Download Ventilation experiments in a seasonal snow cover

Biogeochemistry of Seasonally Snow-Covered Catchments (Proceedings of a Boulder Symposium,
July 1995). IAHS Publ. no. 228, 1995.
41
Ventilation experiments in a seasonal snow cover
MARY R. ALBERT & JANET P. HARDY
U.S. Army Cold Regions Research and Engineering Laboratory, 72 Lyme Road,
Hanover, New Hampshire 03755, USA
Abstract The effects of induced air flow through a layered, seasonal
snowpack due to an imposed horizontally varying surface pressure
distribution are described. Results of a field experiment show that the
thermal signature of air flow through the snow occurred within minutes
of imposition of a surface pressure disturbance and became evident over
much of the 28-cm-deep snowpack. In this low-density snowpack, small
pressure variations (less than three Pascals) were sufficient to cause
significant air movement in the pack. Numerical heat and mass transfer
simulations of the experiment are described. There is very good
agreement between model calculations and measured snowpack
temperatures, which demonstrate diffusion-controlledheattransfer before
the onset of air flow, advection-controlled transfer during the ventilation,
and return to diffusion-dominated transport after ventilation ceased.
INTRODUCTION
The transport of heat, mass, and chemical species through porous media may result from
diffusion, natural convection, or forced convection. In naturally occurring dry snow,
diffusion is commonly presumed to be the dominant exchange mechanism. However,
if natural convection or ventilation (forced convection due to surface pressure gradients)
occur, the potential for rapid transport of heat or gas through the snow is greatly
increased. Knowledge about convective and advective processes in snow and verification
of a working model are important for interpretation of gas flux measurements made in
seasonal snow, and for interpretation of polar ice core records in glacial firn.
There is field evidence that air flow through snow due to natural convection and
ventilation may occur in a natural snow cover. Sturm & Johnson (1991) documented
snow temperature profiles that indicate natural convection effects in a highly permeable
Alaskan snowpack. Benson (1962) found that near-surface (to depths of 1.6 m) snow
temperature changes in Greenland were faster than could be explained by heat
conduction, and attributed the differences to heat advected by ventilation. Clarke et al.
(1987) found warming of the firn in windy areas of Agassiz Ice Cap that cannot be
explained by heat diffusion.
Numerical results give insight into the nature of the effects of ventilation processes.
Albert & McGilvary (1992) presented a numerical model for advective heat and vapor
transport through snow. In one-dimensional simulations, they showed that conductive
and advective vapor transport effects in ventilated dry snow are secondary contributors
to resulting temperature profiles, even though they are important to mass transfer. It was
demonstrated that the major thermal effects of ventilation are controlled by the heat
Mary R. Albert & Janet P. Hardy
42
carried by dry air through the snow and heat conduction due to the temperatures imposed
at the boundaries.
Pressure variations on the snow surface are a forcing mechanism for ventilation of
snow. While no surface pressure measurements have been reported for ventilation, there
have been relevant theoretical calculations. Colbeck (1989) showed that dunes on the
snow surface cause pressure variations from form drag of the air flow across the surface.
Clarke & Waddington (1991) showed that the depth attenuation of surface pressure
fluctuations (due to turbulent air flow over flat terrain) is influenced by both the
temporal and spatial frequency of the pressure signal. Albert (1993) showed that
resulting temperature profiles during ventilation are fairly insensitive to the frequency
in time of sinusoidal surface-pressure forcing as long as the surface pressure amplitude
is sufficient to sustain air movement in the snow.
Clearly, theoretical estimates of ventilation effects need to be verified with field data
before they are applied to gas flux problems. The purpose of this study is to quantify the
effects of air movement through a natural, layered seasonal snow cover under known
(controlled and measured) surface pressure forcing conditions. The theory of air
movement through snow and the numerical model to be used are presented. Results of
a field test of surface pressure variations imposed on an undisturbed natural snow cover
are described, and the field data are compared with numerical simulations.
