5. World Maps of Extreme N-Gradients 



5.1. Development 



The gradient of N near the surface of the 

 earth is of particular importance in many appli- 

 cations of telecommunications ; e.g., extreme 

 values of these initial gradients are responsible 

 for much of the unusual behavior of radio sys- 

 tems. Superrefractive gradients (defined here as 

 values between -100.0 TV/km and -156.9 N/km) 

 are responsible for greatly extended service hori- 

 zons, and may cause interference between widely 

 separated radio circuits operating on the same 

 frequency. Ground-based radio ducts (layers 

 having a negative gradient larger in absolute 

 value than 156.9 N/km) can cause prolonged 

 spacewave fadeouts within the normal radio ho- 

 rizon [Bean, 1954] and allow radar to track ob- 

 jects many hundreds of kilometers beyond the 

 normal radio horizon. On the other hand, subre- 

 fractive gradients (zero or positive gradients) 

 produce greatly reduced radio horizons, and 

 may result in diffraction fading on normally 

 line-of-sight microwave paths. 



In the process of obtaining the mean A r -profile 

 for each station and month, cumulative distri- 

 butions were prepared of the gradients occur- 

 ring between the surface and the 50-m and 

 100-m levels. Each gradient was calculated as 

 the simple difference between the surface TV 

 and the value at 50 or 100 m above the surface, 

 divided by the height interval. For 99 out of the 

 112 stations in the mean N sample, cumulative 

 distributions were also prepared of the gradi- 

 ents and thicknesses of all observed ground- 

 based superrefractive or ducting layers, regard- 

 less of the thickness of the layer (except that 

 no layer less than 20 m thick was included, be- 

 cause the gradients obtained in such cases are 

 not considered to be reliable) . In addition, 

 cumulative distributions were prepared of the 

 minimum trapped frequency for each of the ob- 

 served ducts in the sample. (This sample size 

 averaged 208 pieces of data for each month ; 

 for all months the smallest sample was 30 and 

 the largest, 620). The minimum trapped fre- 

 quency refers to the approximate lower limit of 

 frequencies that will be propagated in a duct in 

 a waveguide-like mode, and is given by [Kerr, 

 19511 



h 



1.2 X 10 5 (c/s) 



(t) Vl [• 



dn 

 dz 



(6) 



"] 



where / min is the minimum trapped frequency in 



c/s, t is the total thickness of the duct in km, 

 dn/dz is the average gradient over the duct 



(n/km), and r is the radius of the earth in km. 



Equation (6) is derived under the assumption 

 of a constant gradient throughout the duct, but 

 moderate departures from this assumption do 

 not seem to affect the results greatly. The /mm 

 corresponds to an absolute attenuation of the 

 guided energy of about 3 dB/km (5 dB/mile) 



[Kerr, 1951]. 



The maps in appendix C were prepared from 

 the cumulative distributions discussed above. 

 The distributions of gradients for the to 

 100-m layer were used to obtain maps of the 

 positive (subrefractive) gradient exceeded for 

 10 and 2 percent of the observations at any lo- 

 cation, and the percent of observations with 

 or positive A T -gradients. Maps were also pre- 

 pared of the extreme values of negative gradi- 

 ents observed ; these are referred to as "lapse 

 rates" of N (i.e., decrease with height, a term 

 normally used in referring to atmospheric tem- 

 perature gradients ; it is used here to avoid the 

 awkwardness of referring to a very strong nega- 

 tive gradient as being "less than" a given nega- 

 tive value). Included in appendix C are maps 

 of the lapse rate of N exceeded for 25, 10, 5, 

 and 2 percent of the observations for the 100-m 

 layer. Cumulative probability distribution 

 charts of the gradients at 22 representative 

 world locations are also presented. 



Other maps in appendix C were prepared 

 from the distributions of superrefractive and 

 ducting layer gradients, thicknesses, and / m m 

 values for ducts. These include the percent of 

 time that the lapse rate of N in the ground- 

 based layer is equal to or larger than 100 N/km 

 and equal to or larger than 157 N/km (ducting 

 gradient) , the percent of superrefractive layers 

 that were more than 100 m thick, and the per- 

 cent of ducting layers that were more than 100 

 m thick (the last two refer to the percent of 

 thick layers out of the number of observed lay- 

 ers of that type) . The distributions of /mm 

 values were used to prepare maps of the per- 

 cent of all observations which showed ground- 

 based ducts having an /,„m value of less than 

 3000 Mc/s, 1000 Mc/s, and 300 Mc/s. 



5.2. Discussion of Gradient Map Contours 

 (Subrefraction) 



Ground-based subrefractive layers may be 



12 



