ATLANT. DEEP-SEA EXPED. 1910. VOL. l) PHYSICAL OCEANOGRAPHY AND METEOROLOGY 



41 



111 other words, about 44 '\'o of tlie quantity of lieat 

 absorbed iu the sea by tlie direct and tlie diffuse solar 

 radiation is consumed by the evaporation. 



The sea may be regarded as a nearly "black body". 

 According to Stef.\n's law the radiation outward, E, is 

 proportional to the fourth power of the absolute tempera- 

 ture (T) of the body: 



E — k T\ 



k being a constant which for a perfectly black body is 

 equal to 1-28 /, 10 '-, when the radiation ^s calculated 

 in gram calories per second per square centimetre of the 

 surface. This radiation is 15 per cent greater at 10*^ C 

 and 33 per cent greater at 20' C than at 0° C. 



On the other hand, heat radiates from the air to the 

 sea. As the temperature of the air generally is lower than 

 that of the sea, the dark heat radiation from the air to 

 the sea is, on an average, smaller than the corresponding 

 radiation the other way. By using the indices s and a 

 for sea and air respectively, we have : 



Q3=^ Qs — Qa =^ ks Ts 



knTaK 



On account of reflection, the intensity of the radiatioii 

 from the very surface of the sea is reduced in such a way 

 ihaiks may be put equal to 0-83XA:X86400^ 918X10™ 10 

 when we calculate the radiation for 24 hours. The factor 

 0-83 is computed by W. Schmidt [1915]. 



k„ is a constant not very different from ks, but 7a 

 is a variable quantity, as the radiation from the atmo.s- 

 phere to the sea takes place up to high levels, varying 

 with cloudiness, humidity etc. Qa is, therefore, difficult to 

 calculate directly. 



The effective radiation Q.^ from the surface of the sea 

 outwards may, however, with sufficient approximation be 

 computed from observations of the nocturnal radiation 

 made by means of a black-bulb thermometer [Angstrom, 

 1915; DoRNO, 1919]. Considering the variations in cloud- 

 iness, we find the effective radiation between 70° N and 

 70° S to be on average equal to 0-78 g. cal. cm.- min., or 



Q., — 112 g. cal./cm.- 24 hours. 



The effective radiation outward from the sea corre- 

 sponds to about 41 7" of the quantity of heat gained by 

 the direct and the diffuse solar radiation. 



We have: 

 Q4 — 275 — 120 - 112 — 43 g. cal. cm. ^ 24 hours. 



W. Schmidt [1915] has calculated the quantities of heat 

 (w) which are at disposal for the evaporation (f) and the 

 convection from the sea to the atmosphere. He has, further, 

 calculated the ratio v/w, and found it to be 0-63 on an 

 average between 70' N and 70° S. This gives Q4 --0-37Q.J 



14 g. cal., cm.- 24 hours, or practically the same value 

 as found above. 



The above calculations do not claim to give more 

 than an estimation of the relative importance of the various 

 causes for the loss of heat from the sea in general. The 

 result is, then, that among these causes the evaporation 

 is the most powerful one. Second to the evaporation in 

 importance comes the excess outioard radiation of dark 

 heat, called Q., above, and finally the direct convection 

 of heat to the atmosphere. By the two latter processes 

 the heat is given off to the air directly above the sea, 

 while the latent heat of the water vapour may be liber- 

 ated far away from the places of evaporation. 



These results refer to the average conditions only. 

 There are many variations in the quantitative relation 

 between the said agencies. It depends upon the actual 

 conditions in the atmosphere (humidity, stability, cloud- 

 iness, wind etc.i and the absolute temperature of the sea 

 surface as well as of the air. We shall, however, not go 

 further into these questions here. 



30. Absorption of Heat in the Sea. 



Ill the previous section it was stated that the average 

 quantity of heat (QJ, absorbed by the sea from direct and 

 diffuse solar radiation amounted to about 275 g. cal. cm^ 

 24 hours. The heat rays in question are of different wave- 

 lengths, and the heat energy of the rays varies with the 

 wave length, as is well known. Generally speaking, this 

 energy increases from the extreme point of the very long 

 infra-red part of the spectrum towards the small visible 

 part of it and still a little further, attaining a maximum 

 in red at a wave length of about 000065 mm. 0-65//. 

 Then it decreases quickly towards the blue and violet part 

 of the spectrum and is very small in the ultraviolet part. 

 Summing up the heat energy of various parts of the 

 spectrum we find that about 60 % of the total heat energy 

 of the normal spectrum (at sea level) is due to the dark 

 rays and about 40 "/" to the visible, assuming that the 

 sun is at medium height [Dokno, 1919]. 



If the solar radiation that penetrates the water and 

 is absorbed there has an initial intensity /,,, it will acquire, 

 after having passed through a length A of the water, a 

 reduced intensity, which may be found by the formula: 



li^Ioe 



-tL 



where e — 2-71828 and t — a quantity generally called 

 the coefficient of absorption (or coefficient of extinction), 

 f may be defined as the reciprocal value of the way which 

 the rays must go in the absorbing medium in order to 

 have their intensity reduced to l/c of the initial value. 



