WATER RESOURCES
RESEARCH,
VOL. 31, NO. 3, PAGES 601-618, MARCH
1995
A model for deuterium and oxygen 18 isotope changes
during evergreen interception of snowfall
H. C. Claassenand J. S. Downey
Water ResourcesDivision, U.S. GeologicalSurvey,Denver, Colorado
Abstract. A one-dimensional,physicallybasednumericalmodel was constructedto
describethe isotopicenrichmentobservedin throughfallof snowinterceptedon
evergreens.The processof enrichmentis similar to that which resultsin formation of
depthhoar in snowpack.On-sitedata were obtainedat a high-altitude(3500 m) watershed
in the Colorado Rocky Mountains.The model includesthe ambient atmosphericvariables
of temperature,relativehumidity,and water vapor isotopiccompositionand the
interceptedsnowvariablesof temperatureprofile, permeabilityfor viscousflux, and
isotopiccomposition.Model simulationsyield resultssimilar to thoseobservedon site and
suggestthat the processis dominatedby diffusiveflux despitethe very high permeability
of freshlyfallen snow.Median enrichmentswere observedto be 2.1%o in oxygen18 and
13%o in deuterium.
snow,other assumptions
regardingthe isotopiccompositionof
the vapor do not changethe model formulation.
Isotopic enrichment of evaporating water has been deOne aspectof interceptionof snowfallby evergreensthat
scribedby Craiget al. [1963],Craigand Gordon[1965],Merlivat affectsthe final isotopiccompositionis the large increasein
and Coantic[1975], and Stewart[1975]. These studiesindicate surfacearea of snowexposedto evaporationoverthat whichis
the importanceof turbulenttransferfrom the water surface, formed when snowfalls on the groundsurface.This resultsin
water vapor pressureand isotopiccompositionof the atmo- higher energyabsorption,and henceevaporation,for a given
sphere,and the possibleeffect of liquid phase diffusionin water equivalentof precipitation.In a forestedwatershed,
denseevergreengrowth may causeover one-half the precipideterminingthe final compositionof the liquid.
The natureof snowasa porousmedium,in contrastto liquid tation to be lost to evaporation[Hooverand Leaf, 1967; Trowater, imposessignificantconstraintson applicationof water endleand King, 1985;Claassenet al., 1986]. Isotopicmodificaisotopeenrichmentmodelsto this medium. Some of the vari- tion of the remainingsnowcould have a significanteffect on
ablesthat affectevaporatingliquid, in whichconstanttemper- the isotopiccompositionof water availablefor groundwater
ature is assumedto prevail,haveminimal effecton the isotopic recharge,resultingin modified interpretationof groundwater
compositionof remainingsnow,primarilybecauseof the tem- isotopedata in water balanceand paleoclimatestudies.
Measurements made at Snowshoe Mountain, a Rocky
peraturegradientsin the snow.Thesegradientsresultin transMountain watershed near Creede, Colorado, have shown that
fer of vapor in snowpore spacefrom regionsof highervapor
significant
enrichment
in waterisotopes
HDO andH2•80 ocpressure(highertemperature)to regionsof lower vapor prescurs while snowfallis interceptedby evergreens.This paper
sure (lower temperature)where condensationoccurs[Seligdescribesthese measurementsand presentsa model of the
man, 1936;Baderet al., 1939;Schytt,1958;Epsteinet al., 1965;
Introduction
Gow, 1965; Trabant and Benson, 1972; Whillans and Grootes,
1985;Sommerfeldet al., 1991;Friedmanet al., 1991]. In addition to intrasnowvapor transfer,lossof snowby sublimation
occursat the surfaceof a body (the poroussnow)that cannot
be assumedmixed(or of constantcomposition)throughoutthe
process.In evaporationof water the potentialfor maintaining
the fluid surfacenearer its originalcompositionexistsby virtue
of viscousflow and diffusionin the liquid. In evaporationof
snow,however,the initial vapor associated
with the snowmay
be the equilibrium vapor, but over a short time the vapor
releasedby the snowshouldapproachthe compositionof the
solid.This must be true becauseisotopegradientscannot be
formed in the solid phaseduring periodsof time the snowis
held on the tree branches,generally hours to a few days.
Although the model presentedhere assumesthat vapor releasedfrom the snowmaintainsthe averagecompositionof the
This paper is not subjectto U.S. copyright.Publishedin 1995 by the
American GeophysicalUnion.
Paper number 94WR01995.
601
process.
Description of Study Area
In a long-term study of water, water isotope, and solute
transport,measurementsof isotopiccompositionof incident
precipitationand evergreenthroughfallhave been made for
severalyearsat Snowshoe
Mountain,locatedabout5 km southof
Creede,Colorado.The throughfallmeasurements
were made at
a site near the summit,at an elevationof nearly 3500 m. The
climateof the site can be characterizedas being cool, havinga
mean annual temperaturenear freezing,and moderatelywet,
havingan annualprecipitation
averageof about53 cm,morethan
one half of whichfallsas snow[Batesand Henry,1928].
On-Site
Methods
and Results
Monthly or quarterlyintegratedsamplesof incidentprecipitation and throughfallwere obtainedfrom 1981 to 1989 using
a 40-cm-diametercylinderwith a lessthan 2-cm restrictionto
minimize evaporationor isotopicexchangewith changingat-
602
CLAASSEN
AND
DOWNEY:
ISOTOPE
CHANGES
DURING
INTERCEPTION
OF SNOW
Clearing
Clearing
Clearing
EXPLANATION
METEOROLOGICAL
DATA
SITE
INCIDENT
PRECIPITATION
COLLECTOR
0
I
•
•
•
•
50 METERS
I
THROUGHFALL
COLLECTOR
Figure 1. Plan view of throughfallcollectionsite, SnowshoeMountain, Colorado.
mosphericcompositions.
Comparisonof precipitationamounts
determined from sample volumes collected in the incident,
open area collectorwith a U.S. standardrain gage showsthe
larger-diametercollectorto be slightlymore e•cient than the
rain gage,and evaporationlosses,therefore,probablyare minimal. The possibilityof isotopicexchangebetweensnowin the
collectorsand the atmosphericwater vapor is more di•cult to
evaluate,but a simplestudydesignedto evaluatethe effect of
exchangeon water storedin this collectorhas showninsignificant impact. A plan view of the site is shownin Figure 1.
A summaryof the data obtainedis availableon diskette.• It
is evidentfrom the data that about one-halfthe input precipitationis lostby interception(Figure2). This occursin summer
(July-September)and winter (October-June). Only winter
samples,however,displayenrichmentin the throughfallsamples.The averagedifferencebetweenthe isotopiccomposition
of incident precipitation and throughfall for the period of
recordisA•D -- 13%oandA•80 = 2.1%o.Thecorresponding
averagedifferencefor the summerperiod is A•D = -0.19%o
andA•80 - 0.03%0,withintheestimated
analytical
accuracy
(20-)of •D = 2%0and•80 = 0.2%0.Saxena
[1986,Table1]
reports similar resultsfor pine forest throughfallin Sweden:
precipitation
lossof about56% anda meanA•80 - 0.25,for
•An electronic
supplement
of thismaterialmaybe obtainedon a
disketteor anonymousFTP from KOSMOS'AGU'ORG' (LOGIN to
AGU's FTP account using ANONYMOUS as the user name and
GUEST as the password.Go to the right directory by typing CD
APEND. Type LS to seewhat files are available.Type GET and the
name of the file to get it. Finally, type EXIT to leave the system.)
(Paper 94WR01995,A model for deuteriumand oxygen18 isotope
changesduringevergreeninterceptionof snowfall,by H. C. Claassen
andJ. S. Downey.)Diskettemaybe orderedfrom AmericanGeophysical Union, 2000 Florida Avenue, N.W., Washington, DC 20009;
$15.00.Paymentmustaccompany
order.
24 samples.It may be concludedthat enrichmentof samples
occurswheneverthe period of interceptionis relativelylong,
suchasoccursduringsnowfall.Althoughno other observations
of snow interception enrichment have been reported in the
literature, Judy et al. [1970] and Moser and Stichler[1974]
describeobservationsof enrichment in snowpack.Quantitatively, their observationsshowsimilar enrichmentto ours.The
observationsof Moser and Stichlerwere followed by laboratory experimentsthat suggested
the enrichmentmaybe related
CLAASSEN
AND
DOWNEY:
ISOTOPE
CHANGES
to vapor transportin snowpackresultingfrom temperature
profilesthat exist in a metamorphosingsnowpack.In more
recentwork,Friedmanet al. [1991]havestudiedenrichmentof
snowpack
by depthhoar formation(Fairbanks,Alaska)and in
experimentaldepth hoar formation [Sommerfeld
et al., 1991].
