Biogeochemistry of Seasonally Snow-Covered Catchments (Proceedings of a Boulder Symposium,
July 1995). IAHS Publ. no. 228, 1995.
157
Snow surface energy exchanges and snownielt at a
continental alpine site
DON CLINE
Department of Geography, University of Colorado, Boulder, Colorado 80309, USA
Abstract The energy balance of an alpine snowpack was studied during
the 1994 snowmelt season at Niwot Ridge (3517 m a.s.L, 40°03'N,
105°35'W), an alpine site in the Colorado Front Range. Radiative,
turbulent, and soil energy fluxes, and snowmelt were measured. Prior to
the onset of snowmelt, the high albedo of the snowpack ( » 90%)
coupled with nearly constant longwave losses caused the daytime
maximum net radiation to remain below 100 W m"2. As the snow albedo
decreased with age, the daytime net radiation receipts began to increase,
and melt began. Little additional snow accumulation occurred following
the beginning of snowmelt, so the albedo continued to decrease to a
seasonal minimum of less than 60%. Consequently, daytime maximum
net radiation increased during this period, and a typical diurnal pattern
of daytime snowmelt ensued. Net radiative fluxes provided 75% of the
total energy available for snowmelt during the season. During this
period, the turbulent fluxes were of small magnitude and usually of
opposite sign, with latent heat losses and slightly larger sensible heat
gains. The net energy supplied by turbulent sources was 25% of the
seasonal total.
INTRODUCTION
To understand and model hydrologie and biogeochemical transfers within snowmeltdominated alpine basins, both under the current climate regime and under changing
climate conditions, we require a thorough understanding of the energy transfers between
the snowpack and the atmosphere. These transfers lead to a gain in energy within the
snowpack and eventually cause snowmelt. The two main components of snowpack
energy transfer are radiative energy exchange, consisting of shortwave (solar) and longwave (terrestrial) energy receipts and losses, and turbulent energy exchange, sensible and
latent heat that is transferred between the surface and the atmosphere by turbulent
processes. A third, but frequently negligible component is energy exchange between the
base of the snowpack and the ground. Numerous studies have examined snowpack
energy exchanges, however relatively few have examined these exchanges for entire
snowmelt seasons. Rarer still are season-long studies at high-altitude locations, thus our
understanding of snowpack energy transfers in high-alpine basins is quite limited.
The purpose of this paper is to examine the role and importance of each of the
components of snow surface energy exchange at a continental alpine site for a complete
snowmelt season. The methods used here to examine the snowpack energy balance and
its components are described below, followed by a brief discussion of the results. The
Don Cline
158
motivation for this study is to provide information for the development of spatiallydistributed physically-based snowmelt models for use in alpine basins.
Site description
The data reported here were collected during the snowmelt season at Niwot Ridge on the
eastern slope of the Front Range of Colorado (3517 m a.s.l., 40°03'N, 105°35'W).
Niwot Ridge is a 10 km interfluve extending eastward from the Continental Divide, and
is characterized by low weathered hills with shallow saddles in between. Treeline in this
area is at approximately 3350 m. The instrument site is located in a relatively flat area
within a broad saddle of the ridge.
The Front Range of Colorado has a dry continental climatological setting due to its
distance from the Pacific coast. Most of the precipitation received at Niwot Ridge
arrives during early spring, as moist air from the Gulf of Mexico is drawn northward
(Barry, 1992). The high elevation and exposure of Niwot Ridge, and typically dry
atmospheric conditions result in large clear-sky atmospheric transmissivity, increased
solar insolation, low magnitudes of incident longwave radiation, low air temperatures,
and high wind velocities. The depth of snow accumulation on Niwot Ridge is extremely
variable, being influenced by the interaction of high wind velocities and topography.
Windswept areas devoid of snow may be found immediately adjacent to depositional
areas with accumulations in excess of 8 m.
METHODOLOGY
The physics of energy exchange at the snow surface are not unique in alpine
environments, although environmental conditions common in the alpine may represent
extreme cases of factors influencing the rate and magnitude of snow surface energy
exchange there. Radiative and turbulent transfer are the two most important processes
affecting snow surface energy exchange. Details of these processes have been reviewed
by many authors, including Obled & Harder (1979) and Male & Granger (1981). The
methods used in this study are described below.
Energy balance
Considered as a volume, the energy balance of a snowpack may be written as (Oke,
1990):
AQS + AQM = Q* +QH + QE + QG
(1)
where:
AQS is the convergence or divergence of sensible heat fluxes within the snowpack
volume,
AQM is the latent heat storage change due to melting or freezing,
Q* is the net all-wave radiation flux,
QH is the sensible heat flux,
Snow surface energy exchanges and snowmelt at a continental alpine site
159
QE is the latent heat flux, and
QG is the ground heat flux.
