，theAlthoughthelowest concentration of discharge

COnCentrationrisesatonceasexactlyasdescribedin

the model．Third，When the discharge returns to theStartlevel，theconcentrationalsofallsexactlybackto

Watermightbe higher thantheconcentrationinsur−

facemeltwateron24th，the dischargeconcentration、
after thelowest，Went up Slowly，0nly a gainoflessthan3メ1eql．1intwohours．Hencewetreatit asthe

Originallevel，butinFig．2itdoesnotuntiltheflow
ratereachesalevellowerthanatthebeginning（Fig． COnCentrationforthemeltwaterofthedayandmake1）．ComparingFig．1withFig．3，itcanbeseenthattheSimi1arcalculationsasmadeforApri121．Theresults
airtemperatureswerelowerintheearlymorningof
are：7．76％〜11．37％forQl（Cl￣）（ABCsegmentinFig．
Apri121，andthesnowpacksurfacefroze，butonApri1 4）6．27％〜9．18％for Q≧（Cl￣）（CDA segmentin Fig．4）
24，thelowestairtemperaturewasaboutOOCandits
and20．30％〜29．73％ for P；9．03％〜12．94％ for Ql
durationwasveryshort，SOthefreeze，ifany，WOuldbe （SO42L）（ABCsegmentinFig．4）6．47％〜9．28％for（込Veryfew．The freezingprocessexcludes andpushes（SO42￣）（CDAsegmentin Fig．4）and21．97％〜31．50％
theimpuritiestothesurfaceofthenewlyformediceforP．Thesevaluesarehigherthanfor21st，andthe（Colbeck，1981）which then acceleratesthe elution． actualdifferencesshouldbelargerthanthesebecause，
Moreover，therewasaboutl．5mm（w．e．）snowfa11in inthemorningof21st，therewasaboutl．5mm（w．e．）

the early morning of Apri121，andits average CIL

COnCentrationwas130JLeql▲1．Therefore，theconcenT

trationsintheoutflowwerehigherandtheirdecreas−

new snow which had a highconcentration．These
differencesshouldarisefromthemeltingandthenthe

dischargedifferencesbetweenthetwodays．Accord−

2g

Bu11etinofGlaciologicalResearch

togetherwithahigherpeakflowrate，WOuldresultin

ValueandthenalargerPvalue．
Surface freeze also affects the estimation of theinapack．Thisistrulythecasefor24thversus21st

frozen part，1ike thatin the unfrozen part，is also

ingthe abovemodel，alarger totaloutflowvolume，

alargerratiooftheelutedsoユutestothetotalamount

totalsolute amount because the solute amountin the

Calculatedusingthepack−uniformedwatersaturation
withtheformerhavinghighervalues（Fig．1andFig．3）
and solute concentration．Thelow concentration of
andfurthermore，thesnowthickness on24thwasO．1
mthinnerthanon21st（Thepeakflowrate，On24th， the surface snow produces meltwater withlow con−wouldbelargerifthesnowwereO．1m thickerthanCentrations，but freezeconcentrates solutes onto sur−theobservedone（Colbeck，1972））．Therefore，although faces of snow grains（Colbeck，1981）and thus

there are some differences in the ratios between the

twodays，theratiosofthemain−Channelspacetothe
wholeporevolumeofthepack arewithin13％，and
the Pvaluesarewithin32％．

enhances the meltwater concentrations，hence theactualconcentrationsdependonthesetwocompeting

processes．Meltwater，atthedepthofO．05mwithinthe

pack，WaSCOllectedbytheporouscupandthevacuum

SyringeonApri121．Theaverageconcentration（Cl￣）Of the water collectedintheinitiall．5hours（10：30−12：00）was135JLeqlrl．Sincetheoutflowratealmost
Intheabovemodelandcalculations，tWOaSSump− reachedits maximum at12：00（Fig．1）theinitial
tionsareessential．Oneisassumingaconstantconcen− concentrationatthewatersaturationsof5−7％could
5．Discussion

tration for the surface meltwaterin one day；and
another，forthecalculationoftotalsoluteamountin
the waterswithin the snowpack，is presuming thedischargeconcentration，beforeflowincreasinginthe
morning，being the average concentration of thewaters at that time．

probably be higher than the adopted value（156FEeql￣1）．ThiswouldalsoresultinalargerPvalueand
wouldn t make the conclusion untrue．

Intheaboveanalysis，Wealsoneglectedthesoluteexchangeinthemelt−freezeprocessbetweenpercolat−

ing water andice grains．As the freezing process

Asmeltingoccursinthesurfacelayer，itswatercontentisthehighest，anditsgraincoarsenlngistheenriches theinfiltrating meltwater（Colbeck，1981）

haverevealedaveryhomogeneousandlowconcentra−

Catedto distinguish them．Feng et al．（2001）ignored

especiallytrueinalatemeltingseason．Sincethedaily
melt thicknessis generally notlarger than O．05m

