Chapter 13 



THEORETICAL ANALYSIS OF ERRORS IN RADAR 

 DUE TO ATMOSPHERIC REFRACTION* 



131 PURPOSE 



This report is a theoretical evaluation of errors 

 in altitude, azimuth, and range caused by atmos- 

 pheric refraction. These errors are compared with 

 the error tolerance specified in military characteris- 

 tics for fire control radar equipment. Regional 

 climatological data are utilized to determine probable 

 refractive index gradients used in the determination 

 of the error. Errors in heightfinding resulting from 

 ducts are also treated. An Evans Signal Laboratory 

 [ESL] report now under preparation discusses errors 

 which may occur during specific meteorological 

 situations and which may exceed the errors indicated 

 in this report. 



13.2 



PROCEDURE 



The variation of the index of refraction perpen- 

 dicular to the path of a radio wave results in a 

 curvature of the ray toward the higher index. The 

 curvature of the ray is approximately equal to the 

 rate of decrease of the index of refraction with 

 altitude. Errors due to atmospheric refraction will 

 therefore depend on the rate of decrease of the 

 index of refraction perpendicular to the ray path 

 and to the range. A simplified equation for the error 

 in azimuth and altitude is derived below and is 

 utilized in this report. This method has been found 

 to check to within a thousandth of a degree with 

 more accurate methods of ray tracing. 



The rate of decrease of the index of refraction in 

 a standard atmosphere is 12 X 10~ 6 unit per 1,000 

 ft up to 4,000 ft above mean sea level. This corres- 

 ponds to a curvature of the path of the ray approxi- 

 mately one fourth the curvature of the earth. The 

 standard atmosphere represents average conditions 

 in temperate zones. In tropical air such as exists in 

 equatorial regions and southeast Asia and southeast 



a By Raymond Wexler, Signal Corps Ground Signal Agency, 

 b Errors in angle of altitude due to a duet with a standard 

 atmosphere above the duct have been computed by members 

 of Group 42 of the Radiation Laboratory. Values computed by 

 the method outlined below under Derivation of Formulas 

 have been found to agree with their results. 



Tor a more detailed analysis of ray tracing methods, see 

 reference 75. 



United States in summer, the average rate of decrease 

 of the index of refraction is approximately 18 X 10~ 6 

 unit per 1,000 ft up to 6,000 ft corresponding to a 

 curvature of the ray % that of the earth. Over trade 

 wind regions of the ocean (latitude 10° to 30°) dry 

 subsiding air exists over a moist tropical layer. The 

 rate of decrease of the index of refraction in these 

 regions is approximately 24 X 10~ 6 unit per 1,000 ft 

 corresponding to a curvature of the ray one-half that 

 of the earth. Within layers of atmosphere designated 

 as "ducts" the curvature of the ray may exceed the 

 earth's curvature and may result in a trapping of the 

 ray within the duct. Errors due to atmospheric 

 conditions in each of the above atmospheres are 

 analyzed. In Table 1 are tabulated values of the 

 index of refraction at selected levels for the standard 

 atmosphere, tropical atmosphere, and tropical dry 

 atmosphere as utilized in this report. 



Table 1. Values of the index of refraction for selected 

 levels in different air masses.* 



(n — 1) 10 6 ; n = index of refraction. 



*Aerological data for Miami and San Diego for July 1943 were utilized to 

 compute the indices of refraction for the tropical atmosphere and the trop- 

 ical atmosphere with dry air above, respectively. 



"■» APPLICATION TO GROUND 



RADAR EQUIPMENTS 



Gxjnlaying (Antiaircraft) Radar 



Military characteristics for gunlaying radar call 

 for a tolerance of 50-yd error in a range of 29,000 

 yd and an angle of 1.5 mils in azimuth and elevation. 

 Initial angles of sight are between 10° and 90°. 

 Results 



In a standard atmosphere, errors in angle of eleva- 



106 



