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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 sheets. In: The Physical Basis of Ice Sheet Modelling (ed. by E. D. Waddington & J. S. Walder) (Proc. Vancouver Symp., August 1987), 169-180. IAHS Publ. no. 170. Clarke, G. K. C. & Waddington, E. D. (1991) A three-dimensional theory of wind pumping. J. Glaciol. 37(125), 89-96. 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 A, 22, 1-32. Sturm, M. & Johnson, J. B. (1991) Natural convection in the subarctic snow cover. J. Geophys. Res. 96(B7), 657-668.