Consider first the sunlight and daylight radiation. At a low sun 

 altitude of from 5 to 10 degrees, for example, a water or ice surface 

 will reflect a considerable part of the sun's rays. A fraction will 

 enter the water and be gradually absorbed, while the transmitted ra- 

 diation will be practically all absorbed by the lower layers of the 

 water body. At a sun altitude of 5" one square centimeter of water 

 surface will receive 0.6 calorie per square centimeter per hour. This 

 is only 0.5 percent of the amount of solar radiation reaching the atmos- 

 phere . 



Under these conditions and with a clear sky, the diffuse daylight 

 from all parts of the sky will give a greater input, namely 3 cal/cm? 

 per hour. If the sky is clouded, the diffuse daylight absorbed by a 

 water surface will be less but will still represent 1 cal/cmr/hr,, which 

 is more than the direct radiation would give at the low sun altitude. 



These figures of heat gained are small compared to heat losses in 

 winter. But when the sun's altitude increases, the incoming radiation 

 direct and diffused will contribute more and more to the heat absorbed j 

 and in the summer the relation will be reversed, as the heat received 

 will exceed the heat lost. 



Restricting the problem to winter conditions, next consider the loss 

 of heat by infrared radiation at a representative air temperature of -10° C, 

 With a clear sky and air temperature -10°C. the heat radiation from a 

 water surface at o C. will be about U+ cal/cmr/hr. 



Nearly all surfaces will absorb almost completely infrared radiation 

 of the type radiated from objects of moderate temperature, and with re- 

 spect to these rays, water is a black body. This is also the case with 

 snow. This means that infrared radiation falling on a water or snow sur- 

 face is completely absorbed in the uppermost layers in a very thin sheet 

 some hundredths of a millimeter thick. On the other hand the same layer 

 emits infrared radiation of the same wavelengths to the atmosphere. 



The next process to consider is the loss of heat by convection. 

 This loss is due to the difference in temperature between the water 

 surface and the air above, but it is also modified by the wind. It is 

 well known that a body is much more rapidly cooled when a wind is blow- 

 ing than when it is calm. The figures relating to a water surface are: 

 heat loss by convection 2.8 cal/cm?/hr. with an air temperature of -10°C. 

 and calm air, and heat loss by convection 11.5 cal/cmf/hr. with a wind of 

 5 meters per second. 



Another heat loss to be considered is the loss caused by evaporation. 

 The evaporation depends first upon the dryness of the air above the water 

 surface, or more exactly upon the vapor pressure, and secondly upon the 

 wind. With an air temperature of -10°C, a vapor pressure of 3.5 milli- 

 bars, and calm air, the loss by evaporation from a water surface at 0°C. 

 is 1.7 cal./cm. /hr., but if there is a wind of 5 meters per second it 

 will increase to 7.7 cal./cm./hr. 