Other studiesof snowpackisotopyhave been done in polar
regions[e.g., Whillansand Grootes,1985]. It is reasonableto
anticipatethat this same processmight be operatingduring
interception.
The data alsoincludevaluesfor the enrichmentratio (AiSD/
DURING
INTERCEPTION
OF SNOW
603
10
I
I
I
9
-
LLI 8
-
•
7
-
6
-
0
$
-
LU
4
-
•)
2
-
A•5•80)for eachwintersample.Figure3 summarizes
these
data in the form of a bar graph showingthe frequencydistribution of enrichmentratio, the most probablevalues lying
between
0
I
0
I
2
3
4
5
6
7
8
9
10
11
12
13
14
4 and 8.
The probableimportanceof temperaturegradientsin interFigure 3. Frequencydistributionof enrichment ratio values
ceptedsnowprompteddesignof a deviceto measurethe time- from throughfallat SnowshoeMountain, Colorado.
variable temperatureprofilesunder typical interceptionconditions(Figure 4). This deviceconsistsof a stackof 0.4-mmdiameterthermistorsencasedin 1-mm x 13-mmglasshousing. shouldbe noted. A further significantobservationis that the
These were mounted on a 3-mm-diameter
x 10-cm wood stalk
interception period generally is terminated when the snow
that could be clamped to an evergreen branch. Spruce temperaturerisesto freezing,regardless
of the air temperature
branchesand needlesform a more or lessplanararraythat acts (Figure6, beginningat 1230localtime (LT)). A smallamount
as an efficientplatformfor snowinterception.Six thermistors of meltingappearsto lubricatethe snow/leafcontactand allow
were placedat 2-cm intervals,and the outputwasconnectedto the snowto slide of[. Many on-site observationssuggestthat
a micrologger.Data collectionwaslimited to periodsof actual clearskyconditions,rather thanwind or air temperature,proobservationsothe depthof snowon the branchcouldbe noted. vide energyto warm the snow and appear to be primary in
Typicalexamplesof resultsare shownin Figures5 and 6. These determininginterceptionresidencetime for appropriatelyorifiguresplot snapshots
of interceptedsnowtemperatureprofiles entedbranchlets.The wide rangein day-nightair temperatures
taken at the times shownon the lower abscissa.Depths are generatesa similarwide rangein snowtemperatures(as shown
shownon the upper abscissa,
and the data pointsindicatethe in Figures5 and6, for example),but threegeneralprofiletypes
temperature profiles. The air temperature measurementis may be recognized:symmetrical(e.g., December 24, 1988,
shownby the horizontalline. The steeptemperaturegradients 0700LT), linear (e.g.,December24, 1988,0300LT), and step
that form after sunrise(Figure 6) and nightfall (Figure 5) (e.g., December30, 1988, 1130 LT). These are illustratedin
Figure 7.
Conceptual Model
2O
Developmentof a modelto simulatethe processes
resulting
in isotopeenrichmentin interceptedsnowrequiresknowledge
of the pore structureof freshlyfallen snowand changesthat
occuras the snowmetamorphoses
duringthe interceptionperiod, which may range from hours to several days. Rogers
[1979], Colbeck[1980], and Gray and Male [1981], provide
excellentsummarieson the physicsof snowformation,deposition,and metamorphosis.
Unfortunately,detailsof the structure of snowthat are pertinentto modelinggastransportin
freshly fallen snow remain obscure[Shirnizu,1970; de Quervain, 1973;Delloff, 1983;Davis et al., 1987;Dozier et al., 1987;
Sommerfeld
and Rocchio,1989]. Thereforethe followingapproachwasusedto model processes
duringsnowinterception
on evergreens.The snowwas assumedto consistof an infinite
platerestingon an evergreenbranch.The plate comprisesa set
of layers(cells)eachof whichhas an associated
temperature
andwatervaporpressure.Becausethisis an isotopemodel,the
water vapor pressureis dividedinto partial pressuresfor each
15
10
waterisotope(H2160,HDO, H2180).The objective
wasto
0
10
20
30
40
50
PERCENT
60
70
80
90
100
LOSS
Figure 2. Distributionof precipitationlossresultingfrom interceptionof snowat SnowshoeMountain, Colorado.
model vapor fluxesbetweencells and to or from the atmosphere,allowfor condensation
and evaporation,and compute
a finalcomposition
of the remainingsnowaftervaryingperiods
of exposure.Both viscousand diffusivefluxeswere considered,
but it was determined
that the viscous flux was less than 0.5%
of the total flux for conditionsexpected at the Snowshoe
Mountain site and was thereforeminimal. The appendixde-
604
CLAASSEN
AND
DOWNEY:
ISOTOPE
CHANGES
DURING
INTERCEPTION
OF SNOW
Inter.'.....!.Pted
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Figure 4. Diagram of interceptedsnowtemperaturemeasurement.
scribes the methods
used to estimate
the relative
amounts
of
diffusive and viscous flux.
Figure 8 showsa stack .of unit cells that sectionthe intercepted snowpack.A unit cell representsthe void volume describedby a unit area perpendicularto the vapor flux vector
multiplied by the cell thickness,which may be varied to suit
individual circumstances.The stack of cells representsvoid
spaceonly.We assumethat voidsaccountfor more than 85%
of the snowpack(fresh snow),that the snowdoesnot impede
gasflux, and that viscousflow to the atmosphere(and between
cells)is minimal.The model alsoassumesthat the supporting
branchletsdo not impedediffusionof vaporfrom the snowpack
to the atmosphere.
The model usesa one-dimensional,steadystateformulation
to estimatethe nonsteadyviscousand diffusiveflux between
cell pairs and betweencells delineatingthe snowboundaries
and the atmosphere.Becausecondensationmay occurin some
cells,it cannotbe assumedthat a steadystatevapor composition is reached during the period of time defined by snow
interception.Therefore a time step mustbe chosenfor which
an instantaneous
flux is representative.The fluxesbetweenall
cells are used to determine changesin vapor compositionin
each cell, taking into accountcondensationor vaporization
necessaryto maintain the equilibriumvapor pressuredetermined by cell temperature. Condensationfollows rules for
equilibriumisotopefractionation.Newly vaporized snowhas
the compositionof the original snowfall.This is an important
assumption:that all evaporatedsnow is original, not recondensed,vapor.This is a reasonableassumptionfor most situationsbecausethe predominantevaporationoccursfrom the
upper (and lower) snowlayers,where the vapor pressuregradientsare largest.Clearly, the assumptionlosesvalidity as the
fraction of snow lost increasesand the recondensedvapor
becomesthe dominantfractionof remainingsolid.It is important to recognizethat this laminar flow model assumesthat the
onlyviscousflux is producedby pressuregradientsarisingfrom
the diffusivefluxespresent in the system.The possibilityof
viscousfluxesresultingfrom eddiesdevelopedby atmospheric
turbulence cannot be dismissed, but on-site observations in
dense evergreen forest suggestthat mean wind speedsapproachzero for much of the region below the canopycrown.
This would not be true for lone trees,forestsof low vegetation
density, or trees at the edge of large clearings.Barometric
pressurefluctuationscan generatefluxesin snowpackon the
ground [Colbeck, 1989], but intercepted snow is subject to
pressurefluctuationson all sidesand, therefore, little or no
pressuregradientsin the snowwill be generated.As is commonlydone in this type of modeling,resultsfor eachtime step
are summedto approximatethe dynamicflux.
Foreachtimestepandeachisotope(H2160,HDO, H2180),
the modelcomputesfluxesacrosseachboundaryand algebraically sumsthe fluxes to arrive at a net vapor composition
changein a givencell. If the net changeis lessthan zero, snow
is vaporizedto bring the total vapor pressurein that cell into
equilibriumwith the chosenconditions(generally,saturation
equilibrium). If the vapor pressureexceedsequilibrium, an
appropriateamount of vapor is condensedaccordingto equilibrium condensationfractionationfactors.This processis continued for each time step, with the isotopiccompositionof
vapor condensedaccumulatedin a separatefile. The isotopic
compositionof vapor lost to the atmosphere,if appropriate,is
also accumulatedin an additionalcomputerfile.
