A Portable Capacitance Snow Sounding Instrument
Michel Y. Louge, Robert L. Foster, Newel Jensen and Ralph Patterson3
Abstract: We describe a penetration field-portable capacitance instrument capable of recording profiles of dielectric permittivity at a horizontal resolution of 2.5 mm through layers of relatively dry snow packs. Using independent calibrations, measurements of the dielectric modulus through a typical winter snow pack provided an accurate profile of density later confirmed by the excavation of a detailed snow cover profile.
Keywords: avalanche forecasting, snow density, snow electrical properties, snow water equivalent, snow stratigraphy
Vertical soundings of the snow pack are essential diagnostic tools for snow hydrologists and avalanche forecasters. The hydrologists require quantitative profiles of snow density from which they can infer the total amount of snow coverage in a region. The avalanche forecasters are concerned with the presence and depth of weak layers in relatively immature snow. In both cases, these professionals must dig a relatively large number of pits or extract many core samples for an accurate assessment of the pack.
In this context, we have developed a penetration field-portable capacitance probe capable of recording profiles of dielectric permittivity through a relatively dry snow pack. The idea is to acquire rapidly several density soundings without multiple excavation. The probe consists of a pole with a wedged capacitance tip allowing penetration through depths of at least 2 m. The tip is connected to a hand-held amplifier for data processing and storage.
We tested a prototype of the probe at Alta near Salt Lake City, Utah by recording the real and imaginary parts of the dielectric constant through a typical winter snow pack. Using independent calibrations of the dielectric modulus, we inferred a density profile, which we later corroborated with a traditional excavation. We begin with a brief description of the sounding probe and its principle.
2. Capacitance Sounding Probe
In general, the purpose of our capacitance instrumentation is to record accurately the complex dielectric permittivity of a material in a well-defined measurement volume. To this end, we design probes consisting of three conductors called the "sensor", "reference" and "guard" electrodes that can detect capacitances three to six orders of magnitude smaller than conventional bridges of similar cost. Acree-Riley and Louge (1989) and Louge, et al (1996, 1997) described several instruments operating upon the same principle for a variety of applications in gas-solid suspensions. Here, we describe another probe geometry specifically designed to penetrate the snow pack.
Louge, et al (1998) summarized the principle of this instrument in a recent paper. When the sounding probe is exposed to ambient air, its processing electronics produces an adjustable output voltage V0 and the phase lag between its oscillator and the voltage of the guard electrode is 180°. When it is immersed in snow, the electronics produces a new voltage V and phase lag f that are related to the complex dielectric permittivity of snow,
|tan f| = , (2)
where e' and e" are, respectively, the real and imaginary parts of the complex dielectric permittivity of snow,
ee ? e' - j e" , (3)
and j2 = -1. Then, by recording V0, V and f, the instrument can extract ee.
While this technique produces accurate records of the dielectric permittivity, its principal challenge is to relate local measurements of ee to snow density. To do so, we employ the capacitance "snow press" of Louge, et al (1997). This instrument includes a piston at the reference voltage traveling in a plastic cylinder . The base features a circular sensor surface surrounded by a guard plate. After a sample is introduced in the press, the piston is progressively lowered to bring it to denser compactions while the corresponding values of ee are measured. The resulting plot of |ee| versus snow density produces an empirical calibration valid for the type of snow present in the pack.
Fig. 1. Tip of the penetration probe.
The tip of our prototype probe is mounted at the end of a rigid pole (Fig. 1). The back face is sharply cut at an angle of 10° to allow its penetration through the snow pack while avoiding excessive density disturbances near its flat vertical frontal surface. The flat sensor/guard assembly is mounted flush within a pocked cut on its face. The sensor consists of two rectangular conductive surfaces located on either side of the vertical symmetry axis and surrounded by a relatively tall guard. The periphery of the probe tip is held at the reference voltage. Louge, et al (1998) calculate the capacitance of this probe geometry and the depth of its measurement volume. With dimensions chosen for the prototype, the probe capacitance in air is about 25 femtoF and the measurement volume penetrates a horizontal distance h = 12 mm into the pack while resolving horizontal layers of thickness d = 2.5 mm.
