A. INTRODUCTION 



The Zubov-Defant ice potential computation technique, although not 

 difficult, is quite tedious and in essence graphical or tabular. Further- 

 more, the results of the computation may indicate that ice formation is 

 very improbable o Clearly there is need for a technique that will indicate 

 with considerably less labor both possible ice formation and the quantity 

 of ice. In addition the technique should be placed on a simple analytic 

 basis to eliminate the need for several large-scale density nomographs or 

 bulky tables. 



B. DERIVATION OF THE ICE POTENTIAL FOR SALINITY > 24.70 %o 



When the salinity of sea water equals or exceeds 24.70 °/oo, the 

 maximum density occurs at the temperature of freezing, 



T f = - 0.0966 CI. -0.0000052 CI 3 , (1) 



where 



CI = (S-0.030)/l.805. (2) 



It can be shown that the results of thermohaline convection, which 

 are obtained by mixing of infinitesimal layers of sea water from the sur- 

 face to a depth h, are identical with those obtained when mixing is con- 

 sidered for the entire layer from the surface to h.# 



The density of freezing, ^f ( h ) , for a column of mixed water of 



depth h and with mean salinity S n h where 



.,h - -R-/ S(z) dz K (3) 



(4) 



is so nearly linear (i.e. the error is less than +0.01) that we can 

 express it as 



°"f (h) =°- t [T f (S 0fh ), $ 0ih ] =0.8104 S 0>h -0.1600 



When considering a graphic representation of the freezing density 

 (Fig. 1), it is quite apparent that ice must be formed to attain thermo- 

 haline mixing of a column of water of depth h, mean salinity S. h , 

 and a density at h, ^ = o" f [ T(h)jS(h) ] j 



if °"h is greater than °f ( h ) . 



The graphical equivalent of this statement is that the point ( S h • ) 



■"See Appendix I 