Values for certainvariablesrequiredto effectthe computations are obtained
as follows.
Withinthesnow,
PH20-- •i Pi wherePH20isthetotalvapor
pressureof water (all isotopes)and Pi is the partial vapor
pressureof eachisotopei (Dorsey[1940],ascitedbyEisenberg
and Kauzmann[1969]):
log10
PH20(•)
=
T
-2445.5646
+ 8.2312 log•0 T
CLAASSEN AND DOWNEY:
ISOTOPE CHANGES
DURING
INTERCEPTION
OF SNOW
605
CENTIMETERS ABOVE BRANCH, 10 CENTIMETERS OF SNOW
0
4
80
4
80
4
80
4
80
4
80
4
80
4
80
4
80
4
80
4
80
4
80
4
8
-10
-15
-
O0
_
_
•
ß
ß
-
000
oøo:
-
-20
o
oo 0 ß
-
-
-25 _temperature
measured
<
_
Air
-
_
ß
-
at north
side
of
tree
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--
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, I , I
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• I , I
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1700
1900
2100
2300
0100
0300
0500
0700
0900
1100
1300
1700
DECEMBER
23,
1988
I
DECEMBER
24,
1988
Figure 5. Southfacingbranchtemperatureprofiles,showingchangesin temperatureprofile occurring
duringa diurnal cycle.
- 1677.006x 10-ST+ 120,514x 10-•øT2
ß 1.00216096 + 1.5576 x 10-78D + 2.0052 x 10-68•80'
1.01325
x106
- 6.757169 760
The equilibriumvaporpressureat T (kelvins)is referencedto
[
CHD
O= CH2160[1.5576
x 10-4] 1+ 1000
ice.
In the atmosphere,
PH20
= PH20(l•)
RH
whereRH is the relativehumidity.Computationally,
the pres-
CH218
O=CH2•60[2.0052
X10-3]1+ 1000]
8180
]
Air diffusivityDAiR/i of eachisotopeis
sures are converted to molecular concentrations for each water
DH216
O = 0.00127TAv-
0.12731
vapor isotopeCi, the valuesbeing a functionof either the
input isotopecompositionof the atmosphereor the vapor
DHDO = 0.00127TAv-
0.13449
DH218
O = 0.00127TAv-
0.13319
inside the snow:
Ci = [PH2oNAv/RT][1+ RSMOW
HDOq-RsMowH2180
q-RSMOWHDO(SD/1000
) q-RSMOWH2•80(8180/1000)]_
1 where
TAV
represents
theabsolute
temperature
average
betweeneachadjacentpair of cells.
whereN^v isAvogadro's
number(6.02x 1023),
R is thegas
constant,and the varioussubscripted
R termsare definedin
the notationsection.Specifically[Fritz and Fontes,1980, pp.
11-13],
CH216
O•
T [6.023
õ15ixiJ
PH20
X1023]
The temperaturedependenceof the diffusivitywas determinedby partial differentiationwith respectto T of the simplifiedrelationfor D derivedfromkinetictheory(asgiven,for
example,by Merlivat[1978,equation(15)]). Temperaturedependenceof diffusivityfor water/airalsowascalculatedusing
equation16.4-13 of Bird et al. [1960,p. 505]. The calculated
valueswere in substantialagreement(0.00122) with values
606
CLAASSEN
AND
DOWNEY:
ISOTOPE
CHANGES
DURING
INTERCEPTION
OF SNOW
CENTIMETERS ABOVE BRANCH, 10 CM OF SNOW
4
o
80
4
80
4
80
4
80
4
80
4
80
4
80
4
80
4
80
4
80
4
80
4
8
+5
ß
--
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ß ßß
ßßß
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ß
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branch
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beginning
at 1133
Air
-lO
temperature
measured
atnorth
--
side
oftree
-15
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--
ßß
ßß
ßßß
ee
ß
Snowfalls
ßß
offbranch
ß ©©
ß ©ß
insolation
ß
at 1310
Snow
Maximum
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ß
begins
--
falling
offtree
at1225
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--
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ß
-20
-25
-3O
-35
0000
0400
0800
1000
1100
1130
1145
1200
1215
1230
1245
1300
DECEM BER 30, 1988
Figure 6. Eastfacingbranchtemperatureprofiles,showingchanges
in temperatureprofileoccurringduring
a semidiurnalcycle.
givenabove.Valuesfor D H20,D HDo/DH2160,
andD H2180
/ wheremr is the massof recondensedwater after interception
time t and # is the rate of condensation.The fraction of
DH216
O arefromMerlivat[1978].
Condensationfractionationfactorsare computedfrom the
followingrelations[Merlivatand Nief, 1967;O'Neil, 1968;Majoube, 1971]:
In aD = [-2.15412T + 706.4594] x 10-3
In a18o=[1.137 x 106T-2- 415.6T -• - 2.0667]
X 10 -3 + 0.003
original snowremainingat time t is
fo=l--fr
Then the isotopiccomposition
of the remainingsnow(primed
species)at time t is
/SD•No= fr(/SDsNoR)+ fo(/SDsNo)
1•180•NO
= fr( • 1SOsNoR)
-Jrfo(I•18OsNo)
Once the model determinesthe steadystatecompositionof
where the subscripts
SNO and SNOR representoriginaland
recondensed
vaporfor a specifiedsetof conditions,calculation
recondensedsnow,respectively.As previouslyindicated,the
of the resultingisotopiccompositionof throughfallis accomenrichmentratiois a usefulparameterin describing
the results:
plishedas follows.The amount of snowremainingat end of
interceptionis givenby
•D•N o -- /SDsN
o
A/SDsNo
mt = mo - mt = dp - tl
er= eD/el8
= {•180•NO
_ {•18OsNoAl•18OsN
O
where rot, rno, and m• are the massof snowremainingafter where eD and e18 are the isotopicenrichmentsin deuterium
interceptiontime t, originalmassof snow,and massof snow and oxygen18, respectively.
lost, respectively;d is depth of original snow;p is densityof
originalsnowand l is the sublimationlossrate per unit area.
Input Values
The fractionof snowthat isrecondensed
at timet is givenby
The variablechoicefor model simulationspresentedhere
fr = mr/mt = tg/mt
wasintendedto explorethe effectof someof the environmen-
CLAASSEN
AND
DOWNEY:
ISOTOPE
CHANGES
DURING
tal conditionsexpectedat the sitewhere throughfallmeasurements were made. The resultswere then compared to the
range of enrichmentsand evaporationlossessuggestedby the
interceptedsnowsamples.Critical variableschosenwere (1)
snow-temperature
profiles,(2) atmosphericwater vapor pressure(temperatureand relativehumidity),(3) isotopiccompositionof atmosphericwater vapor, (4) interceptiontime, and
(5) size of snowfall.Variablesthat are related to model performanceare (1) sizeof time stepand (2) cell size.The latter
two affectthe accuracyof the result in the sameway that any
numericalmodel simulatesa continuousprocessusingdiscrete
computationalsteps.Experiencehas shownthat a step size of
INTERCEPTION
OF SNOW
607
ATMOSPHERE
10-3 tO10-2 s andcellsizesof 0.2to 1.0cmareadequate
for
modelingof snowpacksusingobservedenvironmentalconditions. See the sectionon cell size and amount of evaporation
for further considerations
regardingchoice,of cell size.
The modelacceptsa temperatureprofileasone of the input
variables, which remains constant for the time modeled. Time-
variant temperature profiles cannot be modeled with the
present version of the computer code. For comparisonof
model resultswith environmentaldata, the choice of input
variables
was made
on the basis of limited
observations
of
snow-temperatureprofilesand atmosphericwater vapor isotopic compositions.The choiceof valuesfor the variousinput
parametersis discussedbelow.
ATMOSPHERE
Figure 8. Unit cell used in modelingisotopechangesoccurring in interceptedsnow.
Temperature Profiles of Intercepted Snow
and AtmosphericVariables
Figures 5 and 6 show measuredtemperature profiles for
what is believedto be typicalmidwinterconditions.Examination of these temperature profiles indicatesthe following.
Nighttime conditionssuggestthat in-snowlinear gradientsof
about 0.4øC/cmor step gradientsof about løC/cm are likely.
Air temperatureslag or lead snowtemperaturesby asmuchas
about 5øC.
