THE HEAT BUDGET OF THE OCEANS 53 



calories per square centimeter per minute, which reach a horizontal 

 surface in the indicated localities (computed from Kimball). The 

 differences between the parts of the oceans in the same latitudes are 

 mainly due to differences in cloudiness. 



Few direct measurements of radiation are available from the oceans, 

 and when dealing with the incoming radiation it is necessary to consider 

 average values that can be computed from empirical formulas. Mosby 

 has established such a formula by means of which monthly or annual 

 mean values of the incoming radiation on a horizontal surface can be 

 computed if the corresponding average altitude of the sun and the average 

 cloudiness are known. 



Q = kha - 0.071C) g cal/cmVmin. (IV, 4) 



Here h is the average altitude of the sun. The factor k depends upon the 

 transparency of the atmosphere and appears to vary somewhat with 

 latitude, being 0.023 at the Equator, 0.024 in lat. 40°, and 0.027 in lat. 

 70°. The values computed by means of this formula agree within a few 

 per cent with those derived by Kimball in an entirely different manner 

 (table 6). 



Part of the incoming radiation is lost by reflection from the sea surface, 

 the loss depending upon the altitude of the sun. When computing the 

 loss, the direct radiation from the sun and the scattered radiation from 

 the sky must be considered separately. With the sun 90°, 60°, 30°, and 

 10° above the horizon, the reflected amounts of the direct solar radiation 

 would be, according to Schmidt, 2.0 per cent, 2.1 per cent, 6.0 per cent, 

 and 34.8 per cent, respectively. For diffuse radiation from the sky and 

 from clouds, Schmidt computes a reflection of 17 per cent. Measure- 

 ments made by Powell and Clarke give values on clear days in agreement 

 with the above, but on overcast days, when all radiation reaching the sea 

 surface was diffuse, the observed reflection was about 8 per cent. If the 

 fractions of the total radiation from the sun and the sky on a clear day 

 are called p and q, respectively, and if the corresponding percentages 

 reflected are called m and n, the percentage of the total incoming radiation 

 which is reflected on a clear day is r = mp + nq. On an overcast day, 

 when all incoming radiation is diffused, r = 8 per cent. Table 7 shows 

 approximate values of r at different altitudes of the sun on a clear day. 



Table 7 



PERCENTAGE OF TOTAL INCOMING RADIATION FROM SUN AND SKY 



WHICH ON A CLEAR DAY IS REFLECTED FROM A HORIZONTAL 



WATER SURFACE AT DIFFERENT ALTITUDES OF THE SUN 



Altitude of the sun 5° 10° 20° 30° 40° 50° 60° 70° 80° 90° 



Percentage reflected 40 25 12 6 4 3 3 3 3 3 



The values in the table are applicable only if the sea surface is smooth. 

 In the presence of waves the reflection loss at a low sun is somewhat 



