WATER RESOURCESRESEARCH,VOL. 28,NO. 11,PAGES3043-3054,
NOVEMBER 1992
Climateand EnergyExchangeat the Snow Surface
in the Alpine Regionof the Sierra Nevada
2. Snow Cover Energy Balance
DANNY MARKS
ManTech
Environmental
Technology,
Incorporated,
Environmental
Research
Laboratory,U.S. Environmental
ProtectionAgency,
Corvallis, Oregon
JEFF DOZIER
Centerfor RemoteSensingandEnvironmental
Optics,Universityof California,SantaBarbara
A detailedevaluationof surfaceclimateandenergyexchange
at the snowsurfacein a smallalpine
watershed,typicalof muchof the southernSierraNevada,is presentedfor the 1986water year.
Measurementsof snowfall,meteorological
and snow cover conditions,and snow cover ablation,
describedin part 1 of this paper(Marks et al., this issue),are usedto characterizethe climate. Each
form of energytransfer,radiation,sensibleandlatent heat flux, soil heat flux, and heat flux by mass
advection,is evaluatedseparatelyto determinehow its magnitudechangesduringthe snow season.
These are then combinedto approximatea snowcover energybalance and determine the relative
importanceof eachformof energytransferin theseasonal
energyandmassbalanceof the snowcover.
Radiationand sensibleand latent heat flux dominatethe snow cover energybalancethroughoutthe
snow season.During snowmelt,radiationaccountsfor between66 and 90% of the energyavailable for
melt. Sensibleand latentheattransferduringthistime are of approximatelyequalmagnitudebut are
usuallyof oppositesignand thereforecancel.Calculatedsublimationduringthe entire snow season
accountedfor the lossof about20% (approximately
50 cm snowwater equivalent)of the massof the
snow cover. This experimentshowsthat energyand masstransfercan be adequatelymonitoredat a
remote site usinga combinationof measuredand modeledparametersand that the energy balance of
the snowcover in the alpinezone of the SierraNevada is dominatedby net radiationduring snowmelt.
INTRODUCTION
In part 1 of this paper [Marks et al., this issue]the detailed
surfaceclimate monitoring required for investigationsof the
snowpackenergy balance and melting in remote alpine
watersheds
is presented. Snow metamorphism,melting, and
runoffare controlledby the magnitudeof energyavailableto
top of an arete about 300 m above the lake, and the lake site
is a protected location at the lake inlet.
ENERGY EXCHANGE AT THE SNOW SURFACE
In a seasonalsnowpack, newly fallen snow is thermodynamically unstable, undergoing continuous metamorphism
drivetheseprocesses,and these energy fluxes are deter- until it melts and becomes runoff during spring [Colbeck,
minedby the combinationof local meteorologicalinputsof 1982]. These metamorphic changes and final melting are
precipitation
and energy.Detailed observationsof snowpack driven by temperature and vapor density gradients within
energyfluxes in montane climates are limited. Most of those the snowpack, which are caused by heat exchange at the
thatdo exist come from locationsat lower elevations[Smith snow surface and at the snow-soil interface [Colbeck eta!.,
andBerg, 1982], are from nonalpinelocations[Anderson, 1979; Male and Granger, 1981]. In general, the energy
1976],or have been limited to a single though well- balance of a snowpackis expressed as
instrumented
measurementsite [Davis and Marks, 1980;
(1)
AQ = Shet q- H q- LyE + G + M
Daviset al., 1984]. Here we utilize the climate data presentedin part 1 of this paper to characterizeenergyexchange
at the snowsurfacein a remotealpinewatershedand whereAQ is changein snowpackenergy,and Snet,H, L•E,
G, and M are net radiative, sensible, latent, conductive, and
evaluate
the effect that these parametershave on snow
advectiveenergyfluxes. In temperatureequilibrium, AQ =
distribution,
metamorphism,
andmelt.
Asdiscussed
in part 1, the studysitefor thisworkwasthe 0; a negativeenergybalancewill cool the snowpack,inEmerald
Lakewatershed
in SequoiaNationalPark,in the creasingits cold content(the amountof energyrequiredto
bring it to 0øC), while a positive energy balance will warm
southern
SierraNevada of California,locatedin the Marble
the snowpack.The snowpackcannotbe warmerthan 0.0øC,
Forkof the KaweahRiver drainage,approximately
8 km
fromand700 m abovethe nearestroad. Data from the 1986 and melt cannot occur in significant amounts until the entire
snowpackhasreachedthistemperature,whereuponpositive
wateryear were integrated into hourly averagesfor a
"ridge"and"lake" site,whichrepresent
the extremes
of
themeasured
data.Theridgesiteis anexposed
location
on
Copyright
1992by theAmerican
Geophysical
Union.
Paper
number92WR01483.
0043.1397/92/92WR-01483505.00
values of A Q must result in melt.
In the followingsectionseachof the termsin the energy
balanceequationis presentedin detail,showingthe parameterswhichweremeasuredor calculated.The uncertaintyof
thosemeasurements
and the assumptionsmade in calculatingenergyfluxare evaluated,andthe sensitivityof theresult
3043
3044
MARKSANDDOZIER:CLIMATEAND ENERGYEXCHANGEAT THE SNOWSURFACE,2
to reducecomputational
difficulties
while
to errorsin eachphaseof the calculationis determined.The be parameterized
magnitudeof eachterm in the energybalanceis estimated retainingthe importantspectralfeaturesaffectingnet solar
to
throughthe snowseason,andthe sensitivityof thisbalance radiationat the snow surface.We use their approach
examinenet solarradiationat the snowsurface.Incidentand
to errors in the exchangecalculationsis evaluated.
reflectedsolarradiationare measured
in two wavelength
bands:visible(0.3-0.7/xm)andnear-infrared
(0.7-2.8
NET RADIATION AT THE SNOW SURFACE
The radiant energy flux, or net all-wave radiation,at a
pointis the incidentspectralirradiancelessspectralexitance
integrated over all wavelengths'
Sne
t'" S,• - St
(2)
The irradiance term S $ includes direct and diffuse solar
radiation and longwave radiation emitted from the atmo-
sphere.ExitanceS •' includesboth reflectedand emitted
The net solar radiation at a point is calculated by
Snet,sol
= S • vis(1.0
-- Rvis)+ S $ nir(1.0
- Rnir) (3)
The albedosare calculatedfrom a modelpresentedby Marks
[1988] which is based on effective snow grain radius and
solar zenith angle, as detailed by Marshall and Warren
[1987].
Albedo changeswith sunangleand grain size decayafter
radiation from the surface.
a snowdeposition
event.The decayof albedois inversely
Radiation is the only form of energytransfer that can be
measureddirectly in the natural environment.Incidentradiation can be reliably and accurately measured in broad
wavelengthband widths, using well establishedtechniques
and instrumentation [Monteith, 1973]. Under clear sky con-
related to the square root of the grain radius. The albedo
decaywith increasingsnowgrain size is linear in the visible
and nonlinear in the near infrared. The increase in albedo
with solar zenith angleis a function of the squareroot of the
ditions the distribution of incident radiation can be modeled
linear in both the visible and near-infrared bands, but the
effect is much larger in the near infrared.
