11. Appendix B. World Maps of aN. 



The weather stations from which data were obtained for this study are shown in 

 figure B— 1. Their locations, elevations and the 5-year mean surface refractivity for each 

 month of the year are alphabetically listed in table B-l. 



The monthly aN values between the surface and 1 km above the surface are pre- 

 sented in figures B-2 through B-13. If the &N at a specific location is desired for a cer- 

 tain month and year for which a monthly mean surface refractivity value, N s , is avail- 

 able, the following relationships may be used : 



a~N = b (W s - K) + IN, (B-l) 



where 



N s = N exp -° 1(z) ; z = elevation above sea level in km. 



World maps of N„ (the yearly sea-level value of refractivity), b (the slope of the 



regression line (B-l) ),and aN (the mean annual value of the refractivity difference be- 

 tween surface and 1 km) are presented in figures B-14 through B-16. 



If the A.ZV value were required at a station with an elevation of 300 m and a location 

 of 30 °N and 30 °E, here is the procedure which would be used. Available surface wea- 

 ther reports indicate that the mean N s was 314 for a recent month for which a value of 

 AN is needed. Therefore, at the assumed location, these values are interpolated linearly 

 from the figures : 



Wo = 320 (fig. B-14) 



IN = 48 A r -units (fig. B-l 5) 



b = 0.60 (fig. B-16) 



Jv7= 320 exp- - 110 - 3 ' = 311 

 Using the value of 314 for N s , AN is found to be 50 iV-units. 



In some areas of the world (e.g., where the assumption of an exponential distribution 

 of the wet term is largely invalid ; see sec. 3.4) , the use of the regression method to predict 

 AiV has definite limitations. To delineate these locations, figures B-17, B-18, B-19, and 

 B-20 are presented. The first two figures are world maps of the correlation coefficient and 

 the standard error of estimate of the regression line of aN versus N s for the 60 months of 



station data, and figure B-19 gives the percentage of this standard error to the AiV value. 

 Areas with correlation coefficients < 0.5 (fig. B-17), standard errors > 5 iV-units (fig. 



B-18), and standard errors > 12 percent of aN (fig. B-19) are shaded, but the use of 

 equation (B-l) for any location in these shaded areas may still be valid if: 



(a) a low correlation coefficient occurs with a small standard error (typical of sta- 

 tions with a small seasonal range of variability in both N s and AN) , or 



(b) a large error is found with a good correlation (typical of stations with distinct 

 wet-dry seasons) . 



However, if the coefficient is less than 0.7 (reducing the variance of AiV to <— 50 per- 

 cent) and the standard error is greater than 10 percent of aN (as discussed in sec. 7), it 

 would be reasonable to assume that the yearly dependence of aN upon N s is not sufficient to 

 justify the regression prediction method. Areas represented by these criteria are shaded 

 in figure B-20. 



48 