Thus positive values of radiative and turbulent fluxes indicate a gain of energy in the
snowpack, and negative values indicate a loss of energy in the snowpack. These changes
in energy either change the temperature or the phase of the snowpack. This sign
convention is used throughout the remainder of this paper.
Radiative fluxes
The net all-wave radiation flux is the balance of the incident and reflected shortwave
radiation and the incident and emitted longwave radiation, and is expressed as:
Q* = Ki(l - a) + (Li - LÎ)
= (Ki - Kt) + (Li - L t )
= K* +L*
(2)
where:
Ki is the incident shortwave radiation,
a
is the shortwave albedo of the snow surface,
Kf is the reflected shortwave radiation,
Li
is the incident longwave radiation,
L Î is the emitted longwave radiation,
K* is the net shortwave radiative flux, and
L* is the net longwave radiative flux.
The net all-wave radiation flux was measured directly and each of the four radiative
components were measured individually. The instruments used and their specifications
are shown in Table 1.
Table 1 Instruments used in this study, and their specifications.
Parameter
Instrument
Model
Range
Accuracy
Ki,Kt
Ll.Lt
T
RH
u
P
pyranometer
pyranometer
thermistor
capacitance
propeller
capacitance
Kipp & Zonen CM14
Kipp & Zonen CG2
Vaisala HMP35C
Vaisala HMP35C
Young 05103
AIR-DB-2BX
305-2800nm
5-25 nm
-33°-48°C
0-100%
0.60 ms"1
475-825 mb
+5%
±10%
±0.4°C
+1%
±2%
±0.01 mb
Turbulent fluxes
The sensible and latent heat fluxes were estimated using aerodynamic formulae with
corrections for stability. The sensible heat flux through the surface boundary layer is
expressed as:
Don Cline
160
QH
k «?, - e.)
k (u2 - «,)
4>H (ln(z 2 /z 1
<t>M ln(z,/z
•2"<-i;
(3)
= P (Cp)
and the latent heat flux is expressed as:
' k (q2 - qy)
QE
k (u2 - w,)
= P (Lv)
(4)
<i>E ( M V Z i
'M
H*2'4
where:
p is the density of air,
Cp is the specific heat of air at a constant pressure,
Lv is the latent heat of vaporization of water,
k is von Karman's constant,
4>H is the stability function for heat,
4>E is the stability function for water vapor,
4>M is the stability function for momentum,
Zj and z2 are the instrument heights in the profile,
d] and 62 are the potential temperatures at the given profile height,
q1 and q2 are the specific humidities at the given profile height, and
Uj and u2 are the horizontal wind speeds at the given profile height.
The specific humidity at each level in the profile was determined by (Saucier, 1983):
<? =
0.622(g)
P - 0.378(e)
(5)
where:
P is the atmospheric pressure,
e is the vapor pressure, calculated from the equation:
es(RH)
e =
io<r
(6)
where:
RH is the relative humidity at a given level, and
es is the saturation vapor pressure over ice, calculated from the equation:
e s = 6.11 mb x \o"Ti(T*b)
where:
T is the air temperature (°C) at each level, and
a and b are constants.
(7)
Snow surface energy exchanges and snowmelt at a continental alpine site
161
Table 2 Equations used for calculations of stability functions.
Stability
Richardson criteria
Function
Ri < -0.03
-0.03 < Ri < 0
0 < Ri < 0.19
*M
*M
(1 - lmy025
1-3(*M)
(1 - 18/tt)"0'25
*M
*M
*M
*M
*H
*M
*M
The stability functions were calculated as a function of the Richardson number (Ri) as
described by Ohmura (1981) using the equations shown in Table 2. The Richardson
number was determined by:
Ri = 1
Ôd/ôz
(8)
{ôu/ôzf
where g is the acceleration due to gravity.
Temperature, relative humidity, and wind speed were measured at three levels above
the snow surface. The instruments were mounted on a movable support attached to a
fixed mast; the support was repositioned regularly to maintain instrument heights of
0.5 m, 1.0 m, and 2.0 m above the snow surface. The estimation of turbulent fluxes as
shown in equations (3) and (4) assumes that the fluxes are constant in the atmospheric
layer being measured. However during blowing snow conditions, sublimating ice
particles act as sources of water vapor and sinks of latent heat in the atmosphere, and
the sensible and latent heatfluxesare not vertically constant (Morris, 1989). In an effort
to compensate for this problem, fluxes were calculated between 2.0 m and 1.0 m,
between 1.0 m and 0.5 m, and between 2.0 m and 0.5 m. The averages of these three
flux-interval calculations are reported here. A more appropriate approach towards
calculating the temperature and humidity profiles under blowing snow conditions is
described by Schmidt (1982), but this approach was not feasible for this study.
