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Climatology of Ground-Based Radio Ducts*

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Climatology of Ground-Based Radio Ducts* Iournal of Research of the National Bureau of Standards-D. Radio Propagation Vol. 63D, No.!, Iuly-August 1959 Climatology of Ground-Based Radio Ducts* Bradford R. Bean (January 15, 1959) An atmospheric duct is defined as occurring when geometrical optics indicate t hat a radio ray leavin g the transmitter and passing upwards t hrough the atmosphere is suffi ciently refr acted that it is traveling parallel to t he eart h's surface. Maximum observed incidence of ducts was determined as 13 percent in t he tropics, 10 per ce nt in the ar ctic and 5 percent in the temperate zone by analysis of 3 to 5 years of radiosonde data for a tropical, temperate, and arctic location. Annual m aximums are observed in t he winter for the arctic and summer for t he tropics. The arctic ducts arise from ground-based temperature inversiofls with the gronnd temperature less than - 25 ° C while the tropical ducts are observed to occur with slight temperature and humidity lapse when the surface temperature is 30 ° C and greater. 1. Introduction Thus trapping occurs when the ray IS traveling parallel to the earth, i.e., cos Oa= 1 and The author has recently had cause to investigate the limitations placed upon ray tracing of vhf-uhf (2) radio waves by the occurrence of atmospheric ducts [1] .1 Ducting is defin ed as occurring when a radio ray originating at the earth's surface is suffi­ The angle of penetration at the transmitter, Op, found ciently refracted during its upward passage through by setting \ the atmosphere so that it either is bent back towards (3) the earth's surface or travels in a path parallel to the earth's surface. Although the proper treatmen t of ducting involves consideration of the wave equation divides the ray family into two groups since all ray solution [2] rather than a simple ray treatmen t, the of 00 ::; Op arc trapped within the duct and those rays present study will be based upon a geometrical of Oo> Op are not. The n gradientlfor a given value optics definition of the limiting case in which ray of Op is then given by '- traci.ng techniques may be used . This simple f:.n nt - nd ( criterion is then applied to several years of radio­ -=- - - , (4) sonde observations from stations typical of arctic, f:.r ra - rt temperate and tropical climates to derive e timates of the variation of the occurrence of radio ducts with where, for the ducting case, na must satisfy (3), i.e., climatic conditions. (5) 2. Background The property of the atmosphere basic to radio-ray tracing is the gradient of the radio refractive index of the atmosphere, n. For standard conditions near the surface of the earth n is a number of the order 1.0003 and its gradient is about 40 X 10- 6 p er kilo­ m eter. It is instructive to consider the order of mag­ By rewriting (6), nitude of refractive index gradient needed for trap- L ping for several commonly observed refractive index (7) t profiles. Snell's law may be written, for cylindrical I coordinates, (1) f:.h)-I and expanding ( 1 +~ and cos Op one obtains the where 0 is the elevation angle made b y the ray at the eJi.'})ression point under consideration. The subscripts t and d ( refer to the values of the variables at the transmitter (8) h eight and the top of the trapping layer respectively. -This work was partiall y sponsored by task 31 of the U. S. Navy Weather 4 I Research FaCili ty, Norfolk, Va. by neglecting terms of the order 410 and (1)2r; . I 1 Figures in brackets indicate the literature references at the end of this paper. I I 29 ~ For the case of ep =o and the transmitter at sea are seldom indicated within atmospheric layers. level, (8) reduces to Note how rapidly the necessary gradients increase to the approximate upper limit of gradients derived Lln n 1 . from radiosonde observations; a ground-based layer -A=- ~ - ~157 N umts/km. (9) J..J.r a a 100-m thick attains this gradient at 8.3 milliradians while the maximum observed gradient is intercepted using a= 6,373 km and N =(n-l) 106• Note that by the 30-m layer curve at 4.5 milliradians of eo. A the n gradient is referred to here and hereafter as third example was calculated for an elevated layer parts per million, or in popular parlance, N units. 0.5 km above the ground and 100-m thick by as­ It is seen from (8) that the n gradient necessary suming normal refraction between the ground and to trap a radio ray at a given value of ep is practically the base of the layer and solving for the necessary independent of transmitting antenna height above ducting gradient within the layer. The large values the earth. For example, a ep=o ray will be trapped of the n gradient necessary for this case indicate by an n gradient of - 157.0 N units/km at sea level that elevated ducts would rarely be observed. when ne= 1.0003 while the necessary n gradient at Although the preceding examples were calculated 3 km above sea level will be - 156.9 N units/Ian for a ground transmitter, the combinations of ep , for an ne= 1.0002, thus indicating, for all practical Lln/Llh, and Llh are very nearly the same as would applications, that the necessary n gradient for be obtained for any other transmitter height within trapping is independent of altitude. Further, by the first 3 km above the surface. considering the temperature and humidity gradients encountered in the troposphere one is led to the 3. Description of Observed Ground-Based ~ conclusion that ducting gradients would not be Atmospheric Ducts expected to occur at heights greater than 3 km above the earth's surface. In fact, Cowan's [3) investigation Radiosonde data were examined for the occurrence indicates that trapping gradients are nearly always of ducts. Three consecutive years of data were confined to the first kilometer above the surface. analyzed for the months of February, May, August, A consideration of (8) indicates that the mag­ and November at each of three Weather Bureau nitude of the negative gradient necessary for ducting stations. The three stations were chosen to repre­ is l /a for eo =o but is increased by the amount sent a range of climates: Fairbanks, Alaska for an n e8p 2/2Llh for other values of 8p • The gradients arctic climate, Washington, D. C., for a temperate necessary for atmospheric ducts as a function of climate and Swan Island, West Indies, as an example eo are given for several different but typical n profiles of a tropical climate. The procedure used to de­ in figure 1. An analysis of radiosonde data in­ termine the occurrence of a radio duct was to: dicates that gradients in excess of 500 N units/km (a) D etermine tbe value of N from the expres- sion [4) < 1300 r-------,--------r---,----,--~------,--~__,_~ 1200 1--+-++ I ~ I N=(n_1)106= 7~6 (p+4810iRH} (10) 1100 where P is the station pressure in millibars, RH is 1 1000 the percent of the saturation vapor pressure, e" in 1,.11 millibars at the absolute temperature, T, in degrees O.5km above ~;ound b I ~ 900 I---+--j--- ondO, l km thlck _ Kelvin; 0; No = 320, No.5 ;:, 300 E (b) note all instances when the N gradient " .Q 800 equaled or exceeded the minimum ducting gradient 11 '" indicated by (9), i.e., ~ -t _ ' ._ _ __ <n' 700 -i ~ c !:J.n n 1 . ::J 1 i - - =-,,-,-=157 Numts/km' (11) Z 600 f--------L---I--_+_ W +: !:J.r a a ' Appro.omate upper !tmllof I rodlO sonde - observed gradIents <l<lzlr J 500 " _ , ---l- (c) if, for the instances selected by (b), 400 (2) I 300 where re = a, then the duct, was said to trap rays 200 from an antenna resting on the surface of the earth. Further, under this condition the particular .~ 100 duct would trap all rays from eo =o up to the angle I 0 3 4 5 8 9 10 of penetration, 80 I Millirodians (12) i FIGURE 1. R efractivity gradients needed for radio ducts. 30 I r Th.e ducts selected by procedure (a) th.rough (c) are defined as ground-based ducts. Statisties of ground­ based ducts are given below. SWAN ISLAND The percentage occurrence of ducts is shown on 1 figure 2. The maximlUl1 occurrences of 13. percent for August at Swan Island and 9.2 percent for Fairbanks in F ebruary are significantly greater than the values observed at other times of the year. The ~" 4 1-\--+--/ \\---+---1 \Vashington daLa displ ay a summ ertime maximum ~ of 4.6 peree nt indicating the temperate zone maxi­ 14 Meon mum incidence is about on e-balf Lhe wintertime 21+\23 mo, 30 maximum incidence in the arctic, and about one-t hird of the summertime tropical maximum. ~' , -~,- 9 Mean min min o L---'._...l..-~ __ FEB MAY AU G NOV FEB MAY AUG NOV 14 ~--~~---+---+--~--~--~~t---~-i---­ Numbers on curves are fotal Months of the Year number of profiles analysed F I GU R E 3. A n gle oj penetmtion of g1·ound-based ducts. :::J o I -0 I 2 I-----'----j----j j II __1:---+--1- valu e of 230 N units/km at Fairbanks to a value I -0 of 1 ()O N u ni ts/km at Swan I sland.
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