perature, medium sized, blocky berg, and a de- 

 terioration time of 20 days (2.88X10^ mm.)- 

 The dimensions of the berg selected are 100 meters 

 wide, 100 meters long, and 300 meters in overall 

 height. Using an ice density of 0.9 gm/cm' 

 (Smith 1931) this gives an above the water height 

 of 30 meters. With a total mass of 2.7 X 10'^ gms 

 and a surface area of 1.4 X 10^ cm^. 



Because the berg is constantly being reduced in 

 size, it will be assumed that this reduction is linear 

 as far as its surface area is concerned over the 

 20-day period. This means that a representative 

 area, integrated with respect to time, can be as- 

 sumed to be one-half of the initial surface area 

 which would be 7.0X10" cm^ 



Before proceeding with the analysis a few more 

 assumptions must be m.ade. The net heat added 

 to an iceberg must be utilized for both raising the 

 berg's temperatiu'e to its melting point and for 

 heat of fusion to melt the berg. Barnes (1927) 

 has shoMTi that the icebergs are basically fresli 

 water and can even be compared to distilled water. 

 Due to the bergs glacial origin this seems reason- 

 able and therefore, the physical constants for 

 fresh water such as heat of fusion may be applied 

 to icebergs. 



According to Bader (1961) direct temperature 

 measiu-ements of the Greenland ice cap indicate 

 that as the various glaciers flow towards the sea 

 they assume an internal temperature similar to tlie 

 mean annual ah- temperatiu-es. Furthermore, the 

 internal temperatiu-es are found to be quite uni- 

 form from top to bottom varying only about 1° C. 

 Bader shows that in the xicinity of the Jacobs- 

 haven glacier, postulated by Smith (1931) to be 

 a prime source of bergs, a temperatiu-e of about 

 — 12° C. would apply. For this paper this figure 

 will be assumed to be the minimum mternal 

 temperature of an iceberg. 



Durmg melting, the berg's surface would be 0° 

 C. and it would have a negative internal tempera- 

 ture gradient. This gradient would certamly be 

 a variable and some actual measurements will be 

 required. For the purpose of this treatment it 

 will be assumed that a specific portion of received 

 heat will be utilized for raising the berg's surface 

 temperatvu'e to 0° C. prior to melting and mam- 

 tauiing the thermal gradient. 



The quantities (Qs—Qr) of equation (1) are 

 affected by the icebergs particular properties of 

 absorption and reflection. Q^, the incoming solar 

 radiation, is an environmental property which not 

 only tends to provide direct heat energy for 



melting the bergs surface but also indirect energy 

 for heating the bergs environment. 



The nature of the ice surface on which this 

 incoming radiation (Q^) falls, is an important 

 factor in determinimg the effectiveness of this 

 heat source. Before any heating can take place, 

 the radiant energy must penetrate this surface. 

 The ratio of reflected energy to incident energy, 

 or albedo, provides the first tool for estimating 

 the heat energy available for melting. The 

 albedo percentage must be estimated from meas- 

 urements made on snow fields since no direct 

 observations have been made on icebergs. Clean 

 snow fields are very similar to icebergs because 

 of the extreme whiteness of bergs due to their 

 saturation with air bubbles. The air bubbles 

 decrease the transparency of bergs and cause 

 scattering of the incident radiation increasing 

 the reflection. Albedo measurements have been 

 made for sea ice, however, puddhng, brine pockets, 

 and darkened transparent areas can severely 

 reduce the albedo and prevent comparison. 



Chernigovskii (1939) shows snow albedos range 

 from 87 percent during March to 60 percent 

 during July in the Arctic. This reduction is due 

 primarily to melting, puddling and surface texture 

 changes during the summer. Numerous investi- 

 gators have looked at the albedo of Antarctic 

 snow fields. Hoinkes (1960) indicates that values 

 ranging from 75 to 93 percent have been found 

 for instantaneous measurements. A value of 80 

 percent seems reasonable for a berg and will be 

 assumed until more accurate measurements can 

 be obtained. Actually, the albedo of a snow field 

 should be somewhat lower than a berg's because 

 of the berg's facets. These facets cause random 

 reflection which scatters a great deal of the inci- 

 dent radiation. This phenomena is variable 

 depending on a particular berg's configuration 

 and can be treated in general terms only, how- 

 ever, it is reasonable to suspect that the albedo 

 might be a good deal higher than the assumed 

 80 percent. 



Solar radiation values from Hess (1959) show 

 that at 45° N., a latitude of Ice Patrol interest, 

 the maximum incommg radiation reaching the 

 earth's surface during March and June ranges 

 from 0.14 to 0.38 gm cals/cm^min on a 24-hour 

 basis. Some direct measurements, figure Ic, 

 show that during a week in April 1965 an average 

 of 0.14 gm cals/cm^/min were received in the Ice 

 Patrol area of the Grand Banks of Newfoundland. 



43 



