3. World Maps of N(z) 



3.1. Development 



In order to prepare worldwide maps of upper 

 atmospheric N from the 5-year mean N-profiles 

 described previously, it was decided to reduce 

 the quantity of necessary N (z) maps by ab- 

 stracting each mean profile in terms of a model 

 atmosphere which would use three negative ex- 

 ponential functions of altitude. The three func- 

 tions which are used to represent each mean pro- 

 file are a single exponential for the wet term, W, 

 and two exponentials for the dry term, D. Two 

 exponential functions are necessary for the dry 

 term because of the change in the lapse rate of 

 the temperature from the normal 6.5°C/km in 

 the troposphere to the nearly isothermal strato- 

 sphere where the temperature may increase 

 with height. Least-squares fits were obtained for 

 log W versus height over the interval to 3 km 

 above the surface. The ranges to be covered by 

 the two fits for the dry term were determined 

 from the mean tropopause heights and their 

 standard deviations which had been obtained 

 during the analysis of the A T -profiles in each 

 sample. The tropospheric dry term, D lt was fit 

 over the interval to the tropopause height 

 minus one standard deviation, and the strato- 

 spheric dry term, D 2 , was fit from the tropo- 

 pause height plus one standard deviation to the 

 upper limit of data for that profile. In both 

 cases, log D was fit to height using least squares. 

 The resulting model atmosphere is given by 



+ W exp ( — -gr- J , 



z ^ Zt, 



(3) 



+ TF exp(--|-), (4) 



z >z t ; 



D and W are the mean sea-level values of the 

 dry and wet terms (reduced from the surface 

 values using the free-atmosphere scale heights) , 

 H XI1 is the wet-term scale height, fl a is the tropo- 

 spheric dry-term scale height, H 2 is the strato- 

 spheric dry-term scale height, and z t is the 

 altitude above mean sea level of the point of 

 transition between the tropospheric and strato- 

 spheric dry-term exponentials. The altitude, z u 



may thus be thought of as an effective density 

 tropopause. 



Examples of the application of this model to 

 actual mean refractivity profiles are given in 

 figures 1 and 2: a very good fit (Koror) and one 

 of the worst fits encountered (Dakar). The 

 good fit obtained in figure 1 is especially signifi- 

 cant since Koror represents a climatic type 

 (equatorial station with a very high mean sur- 

 face refractivity, 387.6) for which exponential 

 models of N were previously thought to be un- 

 satisfactory [Mismeet al., I960]. Dakar (fig. 2) 

 is an example of the climatic type (character- 

 ized by a persistent low-level temperature in- 

 version with dry subsiding air above) where 

 this model (or any other simple model) of iV 

 versus z is inadequate to explain the ^-structure 

 at low latitudes. It was found that the behavior 

 of the wet term (measured on figs. 1 and 2 by 

 Sw, the rms error over the first 3 km) was a good 

 indicator of whether or not the data would pro- 

 vide a good fit to the profile. However, it can 

 be noted in figure 2 that, even though the rms 

 wet-term error below 3 km is 14.6 iV-units, the 

 profile at Dakar above an altitude of 6 km is 

 well represented by the three-part exponential. 



Maps were prepared for each of the 4 "sea- 

 sonal" months of the parameters necessary to 

 utilize the three-part exponential in estimating 

 upper-air refractivity. These are the reduced- 

 to-sea-level values, Do and W ; the three scale 

 heights, fl«„ flj, and H 2 ; and the_transition alti- 

 tude, z t . The surface values of N can be recov- 

 ered by substituting the elevation of the surface 

 above sea level at the desired location in (3), 

 which amounts to inverting the process used to 

 reduce the surface values of N to sea level. The 

 series of maps given in appendix A can be used 

 to estimate the mean value of N at any desired 

 altitude for each of the seasonal months at any 

 world location except those areas outlined in 

 figure A-30 (which summarizes the wet-term 

 rms error values found in figures A-26 through 

 A-29). 



3.2. Discussion of N{z) Map Contours 



The world maps of N(z) parameters reveal 

 a number of interesting trends. Some of these 

 are: 



(1) The D, scale height, H, : 



(a) is smaller than average over the arctic 

 seas in winter because of dense stratified air ; 