Ground heat flux
The flow of heat through the soil was measured using a heat flux plate placed 0.05 m
below the soil-snow interface. No significant heat exchange occurred through this level
until the snowpack became very thin near the end of the snowmelt season. Therefore,
no further consideration of the ground heat flux will be given here.
Sensible and latent heat storage changes within the snowpack
Changes in the internal energy of the snowpack are calculated as a residual using
equation (1). Snowmelt was measured using draining lysimeters located approximately
3 m from the instrument tower. The term (AQS + AQM) was converted to mass units
using the latent heat of fusion of water to allow comparison to measured snowmelt.
Don Cline
162
RESULTS
The 1994 snowmelt season discussed in this paper began at maximum accumulation in
the spring of 1994 (25 April, Julian Day (JD) 115) and continued until the snowpack had
ablated completely (6 June 1994, JD 157). The patterns of air temperature, specific
humidity, wind speed, and air pressure during this period are shown in Fig. 1.
Following JD 125, the mean daily air temperature remained above freezing nearly every
day. Although a diurnal fluctuation in specific humidity was evident, there was no
apparent seasonal trend while snow remained on the ground. Wind speed was often quite
variable throughout the day. In general, windier days were associated with the passage
of frontal systems, as indicated by drops in atmospheric pressure.
At the beginning of this study period, the measured snow depth at the instrument site
was 1.29 m, with 0.49 m water equivalence. Snowfall occurred intermittently during
this period, which affected the surface albedo briefly but did not produce significant
additional accumulation.
Complete Ablation
5 670
<- 660
S 650
Q.
640
125
135
Julian Day
155
165
175
Fig. 1 Seasonal patterns of air temperature, specific humidity, wind speed, and
atmospheric pressure recorded at the 2 m level. Complete ablation of the snowpack
beneath the instrument tower occurred on JD 157. In this and subsequent figures, a
brief period following complete ablation is shown to provide some insight of the
characteristics of each factor when snow is not present, but this period is not discussed
in the text.
Snow surface energy exchanges and snowmelt at a continental alpine site
163
Energy fluxes
The patterns of the snow surface albedo, and net shortwave, net longwave, sensible, and
latent heat fluxes are shown in Fig. 2. The albedo was approximately 0.90 following the
last major accumulation of snow of the season. Aging of the snow resulted in a gradual
decrease of the albedo over time, punctuated by brief increases whenever additional
snowfalls occurred. These snowfall events did not produce significant additional
accumulation, and either melted quickly or were blown off of the older, harder snow
surface such that the albedo quickly returned to pre-event levels. The mean albedo for
the entire period was 0.66.
The influence of albedo on K* can be clearly seen, as K* increased from a daytime
maximum of ~ 200 W m~2 early in the season when the albedo was high, to nearly 800
W m~2 prior to complete disappearance of the snowpack. While snow was present and
the atmosphere was clear, L* was an energy sink of up to -126 W m"2. A reduction in
the magnitude of this loss occurred whenever cloud cover was present; under overcast
conditions LA andLT approximately balanced and L* approached zero.
125
135
Complete Ablation
1000
800
600
400 200
0
^f^mPr^W'
-200
175
1000
800 600
400 200
0 -200
125
135
J u l i a n Day
155
165
175
Fig. 2 Seasonal patterns of snow surface albedo, and energy fluxes of .£*, L *, QH, and
QE. The points shown in the plot of albedo are only those that occurred while the cosine
of the solar incidence angle was greater than 0.5 (solar elevation greater than 66°) to
reduce errant values due to low sun angles. The line shown connects the daily median
albedo.
Don Cline
164
Although the magnitude of L* was much less than that of K*, it was a relatively
constant flux both day and night (unless clouds were present) compared to K* which of
course was only present during the daytime. The mean daily L* was -58.3 W m"2.
Although the mean daytime K* was 190.6 W m 2, the mean daily K* (day and night) was
only 96.5 W nf2. Therefore over the entire snowmelt season, radiative processes
resulted in a mean rate of energy flow directed towards the snowpack of only 38.2 W
m"2. Thus nocturnal longwave energy losses were clearly important in terms of the
seasonal energy balance, as discussed below.
The fluxes of sensible and latent heat are shown using the same vertical scale as used
for the radiative fluxes to illustrate the small magnitudes of QH and QE compared to K*.
QH was almost always a source of energy to the snow surface, with a mean value of
28.4Wm' 2 . Conversely, QE was almost always an energy sink with a mean of -15.6
W m"2. Similar to the net radiative exchanges, the turbulent transport processes resulted
in a mean flow of energy directed towards the snowpack of 12.8 W m"2.