Daytime conditionsaffect snow temperature profiles dra-
I
-1(,.)
z
maticallyunder clear skyconditions,lessdramaticallyin overcast.Clear sky,maximuminsolationconditionsappearto producelocal gradientsashigh as2øC/cmfor at leastshortperiods
of time. Air temperaturelag or lead of 9øCappearspossible.
For purposesof illustration,13 temperatureprofile conditions
were chosenand are shownin Figure 9. Nighttime humidity
oftenpeaksat about85% and dropsto about35% duringthe day
whendear skyconditions
prevail(Figure10), about65% under
overcast,and may remainbetween80 and 90% duringsnowfall
(Figure10) (H. C. Claassen,
U.S. GeologicalSurvey,unpublished
data,1992).Basedon the foregoing,the relativehumidityvalues
indicatedwere chosenfor the examplecalculations.
AtmosphericWater Vapor Isotopic Composition
Numerousatmosphericwater vapor sampleswere obtained
by the method of Claassenand Halm [1992] to establishthe
range of values that might contact intercepted snow. This
method uses cryogenic separation of water vapor from a
pumped air sampleand was demonstratedto be nonfraction-
I
I
o
ating.
Fromthese
dataa typical
midwinter
value(&•aOvapo
r -----35%0;•iDvapo
r - -259%0)waschosen
for mostof thecalculations.Variations from this value were determinedusinga
regressiondevelopedfrom the vapor compositiondata and are
noted where appropriate.
Incident Snowfall Isotopic Composition
TEMPERATURE
Fromtheon-site
dataa typical
midwinter
valueof 818OsNo
=
-19%o, •iDsNo -- --142%o was determinedfor use in simulations.
EXPLANATION
TEMPERATURE
PROFILE TYPES
Symmetrical
.....
Linear
Step
Figure 7. Generalizedtemperatureprofile types.
Permeability
Snowpermeabilitymeasurementswere reported by Shimizu
[1970] and Sommerfeldand Rocchio[1989]. Although the reportedvaluesrangewidely,a reasonablemean for new snowis
5 x 10-5 cm2.As is demonstrated
in the appendix,
fluxesare
608
CLAASSEN AND DOWNEY:
lO
ISOTOPE CHANGES DURING
INTERCEPTION
OF SNOW
(B)
(A)
5-
I
-5
-10
10
0
-3o
-25
(F)
(E)
-20
'
z
Snow
thickness
0.4 cm
/
_015
-5
-15
10
u.I
-5
-15
-5
-15
i
(H)
(G)
-10
-5
-15
lO
(J)
(L)
(K)
-30
I
-3•0
-29
10
-24
-16
-1
i
(M)
5 -
-ø10
SNOW
TEMPERATURE,
0
(øC)
Figure9. Temperature
profiles
usedin modelsimulations
of isotope
changes
occurring
in intercepted
snow.
CLAASSEN
i
AND
i
DOWNEY:
ISOTOPE
i
lOO
_
//\
/
!
I
I
I
_
I
I
!
!
/
/
-
I
I
/
/
/
!
\
CHANGES
DURING
INTERCEPTION
OF SNOW
609
layer dimension.Merlivat and Coantic [1975] appliedvarious
diffusionlayer theoriesto the evaporationof water by using
isotopicanalysisof water vapor in wind tunnel experiments.
They presentdata and analysisthat relate wind speedto diffusionlayer thickness.Their data suggestthat a diffusionlayer
thicknessof about 1 cm is reachedas wind speedapproaches
zero (windcurve,Figure 11). For the meanannualwind speed
in forestclearings
at Snowshoe
Mountain,0.45m s-•, a diffusion layer thicknessof 0.85 cm may be estimated.Of course,
periodicgusts,evenin forest,maybe higherthan the average.
Although somewhatarbitrary,an upper wind speedof 2.5 m
s-• (equivalent
to a diffusion
layerthickness
of 0.2 cm) was
chosen for the simulations.
An
illustration
of the effect of
diffusionlayer thicknesson evaporationlossmay be seenby
comparingsimulations3 and 4, or 11 and 12 (Table 1), and by
studyingFigure 11. Simulations3 and 4, or 11 and 12, differ
onlyin choiceof cellsize(diffusionlayerthickness)(0.2 and 1.0
cm, respectively)
and showthe largerevaporationlossassociated with the smallercell size (higherwind speed).Figure 11
suggests
that thesecell sizescorrespondto mean wind speeds
of about2.5and0.45m s-•, respectively,
andthedatain Table
1 (or Figure 11) showthe higherevaporationamountsassociated with the higherwind speeds.The simulatedsnowsublimation amountsshownin Table 1 suggestthat the model can
reproducethe observedamounts.
Deuterium and Oxygen Isotope Changes
-10
Range of enrichment. Modeling results suggestthat the
amount of enrichmentthat occursduring interceptionis controlled primarilyby the sizeof snowfalland interceptiontime,
I
I
I
-15
0
0600
1200
1800
2400
althoughall the previouslystatedvariableshave someeffect.It
TIME OF DAY
shouldbe evidentthat for a givenset of environmentalconditions,viscousand diffusiveflux to the atmosphereis nearlythe
EXPLANATION
samefor a large snowpackas for a smallerone. A smallsnowOCT. 24, 1990 (Dry)
NOV. 1, 1990 (Precipitation
pack
will lose a greater fraction of mass while condensing
occurring)
P
WATER VAPOR PRESSURE
amountsof vapor similar to a larger snowpackand therefore
T
AIR TEMPERATURE
will reflecta larger enrichment.Simulations5, 6, and 7 (Table
RH
RELATIVE HUMIDITY
1) allow comparisonof snow surface losses(simulation 5)
Figure 10. Diurnal variation of water vapor pressure,air relative to lossesthat may be affectedby internal gradientsin
(simulations6, 7). Simulation5 is a two-cell,
temperature,and relative humidityon two typicalwinter days largersnowpacks
at Snowshoe Mountain.
0.4-cmsnowfallwith no internal gradientand therefore representsevaporationlossesdriven only by the vapor pressure
gradientspresent at the snow surface.These gradients are
not stronglydependenton permeabilityfor systemswith large determined by the atmosphericvapor pressure, the snow
boundarylayer vapor pressure(s),and the choiceof cell size.
permeability,suchas freshlyfallen snow.
Simulation6 representsa 2-cm snowfallwith a minimal internal temperature gradient; simulation 7 representsa 2-cm
Results
snowfallwith a larger internalgradient.Comparisonof absolute
evaporationlossesfor all three simulationsreveals no
Model resultsshouldsimulatethe rangeobservedin samples
differences
(datanotshown),
although
ther'•lative
loss
isprowith respectto the followingvariables:(1) amountof evaporation for reasonableinterceptiontimes,(2) enrichmentin D portionally greater for the smaller snowfall of simulation5.
Increasedenrichments,however,are determinedby increased
and•sO,and(3) enrichment
ratio.
internal temperaturegradientsas shownby the larger enrichment shown in simulation 7 over that in simulation 6 and in
Cell Size and Amount of Evaporation
The rate of evaporation is determined by the snow-to- simulation 16 over that in simulation 4.
atmospherevapor pressuregradient.This gradient is formed
Warm conditions,generallyfound just prior to the end of
by differencesin temperatureand relative humidity between interception,producelargelossesandlargeenrichments
(simsnowand atmosphereand the cell size chosen.Cell size func- ulation 13).
tions to discretize the snow temperature gradient but also
Interceptiontime and cell sizemaybe independentlyvaried
determinesthe sizeof the diffusionlayer that controlsthe rate to producesimilar evaporationlosses.Simulations14 and 15
of evaporationlossfrom snowto atmosphere.Therefore the demonstrate that this does not result in similar enrichments.
choice of cell size is not arbitrary but should be related to
Interception time also determineshow much snow is lost
anticipatedenvironmentalconditionsthat determinediffusion and how muchvapor is condensedwithin the snowpack.Rel-
610
CLAASSEN
AND
DOWNEY:
ISOTOPE
CHANGES
DURING
INTERCEPTION
ative lossesand condensationbecomelarger for the smaller
snowfalls, and consequently,the amount of enrichment is
larger. For example,comparethe resultsof simulations1 and
2 with 3 and 4 in Table
1. Absolute
enrichments
OF SNOW
I
in simulation
1 or 2 are much greater becausethe initial amount of snowis
smaller than that used in simulation3. Comparisonbetween
simulations3 and 4 suggestthat much of the enrichmentre-
sultsfromtheincreased
evaporation
(13%versus
3%) induced
8 is -28.8øC
and in simulation
9 is -24øC.
