Field study

As mentioned above, the Old Faithful site was chosen because the area acts as a constant heat source throughout the winter. In addition, the cold climate combined with a low-density snow-pack acts to produce a collapsing snow virtually every winter. Three thermistor stacks were installed in a radial line from the Old Faithful vent. In each stack, two thermistors were buried, one at a depth of 250 mm and the other at 100 mm. In this way the temporal and spatial character of the heat flux into the snow from the ground could be observed. The three stacks were placed at intervals of 6 m at a sufficient distance from the vent (approximately 30 m) to ensure that they would be covered by a good depth of snow. In Figures 1 and 2 the locations of the three stacks are indicated by stations 1, 2 and 3 where station 3 is the farthest from the Old Faithful vent. The temperature regimen in the snow-pack was measured by means of a thermistor probe with a resolution of �0.2 deg., so that a detailed record of the temperature from the air through the pack to 250 mm below the ground level could be observed.

Fig 1. Vertical distribution of density, temperature gradient, and strength at Yellowstone, test on 14 December 1974.

Fig 2. Vertical distribution of density, temperature gradient, and strength at Yellowstone, test 011 18 December 1974.

Meteorological observations were made on a daily basis. They included the minimum and maximum temperatures, the snowfall, and the snow accumulation on the ground. In addition, frequent resistometer readings were made to record snow strength. The resistometer is a probe with a conical point and a spring-mounted handle coupled with a sensitive displacement dial indicator. It is capable of giving accurate spot strength measurements of very weak snow at depth. Finally, snow-pit studies were conducted in regular intervals at all three stations. In these studies the crystal stratification was recorded photographically, density measurements and whisk-broom abrasion tests were made, and the snow strength profile was measured with a resistograph. The information obtained from data collected by these measurements was then used to study the development of euhedral depth hoar and the variation of the mechanical and physical properties of the snow.

Figures 1 through 4 illustrate results of the field investigation. Figures 1 and 2 contain data actually recorded at stations 1, 2 and 3 plus information gathered from the pit studies. Station 1, as it turned out, was located too close to the Old Faithful vent, and consequently it was never covered by a snow-pack of any significant depth. Therefore, no useful data were obtained from that station.

Generally, Yellowstone National Park receives an abundant amount of snow during December. However, in 1974, snowfall was below average and, as can be observed in Figures 1 and 2, the snow-pack did not exceed a depth of 0.40 m during that month. This relatively shallow pack plus the cold weather and steady heat flux from the ground resulted in copious amounts of depth hoar. Therefore, the investigators had ample opportunity carefully to study the process of temperature-gradient metamorphism under field conditions.

The depth hoar was classified into three subgroups: euhedral, subhedral and anhedral. Euhedral depth hoar consists of a large, fully-developed skeletal structure containing cupshaped crystals, plates, sheaths, and needles. This is a large crystal structure (approximately 2 mm) with an unmistakable character. The subhedral depth hoar is similar to euhedral depth hoar but is not so fully developed. The grains are smaller (I mm to 2 mm) with some solid crystal structure and an abundance of plates and sheaths but with little cup construction. The anhedral snow is essentially depth hoar of a solid type with a small, solid crystal structure having flat surfaces and sharp corners. It shows the effects of temperature-gradient metamorphism, but there is no skeletal development, and the crystals generally are no longer than 1 mm.

Figures 1 and 2 show that in the 300 mm of snow pack, depth hoar was found through the first 200 mm of snow. At the time when measurement of these figures were made, the temperature was –6.2°C on 18 December and –13.8°C on 23 December 1974. These figures show also the interesting fact that the weakest snow is in the subhedral region and not in the euhedral snow. Note also the striking correlation between minimum strength, maximum temperature gradient, and local maximum density. This correlation raises some interesting questions concerning the process of heat flux through the pack and its relationship to strength and density. This will be discussed in more detail later. Figures 3 and 4 show the relationship between density, strength, and temperature gradient. Note that when snow type is classified by density and strength, or by temperature gradient and strength, the three types of snow fall into distinct regions as indicated by the Figures.

