1、 Recommendation ITU-R P.834-9 (12/2017) Effects of tropospheric refraction on radiowave propagation P Series Radiowave propagation ii Rec. ITU-R P.834-9 Foreword The role of the Radiocommunication Sector is to ensure the rational, equitable, efficient and economical use of the radio-frequency spectr
2、um by all radiocommunication services, including satellite services, and carry out studies without limit of frequency range on the basis of which Recommendations are adopted. The regulatory and policy functions of the Radiocommunication Sector are performed by World and Regional Radiocommunication C
3、onferences and Radiocommunication Assemblies supported by Study Groups. Policy on Intellectual Property Right (IPR) ITU-R policy on IPR is described in the Common Patent Policy for ITU-T/ITU-R/ISO/IEC referenced in Annex 1 of Resolution ITU-R 1. Forms to be used for the submission of patent statemen
4、ts and licensing declarations by patent holders are available from http:/www.itu.int/ITU-R/go/patents/en where the Guidelines for Implementation of the Common Patent Policy for ITU-T/ITU-R/ISO/IEC and the ITU-R patent information database can also be found. Series of ITU-R Recommendations (Also avai
5、lable online at http:/www.itu.int/publ/R-REC/en) Series Title BO Satellite delivery BR Recording for production, archival and play-out; film for television BS Broadcasting service (sound) BT Broadcasting service (television) F Fixed service M Mobile, radiodetermination, amateur and related satellite
6、 services P Radiowave propagation RA Radio astronomy RS Remote sensing systems S Fixed-satellite service SA Space applications and meteorology SF Frequency sharing and coordination between fixed-satellite and fixed service systems SM Spectrum management SNG Satellite news gathering TF Time signals a
7、nd frequency standards emissions V Vocabulary and related subjects Note: This ITU-R Recommendation was approved in English under the procedure detailed in Resolution ITU-R 1. Electronic Publication Geneva, 2017 ITU 2017 All rights reserved. No part of this publication may be reproduced, by any means
8、 whatsoever, without written permission of ITU. Rec. ITU-R P.834-9 1 RECOMMENDATION ITU-R P.834-9 Effects of tropospheric refraction on radiowave propagation (Question ITU-R 201/3) (1992-1994-1997-1999-2003-2005-2007-2015-2016-2017) Scope Recommendation ITU-R P.834 provides methods for the calculati
9、on of large-scale refractive effects in the atmosphere, including ray bending, ducting layers, the effective Earth radius, the apparent elevation and boresight angles in Earth-space paths and the effective radio path length. Keywords Tropospheric excess path length, Earth-space link, GNSS, numerical
10、 weather product, digital maps The ITU Radiocommunication Assembly, considering a) that for the proper planning of terrestrial and Earth-space links it is necessary to have appropriate calculation procedures for assessing the refractivity effects on radio signals; b) that procedures have been develo
11、ped that allow the calculation of some refractive propagation effects on radio signals on terrestrial and Earth-space links, recommends that the information in Annex 1 should be used for the calculation of large-scale refractive effects. Annex 1 1 Ray bending A radio ray passing through the lower (n
12、on-ionized) layer of the atmosphere undergoes bending caused by the gradient of the refractive index. Since the refractive index varies mainly with altitude, only the vertical gradient of the refractive index is generally considered. The curvature at a point is therefore contained in the vertical pl
13、ane and is expressed by: hnn ddcos1 (1) where: : radius of curvature of the ray path n : refractive index of the atmosphere dn/dh : vertical gradient of refractive index h : height of the point above the Earths surface 2 Rec. ITU-R P.834-9 : angle of the ray path with the horizontal at the point con
14、sidered. This ray curvature is defined as positive for ray bending towards the Earths surface. This phenomenon is virtually independent of frequency, if the index gradient does not vary significantly over a distance equal to the wavelength. 2 Effective Earth radius If the path is approximately horiz
15、ontal, is close to zero. However, since n is very close to 1 equation (1) is simplified as follows: hndd1 (2) It is therefore clear that if the vertical gradient is constant, the trajectories are arcs of a circle. If the height profile of refractivity is linear, i.e. the refractivity gradient is con
16、stant along the ray path, a transformation is possible that allows propagation to be considered as rectilinear. The transformation is to consider a hypothetical Earth of effective radius Re k a, with: eRhnaka 1dd11 (3) where a is the actual Earth radius, and k is the effective earth radius factor (k
