= 9r=(«+4x|^)il. 



Following the reasoning of the preceeding section, we obtain, 



(6) 

 Substituting A. = 80 g-cal, 6j = 0.9, 6^, = 1.0 and 0^,= 1.0 in (6), we obtain 



As can be seen from (7), under the conditions of the problem posed, the supplementary term 

 that I introduced into Stefan's formula is comparatively small. However, if we assume that on 

 cooling to 0°, the lake water, prior to the appearance of the first ice, will be mixed by the wind to 

 a depth greater than the thickness of the ice, the supplementary term in formula (7) will naturally 

 become 0. 



Naturally, it can also be assumed that in the sea, the upper layer of water which exceeds 

 (sometimes considerably) the maximum possible ice thickness will be mixed and cooled to the 

 freezing point by the time the first ice appears. In the sea, however, ice formation involves sal- 

 inification of the upper layer and subsequently, convective mixing to a depth which depends on the 

 vertical temperature and salinity distribution. Thus, in the sea, the supplementary term in for- 

 mula (7) will be zero only in shallows, where the water is cooled and mixes to the bottom and in 

 regions where the density of the upper layer differs so much from that of the lower layers that its 

 salinification occurring during ice formation does not cause convective mixing, which would in- 

 volve new layers in the vertical circulation. 



Now let us apply our discussion to a stratified sea. Let us assume that the entire upper 

 layer is mixed to a certain depth at the moment the sea is cooled to the freezing point. In this case, 

 ice formation will first occur according to formula (1) . 



If the upper layer is sufficiently thick and if its salinity is considerably less than that of the 

 lower layers, with the given number of freezing degree-days, in the region under investigation, the 

 entire process of ice formation could be limited to this layer, and formula (1) would be sufficient to 

 characterize the phenomenon. However, if the first layer is thin, the vertical circulation can in- 

 clude the second and deeper layers. In the latter case, the phenomenon described by formula (1) 

 will continue only until the salinification accompanying ice formation raises the density of the upper 

 layer to the density of the layer second from the top. 



The vertical distribution of oceanographic characteristics below the first layer can be quite 

 diverse, but there can be no inversion of density and salinity; however, a temperature inversion, 

 particularly under arctic conditions, is usual. Let us assume, for the sake of simplicity, that all 

 the lower- lying layers are quite thick and that each of them, taken separately, is uniform. In such 

 a case, after the density of the upper layers becomes equal to the density of the second layer, the 

 heat released to the atmosphere by a unit of ice surface during time dT will, as before, be equal to 



-dT, 



where i is the thickness of the ice formed before the density of the first layer became equal to the 

 density of the second layer. However, this heat will now be released due to cooling of the second 



215 