We tested the prototype on a south facing slope near Alta's Upper Guard Station. In these tests, the capacitance sounding was followed by the excavation of a snow pit and a ram penetration test at the same location.
Fig. 2. Capacitance profiles of e' and e".
Figure 2 shows profiles of the dielectric constant acquired with the capacitance instrument. Rather than pushing the capacitance probe continuously, the latter was progressively driven into the pack by repeatedly striking the pole. This method permitted us to reach the desired incremental depths accurately despite variable strengths of successive snow layers. Depth was recorded by marking the pole every 6 mm. To facilitate the use of this probe in future, the instrument will be modified to acquire its depth automatically.
To infer density profiles from the capacitance measurements, we first evaluated the dielectric properties of samples collected at the site using the "snow press." Faceted ice grains exhibited the largest values of |ee| and the steepest dependence on density. However, as Louge, et al (1997) observed for dry samples originating from the same basin and exhibiting similar temperatures, the density dependence of |ee| could be reasonably captured by a single empirical fit, despite wide variations in snow morphology or the presence of impurities (Fig. 3). The fit then permitted us to infer the snow density r from the capacitance soundings of |ee|. As Fig. 4 shows, the corresponding values of r agree with the direct density measurements obtained from the excavation within individual errors smaller than 20%, while the recorded average density spans a factor of five.
Fig. 3. Variations of the modulus of the dielectric constant with snow density. The various symbols represent different samples at - 4°C. The best empirical fits are |ee| ÷ (r/r0)1.5 for r = 0.29 g/cm3 and |ee| ÷ (r/r1)3.1 for r > 0.29 g/cm3, with r0 ÷ 0.12 g/cm3 and r1 ÷ 0.19 g/cm3.
Fig. 4. Snow density versus elevation inferred from the sounding of Fig. 2 and the calibration of Fig. 3. The line is from the capacitance probe and the symbols represent direct density measurements from the excavation. The dashed lines to the right of the graph mark elevations of observable melt-freeze crusts. The horizontal lines to the left are peaks of the ram penetrometer profiles.
Because the proximity of the Upper Guard Station likely increased the radiation exposure of the snow surface, several melt-freeze crusts were produced in the pack. As Fig. 4 indicates, voids normally associated with these crusts were detected by the capacitance instrument. In addition, the probe also recorded two noticeable peaks of decreased density at 108 and 137 cm, which may suggest more prominent layers than initially observed.
Above the melt-freeze crusts, large diurnal temperature variations produced temperature gradients sufficient to form layers of faceted grains through radiation recrystallization. The high impermeability of the ice layers may also have created further faceting below the crusts by trapping excess water vapor near crystal surfaces (McClung and Schaerer, 1993). Although such faceted crystals are not always apparent by traditional excavation techniques conducted under adverse weather and lighting conditions, they often denote an instability within the snow pack, and thus are crucial to avalanche forecasters.
The capacitance instrument corroborated other features of the traditional profiles. As Fig. 4 shows, large peak in the ram hardness near 22, 63 and 90 cm were accompanied by relatively large densities inferred from the probe. On the other hand, the probe also revealed features too narrow to observe in the traditional excavation. For example, the decreasing density recorded in the first few centimeters above ground indicated the presence of depth hoar, a large crystal formed by the temperature gradient established between the relatively warm ground and cold snow.
In general, the capacitance instrument sampled density with greater resolution than the conventional portable kit, which averaged that quantity in a wedge of 200 cm3 and 4 cm thickness. Nevertheless, the two methods produced similar values of the total snow water equivalent. Our numerical integrations of the capacitance record and the direct density measurements yielded SWE = 453 mm and 485 mm, respectively.
