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 _ ' ._ _ __ 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. I § 10 \-----11--+--- Another proper ty of radio ducLs is their t hi ckness which i giv en in figure 5. Ao-ain there is observed l ~ 9 a slig h t climatic trelld as the median t hi ckness ~ 8 increases from 66 m at Fairbanks to 106 m at Swan 400 ~"' 240 ~ ~ V 350 2' 200 "' 300 " "' ~ 160 " :c ~ r- iO 250 r- - '-' -:--- rl-~-+- g 120 u 0 => 0 "0 200 I i 8.0 E :.---Fairbonks, Aloska ~ => 1'l E 150 - I ' 0 ."0 ---Washing/on, D.C 40 2' I I I I / Swon Island 100 I' - 0.5 10 30 50 70 90 98 9'15 99.9 50 OJ 0.5 10 30 50 70 90 98 99.5 99.9 Pe rce ntage of Observations That Eq ual or Exceed the Ord in ate Value Percentage of Observations Tha i Equal or Exceed the Ordinate Value FIGU RE 5. Ob served ground-b ased d1lct thickness , F IGU R E 6. Maximum around-based duct thickness . One may obtain yet another thickness by linearly extrapolating to obtain the height at which the rays will be trapped by 50 percent of t he ducts gradien t is equal to - } /a, that is, the height cor regardless of location. responding to the gradien t just sufficient to trap the The reader is cautioned that an atmospheri c duct does not have the sharp boundaries of a metallic ray at 80 = 0. These values, shown in figure 6, dis play an increase in the median thickness of about waveguide and thus the minimum jr equ en c i ~s given 25 percent for Swan Island, 100 percent for 'Wash by table 1 do not represent cutoff frequen cIes but, ington, and 200 percent for Fairbanks, which results as Kerr is so careful to emphasiz e, merely yields a in a reversal of the climatic trend of the observed suggested lower limit of the frequencies strongly thickness between F airbanks and Swan Island. affected by the duct under the assumptions of this This increase in height emphasizes the information rudimentary theory. of the preceding figures, namely, Fairbanks is characterized by shallow layers with relatively i ~ intense gradients. T A BLE l. Estimated mininHlm frequency trapped at 00 = 0 These maximum duct widths may be used to es timate the minimum frequencies that are trapped Station l\1in imum frequency in megacyc1 es trapped by the- by reference to a ducting theory that assumes a indicated percen tage of dUCLS lineal' decay of refractive index wi thin the duct Fairbanks, Alaska (Feb· 95% 90% 75% 50% 25% 10% 5% such as that given by Kerr [5] where the maximum ruary) _... _.. _. _____ ._ .. 1,500 1, 300 1, 200 890 690 490 435 wavelength, A, trapped by a given thickn ess, d, is Washington, D.C. (Au· gust) . __. _. __ .. __ . ___. _._ 4, 300 3, 000 1, 100 600 270 180 150 given by Swan Island, Wes t Indies (Angust) . __ ___ . ______. __ 2, 500 1,300 725 500 365 325 225 (13) wh ere c is a constan t and 'Y is a function of the n gradient excoss over the minimum value of !::"N /!::,.H 4 . Temperature and Humidity Distributions = 1 /0.. If Am ax is to be expressed in centimeters, d in meters and Associated with Ground-Based Ducts (14) The temperature and humidity structure within ground-based ducts appears to be somewhat different ( then from that normally encountered in the atmosphere. c= 2.514 X 102. This departure from the normal structure is an aid in distinguishing the different atmospheric mechanisms By the use of (1 3) the minimum frequen cies that give rise to ducts as well as helping the mete trapped during ducting conditions were es timated for orologist forecast ducting from his experien ce with t he maximum duct thicknesses of figure 6. These the normal meteorological variables. values, given in table 1, were determined for the The temperat ure and humidity structure of the month with tho maximum occurrence of ducts, thus atmosphere during ducting conditions may be allowing an cstimate of the radio frequencies likely evaluated by noting that N is composed of a term to be eff ected by ducting conditions. Note, for proportional to the air density, D , plus a term example, tha t tho data of table 1 indicate that 500-Mc involving the partial pressure of water vapor, W . 