THEORY
The air flow is assumed to follow Darcy's law, where the Darcy velocity or volumetric
flux of the air, v(-, is given by
v,. =
- ^
dP_
dx,
(1)
where buoyancy effects are neglected, P is pressure, x, is coordinate direction (/' = 1,2
for the current discussion of two dimensions), ky is permeability, and n is viscosity. The
flow of air through snow in the field is sufficiently slow that air is treated as an
incompressible medium. Conservation of mass is combined with the definition of the
Darcy velocity to give the single equation which governs air flow through ventilation
effects:
a
dP
dxi
dXj
(2)
Heat transport follows an advection-diffusion equation:
-p's
dt
dT
dx,
_d_
dx,
x
dT
» dXj
Qi
(3)
where the heat capacity of the snow is determined by contributions from the air and ice
that comprise snow:
Ventilation experiments in a seasonal snow cover
{pcp\ = <A(pcpa + (l-0)(pCp,.
43
(4)
Here T is temperature, t is time, cp is specific heat, X(y is thermal conductivity, <j> is
porosity, p is density, subscripts s, a, and / denote snow, air, and ice, respectively, and
QT is the thermal source term.
Equation (1) shows that the air flow is driven by the pressure field, and the
permeability regulates the amount of air that can flow for any given set of pressure
conditions. The resulting temperature distribution will depend on the thermal boundary
conditions, and is affected by air flow velocity, thermal conductivity, and any thermal
source in the medium. For the experiment described below, there is no appreciable
thermal source in the snow, so that QT is zero. These equations are solved using a finite
element code developed at CRREL, as described by Albert & McGilvary (1992). The
air flow is calculated from equations (1) and (2), with pressure boundary conditions as
measured in the field experiment. The snow permeability values are also taken from
field measurements, as described below. Equation (3) then calculates the snow
temperature field, using the calculated velocities. Temperature boundary conditions are
taken from the measured snow surface and base temperatures. The thermal conductivity
of the snow was inferred from snow density measurements, as described by Mellor
(1977).
THE EXPERIMENT
The ventilation experiment was carried out on a layered, early-season natural snowpack
at the Sleepers River Research Watershed in northern Vermont. A one-dimensional
vertical array of 30-gauge thermocouples were placed at the site in the fall before
snowfall began, and the thermocouples became covered by naturally-falling snow, with
snow layering resulting primarily from different storm events. Temperatures from these
thermocouples were continuously recorded on a Campbell data logger. Detailed snowpit
observations of the snow stratigraphy, density, crystal type classification (Colbeck etal.,
1990), and grain size distribution were made on the day of the ventilation experiment.
The vertical snowpack profile is shown in Fig. 1. The day chosen for the testing had
overcast skies, no natural wind, and the snow surface was flat, with no drifts or sastrugi.
Snow surface pressure forcing
In order to induce a spatially varying pressure distribution across the snow surface
without disturbing the natural snow surface, a fan was placed on the snow surface beside
the testing site, such that the thermocouple array was 70 cm in front of the fan (Fig. 2).
The fan was oriented to produce a steady, horizontal air flow, primarily parallel to the
snow surface. The blades of the fan serve to induce pressure variations that vary with
the distance away from the fan. The moderate fan speed did not cause any visible
saltation or movement of the grains on the snow surface. After the ventilation
experiment was finished, the pressure distribution from the fan was measured using
pressure transducers at locations along the air flow direction. While pressure
Mary R. Albert & Janet P. Hardy
44
-)(- Stellar Dendrites
/
30
Q ] Faceted Particles
Broken G ains
1
W
j
I
1
I
-
/
D
-
o
Snow Height
i
u
Basal Ice
Mixed Grains
*
Ê20--
M
1
•'T™0
100
_
w
• " • " " * ! " ,
1
f-V
200
,
1
r
|
tBBBHEB
300
25
50
75x10^
Permeability (m 2 )
Snow Density (kg/m 3 )
Fig. 1 Snowpit profile at the ventilation site.
measurements were made at 200 Hz, there was no significant high-frequency time
variation; the pressures were steady over time at each location. The measured surface
pressure distribution due to the fan is illustrated in Fig. 3. Only modest pressure
variations are present, with a peak pressure difference of only 2.5 Pa. Since the snow
surface was flat and there was no natural wind, this pressure variation is due solely to
the forced air flow produced by the fan; this was confirmed in the field by pressure
measurements obtained after the fan was turned off.
" it'v.'âWsE.'V ^ Ï 7 """*
PVC Pes*
pePith
T
z8cm
Fig. 2 Schematic diagram of the experimental setup.