Examplesthat illustratetemporal changesin enrichmentof
40
I
20<
0.5
1T.
00
DIFFUSION LAYER (CELL)
THICKNESS (cm)
cm-•; remember
thatthe top andbottomof snowaresimilar
and the mirror image of a profile producesthe sameresult),
but the gradientfrom the snowsurfaceto the atmospheremust
necessarily
be differentbecauseone snowsurfacetemperature
'
I
by the larger snow-to-airvapor pressuregradient(definedby
choiceof 0.2-cmcell size)usedin simulation3. Another comparison to illustrate the relative enrichmenteffectson small
versuslargesnowpacks
maybe madeusingsimulations8 and 9.
Here the internal temperaturegradientsare the same(0.6øC
in simulation
z
'X'Average
windvelocity
inforest
clearings at the study site
Figure 11. Relation of wind speedand evaporationto diffusionlayer (cell) thickness.
D and•80 arefoundin Figures12and13.Ambientconditions
are specifiedin the figure captions,and snow temperature
profiles simulatedare shownin Figure 9. As the amount of
snow evaporatedincreases,the fraction of enriched, recondensedvaporbecomeslarger,resultingin a nonlinearincrease
in overall snowenrichment.For example,in Figure 12, simulations at 75% relative humidity shov.that at about 2 days
interception,45% of the snowis evaporatedand the snowhas
becomeenrichedabout4.5%oin D andabout0.5%oin •80; at
about 3 daysinterception,62% of the snowis evaporatedand
the snow has become enriched
about 10.6%o in D and about
1.3%o in •80.
Range of enrichment ratios. Enrichment ratio has been
defined and is a convenientparameter to differentiate the
processes
that determinethe isotopicresultof the interception
processes.
Theseprocesses
include(1) inwarddiffusionduring
periods of high humidity or large and rapid changesin air
temperatureand (2) variationsin atmosphericwater vapor
composition.
Figures 14 and 15 illustrate short-term changesin the enrichment ratio of condensedvapor that occur while the described systemsreach steady state compositionof the condensedvapor. As expected,the first vapor to condenseis the
equilibriumvalue for the snowtemperatureprofile specified.
As diffusionand viscousflow proceed,changesin enrichment
ratio from the equilibrium value occur until the steadystate
value is reachedat about 1000s.The ambientrelativehumidity
hasa significanteffecton enrichmentratio, especiallyat higher
valueswherethe atmosphericwatervaporpressureapproaches
or exceedsthe vapor pressurein the snow.Compare the 75%
relative humidity curve usingtemperatureprofile A with the
80% curve(Figure14) or the 75% relativehumiditycurvewith
the 81% curvein Figure 15. Enrichmentratiosincreasesignificantly in both examplesfrom around 5-8 at 75% relative
humidityto 13-14 at the higherhumidity.Note alsothat at low
humidity,enrichmentratio is not stronglyaffectedby a change
in temperatureprofile. ComparetemperatureprofilesA and B
at 30% relative humidity in Figure 14 (enrichmentratios at
steadystate about 3.9 and 3.3, respectively).In contrast,at
75% relativehumidity,changingthe temperatureprofile from
that illustratedby A to B resultsin significantchangesin steady
stateenrichmentratiosof condensed
vapor(about7.8 to about
3.7, respectively).
Not illustratedis the resultthat occurswhen
the atmosphericvapor pressuresignificantlyexceedsthe snow
vapor pressure.This will be discussed
subsequently.
The examplesaboverepresentthe steadystate result of an
unvaryingset of environmentalconditions.Realistically,environmental conditionswill continuouslyvary, sometimesdramatically,as illustratedin Figures5 and 6, which are selected
examplesof on-sitemeasurements.Ordinarily, vapor pressure
gradientsare toward the atmosphere,by virtue of the higher
relative humiditythat existswithin the snow.Occasionally,the
temperaturedifferencebetweensnowand atmosphereis large
enough(atmospherehigher) or the atmosphericrelativehumidity is large enough to produce a vapor pressuregradient
reversal. Because atmosphericvapor is considerablylighter
isotopicallythan vapor ordinarilywithin the interceptedsnowpack, any condensationof this vapor occurringin the snow
would result in the snow'sbecomingisotopicallylighter. The
effect of outward diffusioncombinedwith varyingperiodsof
inward diffusionis illustrated in Figure 16. In this instance,
outwarddiffusionresultsin snowhavingan enrichmentratio of
5.0. An increasein atmosphericrelative humidity from 45 to
75% producesan inward diffusingcondition.If this condition
persistsfor 5% of the interception time, snow enrichment
having an enrichmentratio of about 9 results;if 8% of the
time, an enrichmentratio of 15 will result.A secondexample
is givenin Figure 17 where the snowprofile is warmer and a
larger fraction of inward diffusingcondition is required to
result in a particular enrichmentratio.
Nominal isotopiccompositions
were chosenfor atmospheric
water vapor and snow.Deviationsfrom thesevalueswill affect
enrichmentratios. Figures 18a and 18b illustrate the effect of
varying&D•aRand &•80•aR from the nominalvaluechosen
andthe effectof variations
in &DsNoand&•8OsN
o on enrichment ratios.
Model
Limitations
and Discussion
of Results
As is frequentlythe casewhen modelingcomplexenvironmental systems,many simplifyingassumptions
have been relied on to developan algorithmfor sublimationof intercepted
snow.Some of these assumptions
have been previouslymentioned; the more important are discussedbelow, with an assessmentof their impact on overall results.
CLAASSEN
ANDDOWNEY:
ISOTOPE
CHANGES
DURING
INTERCEPTION
OFSNOW
Table
1.
611
Resultsof SelectedModel Simulations
AmbientAmbient
Recondensed
Vapor
FinalSnow
SimulationIntercep- Air Relative Composition,
Composition,
Enrichment,
Enrichment
Number
Snow
tion
TemperaHumiSnow
%0
%0
%0
Ratio,
and Depth,
Time,Cell ture, dity,Loss,
dimensionProfile*cm dayssize øC
1A 2
1 0.2 -10.5
2A 2
2 0.2 -10.5
3D 10 2 0.2 -10.5
4D 10
2 1.0 -10.5
5F 0.4 0.1 0.2 -10
6I
2
0.1 0.2 -10
7H 2
0.1 0.2 -10
8J 2
5 0.2 -30
9C 10 5 0.2 -30
10K 2
5 1.0 -30
11G 2
0.1 1.0 -10.5
12G 2
0.1 0.2 -10.5
13M 2
0.750.2 -3
14E 4.25 14 0.85 -10.5
15E 4.25 7 0.425-10.5
16B 10 4 1.0 -10
%
68
68
68
68
50
50
50
50
50
50
50
50
68
68
68
68
% ($DsNoR
(•18OsNoR
($D•N
O (•180•N
O A•DA(•18
O less
33 -92.2 -10.03-139.4
-18.522.630.47 5.55
66 -92.2 -10.03-131.5
-17.1210.451.88 5.55
13 -86.8 -9.62 -141.8
-18.970.180.03 5.88
2.7 -86.5 -9.69 -141.8
-18.970.160.03 5.96
48 .......
142.0
-19.000 0
-.9.6 -48.1 +6.48-142.0
-19.00
<0.01
<0.01 3.69
9.6 -46.0 +7.96-141.9
-18.970.120.03 3.56
75 -0.7 +13.06-141.4
-18.870.560.13 4.41
24 +5.4 +16.12-141.8
-18.940.240.06 4.20
24 -27.5 +6.05-135.8
-17.636.251.37 4.57
2.0 .......
142.0
-19.00 0
0
--.
9.9 .......
142.0
-19.000 0
-.68 - 106.5- 10.64- 128.8
- 15.8913.193.11 4.24
51 -88.6 -9.49 -136.0
-17.935.971.06 5.60
51 -88.5 -9.42 -138.9
-18.453.070.55 5.59
31 -63.0 +3.69-139.1
-18.162.930.84 3.48
Three dots indicate no data.
*Snow
temperature
profiles
are
given
inFigure
9(profile
Aappears
inFigure
9a,
profile
BinFigure
9b,
etc.).
Each
simulation
assumed
snow
density
of
0.1;
permeability
of
5
x
10
-5
cm2;
original
snowfall
isotopic
composition
is
$DsN
o
=
--142;
$18OsN
o
=
--19;
ambient
air
moisture
isotopic
composition
is$D•R= --259,
$180^m
-- --35.
