C. DERIVATION OF THE ICE POTENTIAL FOR SALINITY < 24. 70 %o 



When S < 24.70 °/oo, the temperature of maximum density is higher 

 than the freezing temperature, so it is possible for convection to reach 

 a depth, z equal h, under two sets of conditions for some values of ^(h). 

 The following represent all the mutually exclusive conditions in the 

 water column (o,h) that have a bearing on convection: 



°" t ^ >cr max(So,h)> (ID 



{ 



°l (S o ) h )<0 -t ( ^ ) <°max<S 0)h ) (12) 



T o.h* T f (S 0fh >, 



°t (h)^a- f (s oh ), (13) 



raj (s o h )<o- t (h)^ . ^ (u) 



I T o,h > T <r m lS hJ , and 



{ 



af(S 0jh )<a- t (h)^cr mgx (S 0)h ) 



T f (S o,h ) < T o,h < T <r_ (S o,h^ • (15) 



Assuming convection to a depth h, equations 11 and 12 imply the formation 

 of ice; 13 and 14 imply that no ice forms, while 15 may fall into either 

 category. An inspection of Table 2 will reveal that for 



15 < S ? 25 , o- m (S) - o- f (S) 7. ,02j 



10 < S < 15 , o-m(S) - at (S) 1 .05; and 



3 z S < 10 



' o-mVS; - <r f {S) < ,02j 

 , o-m(S) - at (S) < .05; 

 » a nS S ) - o- f (S) = .10. 



