layer (which is J02 thick), not due to the heat of crystallization evolved during the formation of 

 additional layers of ice. Thus we will get 



/C8 



-j-dT = cJu,p.,dt. 

 '1 



(8) 



Integrating, we get 



or 



i 



er = 





d1 



k 86,400 



(9) 



where t is the freezing point. 



If the thickness of the ice which has formed is known, the amount of heat released to the 

 atmosphere by 1 square cm of ice surface due to crystallization can be computed according to 



qi = XSi /. 



(10) 



Since this heat is proportional to ice thickness, which increases parabolically with time, it is 

 clear that the rate of heat release to the atmosphere will gradually decrease if the temperature 

 difference between the air and water remains the same. 



If the ice thickness remains constant, the amount of heat released to the atmosphere due to the 

 cooling of the new layers of the sea included in the vertical circulation, will be constant and equal to 



where t is the initial temperature of the layer and t is the freezing point. 



(11) 



TABLE 73 



Table 73 gives some computations based on the concepts and formulas given above. In this 

 table, p is the thickness of the water layer in meters, t° is the temperature of the layer at the 

 initial moment, 5 0/00 is the salinity of the layer at the initial moment, i is the thickness of the 

 ice (in cm) which creates the salinification required to initiate convective mixing with the lower 

 lying layer, R i is the number of freezing degree-days expended on crystallization, Rf, is the num- 

 ber of freezing degree-days expended on cooling the layer to the freezing point, R is the sum of 

 the freezing degree-days expended on crystallization and on cooling the layer, g ■ is the amount of 

 heat in kg-cal released by 1 cm of ice surface to the atmosphere during the crystallation of the ice, 



216 