I
10
/
fD
lOO
/
/
/fid
I
U.
SD!
8
90
!
!
!
!
/
SNOW EVAPORATED
SNOW
EVAPORATED
70
O
60 >
/ /
/
3
O
50 Z
I.
//
O
LU
SNOW EVAPORATED
//
>
-
80
f180
40
Z
30
LU
20
f180
øo
i
2
3
I
4
5o
INTERCEPTION
TIME (DAYS)
EXPLANATION
Cellsize0.2cm,Tair-10.5øC
--
RH 68%, EnrichmentRatio5.55
RH 75%, EnrichmentRatio7.56
RH 80%, EnrichmentRatio 15.22
Figure
12.Simulated
changes
inisotopic
composition
ofsnow
during
sublimation
of2-cm
snowfall
with
temperature
profileA (Figure9a).
612
CLAASSEN
5.0
AND
I
DOWNEY:
I
ISOTOPE
CHANGES
i
DURING
IN2•RCEPTION
OF SNOW
I
EXPLANATION
Cell size 1.0 cm, Tair-10øC
--
RH 30%, Enrichment Ratio 3.27
RH 50%, Enrichment Ratio 3.36
4.5
RH 79.5%, Enrichment Ratio 3.59
/
/
/
4.0
/
/
/
3.5
/
/
3.0
2.5
/
/
/
/$D
/
2.0
1.5
EVAP
50
1.0
EVAP
•180
0.5
/
EVAP
ujuJ
0
1
2
3
4
5
INTERCEPTION TIME (DAYS)
Figure 13. Simulatedchangesin isotopiccompositionof snowduringsublimationof 10-cmsnowfallwith
temperatureprofileB (Figure9b).
In its presentform the modelassumes
all interceptedsnow
initiallyhasa singleisotopiccomposition;
thereforethe probability that snowfallcompositionchangesduringa stormor
that interceptedsnowcomprisesmultiple snowfallsis not addressed.It is expectedthat resultswouldnot be qualitatively
differentfrom thoseobtainedassuming
snowhomogeneity
becausechangesin isotopecompositionare influencedprimarily
by factorsother than initial snowcomposition.
Temperatureandhumidityprofilesare assumed
constantduringsublimation.
Time-variable
temperature
profilesandvariable
atmospheric
humiditywouldbe computationally
morecomplex,
but the resultsare expectedto lie within the milieu of results
heretoforepresented,becausetime-variableprofilesmay be
viewedaslinearcombinations
of time-constant
profiles.
Sublimationof only originalsnowis assumed.
The effectof
resublimationof condensed
vaporis more ditficultto evaluate
than the effectsof temperature,relative humidity,and initial
snowcomposition.A microphysical
model of the distribution
of condensedvapor within the interceptedsnowwould aid
developmentof an appropriatealgorithm.Studiesof snow
metamorphosisare valuable, but determiningthe relative
amountsof original snow and modified snow available for
subsequent
sublimationwouldbe ditficult,if a physicalanalog
is desired.As discussed
earlier,very little effecton final compositionshouldbe seen,exceptat largesublimationlosses.
The
appropriateform of the algorithm at large sublimationloss
remains obscure at this time.
Giventhe aboveassumptions
a protocolwasestablished
to
demonstratethat the modelcouldsimulatethe rangeof results
obtainedfrom analysisof on-sitesamplesand data.
CLAASSEN
ANDDOWNEY:
ISOTOPE
CHANGES
DURING
INTERCEPTION
OFSNOW
613
EXPLANATION
RELATIVEHUMIDITY,
IN PERCENT
11
,•' 10
79.5
A
78.5
O
77.5
•
Equilibrium
condition
(A)
I-
80
O
A
LU
•
o
•
75
v
70
0
68
[]
50
cAonditio
n(B)
ß
30
(A) Snow temperature
profile (fig. 9)
(B) Snow temperature
profile (fig. 9)
6
A
Tair= -10øC
z
Cell size = 0.2 cm
5
•
'1-
A
4
--
z
LU
B
ß A
B
3
0
0
i
i
500
1,000
i
1,500
2,000
MODELEDINTERCEPTION
TIME (SECONDS)
Figure
14.Simulated
changes
with
time
inenrichment
ratio
asaffected
byambient
relative
humidity.
Ideally,datacollected
froman individual,
instrumentedof snow
fallsin a week.Thissnow
willbeexposed
oneverbranch
foraknown
interception
period
should
becompared
to greens
toa much
larger
extent
thanit would
behadit merely
simulation
results;
however,
thishasnotproven
practical.
The fallenonunvegetated
ground.
Thustheoverall
evaporation
modelis entirelybasedonvaporfluxesanddoesnotaddress
rateofintercepted
snow
islarger
thanthatofsnow
onground.
theenergy
balance
fortheintercepted
snow.
Although
the Themodel
accounts
foroneoftheeffects,
two-sided
exposure
energy
balance
ofsnow
ina forest
isextremely
complex,
esti- ofthesnowonbranchlets.
Themodeldoesnotaccount
forthe
matesof winter solsticeincidentradiationand snowalbedo
increased
exposure
thatresults
fromtheirregular
catchof
indicate
thatsufficient
radiation
canbeabsorbed
toaccount
for
snowfall
bythetrees.Observation
of snow
interception
on
thevapor
fluxes
computed
using
themodel
presented
[LeonardEngelmann
spruce
branches
reveals
thatnotallbranchlets
are
andEschner,
1968].
covered,
evenat highloading.
In contrast,
bridging
of snow
Theconditions
chosen
forillustration
of theinterrelation
of
between
branchlets,
and
even
branches,
occurs
at
greater
snow
variables
weresuggested
by the limitedon-sitedata.Model
runsdemonstrated
that the rangeof enrichment
ratiosob-
loadings.
Twoapproaches
weretakento estimate
theincreased
snow
served
in throughfall
(Figure
3) canbesimulated
byvariousexposure
during
interception
overthatwhich
occurs
onunveg-
combinations
ofoutward
andinward
diffusing
conditions
(see etated
ground.
Oneisa simple
geometric
argument.
A repreFigures14-17 andTable1). The absolute
enrichments
are
sentation
ofanevergreen
asa conical
section
withmajoraxis
increased
byeither
longer
interception
times
(seeFigures
12 4 timestheminoraxissuggests
aneightfold
surface
areainand13)orsmaller
snowfalls
(Table
1),andtherange
observedcrease
over
that
of
the
horizontal
(ground)
area
covered.
This
in the on-sitedata can be simulated.
geometric
argument
probably
exaggerates
thesurface
areainWhereas
themodeled
isotopic
results
maybecompared
to creasebecause
the treeis not a solidwhoseentiresurfaceis
on-sitedataonly,modeled
sublimation
amounts
areexamined
available
for snowinterception.
It maybe safely
assumed,
however,
thattheincrease
inevaporation
surface
maybeinthe
Examination
ofdatafromseven
winter
seasons
(October-vicinityof 800%.
May)indicates
thattheaverage
snowfall
eventisabout0.4cm
Another
approach
istouseleafareaindex
estimates
(LAI,
ofwaterequivalent,
orabout
4 cmofsnow
depth.
Combinedthetotalsurface
area
of
foliage
per
unit
ground
area)
to
apwithsnowfall
frequency
data,it isdetermined
thatabout9 cm
proximate
theincreased
snow
exposure
arearesulting
from
in the followingdiscussion.
614
CLAASSEN
15
AND
DOWNEY:
i
ISOTOPE
CHANGES
DURING
INTERCEPTION
OF SNOW
Interception
losses
wereestimated
at 0.027cmd-•, withabout
i
20% of the watershedcoveredby evergreens.Although the
density of evergreensof Bates and Henry [1928] cannot be
assessed,
it maybe inferredthat the interceptionlossrate for
evergreensis greater than twice the nonforested rate and
14
13
wouldbe about0.135cmd-•. Bergen
andSwanson
[1964]and
Slaughter[1970] reported nonforestedwinter evaporationvalues for another Colorado site that were approximatelyoneeighth the valuesfor the forestedsite at SnowshoeMountain.
