In order to simplify the further calculations, let us suppose, in the first place, that during 

 the melting the average temperature of the ice chunk does not change. * 



With such assumptions we obtain 



Qs+Qi= 0. 



(4) 



The heat currents which penetrate through the upper surface of the ice stem from two sources: 

 the radiation balance, S„ , and the heat exchange between the ice and air, Q . Therefore the first 

 member of the equation (4) can be represented in the form of the sum 



where 



Qs=Qr + Qa, 



(5) 



Q, = R + r{l-A)-E, 



Qa = flw{i,-i,)], 



(6) 

 (7) 



where R = direct radiation, 



r = diffused radiation, 



A = alebedo (light reflecting factor), 



E = effective back radiation, 



w = wind speed, 



ta-t-^ = difference in temperature of air and ice surface. 



The second member of equation (4) is characterized by the processes of accumulation (precip- 

 itation and condensation) and the processes of ablation (melting and evaporation) which occur on the 

 ice surface. 



Evaporation and condensation are in actuality a single physical process. Let us designate the 

 difference between them by the symbol D , prefixing the minus sign to this value when evaporation 

 predominates and the body becomes cooler, and the plus sign when condensation predominates and 

 the body becomes warmer. 



If the melting is now considered for 1 square cm of surface and if the sum of the heat is ex- 

 pressed in small calories, we obtain 



Qi =dD — US. + zM, 



(8) 



*This assumption is actually not true, for although the temperature of the lower surface of the 

 ice is always around the freezing point and the temperature of the upper surface remains around 0° 

 during the melting period, the temperatures in the middle part of the ice remain for a long time 

 below the freezing point of salt water. This explains the summer accretion of ice from beneath on 

 account of heat conduction as we have already seen. Obviously, when we ignore the change of 

 temperature within the ice, we also likewise ignore the influence of this change on the processes 

 which occur at the lower surface of the ice. 



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