These temperatures decrease with increasing depth of the lower layer from the surface and, 

 at a depth of 280 cm (if we continue the curve by geometric extrapolation) become equal to the 

 freezing point of sea-water (in the region of Malmgren's observations, -1.5°). This is the depth 

 which Malmgren considers the average thickness of ice formed in the East Siberian Sea due to heat 

 conductivity . 



UTERATURE: 39, 62, 104. 



Section 89. The Lag of the Temperature Minimum 

 in the Lower Levels of Sea Ice 



Quite naturally, the late appearance of minimum temperatures at the lower levels of sea-ice 

 is the result of the Fourier Laws of the distribution of periodic temperature fluctuations in a uni- 

 form solid body of infinite proportions. However, in sea-ice, this has certain specific 

 characteristics . 



At the lower surface of the ice, the temperature remains near the freezing point, but at the 

 upper surface it is close to the air temperature. Let us assume that the temperature of the ice 

 surface reaches its minimum at a certain moment. After this, the following factors will help in- 

 crease the ice temperature: 1) solar radiation, which raises the temperature of the ice surface, 

 penetrates deep into the ice, and converts into heat there; 2) the heat incident on the ice surface 

 from the air, whose temperature gradually increases; 3) the continuous heat flux, both winter and 

 summer, from the water through the lower surface of the ice, such as the heat of crystallization 

 which is released during the formation of ever newer ice layers at the lower surface of the ice. 

 If we ignore the action of solar radiation on the internal parts of the ice, the temperature at any 

 point of the ice will change according to 



dl 

 dT 



k ldH\ 



(1) 



where t is the temperature, T the time, K is the heat conductivity, c^ is the specific heat of ice 

 and 6 i is the ice density . 



Since the ice surface is warmed through quickly during the spring, at first the vertical tem- 

 perature gradients in the upper part of the ice will be considerably greater than in the lower part; 

 consequently (see figure 83) the minimum temperature level, which decreases in size, gradually 

 drops lower and lower until it assumes a position approximately in the middle of the ice mass. 



Actually, after the temperature of the surface layer increases to the freezing point, i.e. , 

 after it becomes approximately equal to the temperature of the lower layer, and after a situation 

 is established where 



[%),r{pj-.' (2> 



where (9t / bs)^^ is the temperature gradient at a distance s above a given point, (dt /ds )_ ^ is 

 the temperature gradient at a distance s below a given point, i.e. , the arrival of heat from above 

 will be equal to the arrival of heat from below; there will be no reasons for any further descent of 

 the minimum. On examining figure 81, which represents Georgievskii' s observations of ice tem- 

 peratures at Cape Schmidt, and table 80 which gives the temperature observations made by Savel'ev 

 on Uyedineniye Island, we see that these data completely confirm the above hypothesis . 



236 