When the solar zenith angieis 0.0 with respectto the snow
over complexalpineterrain for both solar[Dozier, !980] and
thermal [Marks and Dozier, 1979] wavelength ranges, but
under cloudy conditions, measurementsare necessarybecausethe separatecontributionsof direct and diffusesolar
and emitted thermal radiation from the atmosphere and
cloudsare not easily predicted or modeled. At some sites,
irradiance includes significant contributionsfrom reflection
and emission from adjacent terrain. At Emerald Lake,
incident radiation
is measured
at two sites to calibrate the
estimate of irradiance for terrain effects, atmospheric effects, and cloud cover. Parameters that cannot be reliably
measured are modeled, and net radiation is calculated from
a combination of measured and modeled parameters. Net
radiation at the surface is separatedinto two solar and one
thermal spectral bands.
grainsizeandthecosineof thezenithangleandis essentially
surface,
Rv,o
= Rv,maxavrl/2
(4)
Rnir,O
= Rnir,max
exp[anirr
1/2]
(5)
wherer is the effectivegrainradius,Rv,ma
x is the maximum
visible albedo (1.0), a v is the slope coefficientfor visible
albedo
decay
withgraingrowth
(2.0x 10-3),Rnir,ma
xisthe
maximum near-infrared albedo (0.85447), and anir is the
slope coefficientfor near-infrared albedo decay with grain
growth
(-2.123x 10-2).Thisallows
a lineardecay
ofP•,0
from about0.98 to 0.90, and an exponentialdecayof Pnir,0
from 0.70 to 0.40, when reasonablegrain radii are used.For
sun angles other than 0.0,
Solar Radiation
Solar radiation (effectively 0.3-3.0/•m) is absorbedand
scatteredby terrestrial materials but not emitted. For snow,
absorptionand scatteringare functionsof wavelength,incidenceangle, and the grain size and concentrationof absorbing impurities in the surface layer [Bohren and Barkstrom,
!974; Warren, 1982].
Snow albedo varies spectrally,but detailed spectralmea-
Rv,o= Rv,o+ [rl/2av,
o][1.O
- cos0]
Rnir,
0= Rnir,
0+ [(r!/2anir,
o)+ bnir,#][1.0
- cos0]
(6)
(7)
where0 is the solarzenithangle,correctedfor slope,av,ois
theRv,oslope
coefficient
(1.375x 10-3),anir,
0istheRnir,
o
slope
coefficient
(2.0x 10-3),andbnir,
0istheRnir,
ooffset
coefficient(0.1). The slope and offset coefficientsin the
surements of radiation at the snow surface are difficult under
above equationswere derived from measuredreflectancesat
controlled conditions and not possibleat a remote site. A
spectralapproach to modeling solar radiation [e.g., Dozier,
1980]will give an accurate result under clear skies, but it is
complicated computationally and requires detailed information about the atmosphereand the snow surfacethat cannot
be known when monitoring a remote site. Other investigators have taken a single-band,global approachto modeling
solar radiation over remote alpine areas [Davies and Idso,
!979; Munroe and Young, 1982; Olyphant, 1984]. This
simplifies the calculation of net radiation so that it can be
doneat a remote site, but it ignoresthe distinctdifferencesin
the absorptionand scatteringpropertiesof the snowsurface
in the visible and near-infraredwavelengths.
a snowstudyplot in a similarregionof the SierraNevada.
They are similar,thoughnot identical,to thosereportedby
circulation models(GCMs) parameterize solar radiation into
two wavelengthbandsand suggestthat snowalbedocan also
Largesolarzenithanglesduringwinter causethe lake siteto
Marshall and Warren [1987].
Net solar radiationwas computedfrom the modeled
albedosandmeasured
irradiances
for the two representative
sites in the Emerald Lake watershed. As shown in Table 1,
near-infraredirradiancerepresents53% of the total solar
irradiance at the ridge site and 60% of the total solar
irradianceat the lake site, but it represents85% of the net
solarinput at the ridge site and 89% of the net solarinputat
the lake site. In early winter the ridge site receives more
solarirradiancethan the lake site, but by early springthey
receivethe sameamount,andby late springthe lakesite
Marshall and Warren [1987] point out that most general receivessignificantly
moresolarradiationthantheridgesite.
be shadowed
for a significant
part of the day, but in spri•
MARKS
ANDDOZIER:
CLIMATE
ANDENERGY
EXCHANGE
ATTHESNOW
SURFACE,
2
3045
TABLE 1. SolarRadiationSummary,
MonthlyFluxes,EmeraldLakeWatershed,
1986SnowSeason
SolarIrradiance,W m-2
S • so•
S $vis
Month(0.28-2.8tzm)(0.28-0.7
Nov.
Dec.
Jan.
Feb.
March
95
83
93
96
133
45
39
44
48
68
April
May
217
272
105
129
June
338
154
July
309
143
Season
182
86
Nov.
Dec.
Jan.
Feb.
March
80
73
82
96
171
34
31
35
40
69
April
May
238
298
96
12!
Net SolarRadiation,W m-2
Proportion
Proportion
Proportion
Proportion
Snct,ni
r
of
of
S •,nit
of
Snet,so
1
Snet,vi
s
of
S,Lsol (0.7-2.8
•m) S•,sol (0.28-2.8/xm)
(0.28-0.7
•m) Snet,so
1 (0.7-2.8/.t,m) Snet,sol
0.48
0.47
0.47
0.50
0.51
0.48
0.47
0.46
0.46
0.47
50
44
49
48
65
113
143
184
166
96
0.42
0.43
0.42
0.41
0.40
0.40
0.40
0.39
0.39
0.40
46
41
48
57
102
142
178
204
192
112
Ridge Site
0.52
0.53
0.53
0.50
0.49
0.52
0.53
0.54
0.54
0.53
22
19
22
21
34
62
86
130
119
57
3
2
2
2
5
8
13
21
20
8
0.12
0.12
0.09
O.10
0.13
O.12
0.15
O. 16
O. 17
O. 15
20
17
20
19
30
54
73
109
1O0
49
0.88
0.88
0.91
0.90
0.87
0.88
0.85
0.84
O.83
0.85
20
17
21
25
51
75
101
140
134
65
2
1
2
2
4
7
11
18
17
7
0.08
0.08
0.08
0.07
0.09
0.09
0.11
0.13
0.13
0.11
18
16
20
23
47
68
90
122
117
58
0.92
0.92
0.92
0.93
0.92
0.91
0.89
0.87
0.87
0.89
Lake Site
June
332
128
July
314
122
Season
187
75
0.58
0.57
0.58
0.59
0.60
0.60
0.60
0.61
0.61
0.60
thesunis higher in the sky and this shadowingis reduced.
Moreover,in the spring, reflected radiation from nearby
densityprofileswithin the snow cover [Anderson, 1976], and
terrain adds to the radiation received at the lake site.
these data were not available continuously during the snow
season. The difference between the snow surface layer
Thermal Radiation
temperatureTs and an effective snow surfaceskin temperature Tso was estimatedfor the upper 10 mm of the snow
Thermalradiation (effectively 3.5-50/•m) is absorbedand
emittedby the atmosphere without appreciablescattering
[Paltridgeand Platt, 1976]. Because the emissivity of snow
isspectrallyrather flat [Dozier and Warren, 1982], spectral
variabilityin incoming thermal radiation can be ignored.
Integratedthermal irradiance can be measured, and broadband emissivities can be used for the snow surface and
surroundingterrain. The thermal irradiance in an alpine
regionis a function of the atmosphericconditionsand the
temperatureand configuration of the surroundingterrain
[MarksandDozier, 1979].Net thermalradiationis
Snet,lw
= S• lw- (esrrTs4o)
(8)
cover for each month in the snow season from the magnitude
of the net turbulentheat flux (H + L•,E) and from the snow
surface layer temperature Ts. Daily net thermal radiation,
calculated from the snow surface layer temperature Ts
presentedin part 1 of this paper [Marks et al., this issue] is
shown in Figures 1 and 2 for the ridge and lake sites during
the 1986 snow season. Table 2 shows the monthly net
thermal
radiation
flux calculated
from
the estimated
snow
surfaceskintemperatureTsofor the ridgeand lake sites.