COntent（Zhou et al．，2002）．Alarge flow rate corre−

trations．Followingtherecessionandstopofsurface

beck，1972）andinFig．2，aftertheflowpeak，Wedon

thus thelowest solute concentrationinthe outflowis
Stillhigherthanthesource concentration atthesur−
mostfastest（Zhouetal．，2002）amongallthelayersof
asnowpack．Thesefeatures，tOgetherwiththediurnal faceevenifthemobile−immobileeffectsareignored．
melt−freezecycles，1eadtoalowconcentrationinthe This process occurs simultaneously with both thesurfacelayer．Observations（Ishikawa et al．，1997） dispersionandthediffusion，henceitisrathercompliT
tioninthe upmost O．2m around ofa pack，Whichis

thisprocessintheirmodelingaswell．Thecoarsening
rate of snow grainsincreases withincreasing water

SpOndstoahighwatercontentvalue．Thustheconcen−（Zhou et al．，2002）anditis actually about O．03m on
Apri121，thustheassumptionofaconstantconcentra− tration from the melt−freeze effect wouldincrease
withincreaslng flow rates，Whichis simi1ar to thetionforthemeltwaterproducedinonedayistenable．
diffusioneffect．Yettheincreasingrateforflowrates
Asmentionedabove，differentflowchannelshave
ismuchmore rapid than for water saturations（Col−differentflowrates，elutiondegreesandsoluteconcen−

melting，partOfthewatersinthenon−mainchannels

maybegintoflowbacktothemainchannelsbecause
ofthe quicker flow decreaseinthe mains，andmix

tseeadecreaseintheconcentrationforabout4hours．

Itisunlikelytoconsiderthatthesetwoeffects，inthe
4hours，WereOffsetbytheflowratedecreasingeffectwiththeexistedwater，therefore，thelongerthetime Onthemixingofthesurfacemeltwaterwiththepore
Water，becausethegraincoarsenlngrateisveryslow
frommeltceasing，themorehomogeneousthedistri−bution of solute concentrationsin a snowpack．For

Apri121and24，before flow rising，the discharge

concentrationsvaried onlywithin5JLeql1for6to8
hours，thus solute distributionsin the pack should
havebeen ratherhomogeneousexcept someisolated

watersfarfromtheflowregion．However，theheter・

ogeneitywouldnotchangeourconclusionbecausethewater，from the main channels and having alower
concentration，COnStitutes alarger portion of thedischarge，SO taking the discharge concentration as
the average value for the waters held in the packwould just produce a smal］er total solute amount（Zhou et al．，2002）andtheicecrystalsshouldbevery

Cleanafterexperienclngthelong−timemetamorphism（Colbeck，1981）．
There are some differences between P values

Calculated by Cland by SO42、respectively．These

differencesmayresultfromsolutedistributiondiffer−encesinthe snowpack，Or from the preferentialelu−

tion of which the mechanism has still not been wellunderstood．

Thelargestoutflowratesinthetwodays（Apri1

21，24）wereabove2．00mmh▼1，belongingtothehighlevels．Especially，thelargest rate on24th was2．59

j9

Zhou（ヲfαJ．

mmh￣1beyond which only two days 1argest rates（3．20，3．50 mmh▼1）werein the whole melt season（Suzuki，1991）．Therefore，OurPvaluesmaybeapplied
tothesnowpacksinlatemeltseasons，andmaynot，tO

thepacksinearlyperiodsbecausetheflowchannels，
especiallythemainones，Shouldhavebeendeveloped
gradually and at theinitialstage the snow density，
grain size and stratigraphy all are quite different（Zhou etal．，2002）．Mostprobably，earlyPvaluesare

largerthanlate P values，Which may partly explain
themechanismofpreferentialfractionation．

Res．，34（3）373384．
Harrington，R．F．，Bales，R．C．andWagnon，P．（1996）：Variabil−
ity of meltwater and solute fluxes from homogeneous
meltingsnowatthelaboratoryscale．HydrologlCalProces−
SeS，10，945953．
Harrington，R．and Bales，R．C．（1998a）二Interannual，SeaSOnal，and spatialpatterns of meltwater and solute fluxesin a
SeaSOnalsnowpack．WaterResour．Res．，34（4）823831，
Harrington，R．and Bales，R．C．（1998b）：Modelingionicsolutetransportinmeltingsnow．WaterResour．Res．，34（7）1727
1736．

