420 Tables 135 and 136 



TOTAL DIRECT SOLAR RADIATION REACHING THE GROUND WITH 

 VARIOUS ATMOSPHERIC TRANSMISSION COEFFICIENTS 



The basic formula for computing the direct solar radiation / which falls on a unit 

 horizontal area at the earth's surface in time t is 



if = -§a'««cos* (1) 



at r 



where a is the transmission coefficient of the atmosphere, r is the radius vector of the 

 earth, 7 is the solar constant and z is the sun's zenith distance. The development based 

 on the computations of Milankovitch 1 is similar to the case for the radiation at the top 

 of the atmosphere (p. 414) except that numerical integration is used instead of analytical 

 integration. Jo is assumed to be 1.94 cal. cm" 8 min." 1 

 Some approximations have been made, namely: 



(a) Equation (1) is assumed to apply to total solar radiation although its derivation 



is applicable strictly only to monochromatic radiation. 



(b) Refraction by the earth's atmosphere has been neglected. 



Table 135 gives the direct solar radiation in cal. cm." 2 which reaches a horizontal area 

 at the surface of the earth during one day with various atmospheric transmission coeffi- 

 cients, as a function of terrestrial latitude and solar longitude (or date). 



Table 136 gives the direct solar radiation in cal. cm." 2 which reaches a horizontal area 

 at the surface of the earth during the whole year with various atmospheric transmission 

 coefficients, and also the amounts for the summer and winter half-year (March 21 to 

 September 23 and September 23 to March 21 respectively). 



Computation of diffuse sky radiation. 2 — Table 135 gives only the component of the 

 direct solar radiation which reaches a horizontal surface. To estimate the total radia- 

 tion (direct plus sky) which reaches a horizontal surface under cloudless conditions, the 

 diffuse sky radiation must be added to the values given. The sky radiation may be ap- 

 proximated roughly by use of the following assumption : 3 Of the radiation which is 

 scattered from the direct solar beam, half is scattered forward (downward) and half 

 is scattered back. This assumption is strictly correct only when the scattering particles 

 are small by comparison with the wave length of light. 



The procedure for estimating the sky radiation under this assumption is : 



(1) Find the extra-terrestrial radiation h for the latitude and date desired from 



Table 132. 



(2) Decrease h by 9 percent to allow for water vapor absorption 4 (7 percent) and for 



ozone absorption 5 (2 percent). The remaining radiation is given by 0.91 U. 



(3) Find the appropriate value of the direct radiation reaching the surface of the 



earth from Table 135 and substract from 0.91 h. The resulting difference, S, 

 approximates the energy scattered out of the solar beam. 



(4) Compute S/2. S/2 is the diffuse sky radiation and is to be added to the value 



from Table 135 to give the total radiation reaching the surface of the earth. 



The annual and seasonal values given in Table 136 may be treated in a similar manner 

 with the aid of Table 133. 



Another estimate of the average diffuse radiation for middle latitudes may be ob- 

 tained from Kimball's 6 measurement as a function of air mass. To apply these to 

 Table 135, Kimball's data should be integrated over the day. 



1 Milankovitch, M., Mathematische Klimalehre, Berlin, 1930. Handbuch der Klimatologie, Band I, 

 Teil A. 



2 Fritz, S., private communication, 1949. 



8 Kimball, H. H., Month. Weath. Rev., vol. 63, p. 1, 1935. 



* See Tables 139 and 140. 



8 Fritz, S., Journ. Meteorol., vol. 6, p. 277, 1949. 



•Kimball, H. H., Month. Weath. Rev., vol. 47, p. 769, 1919. 



{continued) 



SMITHSONIAN METEOROLOGICAL TABLES 