Net All- Wave Radiation
Net all-wave radiation is the sum of the net solar and net
thermal. Figures 1 and 2 present daily meansfor the ridge
Considerable
effort has goneinto developmentof simple and lake sites during the 1986 snow season. Table 2 shows
models
of thermalirradiancefrom the atmosphere,but most the monthly fluxes for each component of the radiation
oftheseare applicableonly to clear sky conditions.Cloud balance at the two sites. Thermal and solar radiation make
coverincreasesthermal irradiance at the surface, and as for up approximatelyequalparts of the radiation balance at the
solarradiation,this effectis not easilymodeled.The atmo- ridge site. If the October and August totals were included,
spheric
contributionto thermalradiationgenerallydoesnot the difference between net solar and net thermal would
vary much over an area the size of the Emerald Lake
almostbalance.Thermalradiationis slightlymore important
watershed,and measuredvalues at a few points effectively duringwinter, but by March higher sun anglesand longer
characterize
it, incorporating
the effectof cloudcover.
days cause solar radiation to dominate.
Thermal exitance is a function of the snow surface skin
Solar radiationis more important than thermal during
temperature
andemissivity.The emissivityof snowis0.988-- mostof the snow seasonat the lake site. Only duringthe
0.990
forall grainsizesabover = 75 /•m;for fine-grainedvery cold month of December did thermal radiation domisnow,r = 50 tzm, the emissivitydrops slightlyto 0.985 natetheradiationbalanceat the lake site.Thisis primarilya
topographiceffect. During winter, thermal radiation from
[Dozier
andWarren,1982].
If a coupled
energybalance
is calculated,
theskintemper- adjacentterrainincreasesthermalirradianceat the lake site,
at'ure
ofthesnowcoverT•0canbederived
[Outcalt,
1972], reducingnet radiativecooling,and duringspring,enhanced
butthesecalculations
requiredetailedtemperature
and solarirradiancefrom scatteringby adjacentterrainincreases
3046
MARKSANDDOZIER:CLIMATEANDENERGYEXCHANGE
AT THESNOWSURFACE,
2
Emerald Lake Watershed, 1986 Water Year
Mean
DailyNetAll-Wave
Radiation
(Rn),Ri,d?Sit•
I
I
I
I
I
Obukhov stability length
1
I
,3
I
m
(9)
150
•
Rn
•o
.
+ 0.61E
kgTaCp
.• .•
Friction velocity
-100
uk
-150
'200E,,I Nov
I
Dec
I
Jan
I
Feb
,I
Mar
(10)
I
Apr
May
Jun
In
Jul
..........
Xllsm
zo
Sensibleheat flux (positive toward
the surface)
2OO
(o. - e,)a•ku*pC•
1•o
zr-
In
o
do
zr
- •sh
Z0
-5o
Mass flux (positivetoward the surface)
-lOO
-15o
(q- qs)aEkU*p
-2OO
In
Fig. 1. Daily averagenet all-waveradiation(R n) and net solar
(Rn,so])
(0.28-2.8p•m)andnetthermal(Rn,iw)(3.5-50p.m)radiation
at the ridge site, Emerald Lake watershed, 1986 snow season.
zq- do.-
•sv
zq
zo
The latent heat flux is LyE.
The • functions,•sm for mass,•sh for heat, and•sv for
water vapor, are
solarinput.By March,net solarradiationSnct,so
I is 15-20% Stable (•' = z/L > O)
greaterat the lake site than at the ridgesite. In general,early
in the snow season the radiation budget is dominated by
thermal radiation, but by early springthis beginsto change,
and during melt season, solar radiation predominates.
0<•<1
•r>l
/3s=5
(13)
SENSIBLE AND LATENT HEAT FLUXES
Turbulent energy exchange at the snow surfaceis second
only to radiation in importanceduringthe snowseason.The
turbulent transfer of momentum, heat, and water vapor at
the snow surfaceare the most complicatedforms of energy
exchangeand are not easily measuredin a natural environment. The data required to calculate them are difficult to
measureat a point, and they have a highly variabledistribu-
tion over a topographicsurface.Yet not only doessignificant
energy transfer occur by turbulent exchange, but in the
Sierra Nevada significantmass loss can occur from sublimation [Beaty, 1975; Stewart, 1982; Davis et al., 1984].
Tractable approachesto calculatingsensibleand latent
fluxes have been summarized in textbooks [Fleagle and
Businger, 1980; Brutsaert, 1982]. The method we use is
adapted from Brutsaert [1982]. This method was used because it can calculate turbulent transfer independentof
Emerald Lake Watershed, 1986 Water Year
MeanDailyNetAll-WaveRadiation
(Rn), LakeSite
I
I
200t
z{ ] ] [
150
-tOO
-150
'200F ! "m I
Nov
Dec
I
Jan
I
Feb
!
Mar
I
Apr
I
I
Jun
lV•y
lul
MeanDailyRn•l &Rn,tw,Lake
Sit•
I
I
I
I
Ul
'"""
"'"'
50
a"d
I
!
I
I
I
estimates of net radiation and accounts for variations in wind
speed. It is particularly adapted to high-wind loading sites
like the ridge. The usual condition for data collection at a
remote site is that only one measurementis availablefor air
temperature, humidity, and wind speedand that these may
not all be at the sameheight above the surface.The height
above the snow surfacewill be continually changingas the
snowcover accumulatesand ablates.Air temperatureTa is
measured
atheight
zr, specific
humidity
q ismeasured
atzq,
and wind speedu is measuredat zu. The equationsbelow
iteratively solve for the friction velocity u*:
i•
/ .i , /iJ
-•ol- " •,• ß
' /
i
I
Nov
Dec
'• '
,ti
•
'
•i
n
•1
.-am
iW'.. ,
?•%/
I
I
I
Jan
Feb
Mar
i
Apr
I
May
,
I
Jun
Jul
Fig. 2. Dailyaverage
netall-waveradiation
(Rn), andnetsolar
(Rn,so0
(0.28-2.8/•rn)
andnetthermal
(Rn,lw)(3.5-50/•xn)
radiation
at the lake site, Emerald Lake watershed, !986 snow season.
M•d•KSANDDOZIER:
CLIMATE
ANDENERGY
EXCHANGE
ATTHESNOW
SURFACE,
2
3047
TABLE 2. Net All-WaveRadiation
Summary,
MonthlyFluxes,EmeraldLakeWatershed,
1986
Snow Season
Net Solar
Month
Snet,
(0.28-50/an)
Net Thermal
Snet,so
I, Wm-2 Proportion Snet,lw,
W m-2
(0.28-2.8•m)
Nov.
Dec.
Jan.
Feb.
March
April
May
June
July
Season
-5
-18
- 1
-23
16
23
40
86
85
23
Ridge Site
23
18
22
23
34
63
85
132
114
57
Nov.
Dec.
Jan.
Feb.
March
April
May
June
July
Season
!2
-15
9
9
31
37
44
93
94
35
20
17
21
27
50
77
100
142
128
65
Proportion
of She
t
(3.5--50
/.fill)
of She
t
0.45
0.33
0.49
0.33
0.66
0.61
0.65
0.74
0.80
0.56
-27
-37
-23
-46
- 18
-40
-45
-45
-29
-34
0.55
0.67
0.51
0.67
0.34
0.39
0.35
0.26
0.20
0.43
0.71
0.35
0.64
0.60
0.72
0.66
0.64
0.74
0.79
0.65
-8
-32
-12
-18
- 19
-40
-56
-49
-34
-30
0.29
0.65
0.36
0.40
0.28
0.34
0.36
0.26
0.21
0.35
Lake Site
Unstable(•r= z/L < O)
x = (1 - flue)•/4
flu= 16
ature difference between the two can be very large. Therefore sensibleheat transfer is small, and the net turbulent flux
(14) (H + LyE) is negativeand dominated by latent heat loss.
However, once the air temperature is above 0øC, the snow
surface is constrained, and the temperature difference can
2
2
increasein magnitude,allowing sensibleheat flux to increase
and net turbulent flux to be smaller and finally to become
positive. This is particularly important during spring of the
1986 snow season when air temperatures remained above
freezing
throughoutthe diurnal period from early May on.