Cumulative energy gains and losses by K*, L*, QH, and QE
The fluxes of K*, L*, QH, and QE were integrated to determine the total amount of
energy supplied by each. As indicated by the mean flux values, K* and QHwere energy
sources, contributing a total of 349.6 and 103.0 MJ, respectively; L* and QE were
(a)
600
"
COHplete Ablation
200
^
—
QH_
-200
Lx
125
(b)
100
Julian Day
Fig. 3 Cumulative totals of energy (MJ) over the snowmelt season: (a) individual fluxes
of K*, L*, QH, and QE, and (b) net radiative fluxes and net turbulent fluxes.
Snow surface energy exchanges and snowmelt at a continental alpine site
165
energy sinks, with total losses of -211.3 and -56.7 MJ, respectively. The net energy
gain over the period was 184.6 MJ. The cumulative totals over time for each component
(Fig. 3(a)) indicate that these relationships between the sources and sinks remained fairly
stable throughout the snowmelt season.
The net cumulative totals of radiative energy (Q* = K* + L*) and of turbulent
energy (QH + QE) are shown in Fig. 3(b). Prior to JD 125, Q* remained approximately
balanced by net turbulent losses. After JD 125, the net turbulent transfer was positive.
This change in sign coincided with the onset of recorded melt draining from the base of
the snowpack, discussed below.
Energy balance, snowmelt, and sublimation
The snowpack energy balance was calculated using equation 1. The cumulative total of
snowmelt calculated from (AQS + AQM) is shown in Fig. 4(a) along with the cumulative
total of snowmelt measured at the nearest lysimeter. Melt was first observed draining
through the lysimeter on JD 126. The calculated melt began four days prior on JD 122,
but progressed at approximately the same rate as the measured melt. The total depth of
calculated snowmelt was 555 mm. The difference in time between complete ablation at
(a)
600
r-,
5 0 0
complete Ablation
u
300
™
200
"
100
(b)
15 -
Julian Day
Fig. 4 (a) Cumulative totals over the snowmelt season of measured snowmelt, snowmelt
calculated from the energy balance, and (b) sublimation calculated from the latent heat
flux.
166
Don Cline
the instrument tower and the end of snowmelt at the lysimeter is explained simply by a
shallower snowpack at the lysimeter. Sublimation losses calculated from QE (shown in
Fig. 4(b)) amounted to an additional water loss of 20 mm.
By adding the calculated sublimation loss to the calculated snowmelt, the total
calculated water content of the snowpack at the beginning of the season was 575 mm,
a difference of 17% from the measured water equivalence. Informally considering the
margins of error expected from the radiation instruments (5-10%), the turbulent flux
models ( = 20%), and the measurement of snow water equivalence (5-10%), this
difference is considered to be small. More importantly, the rates of measured and
calculated snowmelt appear to fit well, suggesting that the energy balance calculated
here is reasonably accurate.
Acknowledgments This work could not have been completed without logistical and
financial support provided by the Niwot Ridge Long-Term Ecological Research project
(NSF DEB 9211776), the Mountain Research Station (BIR 9115097), the National
Biological Service Global Change Research program (Colorado Rockies Biogeographic
Area) (COLR-R92-0201 ), a Doctoral Dissertation Research Improvement grant from the
NSF Geography and Regional Science Program (SBR-9304604), and by the NASA
Earth Observing System program (NAGW-2602). Tim Bardsley and Mark Losleben
provided field assistance for this project; Losleben also provided the atmospheric
pressure data. Mark Williams provided the snowmelt lysimeter data. Kelly Elder
provided valuable comments on an earlier draft of this manuscript.
REFERENCES
Barry, R. G. (1992) Mountain Weather and Climate, 2nd edn. Routledge, London.
Male, D. H. & Granger, R. J. (1981) Snow surface energy exchange. Wat. Resour. Res. 17, 609-627.
Morris, E. M. (1989) Turbulent transfer over snow and ice. /. Hydrol. 105, 205-223.
Obled, Ch. & Harder, H. (1979) A review of snow melt in the mountain environment. In: Proceedings on Modeling of
Snowcover Runoff (ed. by S. C. Colbeck & M. Ray), 179-204. U.S. Army Cold Regions Research Engineering
Laboratory, Hanover, New Hampshire.
Ohmura, A. (1981) Climate and energy balanceon arctic tundra. Axel Heiberg Island, Canadian Arctic Archipelago, spring
and summer 1969, 1970, and 1972. Ziircher Geographische Schriften, 3. ETH Geographisches Institut, Zurich.
Oke, T. R. (1990) Boundary Layer Climates, 2nd edn. Routledge, London.
Saucier, W. J. (1983) Principles of Meteorological Analysis. Dover, New York.
Schmidt, R. A. (1982) Vertical profiles of wind speed, snow concentration and humidity in blowing snow. Bound. Lay. Met.
23, 233-246.