While capacitance profiles can be correlated with features of the snow pack through independent density calibrations, they cannot yet supplant a traditional excavation. In particular, it is still unclear how the information contained in the real and imaginary parts of the dielectric constant can alone reveal details of snow morphology.
Another potential difficulty is associated with liquid water content, which can affect the effective dielectric constant and be challenging to measure (Kuroiwa, 1967; Colbeck, 1978; Denoth, et al, 1984; Boyne and Fisk, 1987; Camp and Labrecque, 1992). While the Alta tests were carried out with relatively dry snows, our experience is that excessive amounts of liquid water can produce instabilities in the processing electronics (Louge, et al 1997). It remains to determine how much liquid water our instrument can tolerate.
As Louge, et al (1997) pointed out, the dielectric properties of snow can be significantly affected by temperature. Consequently, for quantitative measurements of density it is important to carry out capacitance calibrations at one or several temperatures characteristic of the snowpack, particularly if substantial temperature variations are anticipated.
For now, because the capacitance method quickly produces a density record of high resolution, it should be regarded as a convenient, rapid, relatively non-invasive complement to standard snow cover profiling techniques. For example, capacitance soundings from multiple locations can be correlated to a single reference excavation profile. Similarly, once a relation is established between dielectric constant and density for snows involved in a specific basin, rapid capacitance soundings should provide the total snow water equivalent at several arbitrary locations with sufficient accuracy for hydrology.
This work was supported by the Department of the Army under Small Business Innovation Research Grant number DAAG55-97-C-0013 and conducted in cooperation with the University of Utah, the Utah Department of Transportation and the Center for Snow Science at Alta. We are particularly grateful to Professor Rand Decker and Messrs. Daniel Howlett, Steve Conger and David Medera for their hospitality and for helping us carry out the tests.
Acree Riley C. and M.Y. Louge (1989) "Quantitative capacitive measurements of voidage in dense gas-solid flows," Particulate Science & Tech., 7 51:59.
Boyne H.S. and Fisk D.J. (1987) "Comparison of snow cover liquid water measurement techniques," Water Resources Research 23, 1833-36.
Camp P.R. and Labrecque D.R. (1992) "Determination of the Water Content of Snow by Dielectric Measurements," 92-18 Special Report AD-A256299, US Army Cold Regions Research and Engineering Laboratory, Hanover, NH, pp. 1-35.
Colbeck S.C. (1978) "Difficulties in measuring the water saturation and porosity of snow," J. of Glaciology 20, 189-201.
Denoth A. , A. Foglar, P. Weiland, C. Mätzler, H. Aebischer, M. Tiuri and A. Sihvola (1984) "A comparative study of instruments for measuring the liquid water content of snow," J. Appl. Phys. 56, 2154-2160.
Kuroiwa D. (1967) "Snow as a material. Chapter J. Electrical Properties of snow," in: Cold Regions Science and Engineering, Part II, Section B: Physical Sciences, US Army Materiel Command, Cold Regions Research and Engineering Laboratory, Hanover, NH, pp. 63-79.
Louge M.Y., R. Steiner, S.C. Keast, R. Decker, J. Dent and M. Schneebeli (1997) "Application of capacitance instrumentation to the measurement of density and velocity of flowing snow," Cold Regions Sci. and Technol. 25, 47-63.
Louge M., M. Tuccio, E. Lander and P. Connors (1996) "Capacitance measurements of the volume fraction and velocity of dielectric solids near a grounded wall," Rev. Sci. Instrum. 67, 1869-1877.
Louge M., R.L. Foster, N. Jensen and R. Patterson (1998) "A Portable Capacitance Snow Sounding Instrument," Cold Regions Sci. and Technol. , in press.
McClung, D. and P. Schaerer (1993) Avalanche Handbook, The Mountaineers, Seattle, WA.