Model simulationsover a broad range of conditionsyield re-
12
sults for loss rates from branchlets
•"•
lO
z
u•
9
80
o
•
is about a factor of 8, evaporationis proportionalto surface
area, and snowis presenton branchletsthe entire winter season. Average lossrates determinedfrom the on-site data are
Equilbrium
z
Condensation
8
0.080cmd- • for denseevergreen
forestandshouldrepresent
79
o
o
7
rr-
6
of less than 0.01 to 0.08 cm
d-•, whichwouldprojectto forestedarearatesof from0.08to
0.64cmd-•, if we assume
theincreased
surface
exposure
area
a realisticupper limit for the site climatic regime. It may be
concludedthat simulationsyield resultsconsistentwith on-site
78.5
observations.
75
z
Summary and Conclusions
A conceptualand computationalmodel is presentedthat
describesthe sublimationlossesand hydrogenand oxygenisotope compositionof throughfallin a high-altitudespruceforest
in southwesternColorado.The model treats the intercepted
snowpackas a temperature-heterogeneous
porous medium
that allowsviscousand diffusivefluxesto flow accordingto
watervaporpressuregradients.Thesegradientsare inducedby
time-dependentchangesin ambient air temperature,relative
z
30
3--
2--
1
--
0
0
I
I
500
1,000
MODELED
1,500
35
INTERCEPTION
TIME (SECONDS)
EXPLANATION
81
Ambient
o
relative
I-
25
humidity (%)
Tair= -3øC
z
Cell size = 0.2 cm
Snow temperatureprofileB
(fig. 9)
Figure 15. Simulatedchangeswith time in enrichmentratio
as affectedby ambient relative humidity.
interception.LAI measurementsof a Douglasfir stand,which
has similar configurationto Engelmann spruce,showedLAI
valuesaround8 [Marshalland Waring,1986]. Becausenot all
leaves(branches)are covered,and becausebridgingoccurs,it
is not knownwhether the effectiveexposurearea is greater or
less than LAI.
Measuredlossrates (Figure 2) indicatethat, on average,
one-half
the snow is lost. To evaluate
loss rates are consistent
with
on-site
whether
modeled
observations
snow
and mea-
•.
•5
z
J
I
lO
PERCENT INWARD
DIFFUSING
PERIOD
Inward diffusing conditions:
Snow temperature profile L {fig. 9)
Cell size 0.2 cm, Tair -10øC, RH 75%
Simulated
time 0.58d
Outward diffusing conditions:
Snow temperature profile L (fig. 9)
surementsmade at other locationsby other means,the followCell size 0.2 cm, Tair -10øC, RH 45%
Simulated time 0.58d
ing comparisonswere made. Estimates of winter snow loss
from the Wagon Wheel Gap, Colorado, forestedwatershed Figure 16. Simulatedchangesin enrichmentratio causedby
(on Snowshoe
Mountain),reportedby BatesandHenry[1928], varyingrelativeamountsof inwarddiffusingatmospheric
water
result in a value of 0.075 cm d -• for the entire watershed.
vapor and usingsnowtemperatureprofileL (Figure91).
CLAASSEN
AND
DOWNEY:
ISOTOPE
CHANGES
DURING
INTERCEPTION
OF SNOW
615
interceptionshouldalsobe studiedin climaticregimesdiffer-
5O
ent from Snowshoe
Mountain.
Exclusiveof the validityof the model to explainand predict
changesin isotopiccompositionof interceptedsnow,one may
speculateon isotopicmodificationof rechargebroughtabout
by the observedenrichmentof throughfall.For example,considera heavilyforestedwatershedclimaticallysimilarto SnowshoeMountain.If this denselycanopiedforestcomprises75%
area coverageand if sublimationlossesfrom snowpackon the
groundare ignored,overall isotopicmodificationmay be esti-
4O
mated.
o
For Snowshoe
Mountain
climatic
conditions
the isoto-
picmodification
ofwintersnowpack
wouldbe A•80 = 1.3%o,
•:• 30
ASD = 7.8%0. If this were the only isotopicmodificationto
precipitation prior to recharge, the climatic interpretation
would suggesta climate that was 2.6øC warmer than if no
isotopic
enrichment
hadoccurred
(1.3%o/0.5%oøC-1).
It may
tt'
be concludedthat isotopicmodificationof interceptedsnow
shouldbe consideredin interpretingthe relationbetweenprecipitationand soilwater and groundwaterisotopes.
20
Appendix: Gas Flux in Porous Media
10
0
10
20
PERCENT
30
40
50
60
70
In the generalcasefor very permeablemedia suchas snow,
Knudsendiffusionand slipflux maybc ignored,and the StefanMaxwell equationsare used to determinethe relative importance of the viscousand diffusivefluxesof water vapor in the
snow[Thorstenson
and Pollock, 1989].The pertinent relations
for a two-componentsystemof air and water vapor follow, all
from Thorstenson
and Pollock[1989]with minor modifications.
INWARD
DIFFUSING
PERIOD
Inward diffusing conditions:
Snow temperature profile B (fig. 9)
Cell size 0.2 cm, Tair -3øC, RH 90%
Outward diffusing conditions:
Snow temperature profile B (fig. 9)
Cell size 0.2 cm, Tair -10øC, RH 90%
N r = Nø + N V
whereN r, N ø, andN V arethetotal,diffusive
andviscous
gas
fluxesof all speciespresent.If the diffusionregimeis assumed
to be molecular, the Stefan-Maxwell equation may be expressedasfollows[seeThorstenson
andPollock,1989,equation
(79)]
Figure 17. Simulatedchangesin enrichmentratio causedby
varyingrelativeamountsof inwarddiffusingatmosphericwater
vapor and usingsnowtemperatureprofile B (Figure 9b).
humidity,and variationsin insolation.Variablesconsideredin
the model include permeabilityfor determinationof viscous
flux; ambient air temperature,humidity,and isotopiccomposition;snowisotopiccomposition;
and snowpackhumidityand
temperatureprofile.Model simulationswere madeusingsnow
profiletemperaturedataobtainedon sitein additionto a range
of anticipatedenvironmentalconditions.The resultsof these
simulationsmirror the range of observationsof isotopicenrichmentundergoneby interceptedsnow.Simulatedsublimation lossrates comparefavorablywith on-site measurements
andvaluesreportedin the literaturefor climaticregimessimilar to the site.
Assumptionsof constanttemperatureand humidityprofiles
and initially homogeneoussnow compositionmay be made
more realisticby (1) algorithmmodification,(2) more extensiveon-siteobservations
of temperatureand humidityprofiles,
(3) sequentialsamplingof snowfallfor isotopesduringstorms,
and (4) accurate measurementsof interception time. The
above could be combinedWith synopticsectioningof intercepted snowpacksfrom various tree locations.Resultsfrom
laboratorystudies,where controllingvariablesmay be regulated, may be comparedto model output.The effectsof snow
(1)
T
T
XH2oNAIR
-- XAIRNH20 PATM
•7Xn20
D H20/AIR
RT
(2)
where X is the mole fraction, X7
X is the mole fraction gradient,
D is the binarymoleculardiffusivity,P^T• is the atmospheric
total pressure,R is the gasconstant,and the subscripts
refer to
the gas speciespresent in the binary system:air and water
vapor.
Assuming
N•i R= 0
one obtainsby substitutionand rearrangementof (2)
T
PATM•7XH2oDH20/AIR
NH20
=
)(AiRR
T
(3)
By introducingDarcy's law and relating the intrinsicKlinkenberg parameter bm to the permeabilityof the medium B•o
Thorstenson
and Pollock [1989, equation(70)] derive an expressionfor the total viscousflux:
M'T
NV_
--
!//1/2
•• H20
_ t•xH20
,,rl/2
. -•r-•
!,,fl/2
(bI'AIRbm/PATM)
+ Xn20/V•n20
+ XAIR
AIR
(4)
where M is the molecularweight and/• is the viscosityof the
specifiedgas. But [Thorstenson
and Pollock, 1989, equation
(63)]
616
CLAASSEN AND DOWNEY:
I
ISOTOPE CHANGES DURING
I
I
I
I
INTERCEPTION
OF SNOW
I
EXPLANATION
Air
•
•18Osn
O
•18Oai
r
I Nominal
value
-16
-32
-19
-35
-22 •180sno
%o
-38 •18Oeir
%o
EXPLANATION
•5Dsno
• Dair
I Nominal
value
I
I
I
-129
I
I
I
I
-262
-266
-270
-141
-246
-250
-254
-258
-157 •5Dsno%0
-274 •5Dair%o
Figure18. (a) Effectonenrichment
ratioof varying
oxygen
isotope
composition
of air andsnowfromthe
nominal value used in most simulations.Conditionsheld constant:Temperature profile B, 2-cm snow,
TAm -- -3øC, ;SD^m- -259, ;SDsNo= --142. (b) Effectof enrichment
ratio of varyingdeuterium
composition
of air andsnowfromthenominalvalueusedin mostsimulations.
