Table 160 (continued) 453 



HORIZONTAL VISIBILITY 



Tables 160-A1 and 160-A2. — Transmissivity as a function of extinction coefficient, and 

 extinction coefficient as a function of transmissivity 



Assumptions and Computations: 



Assuming uniform conditions regarding scattering of available light toward the observer 

 along the path of sight and attenuation of light emanating from the object under view 

 by scattering and absorption of luminous flux through the action of the atmospheric 

 aerosol, the capacity of the atmosphere for transmitting such flux may be expressed 

 either in terms of the (generalized) extinction coefficient, <r, or of the transmissivity, T. 



In defining these quantities we consider a ray of light propagated along the jr-axis 

 in an atmosphere having uniform optical properties (homogeneous in composition, den- 

 sity and concentration of suspensoids). Since the quantities represent the attenuation of 

 luminous flux in the medium, they relate to the ratio of illumination on two imaginary 

 surfaces placed normal to the .r-axis and separated by unit distance. Thus 



let E = illuminance (luminous flux incident per unit area of surface) at distance 



x from the chosen origin; 

 £0 = illuminance at the origin x = 0. (This is generally taken immediately in 

 front of the light source or object being viewed, on the observer's side.) 



Then the extinction coefficient and transmissivity are related to these two quantities by 

 the equations : 



E = E e- ffX =EoT* (1) 



Hence 



T = e-' (2) 



<r=-log 9 r (3) 



Description: 



Table 160-A1 gives values of T as a function of <r, in accord with equation (2), and 

 Table 160-A2 gives values of a as a function of T or of logarithms to the base 10 of T, 

 whichever is most convenient, in accord with equation (3). 



Certain conventions have been adopted to conserve space. In Table 160-A1, with 

 regard to the range of a from 0.00 to 10.0, the tabular values are to be appended to 

 the quantities in the indicial column which immediately follows the column of arguments 

 headed "Extinction Coefficient." 



The superscript associated with quantities in the indicial column indicates the total 

 number of ciphers to be placed following the decimal point. If the tabular value is 

 prefixed by an asterisk, the tabular value is to be appended to the quantity in the next 

 lower line of the indicial column. 



Examples : 



a T 



0.00 1.0000 



0.01 0.9900 



4.60 0.01005 



4.61 0.009952 

 6.90 0.001008 

 7.00 0.0009119 



In the lower portion of the second page of Table 160-A1, giving T as a function of a 

 in the range from a = 1 to 1000 km" 1 , the value of T is found by multiplying the tabular 

 value by the factor 10 raised to the power shown in parentheses. 

 Examples : 



a T 



1 3.679 X 10- 1 



3 4.979 X lO" 2 



40 4.248 X 10"* 



Table 160- A2 gives values of a as a function of T or P where T = 10 p , (P = logioT). 

 Examples : 



T a 



2 X 10-* 8.5172 



0.75 0.2877 



lO" 210 552.620 



lO" 6 11.513 



(continued) 



SMITHSONIAN METEOROLOGICAL TABLES 