Ishikawa，N．，Narita，H．．Ishii，Y．and Kodama，Y．（1997）：
Acidity variations along hydrologlCalprocesses of snow
deposit，SnOWmelt and runoff．Journalof Agricultural
Meteorology，52，SpecialIssue，521−524．
6．Conc山sion
Kattlemann，R．C．（1985）：Macroporesin snowpacks of the
Sierra Nevada．Ann．Glaciol．，6，272273．
Ontheassumptionsthatsnowsurfacemeltwater
Kutilek，M．andNielsen，D．（1994）：SoilHydrology．Reiskirchen，Germany：CatenaVerlag，370pp．
hasauniformsoluteconcentrationinonedayandthat
Leivestad，H．andMuniz，I．P．（1976）：FishkillatlowpHina
the solute concentration，inthe outflow before theNorwegianriver，Nature，259，391392．
dischargeincreaseinthemorning，equalstheaverage
Marsh，P．and Woo，M．−K（1984）：Wetting front advance and
COnCentration ofthe waterswithin the snowpack at
freezingofmeltwaterwithinasnowcoverl．Observations
the same time，the eluted solute amount，from theintheCanadianArctic．WaterResour．Res，，20，1853−1864．
Ohno，H．andNakawo，M．（1998）：Heatbudgetofasnowpack．
PaCkinonedayinthelatemeltseason，aCCOuntSfor
In二Nakawo，M．and Hayakawa，N．SnowandIceScience
lessthan23％ofthetotalamountinthewatersheldin Hydrology．Nagoya：IHAS，Nagoya University andin the pack before dischargeincreaslnginthe day．
UNESCO，6988．
Basedonthepreferentialflowmodel，thisratiocanbe
Smedt，F．D．andWierenga，P．J．（1984）：Solutetransferthroughinterpretedintospatialratiosofthepreferentialflow．
COlumnsofglassbeads．WaterResour．Resリ20（2）225−232．
Suzuki，K（1991）：Diurnalvariationofthechemicalcharacteris−
Itisestimatedthatthespatialratioofthepreferential
ticsofmeltwater．Seppyo，53（1）：2131（InJapanesewith
flow channels to the whole pore volume of the
Englishsummary）．
SnOWpaCkisbelow32％，Whichincludes13％for the
Suzuki，K．（1993）：Translatory flow of snow meltwaterin a
mainchannelsand19％forthenon−mainchannels．
SnOWpaCk．GeographicalReviewofJapan，66A−7：416424（InJapanesewithEnglishsummary）．
Suzuki，K．，Ishii，Y．，Kodama，YりKobayashi，D．andJones，
Acknowledgments
G．（1994）：Chemicaldynamicsinaborealforestsnowpack
duringthesnowmeltseason．In：Jones，H．G．andDavies，T，This work was supported by the Ministry of
D．Snow Cover anditsInteractions with Climate and
Education，Science，SportsandCultureofJapan，theEcosystems，PublicationoftheInternationalAssociationof
NationalNaturalScience Foundation of China（No．
HydrologicalSciences，223，313322．
Young，D．F．and Ball，W．P．（1995）：Effects of column condi−
40371027）andtheScientificResearchFoundationfortions on the first−Order rate modeling of nonequilibrium
theReturnedOverseasChineseScholars，StateEduca−
SOlutebreakthrough、Water Resour．Res．，31，21812192．
tionMinistryofChina．
Zhou，S．，Nakawo，M．，Hashimoto，S．，Sakai，A．，Na
Ishikawa，N．（2001a）二Isotopic fractionation and profile
References
evolutionofameltingsnowcover．ScienceinChina（SeriesE），44（Supp．），35L40．
Zhou，S．，Nakawo，M．，Hashimoto，S．and Narita，H．（2001b）：
Colbeck，S．C．（1972）：A theory ofwaterpercolationinsnow．
Mathematicalmodeling of water percolationin snow．
JournalofGlaciology，11（63）369−385．
JournalofHydraulicEngineering，1，610（InChinesewith
Colbeck，S．C．（1981）：Asimulationoftheenrichmentofatmo−
English abstract）．
Spheric pollutantsin snow cover runoff．Water Resour．
Zhou，S．，Nakawo，M．，Hashimoto，S．，Sakai，A．，Na
Res．，17（5）1383−1388．
Ishikawa，N．（2002）：Densificationandgraincoarseningof
Feng，Ⅹ．，Kirchner，］．W．．Renshaw，C．EリOsterhuber，R．S．，
melting snow．Journalof Glaciology and Geocryology，Klaue，B．andTaylor，S．（2001）：Astudyofsolutetransport
24（3），275−281（InChinesewithEnglishabstract）．
mechanismsusmgrareearthelementtracersandartificial
Zhou，S．，Nakawo，M．，Hashimoto，SリSakai，A．，Narita，H．
rainstormsonsnow、WaterResourL Res、，37（5）14251435．
Ishikawa，N．（2003）：FieldMeasurementsoftheIrreducible
Goto−Azuma，K．（1998）：Changesinsnowpackandmeltwater
Water Saturationin Snow．In：Hayakawa，N．，et al．Pro−
Chemistry duringsnowmelt．In：Nakawo，M．and Hayak−
CeedingsoftheinternationalsymposiumondisastermitigaLawa，N．Snow andIce Sciencein Hydrology．Nagoya：tion and basin−Wide water・management．Niigata，Japan，
IHAS，NagoyaUniversityandUNESCO，119133．

Griffioen，］．W．，Barry，D．A．and Parlange，］．−Y．（1998）：Inter− 514−520．
Pretationoftwo−regionmodelparameters．WaterResour．