10. Appendix A. World Maps of N(z) Parameters 



Data from the weather stations listed alphabetically in table A-l were used to prepare 

 the maps in this appendix. Each station is preceded by a number to identify its location 

 on figure A-l and followed by a listing of surface refractivity values at the 1, 5, 50, 95, and 

 99 percent cumulative distribution levels for the 4 months of February, May, August, and 

 November. 



The N(z) parameters (all referenced to sea level) which are necessary to calculate N 

 at any altitude, z, in kilometers, are D , W , H u H 2 , H w , and z t . These are given in figures 

 A-2 through A-25. The z t chart for any particular month will determine which of the dry- 

 term curves will be used. If the desired altitude (above sea level) of N (z) is below the z% 

 value at the specified location, use the tropospheric equation 



N (z) = D„ exp | - jj- \ + W exp < - ^ \ . (A-l) 



If the desired altitude is above the z t value, use 



N(z) = D exp { -f- r (JL =^ }■ + Wo exp \ ~£\. (A-2) 



All three scale heights are required for equation (A-2) , whereas only two, H 1 and H w , 

 appear in the tropospheric equation. If the surface altitude of the location is greater than 



1 km, it is suggested that the "standard atmosphere" value of 3 km be substituted for H w 

 (see sec. 3.3). 



To illustrate the step-by-step procedure for determining refractivity from the N(z) 

 parameters, the following example (assuming heights of 2 km and 20 km above the surface 

 at a location 200 m above sea level, at latitude 15°N and longitude 0°, in August) is given: 



(a) Refractivity at 2 km above the surface: 



(1) At the assumed location, interpolate linearly between contours on figures A-19 

 to obtain z t (13.8 km) to see whether the altitude above sea level, z (2.2 km), is above or 

 below the z t value. It is below, so equation (A-l) should be used. 



(2) The map values at 15 °N and 0° of the parameters needed to calculate (A-l) 

 are: 



Do = 267.5 N-units (fig. A-14) 



Wo = 105.0 iV-units (fig. A-15) 



H, = 9.35 km (fig. A-16) 



H w =2.19 km (fig. A-l 8) 



(3) If these values are substituted in (A-l), N (z) is found to be 249.9 iV-units at 



2 km above the surface. (Probable errors due to contouring and data restrictions would 

 suggest the use of only three significant figures, i.e., 250 iV-units.) 



(b) Refractivity at 20 km above surface: 



(1) Check to see whether the assumed altitude (2 = 20.2 km above sea level) is 

 above or below the z t value. Since it is above, (A-2) should be used. 



(2) All the parameters are needed for this calculation. In addition to the four 

 values listed in calculation (a) above, these are required : 



H 2 = 5.90 km (fig. A-l 7) 



z t =13.8 km (fig. A-19) 



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