Fig 3. Graph showing the relationship between temperature gradient, strength, and crystal structure.

Fig 4. Graph showing the relationship between density, strength, and crystal structure.

Laboratory investigation

Depth hoar was grown under laboratory conditions in an effort to study carefully the temporal variation of strength during the periods when the snow was subjected to temperature gradient metamorphism. Figure 5 illustrates the apparatus used to grow depth hoar. This apparatus, which was patterned after the experimental facility of Reference AkitayaAkitaya (1974), consists of a box insulated on all four vertical sides, heated on the bottom surface, and kept at cold-room temperature on the top surface. The bottom surface was held at –1.5 ± 0.3°C, a temperature which occurs characteristically at the bottom of typical snow-packs. The snow was cut into four identical rectangular columns of dimensions 10 × 10 × 40 cm³ and each column was placed inside four foam jackets.

Fig 5. The apparatus used in the depth-hoar experiment.

When a test was begun one column was removed and cut into four 100 mm long specimens and then tested for strength and density. Each specimen was strength tested in an Instron testing machine by compressing it at a crosshead rate of 0.038 m/min and thus measuring the stress at which fracture occurred. The density and crystal structure were also recorded for each specimen at this time. The other three specimens were placed in the depth-hoar apparatus and a solid foam insert was placed in the space which would have been occupied by the column previously tested. Then, the heating element at the bottom was turned on, thereby producing a heat flux up through the three columns in the apparatus. After four days a column was removed, cut into four specimens, and tested as above. This was repeated again at eight days and twelve days. The temperature was recorded at 100 mm increments by means of thermistors as illustrated in Figure 5. The bottom two specimens became extremely fragile as time went on due to the metamorphism, but the foam jackets allowed these specimens to be handled without damage.

In all, about 8 experiments were run at various densities and temperature gradients. In all cases the original snow was fin e-grained granula r snow. For the sake of brevity, not all the 8 test results are illustrated in this pa per. Figures 6 to 9 illustra te some of the typical test results. Figures 6 and 7 show the variation of snow strength with time in two tests. Figure 8 illustrates typical temperature profiles in the material. Figure 9 shows the varia tion of Young's modulus with time during three typical experiments. The drop in strength of the lower-density snow was invariably much sharper than the drop in material stiffness as indicated by the value of Young's modulus. Young's modulus was determined by measuring the slope of the load response curve for each fracture test. Assuming that the strain-rate was constant, the stress-rate then gave Young's modulus E from the relationship

Fig. 6 (left) and Fig. 7 (right). Graphs showing the variation of fracture stress and crystal structure.

Fig 8. Steady-state temperature profiles.

Fig 9. Variation of Young's modulus with time during metamorphosis.

(1)

where T is the axial stress, and e is the axial strain. Since fracture occurred within a few seconds of the time the compression was started, this approximation was considered valid.

Observations

In the field investigation, the combination of thin snow cover and a period of cold weather produced an abundant quantity of depth hoar. Three well-defined zones of depth hoar appeared: euhedral, subhedral, and anhedral depth hoar. Both the whisk-broom abrasion tests and resistograph readings showed a definite band of weakness in the subhedral layer, whereas the fully metamorphosed euhedral snow was significantly stronger than the subhedral structure. This result was also verified in the laboratory experiments (Figs 6 and 7). For densities of 250 kg/m² or less, the strengthening invariably appeared in the laboratory experiments. The bottom layer would lose strength as it metamorphosed into the subhedral structure, and, as a fully developed euhedral stage was approached, the strength would begin to increase.

Usually, in the field tests, density was found to reach a local maximum at the weakest zone. This occurred in every test but one. Density readings taken in the laboratory were too inaccurate to verify the field results. By the time that the compression test was completed they had been damaged by the testing machine too extensively to allow an accurate measurement of density.