The three most critical terms in the above equationsare
Because
the magnitudes of latent and sensible heat fluxes
thewindspeedu, the temperaturedifferencebetweenthe air
are
controlled
by the wind speed, they are smaller at the lake
andthe surface, Ta - Ts, and the humidity difference
between
the air and the surface,q - qs- Turbulenttransfer site than at the ridge site. The direction (positive toward and
•sm---2In 2 +In,1+X - 2arctan
x+- (15)
,
,,
•sh(•')
= •sv(•')
= 2 In 2
(16)
ofheatand mass is controlledfirst by the magnitudeof the negative away from the surface) of these fluxes is controlled
w•d speed and then by the temperatureand humidity by the sign of the temperature and humidity gradients.
gradientsbetween the snow surface and the air. As in Latent heat flux is therefore negative at both the ridge and
calculation
of thermal exitance, the snow surfacetempera- lake sitesthroughoutthe year. Sensible heat flux is usually
tureis important, first, in determinationof the temperature positiveat both sitesthroughoutthe year and alwaysposigradientbetween the air and the snow cover, and second, tive during spring once the air temperature does not go
because
humidityat the snowsurfaceqs is calculated
asthe below freezing at night.
Figure 3 presentsdaily averagesof calculatedsensibleand
saturation
humidityat Ts. Becausethe snow cover is por0us,turbulentexchangeis betweenthe atmosphereandthe latent heat transfer for the ridge and lake sites during the
first 15-25 cm of the snow cover. Therefore sensible and 1986snow season.As expected, the magnitudeof turbulent
latentheat flux were calculated from the surface layer exchangeis larger at the ridge site than at the lake site, and
temperature
Ts ratherthan the snowsurfaceskintempera- in general,latent heat transfer is away from, and sensible
turerso.
heat transferis toward, the snow surface.What is striking
Climatic conditions in the Emerald Lake basin, as re- about these calculations is that the latent and sensible
portedin part 1 of this paper [Marks et al., this issue], transfers tend to mirror each other most of the time. For
showed
that while the lake site is significantly
lesswindy both to be negative the air must be both colder and less
thantheridgesite,thereis seldoma longperiodof calm humid than the snow surface. This condition occurs occaconditions
at either site. Except under very cold, calm sionallyduringwinter but does not persist, as the snow
conditions
or duringstorms,the vaporpressure
of theair is surfaceeithercoolsto theair temperature
or the air temperalways
lessthanthat of the snowsurface.As longasthe air atureincreasesduringa diurnalcycle. It almostneveroccurs
temperature
is lessthan0øC,snowsurfacelayertemperature during springin Emerald Lake watershed. In a mid-latitude
willtrackairtemperature,
soit is unlikely
thatthetemper- alpine environment,above-freezingair temperaturesare
3048
MA•KSANDDOZIER:
CLIMATE
ANDENERGY
EXCHANGE
ATTHESNOW
SURFACE,
2
partsof thenetturbulent
transfer(H + LyE) at bothsites,
Emerald Lake Watershed, 1986 Water Year
MeanDailyH &LYE, OverSnow,
RidgeSite
I
I
I
I
1
I
I
....
thoughL•,E is slightlyfavored.We calculatethat626mmof
snowwater equivalent(SWE) sublimatedat the ridgesite
and487 mm of SWE sublimated
at the lake siteduringthe
,
I
I
150'
1986snowseason.
Turbulenttransferis slightlymoreimpor.
100
so
•
(Win-2)
j •3te4.
I•.• ,
.....
-100
L•E
-150 -
-
-200
Nov
Dec
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
MeanDailyH & LuE, OverSnow,lake Sit•
200•' ' ' ' ' ' ' ' ' '
'•"-- "•
....
•'"
•
'I
'-
' "•
tant at the ridge site than at the lake site, but althoughthe
magnitudesof both H and LyE are larger at the ridgesite
throughoutthe snowseason,differencesin the net turbulent
transfer are not large. Latent heat exchange dominatesat
both sites during winter but is replaced by sensibleheat
transfer during spring melt. Though the magnitudeof//
duringspringis largerthan L,,E duringwinter, L•,E is also
largeduringspring,unlike H duringwinter. The effectof//
on the net turbulent exchange is therefore reduced. The
crossoverbetween negative and positive net turbulentexchangeis made duringMay and June when H and L•,E are
about equal in magnitude.This is important becausethese
were the months of maximum snowmelt runoff generation
duringthe 1986snow season.Errors in the estimationof the
sumof H andLyE duringthis periodwould havea minimal
-150
-2•
¾
effect on calculation of snowmelt.
-
-
-
Nov
•
Fig. 3. D•y
I•
F•
•
Apr
•y
5•
l•
CONDUCTION AND ADVECTED HEAT TRANSFER
TO THE SNOWPACK
Aug
averageturbulent•ransfer(H and L•E), Hdgeand
lake sites, Emer•d Lake watershed, 1986 snow season.
Both conductive
and advective
heat transfer tend to be
small when comparedto the seasonalenergy balanceof the
snowpack.They can thereforebe ignoredor greatly simplified. One-dimensional,steady state heat flow in a homogelikely during part of the day throughoutthe snow season,
neous layer is
and very cold temperaturestend to occur duringperiodsof
low wind speeds. The air temperature did not go below
aT
G = K -(17)
freezing at either site after early springduring 1986.
For both to be positive the air must be warmer and more
humid than the snow surface. These conditions occurred
Because soil and snow temperatures near their interface
very infrequently during either snow season, only during are usually very similar, the calculation of heat transfer
stormsor during very cold, calm conditions.A warm rain
event duringspringwould be an extreme caseof combined
positiveturbulenttransferat the snowsurface,but theseare
Emerald Lake Watershed, 1986 Water Year
rare and of short duration.
MeanDailyH +LuE OverSnow,RidgeSite
Over time then, the magnitudesof sensibleand latent heat
transferover a snow surfaceare of oppositesign,and their
I
sum tends to minimize
their effect on the overall
,
,
,
I
,
I
,
J
150
0
transfer at the snow surface
during the 1986 snow season.
The valuesof the coefficientsa u, a e, k, do, and z0 used
-150
-200
in the turbulent transfer calculations are not precisely
known, although Brutsaert [1982] states that they can be
Nov
estimated to within 10% of their true values from an evaluation of conditions at the data collection site. The values
used for these calculations are in the notation list. This
uncertainty, however, affects the magnitudebut not the sign
of the calculations.
,
snow
surface energy balance. This sum, designated"net" turbulent transfer and shownas daily meansin Figure 4, illustrates
the overall effect of turbulent
'
Thus the sum of sensible and latent heat
transfer should not be affected over a period of a day or
Dec
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
MeanDailyH + LuE OverSnow,
200-I I I I I' 1 I I I
150
11X
-
.
•Wm
4
more. Mass flux will be affected, however. Calculations of
massflux are approximationswith an uncertaintyof at least
10% over a time period of a day or less. Over a longertime
periodthis uncertaintyshoulddiminishbecausepositiveand
3 summarizes
turbulent
-150
-200 -
negative errors will tend to cancel.
Table
-50
-100
heat and mass transfer
Nov
De.z:
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
during the 1986 snow season. Over the snow season, sensi-
Fig. 4. Daily average"net" turbulenttransfer(H + LYE), ridge
ble (H) and latent (L,,E) heat transfermake up aboutequal
and lake sites, Emerald Lake watershed, !986 snow season.
MARKS
ANDDOZIER:
CLIMATE
ANDENERGY
EXCHANGE
ATTHESNOW
SURFACE,
2
3049
TABLE 3. Turbulent
Transfer
Summary,
MonthlyFluxes,Emerald
LakeWatershed,
1986Snow
Season
Sensible Heat
Exchange
Net
(H +LvE)
H,
W m-2
Nov.
Dec.
Jan.
Feb.
March
April
-45
-26
-61
-43
-54
-59
10
0
7
8
12
27
May
June
July
Season
-8
32
42
-25
67
110
115
39
Nov.
Dec.
Jan.
Feb.