17、-factor). With this geometrical transformation, ray trajectories are linear, irrespective of the elevation angle. Strictly speaking, the refractivity gradient is only constant if the path is horizontal. In practice, for heights below 1 000 m the exponential model for the average refractive index pro
18、file (see Recommendation ITU-R P.453) can be approximated by a linear one. The corresponding k-factor is k 4/3. 3 Modified refractive index For some applications, for example for ray tracing, a modified refractive index or refractive modulus is used, defined in Recommendation ITU-R P.310. The refrac
19、tive modulus M is given by: ahNM (4) h being the height of the point considered expressed in metres and a the Earths radius expressed in thousands of kilometres. This transformation makes it possible to refer to propagation over a flat Earth surmounted by an atmosphere whose refractivity would be eq
20、ual to the refractive modulus M. 4 Apparent boresight angle on slant paths 4.1 Introduction In sharing studies it is necessary to estimate the apparent elevation angle of a space station taking account of atmospheric refraction. An appropriate calculation method is given below. Rec. ITU-R P.834-9 3
21、4.2 Visibility of space station As described in 1 above, a radio beam emitted from a station on the Earths surface (h (km) altitude and (degrees) elevation angle) would be bent towards the Earth due to the effect of atmospheric refraction. The refraction correction, (degrees), can be evaluated by th
22、e following integral: h xxn xn dt a n(5) where is determined as follows on the basis of Snells law in polar coordinates: )()(c o s xnxr c (6) c o s)()( hnhrc (7) r : Earths radius (6 370 km) x : altitude (km). Since the ray bending is very largely determined by the lower part of the atmosphere, for
23、a typical atmosphere the refractive index at altitude x may be obtained from: )(e x p1)( bxaxn (8) where: a 0.000315 b 0.1361. This model is based on the exponential atmosphere for terrestrial propagation given in Recommendation ITU-R P.453. In addition, n (x) is the derivative of n(x), i.e. n (x) a
24、b exp (bx). The values of (h,) (degrees) have been evaluated under the condition of the reference atmosphere and it was found that the following numerical formula gives a good approximation: (h, ) 1/1.314 0.6437 0.02869 2 h (0.2305 0.09428 0.01096 2) 0.008583 h2 (9) The above formula has been derive
25、d as an approximation for 0 h 3 km and m 10, where m is the angle at which the radio beam is just intercepted by the surface of the Earth and is given by: )( )0(c o sa r c hnnhr rm(10) or, approximately, hm 875.0 (degrees). Equation (9) also gives a reasonable approximation for 10 90. Let the elevat
26、ion angle of a space station be 0 (degrees) under free-space propagation conditions, and let the minimum elevation angle from a station on the Earths surface for which the radio beam is not intercepted by the surface of the Earth be m. The refraction correction corresponding to m is (h, m). Therefor
27、e, the space station is visible only when the following inequality holds: 0),( mm h (11) 4 Rec. ITU-R P.834-9 4.3 Estimation of the apparent elevation angle When the inequality in equation (11) holds, the apparent elevation angle, (degrees), can be calculated, taking account of atmospheric refractio
28、n, by solving the following equation: 0, h (12) and the solution of equation (12) is given as follows: 00 , hs (13) where the values of s (h, 0) are identical with those of (h, ), but are expressed as a function of 0. The function s (h, 0) (degrees) can be closely approximated by the following numer
29、ical formula: s (h, 0) 1/1.728 0.5411 0 0.03723 02 h (0.1815 0.06272 0 0.01380 02) h2 (0.01727 0.008288 0) (14) The value of calculated by equation (13) is the apparent elevation angle. 4.4 Summary of calculations Step 1: The elevation angle of a space station in free-space propagation conditions is
30、 designated as 0. Step 2: By using equations (9) and (10), examine whether equation (11) holds or not. If the answer is no, the satellite is not visible and, therefore, no further calculations are required. Step 3: If the answer in Step 2 is yes, calculate by using equations (13) and (14). 4.5 Measu
31、red results of apparent boresight angle Table 1 presents the average angular deviation values for propagation through the total atmosphere. It summarizes experimental data obtained by radar techniques, with a radiometer and a radiotelescope. There are fluctuations about the apparent elevation angle
32、due to local variations in the refractive index structure. TABLE 1 Angular deviation values for propagation through the total atmosphere Elevation angle, (degrees) Average total angular deviation, (degrees) Polar continental air Temperate continental air Temperate maritime air Tropical maritime air
