Using an albedo of 80 percent, a figure for solar 

 radiation into the berg {Q,— Qt) of 0.03 gm cals/ 

 cmVmin is obtained. Applying this figure to the 

 hypothetical berg described above, and taking 

 only that portion of the berg above the water that 

 receives this radiation, it is found that 1.1 

 XIO' cm-X0.03 gm cal/cmVminX2.88X 10* min 

 = 0.095X10'^ gm cals of heat received by the 

 berg during its 20-day decay period. 



Back radiation (Q,,) from a berg represents a 

 loss of heat in the budget. Surface and near 

 surface radiative losses will be the most important 

 and would certainly be more intense than any 

 radiation from the colder interior. The Stefan- 

 Boltzman radiation law states that Q=kcT*; 

 where a is the universal cgs units constant of 

 8.312X 10-" gm cals/cm7°K* min, Tis the absolute 

 temperature degrees Kelvin, and k is blackbody 

 or perfect radiation constant. According to 

 Shumskiy et al. (1964) the radiative ability of 

 snow, the k constant, is as high as 0.99. If 0° C. 

 is assumed for the surface, an upper value of 

 radiated heat loss from the berg can be estimated 

 and would be on the order of 0.46 gm cals/cmVmin. 

 Assuming radiative heat loss from the total surface 

 of the hypothetical berg results in a Qtr of 0.46 

 gm cals/cm7mmX2.88X10* minX7.0X10» cm^ 

 = 9.26X10'^ gm cals during the decay period. 



It should be pointed out that the maximum 

 radiative intensity from the sun comes in at about 

 0.48/i, indicating that the greatest mtensity lies in 

 the visible range. The reradiated energy from the 

 berg wUl follow the Wien's displacement law which 

 states that the maximum radiative frequency 

 (^max) is a function of temperature: 



2897 



"max rpo 



where T is in degrees Kelvin. This says that the 

 berg will radiate energy in the vicinity of lO/i or 

 long wave radiation. The frequency of emission 

 is also the frequency of greatest absorption 

 therefore a berg will readily receive long-wave 

 radiation from its fluid environment. 



Radiative heat transfer from the berg's en- 

 vironment (Qaw,) involves so called blackbody 

 radiation based on the environmental absolute 

 temperatures. Using the Stefan-Boltzman radia- 

 tion law and assuming perfect blackbody radiation 

 for temperatures from 0° C. to 20° C, it is found 

 that the radiative heat transferred to a berg varies 

 from 46.1X10-' gm cals/cmVmin to 61.3X10"- 

 gm cals/cm7min as shown in figure 6C. This trans- 



fer of heat will affect the berg proportionately as 

 the air and/or sea temperature varies. The 

 fluid environment radiation is not perfect black- 

 body radiation as is the sun's but is considered 

 more of a greybody type. However for the pur- 

 poses of this paper, perfect radiation will be as- 

 sumed to obtain maximum heat transfer values. 

 Because most of the berg's mass is below the water 

 surface, the water will dominate the radiative heat 

 transfer quantities. This long-wave radiation is 

 absorbed most readily by a berg and since the 

 fluid environment is surrounding the berg on all its 

 facets, reflection due to angular mcidence would 

 be minimal. For this reason, consideration of an 

 albedo would probably not apply in this situation. 

 As can be seen from figure 6C, even with the air 

 at a higher or lower temperature than the water, 

 the overall radiative effect will be little changed. 

 This is true not only because of the small magni- 

 tude change m Q due to warmer or cooler air, 

 but because of the smaller surface area presented 

 to the air compared to that bathed in the sea. 

 Usmg the total hypothetical berg surface area and 

 equal air and water temperatures, arbitrarily taken 

 at 2.2° C, gives a heating contribution of 0.48 

 gm cals/cmVminX 7.0X10* cm2X2.88X10' min = 

 9.67X10'' gm cals. 



Summing up the computed quantities thus far: 



Q,-Q,=0.095X10'2 gm cals 



Qa^r=+9.67X10''gmcals 



-9.26X10'''gm cals 



Qir- 



" 0. 505 X 10*2 gm cals 



net heat added. 



As mentioned, the net heat added to a berg is 

 utilized for both melting and raising the berg's 

 temprature to 0° C. The amount of heat needed 

 to raise the hypothetical berg's 2.7 X 10'^ gms of ice 

 from — 12° C. to 0° C. will be given bv: 



where : 



Q^r = c,XAT°XM 



Af=mass of the berg 



Cp=specific heat of ice at —12° C. 



therefore : 



Q^r=0A9 gm cals/gm °C.X 12°X2.7X 10'' gm 



= 1 5.85 X 10"' gm cals. 



The rest of the added heat must go into the 

 heat of fusion which would equal: Q/=hfXM 



44 