March
April
May
June
July
Season
-28
-59
-54
-28
-28
-33
-4
21
23
-21
8
21
16
7
18
15
50
92
69
33
Month
Latent Heat Exchange
Proportion LyE,
ofNet
W m-2
Proportion MassFlux,
ofNet
kgm-2
Ridge Site
0.16
0.02
0.09
0.13
0.!5
0.24
0.47
0.59
0.61
0.38
-55
-27
-68
-51
-67
-86
0.84
0.98
0.91
0.87
0.85
0.76
-51
-25
-61
-54
-61
-83
-75
-78
-73
-64
0.53
0.41
0.39
0.62
-65
-73
-64
-538
-35
-80
-70
-35
-46
-48
-54
-71
-46
-54
0.82
0.79
0.81
0.84
0.72
0.76
0.52
0.43
0.40
0.62
-34
-73
-64
-36
-43
-46
-49
-66
-40
-451
Lake Site
0.18
0.21
0.19
0.16
0.28
0.24
0.48
0.57
0.60
0.38
betweenthem is based on the assumption that the two
represent
homogeneouslayers in contactwith each other. If
Pø
[Ts'Ilnr
De=De,0
•aa
[TmeltJ
weknowthetemperature,
Ts,tandTg, of theselayersand
estimate
their thickness(usuallythe distanceof the temperaturemeasurement above and below the interface), heat
transfercan be approximated by
G=
2Kes,lKeg(Tg-Ts,t)
KegZs,l
+ KesdZg
(18)
(20)
The temperature exponent was empirically determined by
Andersonto be • 14. Becausethe temperature for a snow or
soil layer is nearly always close or equal to 273.16 K during
the snow season,and P a is always equal to or less than the
sealevel value, precisionof n r is not critical. The effective
diffusioncoefficientDe is always small and relatively stable,
Thethermalconductivity
of soil,Kg, is assumed
essen- varyingfrom10-5 downto around0.5 x 10-5 m-2 s-• for
tiallyconstant[Davis, !980]; we use the value for a moist
an air pressureof 65 kPa and snow temperaturesbetween
coarse
sand(2.2 J m-• K -• s-1) [Oke,1978].Therearea
273.16 and 250.0 K.
varietyof empirical methods for estimatingthe thermal
Thermalconductivitiesare adjustedfor vapor transportby
conductivity
of the snow as a function of density, summa- an empirical correction based on the effective diffusion
rizedby Yen[1969]and morerecentlyby Langham[1981]. coefficient(this is an empirical correctiondevelopedby
The methoddescribedby Yen [1965], selectedas most Anderson [1976] and is not dimensionally correct):
appropriatefor use in the Emerald Lake basin, is used to
computethermal conductivity of a snowpack layer as a
function
of snowdensity
Ps,l(kilograms
percubicmeteD:
2
Ks,l = 3.2238x 10-8 Ps,t
(19)
Because
the air fractionof the snowpackis alwaysat
Kes,l= Ks,1+ [ZvDeqs,l]
(21)
Keg= Kg + [LvDeqg]
(22)
While the latent heat of vaporization or sublimation is a
it is alwayslarge (>2.5 x 106 J
saturation,
andthe air fractionof soilis usuallyat saturation, functionof temperature,
vapor diffusion is estimated as a function of snow and soil
temperature
and air pressure.Both the snowand soilther-
kg-•), sothiscorrection
canhavetheeffectofincreasing
the
thermal conductivity of snow by a factor of 10 or more.
During springat EmeraldLake we found the following
malconductivities
Ks,t andKg arecorrected
for vapor typical
conditionsat the base of the snow cover:
diffusion
by addinga valuethat is basedon theirspecific
humidities
q•,landqgandthecalculated
vapordiffusion Ps= 600kg m-3
coefficientfor each. The effective diffusion coefficient for
Pa = 75 kPa
Ts,l= 273.16K
andsealevelairpressure
De,0wasdetermined
experimen- Tg=273.16K
watervapor in snow or a saturated,inorganicsoil at 0.0øC
tallyby Yen[1965]to be around10-5 m-2 s-•. Anderson De =1.351 x 10-5 m2 s-•
[!97.6]
developed
thefollowing
relationship
fordetermining qs,l= 4.847x 10-3
thediffusion
coefficient
at othertemperatures:
qg=4.847x 10-3
3050
MARKSANDDOZIER:CLIMATEANDENERGYEXCHANGE
AT THESNOWSURFACE,
2
TABLE 4. SnowcoverEnergyand MassBalanceSummary,MonthlyFluxes,EmeraldLake
Watershed, 1986 Snow Season
MassFlux, kgm-2
Energy
Transfer,
W m-2
Month
She
t
H + LyE
G
M
AQ
Nov.
Dec.
Jan.
Feb.
March
-5
-18
-1
-23
16
-45
-26
-61
-43
-54
7
5
4
3
2
-0
0
-0
2
-1
Ridge Site
-43
-51
-39
-25
-58
-61
-61
-54
-37
-61
0
0
0
-26
-18
0
0
0
-26
-18
298
413
152
1249
427
Aphl
May
23
40
-59
-8
2
1
0
-0
-34
33
-83
-65
-12
-8
-12
-261
49
34
2197
1905
June
86
32
1
0
119
-73
-4
-940
0
892
July
85
42
2
0
129
-64
-15
-1020
0
-538
-83
-2277
Total
Es
qbase qmelt [pppZpp] SWE
2622
247
635
726
1895
2243
0
-192
Lake Site
Nov.
Dec.
Jan.
Feb.
March
12
-!5
9
9
31
-28
-59
-54
-28
-28
8
8
6
5
3
-0
0
-0
2
-1
-8
-66
-39
-12
5
-34
-73
-64
-36
-43
0
0
0
-36
-25
0
0
0
-36
-40
298
413
152
1249
427
Apdl
May
37
44
-33
-4
2
1
0
-0
6
41
-46
-49
-13
-8
-47
-324
49
34
2169
1830
June
93
21
1
0
115
-66
-4
-908
0
856
July
94
23
1
0
118
-40
-11
-932
0
Tot•
Lv=2.834x 106J kg-1
Ks,t=0.0116
J m-1 K -1 s-1
Kg=2.2J m-I K-I s-1
Kes,l=O.1971
J m-1 K-I
Kea=2.3971
J m-• K-• s-1
Though there is nearly a twentyfold increase in the thermal
conductivity of the snow when it is corrected for vapor
diffusion,this is still a very low conductivity; it is more than
an order of magnitude lower that the corrected thermal
conductivity of the soil.
Heat transfer between the soil and the snowpack was
computedfor the ridge and lake sites for the 1986 snow
season.Included in Table 4 is a summary of these calculationsfor the 1986 snow season.The flux is small and slightly
positiveduringthe snow seasonat both sites. Over the snow
-442
-98
-2287
2622
264
604
692
1869
2213
0
-116
melt is 100% of total snowmelt only during February, with
surfacemelt beginningto contribute as early as March. The
contribution of base melt during the snowmelt monthsof
May, June, and July was insignificant at both sites.
Advected
heat transfer at the snow surface occurs when
mass,in the form of precipitation (rain or snow), is addedto
the snowpack. If there is a temperature differencebetween
the added precipitationand the snowpack, the energytransfer (Joulesper squaremeted is a function of the massadded
and the magnitudeof the temperature difference:
M = Cpppppzpp[TppTs]
(23)
Becausethe temperaturedifferenceis not likely to be large,
the magnitude of advection is largely controlled by the mass
of precipitation
(pppzpp)
deposited
on the snowsurface.
season
thisrepresents
anaverage
fluxof lessthan3 W m-2 Advection is treated as an event occurrence because no
at theridgesiteandlessthan4 W m-2 at thelakesite.This reliable data exist on deposition rates or conditions.The
flux is slightly larger at the lake site during winter than at the
ridge site, but by springboth sitesare the same. Though the
flux is small, it will generate melt at the base of the snow
cover once the temperature of the lower snow cover layer is
0øC. This had occurred by February at both sites, and as
shown in Table 4, significant base melt occurred at both
sites. The magnitude of soil heat flux decreased from midMarch until the end of the snow seasonbecauseliquid water
percolationinto the soil removesmost of the temperature
gradient,reducingbasemelt. Davis [1980], utilizinga similar
but more detailedmodel at severalsitesin the alpine Sierra
Nevada, got the sameresult becausetemperaturegradients
were always small. In February, base melt is equivalentin
magnitudeto evaporation at the lake site and to nearly half
the magnitude of evaporation at the ridge site. However,
qbasediminishes each month after that, until it is only
mean air temperatureduring the precipitation event is as-
sumedto be the precipitationtemperature.If precipitation
is
warmer than the snowpack,M will be positive. Advection
will be relatively smallunlessthe temperaturedifferenceis
large, which is not usually the case. Even rain-on-snow
events tend to be at or very close to freezing temperatures.