The temperature profile in nearly every case showed a marked increase in the temperature gradient at the weakest zone, as is clearly shown by Figures 1 and 2. This result was not verified by the laboratory studies. Figure 8 indicates that the temperature profile in the laboratory studies was well behaved with no indication of a local maximum in the temperature gradient. However, the spacing of the thermistors was 100 mm, and consequently a small zone with a high temperature gradient may not have been detected in the laboratory. Note however the strong non-linearity of the temperature profile in the laboratory experiments, as indicated by Figure 8. This result was also mentioned briefly by Reference AkitayaAkitaya (1974). In the field tests, the temperature in the anhedral and euhedral zones appeared also to have a similar non-linearity. However, the transient weather conditions in the field make a complete comparison difficult.

During the final period of observation in the field the pack exceeded 400 mm in depth, and the density and strength anomalies disappeared even though the three zones were still visible in the crystal texture. Throughout the period when the subhedral zone was extremely weak, the snow-pack had a strong tendency to collapse, this might account in part for the disappearance of the strength anomaly. Figures 3 and 4 show the strong correlation between snow type, density, temperature gradient, and strength, and also indicate that the three types of depth hoar can be grouped when plotted parametrically against two parameters.

One of the more striking results is illustrated in Figure 9 which depicts the time variation of Young's modulus during the temperature gradient metamorphism. Young's modulus never dropped to less than 50% of its original value in any of th e experiments, whereas fracture stress in some of the experiments dropped to 10% of the original strength. It was also observed that in the laboratory experiments involving more dense snows (density greater than 300 kg/m³), Young's modulus and the strength actually increased from the original values. In this case, “hard depth hoar” was found to form in much the same manner as described by Reference AkitayaAkitaya (1974).

Conclusions

In both field and laboratory experiments, temperature-gradient metamorphism has been observed to produce an advancing wave of change in the snow-pack. This wave, which moves upward from the ground level, initially weakens the snow as it metamorphoses from fine-grained granular snow through anhedral depth hoar to the subhedral stage. At this point, the strength has reached a minimum. Under a continuing temperature gradient, the snow then undergoes further recrystallization and gradually strengthens until it reaches the euhedral depth-hoar stage. Apparently, the weakest zone in the pack is not fully-developed depth hoar, but is a zone of subhedral depth hoar directly above the euhedral zone.

The temperature gradient a normaly quite probably bears a close relationship to the metamorphic state of the snow. Heat flux through the pack, as indicated by Reference AkitayaAkitaya (1974), is due to two prima ry mechanisms: solid heat conduction through the snow, and sublimative heat exchange. The solid heat conduction is highly dependent upon the average cross-sectional area of the bonds and necks connecting the grains in the crystalline structure. In the subhedral snow, which has little strength, these bonds necessarily are small and thereby decrease the effective thermal conductivity of the snow. In order to accommodate the heat flux supplied by the lower layers an increase in temperature gradient results, thus, locally increasing the heat flux due to both sublimative heat exchange and solid heat conduction.

The non-linear nature of the temperature profile observed in the laboratory experiment may also be explained in part by differences in thermal conductivity. Certainly the metamorphosed snow near the bottom had a lower thermal conductivity than the upper colder layers, since these upper layers remained practically invariant during the testing period. The strength, in Young's modulus, of these two layers retain its initial values during the experiments, implying that good intergranular bonding was maintained. Therefore, heat could be conducted more readily through these layers with relatively small temperature gradients.

One interesting observation is that the material stiffness (manifested in the Young's modulus) did not undergo a ny large decrease during the temperature gradient metamorphism ; avariation was observed in the strength. While strength must be related, for the most part, to the load-bearing capacity of the grain bonds which occupy in relatively small portion of the material mass, Young's modulus must be determined by the deformation of the entire crysalline structure, i.e. the grain bodies as well as intergranular bonds. This would appear to indicate that the recrystallization does not radically affect the stiffness in the ice grains themselves.