148 N CLIMATOLOGY 



beyond the horizon. The high signal strength is in keeping with the 

 properties of a surface duct. Nevertheless, deep, prolonged fadeouts 

 can occur in regions beyond the horizon as well as within the horizon. 



Price [37] has theoretically determined regions of deep radio fading 

 associated with surface ducts, which he has termed "shadow zones." In 

 the case of a transmitter above a surface duct, a representation of what 

 occurs is shown in figure 4.43. It shows the location of a shadow zone 

 above the radio horizon line in the normal interference region. In the 

 interference region, a fadeout of signal strength due to the presence of 

 superrefraction must be compared with the value of the field when only 

 the interference pattern is present. Papers such as those by Norton [38] 

 and Kirby, Herbstreit, and Norton [39] give methods for calculation of 

 the normal interference field. Ikcgami [40] gives a more general method 

 for the calculation of received power in the presence of ground based ducts. 



Ikegami's procedure is based on a simple geometrical optics ray-tracing 

 technique of determining the power relative to free space transmission 

 that is received at different locations from the transmitter. A more 

 refined, yet more complex, procedure is the field-strength calculations 

 along the lines followed by Doherty [41], in which a strict mode-theory 

 treatment of the problem reveals that geometrical optics is not sufficient 

 in the presence of refraction anomalies. Doherty expands techniques 

 originally considered by Airy [42] to determine relative field strengths in 

 the neighborhood of caustics (apparent ray intersections) that result 

 vicinal to refraction anomalies such as ducts. 



In the procedure that follows, a model for the determination of the 

 location and extent of shadow zones, rather than the determinations of the 

 actual received field strengths and powers at any particular point, will be 

 given for conditions typical of the temperate climate to aid the radio cir- 

 cuit engineer in avoiding these troublesome interference areas. 



Washington, D.C., is taken to represent an average temperate zone 

 climate. Fairly extensive work has been done in determination of various 

 ducting conditions at this station as well as with the average exponential 

 refractivity above this station. Therefore, Washington, D.C., will be 

 used as a model for all following calculations. 



The gradient of A^ with height determines whether or not a surface 

 duct will exist. Therefore, a surface ducting atmosphere corresponding 

 to conditions at Washington, D.C., consisting of a ducting gradient up to 

 any desired height, and the N s = 313.0 exponential atmosphere [9] above 

 this height, have been chosen for this study. The ducting gradients 

 chosen are maximum, mean, and minimum values for February, May, 

 August, and November (representing the middle of winter, spring, sum- 

 mer, and fall, respectively) taken from figure 4.38 and given in table 4.8. 

 Also in this particular model the duct is assumed to be of uniform height 

 throughout the region considered in the calculations. 