Heat transferduringrain on snowis usuallydominated
by
condensation
rather than advection.
Seventeenprecipitationeventswere recordedduringthe
1986 snow season. The total advected heat from all events
wasrelativelysmallduringthe 1986snowseason,thoughthe
massof depositionwas very large. The directionof the
transferhad no seasonalpattern,thoughmost of the advectedheattransferoccurredduringlarge-volume
eventsin
February and March.
Table 4 also summarizes advected heat and mass transfer
15-20%of the magnitudeof evaporativelossby May. Base for the 1986snowseason,presenting
monthlyfluxesand
melt represents100%of total snowmeltqrneltduringFebru- totals. (The November values include heat transfer and mass
ary, March, and April at the ridge site. At the lake site, base flux from Octoberprecipitationevents.) Advection is always
MARKS
AND
DOZIER:
CLIMATE
AND
ENERGY
EXCHANGE
ATTHE
SNOW
SURFACE,
2
3051
TABLE
5. Snow
Cover
Energy
Balance
Summary,
Monthly fluxes.Table5 presentsa summaryof the relativemagniPercentages,
EmeraldLake Watershed,1986SnowSeason
tudesof energytransfer,andTable 6 presentsa summaryof
,
the relative magnitudesof mass flux at both sites.
Proportionof EnergyTransfer
Month
Snet
H + LyE
Nov.
Dec.
Jan.
Feb.
March
April
May
June
July
0.09
0.37
0.02
0.32
0.22
0.28
0.82
0.72
0.66
0.79
0.53
0.92
0.61
0.74
0.70
0.16
0.27
0.32
Nov.
Dec.
Jan.
Feb.
March
April
May
June
July
0.25
0.18
0.13
0.20
0.49
0.51
0.90
0.81
0.80
0.58
0.72
0.78
0.64
0.44
0.46
0.08
0.18
0.19
In general,AQ is greaterin magnitudeat the ridge site
throughoutthe snowseason,thoughthis differenceis not
large.At the ridge site the transitionfrom a negativeto a
positiveAQ occursin late April or early May, while at the
lakesitethistransitionoccursin late February.The critical
termsin determining
the energyare net radiationSnet and
net turbulenttransferH + L•,E. As shown in Table 5,
turbulenttransferis moreimportantat the ridgesitethanat
the lake sitethroughoutthe snow season.It dominatesthe
energybalancethroughApril at the ridgesitebut dominates
onlyuntilFebruaryatthelakesite,whichcorresponds
to the
transitionof AQ fromnegativeto positiveat bothsites.The
importance
of energytransferby conduction
from the soil,
(7, is slightlygreaterat the lake site,but it is alwayssmall
andis especially
unimportant
duringspringmelt. Its signif-
G
M
AQ
0.12
0.10
0.06
0.04
0.03
0.02
0.02
0.01
0.03
0.00
0.00
0.00
0.03
0.01
0.00
0.00
0.00
0.00
1.00
1.00
1.00
!.00
1.00
1.00
1.00
1.00
1.00
0.17
0.10
0.09
0.11
0.05
0.03
0.02
0.01
0.01
0.00
0.00
0.00
0.05
0.02
0.00
0.00
0.00
0.00
1.00
1.00
1.00
1.00
1.00
of basemelt duringlate
1.00 icanceis primarilyin generation
AdvectedenergytransferM hasno
1.00 winterandearlyspring.
1.00 significant
effecton themagnitude
of AQ at eithersite.
1.00
The absoluteuncertaintyof the energytransferterms
Ridge Site
Lake Site
presentedcannotbe determinedin the field. However, an
estimateof the uncertaintyis presentedin Table 7 for the
criticalparameters
affecting
the magnitude
of eachenergy
season's
precipitation
occurred.
The massof precipitationtransferterm. Radiationand turbulent transfer each contribin thetotalenergybalance.
falling
during
a snowseason
willdominate
themagnitude
of uteabouthalfof theuncertainty
These
estimates
are
for
conditions
duringsnowmelt
andare
advected
heat transfer.The fact that the 1986snowseason
small,
butit was largestduringFebruarywhenmostof the
wasone of the largeston record makesit clear that the
basedon the estimatedprecisionof the recordeddata
for bothmeasurement
anddatarecordingerror.
magnitude
ofthisformofenergy
transfer
willalways
bevery accounting
They representthe maximumrangeof variancethat could
occurfor alltermsconsidered.
Uncertaintyshoulddiminish
small.
SNOWCOVERENERGYANDMASSBALANCE
if averaged
overa longerperiod,andit is likelythatthe
combination
of positiveand negativeerrors in individual
Theenergytransfertermsdiscussed
in previous
sections parameters would tend to cancel.
determine
the thermalconditionand the ablationratesfor
Figure 5 presentsdaily averagevaluesfor net all-wave
theseasonal
snowcover.To precisely
specify
theenergy radiationand net turbulentenergyexchange,calculated
andmass
balance
of the snowcoverrequires
a coupledusingsnowsurface
layertemperature
Ts, whichmakes
up
energy
balance
modelsuchasthatdescribed
by Anderson mostof the energybudgetat the ridgeandlake sites.It is
[1976].
Thiswasbeyond
thescope
ofthisinvestigation,
but noteworthy
thatthemagnitude
of thehourlyaverages
ofAQ
aneffort
wasmadetoindependently
estimate
themagnitudecanbelarge(greater
than-+500W m-2), though
thedaily
ofeach
formofenergy
transfer.
Table4presents
a summaryaverages
areseldom
greater
than---200
W m-2, andmonthly
oftheenergy
terms
estimated
independently
during
the1986 averagesare even smaller. The
effect of these short-term
snowseason,for the ridge and lake sites, and the mass periodsoflarge-magnitude
energyfluxonthe snowcoverare
balance
ofthesnow
cover
derived
fromtheestimated
energymaskedwhenonly longer-termaveragesare considered.
TABLE6. SnowCoverMassBalance
Summary,
Monthly
Percentages,
EmeraldLake
Watershed, 1986 Snow Season
RidgeSite,Proportion
Snowmelt
Month
Nov.
Dec.
Jan.
Feb.
March
April
May
June
July
Total
Precipitation Runoff
0.11
0.16
0.06
0.48
0.16
0.02
0.01
0.00
0.00
1.00
0.00
0.00
0.00
0.00
-0.01
-0.05
-0.23
-0.38
-0.26
-0.83
of Mass Flux
Evaporation Melt
-0.02
-0.02
-0.02
-0.02
-0.02
-0.03
-0.03
-0.03
-0.02
-0.21
0.00
0.00
0.00
-0.01
-0.01
-0.01
-0.10
-0.36
-0.39
-0.88
LakeSite,Proportion
of Mass Flux
Evaporation Melt
-0.01
-0.03
-0.02
-0.01
-0.02
-0.02
-0.02
-0.03
-0.02
-0.17
0.00
0.00
0.00
-0.01
-0.02
-0.02
-0.12
-0.35
-0.36
-0.88
3052
MARKS AND DOZIER: CLIMATE AND ENERGY EXCHANGEAT THE SNOW SURFACE,2
TABLE 7. Estimated Parameter Uncertainty, Melting
Conditions, Emerald Lake Watershed, Spring 1986
Uncertainty
terms.Evaporation
is calculated
fromlatentheatlossL,E,
Snet,so
I
$net,lw
-+10W m-2
-+10W m-2
depthtimesdensity(PvvZvv),
andtheestimated
SWEonthe
--+20
W m-2
-+10W m-2
+-5W m-2
ground at the end of the month is shown as cumulative
precipitationlessmelt and evaporativelosses.By the endof
Rvis
Rnir
ñ0.01
-+0.02
S,• lw
-+10Wm-2
es
Ts
-+0.001
-+0.01øC
and lake sites. Calculated snowmelt plus evaporationis
within7%, or 192mm of SWE, of the measuredprecipitation
at the ridge site and within 4%, or 119 mm of SWE, at the
lake site. This discrepancyis within the uncertainty of the
energybalance, and the precipitationdata, and is a good
verification of the energy flux calculationsduring snowmelt.