33、1 2 4 10 20 30 0.45 0.32 0.21 0.10 0.36 0.25 0.11 0.05 0.03 0.38 0.26 0.12 0.06 0.04 0.65 0.47 0.27 0.14 Day-to-day variation in (for columns 1 and 4 only) 1 10 0.1 r.m.s. 0.007 r.m.s. Rec. ITU-R P.834-9 5 5 Beam spreading loss for propagation through the atmosphere Beam spreading loss, , is a non-o
34、hmic loss due to spreading of the antenna beam in the vertical elevation plane due to the variation of the radio refractive index vs. height. This effect is insignificant for elevation angles above 5. The signal loss due to beam spreading for a wave propagating through the total atmosphere in the Ea
35、rth-space and space-Earth directions is )log(10 BAbs (dB) (15) where: = 1 0.5411+0.074460+(0.06272+0.02760)+20.0082881.728+0.54110+0.0372302+(0.1815+0.062720+0.013802)+2(0.01727+0.0082880)2(16) where: 0: elevation angle of the line connecting the transmitting and receiving points, (degrees) (0 10) h
36、: altitude of the lower point above sea level, (km) (h 5 km). 6 Excess radio path length and its variations Since the tropospheric refractive index is higher than unity and varies as a function of altitude, a wave propagating between the ground and a satellite has a radio path length exceeding the g
37、eometrical path length. The difference in length can be obtained by the following integral: BAsnL d)1( (17) where: s : length along the path n : refractive index A and B : path ends. Equation (17) can be used only if the variation of the refractive index n along the path is known. When the temperatu
38、re T, the atmospheric pressure P and the relative humidity H are known at the ground level, the excess path length L can be computed using the semi-empirical method explained below, which has been derived using the atmospheric radio-sounding profiles provided by a one-year campaign at 500 meteorolog
39、ical stations in 1979. In this method, the general expression of the excess path length L is: ),()c o t1(s i n 02/1020 VV LkLL (18) where: 0 : elevation angle at the observation point LV : vertical excess path length k and (0, LV) : corrective terms, in the calculation of which the exponential atmos
40、phere model is used. The k factor takes into account the variation of the elevation angle along the path. The (0, LV) term expresses the effects of refraction (the path is not a straight line). This term is always very small, 6 Rec. ITU-R P.834-9 except at very low elevation angle and is neglected i
41、n the computation; it involves an error of only 3.5 cm for a 0 angle of 10 and of 0.1 mm for a 0 angle of 45. It can be noted, moreover, that at very low elevation for which the term would not be negligible, the assumption of a plane stratified atmosphere, which is the basis of all methods of comput
42、ation of the excess path length, is no longer valid. The vertical excess path length (m) is given by: LV 0.00227 P f (T ) H (19) In the first term of the right-hand side of equation (19), P is the atmospheric pressure (hPa) at the observation point. In the empirical second term, H is the relative hu
43、midity (%); the function of temperature f (T ) depends on the geographical location and is given by: f (T ) a 10bT (20) where: T is in C a is in m/% of relative humidity b is in C1. Parameters a and b are given in Table 2 according to the geographical location. TABLE 2 Location a (m/%) b (C1) Coasta
44、l areas (islands, or locations less than 10 km away from sea shore) 5.5 104 2.91 102 Non-coastal equatorial areas 6.5 104 2.73 102 All other areas 7.3 104 2.35 102 To compute the corrective factor k of equation (18), an exponential variation with height h of the atmospheric refractivity N is assumed
45、: N(h) Ns exp ( h / h0) (21) where Ns is the average value of refractivity at the Earth surface (see Recommendation ITU-R P.453) and h0 is given by: sVNLh 1060 (22) k is then computed from the following expression: 20 )()(1 oss hrhn rnk (23) where ns and n (h0) are the values of the refractive index
46、 at the Earth surface and at height h0 (given by equation (22) respectively, and rs and r (h0) are the corresponding distances to the centre of the Earth. Rec. ITU-R P.834-9 7 For Earth-space paths with elevation angles, the tropospheric excess path length, L(), (m) can be expressed as the sum of hy
47、drostatic and wet components, LH() and LW(). The excess path length along a vertical path, LHv and LWv can be projected to the elevation angle, , greater than 3, using two separate mapping function for the hydrostatic and wet components, mH() and mW(): WWvHHvWH mLmLLLL m (24) The hydrostatic vertica
48、l component at the Earth surface, LHvs, can be derived using: smsdH vs pkgRL 1610m (24a) The wet vertical component at the Earth surface, LWvs, can be derived using: mssmsdW v s TekgRL )1(10 26 m (24b) where: ps, es: air total pressure and water vapour partial pressure at the Earth surface (hPa) Tms: mean temperature of the water vapour column above the surface (K) : vapour pressure decrease factor Rd : R/Md = 287.0 (J/kg K) R: molar gas constant = 8.314 (J/mol K
