-w 



-20' 



~9/)0 



-SO 



// X A/ x// / // /// /<^ t^ y/ v// s/in 



Figure 80 . Annual variation of monthly ice temperatures at 

 different depths from the ice surface, according 

 to Malmgren. Observed temperatures ( — ) and 

 temperatures computed by the harmonic 

 formula ( — ). 



The branches of these curves corresponding to a temperature increase are steeper than those cor- 

 responding to a temperature decrease. This phenomenon is in agreement with the following: 

 during a temperature increase, the increase takes place from above and from below at every point 

 in the ice, but during a temperature decrease, when there is a steady flow of heat from below 

 (from the water), the cooling occurs only from above. 



The following formula is often used to calculate the annual temperature variation on the basis 

 of mean monthly temperatures 



/^ = T^ + asin(A+m), 



(1) 



where tpi is the mean monthly temperature, T-g^ is the mean annual temperature, a is the ampli- 

 tude of variation, A is the initial phase and m is an angle reckoned from the middle of January, 

 representing the number of months . 



Obviously, when this formula is used, the annual temperature variation at different levels 

 will be represented by sinusoids that differ from each other in amplitude and phase . For ice depths 

 of 75 cm and 200 cm, these sinusoids appear as the dashed lines in figure 80, which was constructed 

 on the basis of Malmgren' s computations. 



As was to be expected, all anomalies are eliminated by the sinusoids. There is no January 

 anomaly and there is no difference in the slope of the inclines , but the lag of the minimum average 

 temperatures in the deeper layers of the ice, as compared with the time during which these same 

 temperatures occurred in the layers near the surface, is shown in greater relief. 



Table 80 shows the mean monthly air and ice temperatures , according to the observations 

 made by Savel'ev on Uyedineniye Island In 1939. The table shows the characteristic decrease of 

 the minimum temperature level and the sharp decrease of the average ice temperature by May and 

 June, despite the steadily increasing ice thickness. 



233 