32 These componenLs are given by duct that was contributed by the gradient of the dry and wet terms. The median co ntribu tion of the D = 77.6 P (15) dry term gradient, summarized in table 3, displays '1 ' -, strong seasonal and geographic difrel'ence . The a nd dry term contribution decreases from summer to TV 3 .7 3 X~~ 5es RTl . (16) win ter and from arctic to tropical climate. The Swan Island ducting gradients are at least 90 percent due to humidity lapse, while the Fail'banks The gradicnL, t::, N, wiLh respecL Lo height ma.\' Lhen wintertime maximum is due to the strong tempera be ex pressed : ture inversion associated with very low surface (17) temperatures. In fact, under these conditions at Fairbanks the vapor pressure actually increases with Average values of t::, N, t::,D , a nd t::,1IfT are given for height with t he r esult that the dry term contributes twoincrell1 en ls between t llC earth's surface and 1 km more than 100 percent of the ducting gradient. above sea level for Fairbanks, Alaska, Washington, TAB L E; 3. M edian contribution of L\D /MI to L\N/L\H for D .C., and Swan Island , W.I., in table 2. These ducting conditions data were determined from the Weather Bureau publicaLion on long term mean upper air data [6]. F a irbanks W ashington, Swan I sland D.C. T A B LE 2. Gmdient of N, D, and W (N units/km) % % % F e bruar y ______.. ______lO3 . 0 73.0 9.5 M ay______F ebru ary Aug us t 40.5 33.5 2. 0 Au g u s L ~ ______• ___ ._. __ 37. 0 26.5 4. 5 Il cL~h t in c r~ m e nt I__ ~_~_II ____~ __ Station )[ovcmbCI" ______. _____ . ______62. 0 55. 0 6. 0 -AN -AD -A IV - AN - AD - A IV ------1------1------The data for ·Washington, D. C. , however , appears F airbanks, Alaska _ surrace to 0. 5 kill 37 4t -4 31 27 4 0.5 kill to 1.0 kill 35 35 0 36 24 12 Lo indicaLe that temperate zone du cting arises from a mixtlll'e of the arctic and tropic mechanisms de W ashington, D.C __ surrace to 0.5 km 41 34 7 60 28 32 0.5 kill to 1.0 kill 30 26 4 46 24 22 pendent upon the season. It appears that the Swan Island, " rest surrace to 0.5 kill 39 24 15 47 26 21 wintertime ducts in the temperate zone are of the Indies _____ 0.5 k ill to 1.0 k ill 58 24 34 66 24 42 clr :\~ -term arctic type wbile the summertime ducts are of the tropical humidity-lapse variety. Several general observations may be made of the 300 data of table 2. The gradient of t he dry term is - f--- relatively less variable than t hat of the wet term when co nsidered as a fun ction of season or height; 200 f- t he increase of t::, N from win tel' to summer at a -I.- l- particular location or from arctic to tropical climate 100 1= at a given time is most strongly refl ected in t::, TV rather Lhan ill t::,D. T he marked increa e of gradient t - with heigh t for Swan Ts land refl ects the drop of 0 '"v 300 refracL ivity across t he in ted ace of the tr ade wind 0; :2 [D.C. inversion wb ere dry subsiding air overlies the moist - WASHIN~[TON, oceanic surface layer. Note, however, t hat in all 8-19-53, 0900GMT u'" f---~ cases the average N gradient is significantly less 200 - -- - f---- ~ t han the - 157 N units/km needed for ducting. (f) - f---- - Examples of the temperature and humidity oS'" structures within ducts typical of each of our three ~ 100 .8 1- - f-.-f--1---1-- - . - I!- climates are shown in figure 7. The F airbanks duct 34