1、 Recommendation ITU-R P.834-7 (10/2015) Effects of tropospheric refraction on radiowave propagation P Series Radiowave propagation ii Rec. ITU-R P.834-7 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, 2015 ITU 2015 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.834-7 1 RECOMMENDATION ITU-R P.834-7 Effects of tropospheric refraction on radiowave propagation (Question ITU-R 201/3) (1992-1994-1997-1999-2003-2005-2007-2015) Scope Recommendation ITU-R P.834 provides methods for the calculation of larg
9、e-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 weather p
10、roduct, 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 developed that a
11、llow the calculation of some refractive propagation effects on radio signals on terrestrial and Earth-space links, recommends 1 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 (non-ioniz
12、ed) 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 plane and
13、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 2 Rec. ITU-R P.834-7 h : height of the point above the Earths surface : angle of the ray path with the horizontal at the point considered.
14、 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 horizontal, i
15、s 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 constant a
16、long 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-factor
17、). 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 profile (s
18、ee 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 refractive mo
19、dulus 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 equal to
20、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.834-7 3 4.2 Vis
21、ibility 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 the follo
22、wing 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 a typic
23、al atmosphere the refractive index at altitude x may be obtained from: )(e xp1)( bxaxn (8) where: a 0.000315 b 0.1361. This model is based on the exponential atmosphere for terrestrial propagation given in Recommen-dation ITU-R P.453. In addition, n (x) is the derivative of n(x), i.e. n (x) ab exp (
24、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 derived as an
25、 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 elevation ang
26、le 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). Therefore, the
27、space station is visible only when the following inequality holds: 0),( mm h (11) 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 refraction, by solving the following
28、equation: 4 Rec. ITU-R P.834-7 h, 0 (12) and the solution of equation (12) is given as follows: 0 0s h , (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 numerical f
29、ormula: 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 desig
30、nated 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 Measured re
31、sults 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 due to
32、 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 1 2 4
33、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.834-7 5 5 Focusing and defocusing of a wave for propagation through the atmosphere Changes in signal level m
34、ay also result from spreading or narrowing of the antenna beam caused by the variation of atmospheric refraction with the elevation angle. This effect should be negligible for elevation angles above 3. The equation below can be used to calculate the signal loss or gain due to refraction effects for
35、a wave passing through the total atmosphere )log(10 Bb where: 202200200200)008288.001727.0()0138.006272.01815.0(03723.05411.0728.108288.00276.006272.007446.05411.01hhhhB0: elevation angle of the line connecting the transmitting and receiving points, (degrees) (0 10) h: altitude of the lower point ab
36、ove sea level, (km) (h 3 km) b: change in signal level for the wave passing through the atmosphere, compared to free-space conditions, (dB) the sign in the equation for b will be negative “” for a transmitting source located near the Earths surface and positive “+” for a source located outside the a
37、tmosphere. 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 geometrical path length. The difference in length ca
38、n be obtained by the following integral: BAsnL d)1( (15) where: s : length along the path n : refractive index A and B : path ends. Equation (15) can be used only if the variation of the refractive index n along the path is known. When the temperature T, the atmospheric pressure P and the relative h
39、umidity 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 meteorological stations in 1979. In this method, the general
40、expression of the excess path length L is: ),()c o t1(s i n 02/1020 VV Lk LL (16) where: 0 : elevation angle at the observation point 6 Rec. ITU-R P.834-7 LV : vertical excess path length k and (0, LV) : corrective terms, in the calculation of which the exponential atmosphere model is used. The k fa
41、ctor 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, except at very low elevation angle and is neglected in the computation; it involves an error of only 3.
42、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 computation of the excess path length, is no longer vali
43、d. The vertical excess path length (m) is given by: LV 0.00227 P f (T ) H (17) In the first term of the right-hand side of equation (17), P is the atmospheric pressure (hPa) at the observation point. In the empirical second term, H is the relative humidity (%); the function of temperature f (T ) dep
44、ends on the geographical location and is given by: f (T ) a 10bT (18) 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) Coastal areas (islands, or locations less than 10 km awa
45、y 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 (16), an exponential variation with height h of the atmospheric refractivity N is assumed: N(h) Ns exp ( h / h0) (19) where Ns is the avera
46、ge value of refractivity at the Earth surface (see Recommendation ITU-R P.453) and h0 is given by: sVNLh 60 10 (20) k is then computed from the following expression: Rec. ITU-R P.834-7 7 20 )()(1 oss hrhn rnk (21) where ns and n (h0) are the values of the refractive index at the Earth surface and at
47、 height h0 (given by equation (20) respectively, and rs and r (h0) are the corresponding distances to the centre of the Earth. For Earth-space paths with elevation angles, the tropospheric excess path length, L(), (m) can be expressed as the sum of hydrostatic and wet components, LH() and LW(). The
48、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 (22) The hydrostatic vertical component at the Earth surface, LHvs, can be derived using: smsdH vs pkgRL 1610 m (22a) The wet vertical component at the Earth surface, LWvs, can be derived using: mssmsdW v s TekgRL )1(10 26 m (22b) where:
