JOURNAL OF RESEARCH of the National Bureau of Standards- D. Radio Propagation Vol. 67D, No. 2, March- April 1963 Empirical Determination of Total Atmospheric Refraction at Centimeter Wavelengths by Radiometric Means Alan C. Anway Contribution from Collins Radio Company, Cedar Rapids, Iowa (Received October 5, 1962) The experimental p rocedures and data analys is methods used i n t he determ in ation of total atmospheric refract ion by radiometric means a re described. The resul ts of fi vo months' oboervation are presen ted in plots of t he mean refraction, its standard deviation , and stand­ ard error of estimate for specifi ed altitude angles between 2 and 65 degrees. The a.m. values of refraction are significantly greater than those of the p.m . at the sa me altitude angle. This effect is attri b uted to t he diurnal cycle. The measured total refraction exhibits a strong linear correlation with surface refractivity 1. Introduction ure total atmospheric mi cro w ~1V e r efraction over a wide r ange of altitude angles and wi th the norm al Developmen t of a prec ise radiometric sextant has variation of meteorological parameters of the atmo s­ made possible the mcaS Ul'cmen t of the eff ect of the phere. To the knowledge of the author, the only earth's atmosphere on the direction of propagation studies whi ch closely approach the prcsen t one were of 2-cm wavelength rad io waves. In par ticular, this those of M arncr and Ringoen [1956 ], and M arner paper considers the problem from a phenom enological and Stewart [1955] at 8.7 mm . Ringoen et aI. , [19 52] point of view, and r eports the perform ance and anal­ did perform som e meaSUl'em ents at 1.91 cm ·wi th a ysis of empirical observations over a wide rang'e of radio sextant of significan tly lower precision than observed altitude angles and for the val'l ety of the on e used in this study. H owever, the refin emen ts weather conditions found in nature. R efractive of equipmen t and analysis technique used her e are bending eff ec ts in the ver tical plane (that is, the alti­ bel.ieved important enough to m ake Lhis study tude coordinate) are considered since, under the usual umque. assumption of spherical stratification , azimuthal re­ The plan was to use a r adiometric sextant to track fraction do es not exist. Further, ionospher ic eff ects the sun as it traversed the sky, a,nd to record the are assumed n egligible at 2-cm wavelengths; there­ observed values of the sun's altitude angle at certain fore, only tropospheric phenomena are being con­ precisely determined tim es throughout the day. The sidered. measurements were obtained at Cedar R apids, Iowa, Smar t [195 6] has shown that, in general, atmos­ between August and December 1959. The observed pheric refraction depends on the index of refr action altitude angles were limited by ground effects and profile. However, if the observed altitude is r e­ by the maximum observed solar altitude angle to stricted to relatively high angles (that is, greater within 2 and 65 deg respectively . The U.s. Naval than 20 deg), total atmospheric refraction is found to Observatory made available highly accurate ephem­ depend only on the surface value of refrac tivity and eris data from which the sun's position was computed the observed altitude angle. Extension of the ana­ for any specific time for which a radio sextant obser­ lytical consideration to low-altitude angles becomes vation was made. These computed values were con­ ~ very complex, and generally ray-tracing techniques ceived to be true values, a nd any deviation from have been followed in this case. The usual procedure them was due to error-producill g causes in the equip­ is to measure the refractivity profile with a radio­ ment, the a tmosphere, or the cen ter of microwave sonde instrument and then compute, from this profile, radiation from the celes tial source. The difference the total atmospheric refraction by numerical inte­ between the observed and true altitude angle was gra tion methods [Shulkin, 1952]. the total error produced by all causes, among them In spite of the wide use of computed values of at­ atmospheric refraction. Fortunately, atmospheric mospheric refraction, it appears that little informa­ refraction was the largest of all errors, so its effect tion is available on precise measurements of this was distinguished easily . quan tity at r adio wavelengths. Anderson et a1. Operation of a radio sextant system depends on [1960] used a beacon tracking r adar to measure low­ microwave radiation emanating from the sun. In angle refraction through par t of the atmosphere. the 2-cm microwave reg ion, the sun radiates therrnal Experimental studies of very low-angle (horizon tal) noise