Parameter
Radiation
Sne
t
S 4,v
S ,[.nir
Turbulent Transfer
H
-+14 W m -2
LyE
--+6
W m-2
Ta
Ts
ea
es
u
zo
+-0-4øC
-+0.01øC
-+25 Pa
-+0.5 Pa
-+0.5 m s -•
-+0.0001m
G
-+0.5W m-2
Tg
Ts,l
Os
+0.25øC
-+0-25øC
-+25kgm-3
Advection
M
-+0.1 W m -2
Tpv
-+0.5øC
Ts
-+0.25øC
pv•
-+25kgm-3
Zpp
-+0.22m
Energy Balance
-+40.5 W
•Q
m
-2
This is especially true during spring melt when significant
melt may occur only during half of the diurnal cycle.
To evaluate changes in the relative magnitudes of net
and net turbulent
transfer we must consider that
net radiation is computed using Tso while net turbulent
transfer is computedusing Ts. During melting conditions
this is insignificant because snow temperaturesare constrainedto be 0øC.Duringwinter, however,estimatesof A Q
are much more uncertain
because combined
basemelt is from soilheatflux G, andtotal snowmeltisfrom
AQ. Mass input is shownas the total monthlyprecipitation
Julythesnowcoverhadessentially
ablatedat boththeridge
Estimates of snowmelt runoff shown in Table 6 are based
on measuredflow volumes from the outflow of Emerald Lake.
The basinis a granitecirque, with virtually no soil, and hasno
Conduction
radiation
Evaporation
Es,basemeltqbase,
andtotalsnowmelt
qmelt
shownin Table4 arecalculatedfromthe monthlyenergyflux
appreciablesubsurfacestorageor baseflow. In summer,rainfall on the watershedis measuredin the outflowdischarge
withinan hour or two. Effectivelyall the dischargeduringthe
snowseasonis from snowmelt.That the measureddischarge
duringthe snowseasonwas 83% of the measuredprecipitation
inputsuggests
that the volumeof evaporativelossshouldbeof
the order of 500 mm of water duringthe 1986 snow season,
whichis verifiedby both the relativemagnitudeandthe volume
of calculatedevaporationfrom the snow cover. Thoughthe
data indicate that the ridge and lake do not differ greatlyin
terms of energy transfer, we observed many locationsin the
watershedthat either receive more energy early in the season
or remain colder longer into the spring. The snow coverat
these sites either ablated earlier or persistedthroughoutthe
summer. This is reflected in the snowmelt runoff volumes,
which show initial melt occurringin March and April and
Emerald Lake Watershed, 1986 Water Year
MeanDailyRn & H +LoE , RidgeSit•
t I I I I I I
200
Rn
150
H+L•E
100
0/ ,, .....
a..•d•
effects of solar
heating and radiant cooling, and sensible warming and
evaporativecooling, all depend on the correct estimateof
snow surface temperature. The estimatesof latent heat and
mass flux using snow surface layer temperature Ts are
reasonable because the vapor source for the exchange is
likely to come from the upper 25 cm of the snow cover.
However, the estimates of sensibleheat flux during winter
'•1
I
Nov
I
•
I
J•
I
F•
MeanDailyRn & H +LyE, •e
[
I
I
,
I
•
I
A•
•y
Site
,
,'
I
,
,
]
usingsnowsurfacelayer temperatureassumethat Ts does
not depart significantlyfrom Ta and are thereforeof limited
magnitude.If a colder snow surfacetemperature,such as
Ts0, were used, the temperaturegradientbetweenthe snow
andthe atmosphere,and subsequentsensibleheating,would
be larger, and the magnitudeof net turbulent transfer would
be reduced during winter. Therefore our estimates of the
magnitudeof energyflux during winter are probablytoo
largebut are reliableduringthe snowmeltperiodof April,
May, June,andJulyat the lake siteandMay, June,andJuly
at the ridge site.
50 ,
,
•. .,j91d•,
j
o•,,..aa,, , a•.•^ •,•••,7.•'
-
' •
I• I
Nov
•
I
Jm
I
F•
I
•
I
A•
_
I
•y
I
J•
Fig. 5. DaVyaveragenet taxation •d "net" turbulentt•sfer
(Rn and H + LyE) for the ridge •d lake sites,Emer•d
watershed, 1986 snow season.
MARKS
ANDDOZIER:
CLIMATE
ANDENERGY
EXCHANGE
ATTHESNOWSURFACE,
2
3053
continuing
intoAugustandSeptember.
However,87%of the Kes,! effectivethermalconductivityof lower snowlayer
(J m-• K-1
mowmelt
runoffoccurred
in May, June,andJuly,andthese
volumes
correspond
closelywiththemeltvolumes
calculated K# thermalconductivity
of moistcoarsesandJOke,
1978](2.2J m- 1 K-l s- 1).
at theridgeand lake sites.Thesedataindicatethat the
-1
calculated
meltvolumesarereasonable,
eventhoughtheyare
Ks,l thermal
conductivity
of lowersnowlayer(J m
K-1
based
on generalized
characteristics
of the snowcoverand
L Obukhov stability length (m).
meteorologic
conditions.
L•, latentheatof vaporizationor sublimation
(J
SUMMARY AND CONCLUSIONS
Thispaperpresents
a detailedevaluation
of alpinesurface
climate,energyexchange,and snowmelt.A combinationof
meteorological
measurementsand model parameterswere
usedto calculatethe net energytransfer to the snow cover
bysolarandthermalradiation,sensible
andlatentheatexchange
with the atmosphere,
conduction
from the soil,and
advected
heattransferfrom precipitation.The magnitudeand
relativeimportanceof each form of energytransferwere
evaluated
to determinewhich measuredparameterswere most
critical
andwhattype of simplifyingassumptions
mightbeused
in snowmeltcalculations.During the 1986 snow season,net
radiation
contributedthe largestamountof energyfor snowmelt,followedby sensibleand latent heat exchange.Soil
conduction
and advectionprovidednegligibleenergyflux, but
soilconduction
generatedsignificantbasemeltduringmidwinter.Duringthe snowmeltseason(May, June,and July in 1986),
netradiationcontributed5 to 10 times the energyfor melt over
the combination of all other forms of heat transfer. This is an
encouraging
resultbecauseradiationis easilymeasured,andits
distribution
over a topographicsurface can be modeled. It
shouldbe noted, however, that this result was achieved at a
mid-latitude,
alpine site and may not be true duringsnowmelt
inforested,prairie, or high4atitudelocations.
Calculationsof snowmelt based on summingthe totals of
eachenergytransfer term resulted in a massbalance which
wasvery close to the measuredprecipitationinput, and to
measureddischarge from the watershed during the same
periodof time, showingthat the calculationsof energyflux
arereliable during melting conditions. The combinationof
meteorologicalmonitoring and physical measurementsof
snowfall
andthe seasonalsnowcover, andrelativelysimple
modelsof snow albedo and surfacetemperature,provided
adequate
inputdata for calculationsof energytransferin the
alpinewatershed.
