t s time, and 



K'= K + T X (C 2 ^-C,J, 



From this equation, it appears that the larger the depth H to which winter 

 vertical convection reaches,, the higher the mean temperature of the layer, 

 and the smaller the coefficient of turbulent heat conductivity, the more 

 important this term becomes. The relative effect of the heat of the 

 water mass is decreased by an increase in the thickness of the snow and 

 ice layers. This effect could be foreseen intuitively, since both the 

 ice and snow layers act as excellent insulators and considerably decrease 

 the flow of heat from the water mass outwards, thus keeping the latter 

 from cooling. 



Taking a resultant temperature of -20°C, the freezing point of sea 

 water (T >^ ) as -1.8°C, the average temperature of the layer T2 as 0.5°C. 

 and the turbulent heat conductivity of sea water (A2) as 8, the following 

 expression results: 



47 x10 s (*■)* (2n-l) £ 



2 76 Hj^ jj^f- • (25) 



The evaluation of the infinite series of (25) is not particularly dif- 

 ficult, as it is rarely necessary to carry the computation to more than 

 3 or 4 terms to secure the required degree of accuracy,* Carrying out 

 the evaluation of equation (2&) by using the parameter values as in equa- 

 tion (25) and multiplying by a^ and dividing by the right hand side of 

 equation (22) evaluated for an air temperature of ~20°C. yields the re- 

 sults shown in Figure 10, where the horizontal scale is in days of 

 freezing time added for an air temperature of -»20°C« S and the vertical 

 scale is ice thickness in cm. Each isoline of mean water temperature 

 indicates the freezing time added by mean temperatures ranging from 

 -1.5° to 0.5°C. in the water layer, which is assumed to be 100 m. thick, 

 and the freezing point of sea water T^is taken as -1,8°C. The figure 

 shows that the heat of the water mass adds to the freezing time least 

 when the water temperature la lowest. At a mean temperature of -1.5°C. 

 the heat of the water mass increases the time for freezing 10 cm. of ice 

 from an initial thickness of 15 cm. by about 1.1 days, and to the time 

 for adding a thickness of 70 cm. to an initial thickness of 15 cm. by 

 about 7.6 days. The variation between these two points is essentially 

 linear. At the warmest mean water temperature of 0.5 6 C., the heat of 

 the water mass add3 about 10 days for the 10 cm. addition (to the initial 

 thickness of 15 cm.) and about 54 days for the 70 cm. increment of ice 

 thickness. At this water temperature the variation is nonlinear, show- 

 ing a slower rate of time increase at high ice thicknesses than at lower 

 ones. Figure 11 shows the total freezing time for ice thickness incre- 

 ments varying from 10 to 70 cm., including the time added by the heat of 



20 