Ventilation experiments in a seasonal snow cover
2.5
1
U1 1
1
1
•
1
45
'
Measured
—
2.0
1.5
—
Model
Input
/
—
0.
0.5
0
^
' 0
!
0.4
t
!
i
I
I
0.8
1.2
Distance from Fan (m)
I
.
1.6
2.0
Fig. 3 Snow surface pressure distribution for the ventilation test. The solid line is the
model input, and the circles are measured values.
Measured snow temperature profiles
The resulting snow temperature measurements at seven depths are shown as a function
of time in Fig. 4. On the time axis of the graph are markers indicating important events
relevant to the experiment. At 10:20, a thermocouple that had been suspended in the air
was placed directly on the snow surface; the fan was turned on at 10:33, and was turned
off at 12:04. The temperature distribution in the snow before the fan was turned on is
typical of the almost linear temperature profiles that are characteristic of the heat
conduction process. Note that while the snow surface temperature remained fairly
constant throughout the test, the change in internal snowpack temperatures is dramatic.
The air flow through the snow changes the snow temperature by several degrees within
minutes of the onset of ventilation. When the fan was turned off, the data logger was set
to record on ten minute intervals. The return of the snow temperature toward diffusioncontrolled heat transfer is evident.
Snow permeability measurements
A series of snow permeability field measurements have been made near the test site and
at other locations using a snow permeameter developed at CRREL (Chacho & Johnson,
1978; Hardy & Albert, 1993). The apparatus uses a pump to draw air through an
isolated snow sample, within a double-walled cylinder as suggested by Shimizu (1970)
to minimize edge effects. Several measurements of pressure are made at different,
measured flow rates in order to derive permeability using Darcy ' s law. While these tests
46
Mary R. Albert & Janet P. Hardy
-8.
I;
|;
I
|
|
p ^
YV^
f
3 cm
01
U u
10:00
10:30
1
I
I
I
I
Li I
I I
11:00
11:30
12:00
12:30
Time of Day
Fig. 4 Measured snow temperatures at seven heights in the snow as a function of time
during the ventilation test. At 10:20 a thermocouple in the air was placed on the snow
surface. The fan was turned on at 10:33. At 12:04 the fan was turned off and the data
logger set to record at ten minute intervals.
were not performed at the same time as the ventilation test, permeability measurements
from similar snow types near the test site are used to provide the best available permeability estimates for modeling this snowpack. The permeability values are presented in
Fig. 1. These measurements are in fair agreement with Shimuzu's empirical formula
(Shimizu, 1970) for estimates of permeability given snow density and grain size.
MODEL RESULTS
The finite element model described above is used to calculate air flow velocities within
the snow (equations (1) and (2)) using the measurements of snow surface pressure
distribution and permeability. The model then uses those velocities to calculate internal
snowpack temperature (equation (3)), using measured snow surface and bottom temperatures as boundary conditions. The resulting calculated temperature profile 1.5 h after the
onset of ventilation is shown in Fig. 5. Here, the influence of the nonuniform surface
pressure forcing is evident, and clearly shows the multidimensional thermal effects of
air flow induced by surface pressure variations. Because the heat flux profile is the
gradient of the multidimensional temperature profile, the heat flux though the snow will
also change in space and time due to the changes in time of the snowpack temperature
(Fig. 4). In situations where ventilation occurs over an extended period of time, the
changes in temperature and heat flux profiles may induce changes in snow crystal
Ventilation experiments in a seasonal snow cover
47
0.24
E 0.16
-
0.08
0.8
1.2
2.0
Distance from Fan (m)
Fig. 5 Isotherms from the calculated two-dimensional temperature profile 1.5 hours
after the onset of ventilation.
metamorphism, but that is not the case for the test of short duration discussed here.
In this situation of surface pressure forcing that is steady in time but is spatially
nonuniform, the resulting temperature profile within the snow is also highly varied
spatially, so that the sampling location for temperature measurements must be clearly
defined. This indicates that field measurements of natural ventilation under nearly steady
surface pressure conditions, e.g. ventilation caused by surface dunes, will also be highly
0.28
1
~i—r®—
\
0.24
0.20
'
O 10:30 Data
® 12:00 Data
ol
—
—
—
^
\
m \
0.16
1
'
Conduction
(computed)
_
—
0.12
\
0.08
—
0.04
—
n
-8
Ventilation^^-^"^~~^a
(computed)
—
V
Mo
I
I
-6
I
I
-4
Temperature (°C)
i
-2
,!