NOTATION
L•,E latentheatexchange
(W m-2).
M heattransfer
by advection
(W m-2).
P0 reference
air pressure,
usuallystandard
sealevel
air pressure(101,342 Pa).
P a air pressure(Pa).
AQ change
in snowcoverenergy(W m-2).
Rnir near-infrared
(0.7-2.8/zm)albedo(dimensionless).
R vis visible(0.28-0.7 •m) albedo(dimensionless).
Snct netall-wave
radiation
(W m-2).
Oenet,/w
netthermal
radiation
(3.5-50
t•m;W m-2).
Snet,ni
r netnear-infrared
radiation
(0.7-2.8/•m;
W m-2).
Snet,so
I netsolar
radiation
(0.28-2.8/.cm;
W m-2).
Snet,vi
s netvisible
radiation
(0.28-2.8/•m;
W m-2).
$ irradiance
on snowsurface(W m-2).
lw thermalirradiance(3.5-50/.•m) on snowsurface
(W m-2).
nir near-infrared
irradiance(0.7-2.8 tzm)on snow
surface(W m-2).
sol solarirradiance(0.28-2.8 p,m)on snowsurface
(W m-2).
vis visibleirradiance(0.28-0.7/•m) on snowsurface
(W m-2).
SWE snow water equivalent (m H20).
T temperature (K or øC).
Ts averagetemperatureof the entire snow cover (K
or øC).
Ta air temperature (K or øC).
Tg soiltemperature
(K or øC).
True
k melting temperatureof ice (273.16 K).
Tpp precipitation
temperature
(K).
Ts snow surfacetemperature (K or øC).
T,,• averagelower snowlayer temperature(K).
Tso snow surfaceskin temperature (K or øC).
a, ratio of eddy diffusivity and viscosityfor water
a•
vapor (•--1.0, dimensionless).
ratio of eddy diffusivity and viscosity for heat
(= 1.0, dimensionless).
Cp specific
heatof dry air, constant
pressure
(1005J
kg-1 K-l).
do zero-planedisplacementheight(=(2/3)7.35z0, m).
Cpp specific
heatofprecipitation,
ice,orwater(Jkg-
k yon Karman's constant (=0.40, dimensionless).
n r temperatureexponent for calculation of diffusion
De (=14, dimensionless).
K-l).
De effective
vapordiffusion
coefficient
(m2 s-•).
De,0 effectivevapordiffusioncoefficient
at sealevelair
pressure
and0.0øC(m2 s- 1).
E massflux by evaporationor condensation
from
thesnowsurface(kgm
Es massof evaporationor condensation
fromentire
snowcover(kgm-2).
G heattransferby conductionand diffusionbetween
snowcoverandsoil(W m-2).
H sensible
heatexchange
(Wm-:).
K thermal
conductivity
(J m- 1 K- • s- l).
Key effectivethermalconductivity
of the soillayer(J
m-• K-! s-l).
g acceleration
of gravity(9.80616m s-2).
q specific
humidity
of theair(g kg-•,
dimensionless).
qbase snowmeltvolume from the base of the snow
cover(kg m-2).
qa specific
humidity
of thesoillayer(g kg-1,
dimensionless).
qmelt snowmeltvolumefrom entire snowcover (kg
m-2).
qs specific
humidity
at thesnowsurface
(g kg-•,
dimensionless).
qs,• specific
humidity
of thelowersnowlayer(g kg-1,
dimensionless).
3054
MARKS AND DOZIER: CLIMATEAND ENERGYEXCHANGEAT THE SNOWSURFACE,2
r
effective snow grain radius (/am).
u windspeed(m s-•).
u* frictionvelocity(m s-•).
z height, length, depth, or thickness(m).
z0 snowsurfaceroughnesslength(in the range 1.0 x
zt
snowpack,
M.A. thesis,
60pp.,Dep.of Geogr.,Univ.ofCalif.,
Santa Barbara, 1980.
Davis, R. E., and D. Marks, Undisturbedmeasurement
of the
energyandmassbalanceof a deepalpinesnowcover,
Proc.West.
Snow Conf., 48, 62-67, 1980.
Davis, R. E., J. Dozier, and D. Marks, Micrometeorological
mea-
10-4 to 5.0 x 10-3 m).
surements
andinstrumentation
in supportof remotesensing
heightabovesnowsurfaceof air temperature
52, 161-164, 1984.
measurement (m).
za depthbelowsoilsurface
of soiltemperature
measurement (m).
z•,•, depthof precipitation
(m).
zq heightabovesnowsurface
of humidity
measurement (m).
Zsd thicknessof the lower snowlayer (m).
zu heightabove snow surfaceof wind speed
measurement (m).
19 potential temperature (K).
O a potential temperatureat the air temperature
measurement elevation (K).
Os potential temperatureat the snow surface
elevation (K).
Fs snow surfaceemissivity(-•0.99, dimensionless).
ps average density of the entire snow cover (kg
observations
of analpinesnowcover,Proc.West.SnowConf.,
Dozier, J., A clear-skyspectralsolar radiation model for snow-
coveredmountainous
terrain,WaterResour.Res.,16, 709-7i8,
1980.
Dozier, J., and S. G. Warren, Effect of viewing angleon the infrared
brightnesstemperatureof snow, Water Resour. Res., 18, 14241434, 1982.
Fleagle,R. G., andJ. A. Businger,An Introductionto Atmospheric
Physics,2nd ed., 432 pp., Academic, San Diego, Calif., 1980.
Langham,E. J., Physicsand propertiesof snowcover,in Handbook
of Snow,editedby D. M. Gray and D. H. Male, pp. 275-337,
Pergamon, New York, 1981.
Male, D. H., andR. J. Granger,Snowsurfaceenergyexchange,
Water Resour. Res., 17, 609-627, 1981.
Marks, D., Climate, energy exchange, and snowmelt in Emerald
Lakewatershed,
SierraNevada,Ph.D.dissertation,
158pp.,Dep.
of Geogr. and Mech. Eng., Univ. of Calif., Santa Barbara, 1988.
Marks, D., and J. Dozier, A clear-sky longwave radiation modelfor
remote alpine areas,Arch. Meteorol. Geophys. Bioklimatol., Ser.
B, 27, 159-187, 1979.
Marks,D., J. Dozier,andR. E. Davis,Climateandenergyexchange
m-3).
pp•, density
ofprecipitation
(kgm-3).
Ps densityof a snowcoverlayer(kgm-3).
Ps,l average
density
ofthelowersnowlayer(kgm-3).
cr Stefan-Boltzmann
constant
(5.6697x 10-8 W
m-2 K-i).
ff stability factor for calculation of turbulent transfer
H and Lv E (dimensionless).
at the snow surfacein the alpine region of the Sierra Nevada,1,
Meteorological measurements and monitoring, Water Reso•.
Res., this issue.
Marshall, S. E., and S. G. Warren, Parameterization of snow albedo
for climate models, in Large Scale Effects of Seasonal Snow
Cover, IAHS-AIHS Publ. I66, edited by B. E. Goodison, R. G.
Barry, and J. Dozier, pp. 43-50, International Associationof
Hydrological Sciences,Wallingford, England, 1987.
Monteith, J. L., Principles of Environmental Physics, 241 pp.,
Edward Arnold, Baltimore, Md., 1973.
Acknowledgments. This work was funded by California Air
ResourcesBoard grant CARB-A3-106-32. Additional supportcame
from University of California Water ResourcesCenter grant W-546,
NASA grant NAS5-28770, and the U.S. Environmental Protection
Agency through contract 68-C8-0006 with ManTech Environmental
Technology.This documentwas preparedat the EPA Environmental ResearchLaboratory in Corvallis, Oregon.It hasbeensubjected
to the Agency's peer and administrativereview and approvedfor
publication. All references to specific manufacturers,instrument
brand names, or model types are for informationpurposesand are
not to be considered a product endorsementby the author, the
University of California, NASA, EPA, or the California Air Resources Board.
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