It can be seen from the figure that on 28 January 1942, for example, the average thickness of 

 the ice beneath a snow cover 15 to 40 cm thick was 58 cm (maximum 63 cm, minimum 48 cm); but 

 on the snow-free roadbed, the average ice thickness was 83 cm (maximum 89 cm, minimum 73 cm). 

 Thus, snow-free ice proved to be almost 1 1/2 times thicker than ice covered with a natural snow 

 cover. This knowledge is always used when building ice crossings and all sorts of roads on river 

 and shore ice . 



To solve the problems of the effect of a snow cover on the rate of ice growth, 1 have assumed 

 that the heat flow through the snow and through the ice is in equilibrium at all times , or 



^ - s i ' ^ ' 



where feg is the heat conductivity of snow, fej is the heat conductivity of ice, S is the snow depth, 

 i is the ice thickness, t^ is the air temperature and also the temperature of the upper surfaces of 

 the snow, *ui is the water temperature and also the temperature of the lower surface of the ice, t 

 is the temperature at the ice-snow interface and T is the time. 



From formula (1) it follows that 



ki s+ks i • (2) 



To be sure, the temperature at the interface changes constantly in connection with ice accretion 

 which assures a flow of heat to the atmosphere, but this change can be ignored for com.paratively 

 short periods of time . 



Furthermore, I have assumed that the investigated ice field is in isostatic equilibrium (see 

 Section 103); in other words, the following equation holds at each vertical 



S6s + i5i = ^„z, (3) 



where 6g is the snow density, 6 y is the ice density, Sj^ the water density, and s is the distance 

 between the water-line and the lower surface of the ice. 



According to Abel's, the heat conductivity of snow is determined by its density according to 



ks = 0.0067 8f . (4) 



Figure 77 is constructed according to formulas (1) to (4) and the foUowdng values are as- 

 sumed (for pure monolithic ice formed from fresh water): i = 100 cm, t(j = -20°, tjy = 0°, 

 6 = 1.0, 6,- = 0.9, 6„ = 0.5, fc, = 0.0054 and fe, = 0.0018. 



On examining figure 77, we see the following: 



1. The ice bends under the weight of the snowdrift, and under the given conditions, the 

 upper surface of the ice sinks below the water level, even when the snow layer is 20 cm thick. It 

 is understandable that when the snow cover is very thick and when there are through-cracks in the 

 ice, the water will come to the surface of the ice, and, on wetting the lower layers of the snow, 

 will freeze there (see columns 5 and 6 in table 70) . 



2. The isotherms bend upward beneath a snowdrift . Thus, after a snowfall, the higher the 

 drift, the higher the ice temperature rises. 



221 



