The Editor,

Journal of Glaciology

Sir,

In our recent paper in the Journal of Glaciology (Vol. 4, No. 36, p. 689–708), we made a rather hasty speculation about the origin of vertical c-axis ice on Peters Lake, Alaska. The speculation offered does not explain every case but suggests only one possibility. We should like to offer another explanation.

Reference KnightKnight (1962) has observed that wind is a primary factor in the formation of ice having c-axes which are predominantly vertical or predominantly horizontal and the break-up of the initial ice skim which results from wind action is also important.

Reference Arakawa and HiguchiArakawa and Higuchi (1952) and Reference ArakawaArakawa (1954, Reference Arakawa1955) have determined the physical conditions under which disc crystals are produced and continue to grow in stellar form, as a result of a series of detailed studies on freezing water. A disc crystal floating on the water surface has a vertical c-axis and can only be produced when the water temperature is very close to the ice point.

Since supercooling, heat conduction and convection should be considered important in the freezing process, it is difficult to explain how an initial ice skim with vertical c-axes can be produced over an extensive lake area under natural conditions. In an ordinary case, the distribution of the c-axes should be random. The initial ice skim would be formed by various types of ice crystals, i.e. needle, feather, and disc or stellar forms (Reference Arakawa and HiguchiArakawa and Higuchi, 1952). The mode of formation is illustrated in Figure 1. If the supercooled water layer is thick, barb-like vanes with c-axes normal to the plate of the vane will grow rapidly in the supercooled water from the needle crystal on the surface, because of the rapid growth of basal planes of ice crystals (Reference Lyons and StoiberLyons and Stoiber, 1962). Even if crystals of disc or stellar form are produced among the needle crystals floating on the water surface, their growth will be restricted by the rapid growth of the needle and barb-like vane crystals on the water surface and in the water. This might be called the first step of orientation selection by grain growth, which is characterized by a predominance of horizontal c-axis crystals.

Fig. 1. The mode of formation of the initial ice skim

Wind breaks the initial ice skim, so that each of the barb-like vanes is freed and may then float on the water surface. Since the c-axis orientation of each feather-like crystal is normal to its vane plate, the newly formed ice skim has vertical c-axes. Wind would also push this newly formed ice skim towards the edge, so that the ice in this part of the lake would have vertical c-axes. The orientation of the c-axes in the ice skim would greatly affect the c-axis orientation of the ice which subsequently grows in the water.

The mode of random distribution of c-axis orientation is necessary for a clearer understanding of the histograms of c-axis orientation given in our previous paper (Reference Muguruma and KikuchiMuguruma and Kikuchi, 1963). Random distribution of c-axis orientation means in a statistical sense that c-axis orientation is distributed uniformly on a hemispherical surface. Then it is expressed as the ratio of the area of the hemisphere to the area of a zone which is cut at an arbitrary latitude as shown in Figure 2. The latter area can be calculated by the following equation:

Fig. 2. The hemispherical surface with a zone cut at an arbitrary latitude, used for calculation of a random distribution of c-avis orientation

where S is the area of the zone, and α ₁ and α ₂ are the latitudes of the upper and lower ends of the zone. Taking α ₁−α ₂=10°, the mode of random distribution of the c-axis orientation is shown in Figure 3. This figure shows that even if 50 per cent of the ice grains have a c-axis orientation of θ=60~90°, the ice cannot be said to have predominantly horizontal c-axes. When the distribution of the c-axis orientation is considered, the mode of random distribution of the c-axis should always be kept in mind. Statistical treatment is also necessary for detailed analysis of the data of c-axis distribution. In this sense, the data obtained by observing Tyndall figures at Peters Lake support the conclusion that the ice has a predominantly horizontal c-axis orientation.

Fig. 3. Histograms illustrating random distribution of c-axis orientation

We are grateful to Drs. K. Arakawa and C. A. Knight for their valuable suggestions and discussions.

3 February 1964