Conditions
heldconstant
are
the same as in Figure 18a.
11//1/2
/
bm= /•
t,,AIR•',
AIR/jULAIR
(5)
wherebAiR is the measuredKlinkenbergparameterfor air,
and[Thorstenson
andPollock,1989,equation(69)] (modified
for the units usedin this paper)
(6)
By substituting
(5) and (6) into (4) we obtain
}kit
11//1/2
, vH20
zrx
H20a•1/2
f•O •:?-0.39 i//1/2 /D
39.9,,.,•,k
Fick
___PATMDH20/Ai
R•7
XH2o/R
T
H20
bAiR-- 39.909B/ø'39
Nv =
The molar water vapor flux arisingfrom diffusioncalculated
usingFick'sfirstlaw [Thorstenson
andPollock,1989,equation
(84)] is
.
11//1/2
,- AIR/ZATMq- XH2Od¾1H20
q- /•AIR•vxAIR
(7)
(12)
Examinationof the foregoingequationsrevealsseveralfacts
pertinentto the relativewatervaporfluxesin snow.First,the
total watervaporflux is significantly
determinedby the vapor
pressuregradient(equation(3)), whichin the snowis determinedby the temperaturegradientandin the atmosphere
by
temperature
andrelativehumidity.Second,theviscous
fluxof
watervaporis onlyweaklydependenton permeability(equa-
tions(7) and(8)) untilthepermeability
drops
to about10-7
Equation(7) allowscalculation
of the totalviscous
fluxin the
cm2 (10 darcy).As permeability
decreases,
thetermthatcon-
snow from known values of the variables. The viscous flux of
tainspermeabilityin (7) becomeslarger.It becomesgreater
than 2% of the sum of the other two terms in the denominator
water vapor is then obtainedfrom
v
v
NH2O= XmoN
(8)
The total diffusiveflux is obtainedfrom (1), recallingthat it
wasassumed
thatN,•iR = 0'
whenpermeability
is decreased
to 10-7 cm2.Thusfor larger
permeabilities
NV isa constant,
andN•:O depends
primarily
on XI-i:oper (8). Largerviscous
fluxesin the snowwould
therefore be associatedwith warmer snow temperatures.
Two examplesare givento demonstrate
the relativecontri-
N ø = N r - N V = NH2O
r _ NV
(9)
butionsof viscousand diffusivefluxesto water vapor flux. The
firstexamplerepresents
typicalnear-surface
conditions
where
[Shimizu,1970;Sommerfeld
andRocchio,1989]
Then
D
T
NH20= NH20-- XH20
N
V
(10)
The molarwatervaporfluxarisingfrom moleculardiffusionis
[Thorstenson
andPollock,1989,equations
(74) and(77)]
JH20
-" /•20 -- XH20
ND
PATM= 6.8 x 10s dyncm-2
RH = 0.75
TAiR= TSN
o = 253øK
Bk = 10-s cm2
The last value is from Shimizu[1970] and Sommerfeldand
( 11) Rocchio[1989].Also,
CLAASSEN AND DOWNEY: ISOTOPE CHANGES DURING INTERCEPTION OF SNOW
DH20/Ai
R--'0.194 cm2s-1
XH20
= 1.309 X 10-3
617
l sublimation
lossrateperunitarea(Mt- •).
mI massof snowper unit area lost to
VXmo= 3.68 X 10-4 cm-1
atmosphere
after interceptiontime t (M).
mo originalmassof snowper unit area at
Then
T
Nmo = -2.311 x 10-9
v
Nmo = -2.374 x 10-•2
Jmo = -2.308 x 10-9
N V= -1.814
x 10 -9
D
NH2o = --2.309 X 10-9
jFick
H20 --' --2 ß308 x 10 -9
Therefore the water vapor flux is 99.9% diffusiveand 0.1%
viscous
undertheseconditions,
andthe Fick'slaw approximation to molecular
diffusion flux is valid.
The secondexamplerepresentsconditionsthat may be
foundwithinthe interceptedsnowduringmaximummidwinter
insolation:
beginningof interception(M).
mr massof recondensed
water vaporper unit
area after interceptiontime t (M).
mt massof snowper unit area after interception
time t (M).
M• molecularweightof specifiedgasi (M
mol-•).
NAy Avogadro's
number(molecules
mol-•).
N•ø totalmolardiffusive
gasfluxacross
a specified
boundaryof gasi (no subscriptdenotesall
gases)(molL - 2 t- •).
N•r totalmolargasfluxacross
a specified
boundaryof gasi (no subscriptdenotesall
PATM= 6.8 X l0 s dyncm-2
RH = 0.50
TAIR= 263øK
TSNO= 270øK
Dmo/Am
= 0.216 cm2s-1
Bk = 10-5 cm2
XH2O
= 4.454 X 10-3
VXi-i:o= 1.695 X 10-3 cm-1
gases)(molL - 2 t- •).
N•V totalmolarviscous
gasfluxacross
a specified
boundaryof gasi (no subscript
denotesall
gases)(molL - 2 t- •).
PA*M ambientatmospheric
pressure
(MLP• vaporpressureof specifiedwatervapor
Then
P•o
T
Nmo = -1.129 x 10-8
Nmo = -3.948 x 10-•
J}•o- -1.124 x 10-8
N V= -8.864
x 10 -9
P•2o(•>total
water
vapor
pressure
inequilibrium
with
ice (ML - • t- 2).
R gasconstant
(ML 2 t -2 T-• mol-•).
D
Nmo = -1.125 x 10-8
isotope/(ML - •
totalwatervaporpressure
(ML- • t-2).
RH relative
humidity
(dimensionless
decimai
jFick
H20 --' -- 1' 124 x 10-8
fraction).
R•vo = C•vo/C•% (dimensionless).
R•o = C•o/C•o
(dimensionless).
In this instance,the water vapor flux is 99.6% diffusiveand
0.4% viscous,and the Fick'slaw approximation
to molecular RsMowI-too= 1.5576X 10-4.
diffusionis valid. Decreasingthe permeabilityto 10-6 cm2 Rs•owI_i•8
o - 2.0052X 10-3.
decreasesthe portion of viscousflux to 0.3%.
t time.
T absolutetemperature(T).
TAV averageabsolutetemperaturebetweenpair of
Notation
DimensionsareM, mass;L, length;t, time; and T, absolute
temperature.
ar• Rx-moliquid/Rx_mo
vapor(dimensionless).
ao RI_12•80
liquid/RI_i•80
vapor(dimensionless).
b Klinkenberg
parameter,measured
using
cells(T).
X• mole fractionof specifiedgasi
(dimensionless).
VX• molefractiongradientof specified
gas(L-•).
•D=[(RI_mo/Rs•owI_mO
) - 1] x 103 (permil).
•80=[(RI_i:•o/Rs•owI_i:•o)
- 1]x 103 (permil).
•JDsNo,
•j•8OsN
o isotopic
valueof snowfall
at beginning
of interception(per mil).
specified
gasi (ML - • t- 2).
bm intrinsicKlinkenbergparameter,characteristic
of theporous
medium(M •/2 mol-•/2 t-•).
Bk permeability
(L2).
•JD•No,
•j•aO•N
o isotopic
valueof intercepted
snowat
interceptiontime t (per mil).
•JDsNoR,
•j•8OsNoR
isotopic
valueof recondensed
vaporat
interceptiontime t (per mil).
Ci molecularconcentration
of specifiedgasi
(molecules
L-.3).
d depthof snowat beginning
of interception
A•D, A•80 change
in isotopic
valueresulting
from
sublimationof snow(per mil).
p densityof snowat beginning
of interception
(•).
D i binarymoleculardiffusivity
of specifiedgasi
(L 2 t-•).
tz• viscosity
of specified
gasi (ML - • t- •).
eo isotopicenrichmentof HDO (per mil).
e•8 isotopic
enrichment
of H2•80(permil).
f fraction(dimensionless).
g rate of watervaporcondensation
per unit
area(mt- •).
Ji molar flux of specifiedgasarisingfrom
molecular
diffusion
(toolL - 2 t- •).
j•ick molarfluxof specified
gasi calculated
using
Fick'slaw(molL - 2 t- •).
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