0
Fig. 6 Vertical temperature profiles in the snow at two times. Lines indicate calculated
results, symbols indicate temperature measurements.
48
Mary R. Albert & Janet P. Hardy
dependent on sampling location; the precise location of the measurement relative to the
dune must be noted.
The temperature measurements were taken at location* = 0.7 m in front of the fan.
From Fig. 3, it is evident that, at this location, the positive pressure on the snow surface
was forcing air down through the snow, which cooled the snow and caused the nearsurface snow temperatures to become more uniform. At this location, the measured and
modeled vertical temperature profiles are shown for two times in Fig. 6, where the solid
lines are computed results and the dots are data. The line with less curvature in both
measured and computed results show the temperature profile at 10:30, before the fan
was turned on. This nearly-linear profile is characteristic of the heat conduction process.
The curved profiles show the measured and computed results for the temperature profile
1.5 h after the onset of advection (12:00). Air movement down through the near-surface
snow causes a more uniform temperature profile there. Closer to the bottom of the pack
and basal ice layer, the decreased permeability allow less air flow, so that heat transfer
is dominated by heat conduction in the basal ice layer. Considering that the thermal
conductivities were estimated from snow density graphs, and permeabilities were
estimated from samples considered to be similar on the basis of density and crystal type,
the agreement between the model and measurements is very good.
CONCLUSIONS
The results of the field experiment show that the thermal signature of forced air flow
through snow occurred within minutes of imposition of a surface pressure disturbance,
and had an effect through most of the 28 cm deep pack. In this low-density snowpack,
small pressure variations, less than three Pascals, were sufficient to cause significant air
movement in the snow. Numerical (finite element) heat and mass transfer simulations
of the experiment show good agreement between model calculations and measured
snowpack temperatures, which demonstrate diffusion-controlled heat transfer before the
onset of ventilation and advective effects during the ventilation. Surface pressure
variations that are steady in time tend to minimize horizontal mixing effects, so that
sampling location for temperature measurements is important. Future work will
concentrate on time-varying pressure, temperature, and gas flux modeling and
measurements.
Acknowledgments This project was funded by U.S. Army AT24-SS-E09, Surface-Air
Boundary Transfer Processes. The authors thank Steve Flanders for help with an
illustration. We also thank Ted Arons, Bert Davis, Sam Colbeck, and anonymous
reviewers for their helpful technical reviews.
REFERENCES
Albert, M. R. (1993) Some numerical experiments on firn ventilation with heat transfer. Ann. Glaciol. 18, 161-165.
Albert, M. R. & McGilvary, W. R. (1992) Thermal effects due to air flow and water vapor transport in dry snow
/. Glaciol. 38(129), 273-281.
Benson, C. S. (1962) Stratigraphie studies in the snow and firn of the Greenland ice sheet. U.S. Army CRREL Res Report
70.
Ventilation experiments in a seasonal snow cover
49
Chacho, E. F., Jr. & Johnson, J. B. (1987) Air permeability of snow. EOS (Trans. AGU) 68, 1271.
Clarke, G. K. C , Fisher, D. A. & Waddington, E. D. (1987) Windpumping: a potentially significant heat source in ice
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Colbeck, S. C. (1989) Air movement in snow due to windpumping, J. Glaciol. 35(120), 209-213.
Colbeck, S. C , Akitaya, E., Armstrong, R., Gubler, H., Lafeuille, J., Lied, K., McClung, D. & Morris, E. (1990) The
international classification for seasonal snow on the ground. Int. Coram. Snow and Ice (ICSI), (available from World
Data Center, University of Colorado, Boulder).
Hardy, J. P. & Albert, D. G. (1993) The permeability of temperate snow: preliminary links to microstructure. Proc. 50th
East. Snow Conf. (Quebec City, Canada), 149-156.
Mellor, M. (1977) Engineering properties of snow. J. Glaciol. 19(81), 15-66.
Shimizu, H. (1970) Air permeability of deposited snow. Contributionsfrom the Inst, of Low Temp. Sci., Hokkaido Series
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