SECT. 7] THE PHYSICS OF SEA-ICE 835 



through the water. A number of attempts have been made to obtain more 

 general solutions of the problem. Kolesnikov (1958) gives a discussion with 

 references. Most of these solutions have been too involved to be of much use in 

 practical calculations. Stefan's equation works sufficiently well that a number 

 of equations based on it are frequently used; Assur (1956) may be cited as an 

 example. In these, equation (3) or a slight modification of it is usually assumed, 

 but with an empirical coefficient dependent on snow cover and type of ice. 



The decay of an ice cover is largely controlled by solar radiation and by the 

 albedo of the surface. The ice stops growing and starts to decay a considerable 

 time before the air temperature rises to the melting point of ice. The later 

 stages of the decay of an annual ice cover in the Arctic are startlingly rapid. It 

 takes place at a season with 24-h daylight and, until there are significant 

 amounts of open water, under usually cloudless skies. The albedo of the snow 

 cover changes within days or even hours from a value of 0.9, typical of clean 

 snow, to as low as 0.45. The snow cover melts rapidly leaving wet ice whose 

 albedo is almost as low. An ice cover 8 ft thick can melt completely within 

 6 weeks. 



The discussion above applies to annual sea-ice. The regime of the perennial 

 pack-ice in the Arctic and Antarctic is more complex. In winter this ice grows 

 by accretion of sea-ice at its bottom surface ; in summer the upper surface 

 melts. Since the ice cover is broken into floes at this time, the relatively fresh 

 meltwater drains to the underside of the ice and may refreeze there since its 

 freezing point is higher than that of the saline water. These processes lead to 

 an ice cover of fairly constant thickness of between 3 and 4 m. Solar radiation 

 seems to be the dominant control. For more details see Yakovlev (1958) and 

 Untersteiner and Badgley (1958). 



6. Theory of Sea-Ice Structure and Properties 



Important theoretical developments were reported in Anderson and Weeks 

 (1958), Anderson (1958) and Assur (1958). The primary purpose of these 

 theories is to account for the extreme variation with temperature and salinity 

 of the strength of sea-ice, from much less than that of pure ice at high tempera- 

 tures to at least twice as great at low temperatures. Space permits only a brief 

 and over-simplified summary of the arguments. It was pointed out earlier 

 that a sea-ice crystal contains brine inclusions distributed regularly in parallel 

 planes which are perpendicular to the c-axis. For stress applied parallel to the 

 c-axis, which is the direction of minimum tensile strength of the ice, these liquid 

 cells reduce the effective cross-sectional area. In addition they act as stress 

 concentrators. Anderson explains the reduced strength of sea-ice as jointly 

 caused by these two effects and writes the general equation 



a = crp{l-^e)lk, (4) 



where a and o-j, are the strengths of sea-ice and pure ice, /3e is the fraction of 

 unit area of the failure plane occupied by brine, and k is the stress concentra- 

 tion factor, which is equal to 3 for small, isolated, circular cylinders. Assur 