energy similar to a blackbody of temper ature refraction through the en tire atmosphere h ave been approximately 7,000 Ole The space surrounding the performed by Aarons et al. [1958]. sun also radiates a very minute amount of energy It is beli eved that the investigation reported and appears as a blackbody of temperature very her ein represen ts the first attemp t to prec isely meas- near absolute zero. 153 A sensitive microwave receiver connected to a causes, and are known functions of the several highly directional antenna senses when the sun is in independent variables x,y, ... and perhaps the de- the antenna beam by an increase in noise output pendent variable h. Rh(a,b, .. ) is the residual error from the receiver. If the sun were directly centered in the altitude coordinate, and is some unknown in the beam, the noise output would be maximum, function of the infinite variety of independent and if the sun were displaced sli ghtly from boresight, variables a, b, . .. That is, R,,(a,b, . ) is random the output would be reduced. Assuming symmetry in that we cannot predict its precise value from a of the al1 tenna beam and of the temperature distri­ knowledge of only a finite number of independent bution of the source, circular scanning of th e sun's variables. disk with the antenna beam can provide tracking To arrive at a model which is useful for the digital error information. That is, if the sun is centered in computations performed in this analysis (1) must be the scan pattern, no change in d-c output level is expressed in discrete, rather than analog form. obtained over the scan cycle, since the beam always Thus, for the.ith observation, we have sees the sam e effective source temperature. If the sun is not centered on the scan axis, the d-c output hj=hO j+t:.hij + t:.h2 j+ ... t:.hkj+ej) (2) is modulated at the scan rate and correlated (phased) with the direction of the scan-axis to source-center where t:.hkj is the error due to the kth assignable displacement. The modulation arises since during cause under the specific conditions existing at the part of the scan cycle the beam predominantly sees instant the .ith observation was made. The residual the cold space, and during the remaining part of the random error at the instant of observation is Cj . cycle it sees the hot sun. In effect then, f>hkj is a correction term due to the After suitable a-c amplification, the modulated kth cause which must be added to the observed value signal is synchronously detected to provide a pair of of altitude angle to make it more nearly correct. d-c voltages, one in up-down, the other in right-left For example, f>hlj might be the correction due to coordinates, which are proportional in magnitude atmospheric refraction and !J.h2J might be the cor­ and polarity to the magnitude and diTection of the rection due to a systematic error in the angular sun's displacement in line-of-sight coordinates. These readou t mechanism. For this analysis, the residual signals are used to achieve automatic tracking. error is assumed to be nonnally distributed with An air-supported radome was used to provide a mean value (JJ-) of zero and standard deviation, u. temperature controlled environment for the sextant Let the fu'st correction term, f>h 1 • be the total and to protect it from the effects of weather and measured atmospheric refraction. T. Then, from wind. This radome was made by cementing sections the true and observed altitude angles and the re­ of neoprene-coated nylon fabric into the shape of a maining correction terms, the atmospheric refraction truncated sph ere. It was fastened at its base to a can be computed from circular ring which was free to rotate in the hori­ zontal plane. The ring was driven by an electric motor so that the radome rotated 360 deg in azi­ muth every 20 sec. Radome rotation was necessary to remove refractive errors produced by localized As long as the conditions assumed for ej hold, (3 ) differences in the radome material. Rotating the is an unbiased estimate of the true value of measured radome caused rapid fluctuations in apparent posi­ refraction. Notice that refraction cannot be deter­ tion of the source which were effectively filtered, or mined perfectly, it can only be estimated to within averaged by the tracking-servo time constant. a standard error of u . Thus, the sextant follo wed the mean apparent posi­ The problem in making precise determinations of tion of the source. There is adequate evidence atmospheric refraction by this method reduces to beyond the scope of this paper that radome rotation one of evaluating the various errors introduced by successfully removed the effects of radome structural the measuring instrument and by the sun.