1、21 4 ITU-R RECMN*PN- 834-L 94 48552112 0521960 549 = Rec. ITU-R PN.834-1 RECOMMENDATION ITU-R PN.834-1 EFFECTS OF TROPOSPHERIC REFRACTION ON RADIOWAVE PROPAGATION (Question ITU-R 201/3) ( 1992- 1994) The ITU Radiocommunication Assembly, considering that for the proper planning of terrestrial and Ear
2、th-space links it is necessary to have appropriate calculation a procedures for assessing the refractivity effects on radio signals; b) signals on terrestrial and Earth-space links, that procedures have been developed that allow the calculation of some refractive propagation effects on radio recomme
3、nds 1. that the information in Annex 1 be used for the calculation of large-scale refractive effects. ANNEX 1 1. Ray bending A radio ray passing through the lower (non-ionized) layer of the atmosphere undergoes bending caused by the gradient of the refractive index (see Recommendation ITU-R PN.369).
4、 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 is expressed by: where: P: n: dnldh : h: p: radius of curvature of the ray path refractive in
5、dex of the atmosphere vertical gradient of refractive index height of the point above the Earths surface angle of the ray path with the horizontal at the point considered. This ray curvature is defined as positive for ray bending towards the Earths surface. This phenomenon is virtually independent o
6、f frequency, if the index gradient does not vary significantly over a distance equal to the wavelength. 2. Effective Earth radius on an approximately horizontal path If the path is approximately horizontal, cp is close to zero. However, since n is very close to 1, equation (i) is simplified as follo
7、ws: 1 dn p-dh -_ - It is therefore clear that if the vertical gradient is constant, the trajectories are arcs of a circle. ITU-R RECMNaRN. 834-3 94 4855232 05239bL 480 215 A well-known transformation allows propagation to be considered as rectilinear above a hypothetical Earth of Rec. ITU-R PN.834-1
8、 effective radius Re = k a, where: Elevation angle 8 (degrees) 1 2 4 10 20 30 1 10 1 1 dn 1 - +- ka a dli - Re - Average total angular deviation, A0 (degrees) Polar Temperate Temperate Tropical maritime continental air continental air maritime air air 0.45 - - 0.65 0.47 0.32 0.36 0.38 0.21 0.25 0.26
9、 . 0.27 0.10 0.1 1 0.12 O. 14 0.05 0.06 0.03 0.04 Day-to-day variation in A0 (for columns 1 and 4 only) o. 1 r.m.s. 0.007 r.m.s. (3) where a is the actual Earth radius, and k is the effective earth radius factor. The exponential model of the refractive index (see Recommendation ITU-R PN.369), used i
10、n the first kilometre of the atmosphere, can be approximated by a linear one corresponding to an effective Earth radius with 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
11、ITU-R PN.310. The refractive modulus M is given by: M=N+; h (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 who
12、se refractivity would be equal to the refractive modulus M. 4. Apparent boresight angle on slant paths The decrease in refractive index with height will produce an increase A0 in the apparent elevation angle for an elevated source. There will be fluctuations about this apparent angle due to local va
13、riations in the refractive-index structure. 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. TABLE 1 Angular deviation values for propagation throu
14、gh the total atmosphere 21 6 5. Rec. ITU-R PN.834-1 Beam spreading on slant paths Signal loss may also result from additional spreading of the antenna beam caused by the variation of atmospheric refraction with the elevation angle. This effect should be negligible for all elevation angles above 3“.
15、Figure 1 gives an estimate of the losses through the total atmosphere due to atmospheric refraction effects. Losses should be independent of frequency over the range 1-100 GHz where water vapour is contributing to the refractive profile. FIGURE 1 An estimate of loss due to the additional spreading o
16、f a beam and standard deviation about the average Rec. ITU-R PN.834-1 217 6. Effective radio path length and its variations Since the tropospheric refractive index is higher than unity varying as a function of altitude, a wave propagating between the ground and a satellite has a radio path length ex
17、ceeding the geometrical path length. The difference in length can be obtained by the following integral: B AL = J(n - 1) ds A where: S: length along the path n: refractive index A and B: path ends. Equation (5) can be used only if the variation of the refractive index n along the path is known. When
18、 the temperature T, the atmospheric pressure P and the relative humidity H are known at the ground level, the excess path length AL will be computed using the semi-empirical method explained below, which has been prepared using the atmospheric radio-sounding profiles provided by a one-year campaign
19、at 500 meteorological stations in 1979. In this method, the general expression of the excess path length AL is: where cpo is the elevation angle at the observation point, A LV is the vertical excess path length and k and 6 (cpo, ALv) are corrective terms, in the calculation of which the exponential
20、atmosphere model is used. The k factor takes into account the variation of the elevation angle along the path. The S(cp0, ALv) 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 comput
21、ation; it involves an error of only 3.5 cm for a cpo angle of 10“ and of 0.1 mm for a cpo angle of 45“. It can be noted, moreover, that at very low elevation for which the 6 term would not be negligible, the assumption of a plane stratified atmosphere, which is the basis of all methods of computatio
22、n of the excess path length, is no longer valid. The vertical excess path length (m) is given by: A Lv = 0.02228 P / g + f(T) H (7) In the first term of the right-hand side of equation (7), P is the atmospheric pressure (hPa) and g is the acceleration due to gravity (m/s2) at the observation point.
23、In the empirical second term, H is the relative humidity (%): the function of temperaturef(T) depends on the geographical location and is given by: f(T) = a 10bT where: Tis in (OC) a is in (m/%) of relative humidity b is in (OC-). Parameters a and b are given in Table 2 according to the geographical
24、 location. 218 Location a (d%) ITU-R RECMN*PN- 834-3 94 4855232 05219bY 39T = b (OC-I) Rec. ITU-R PN.834-1 CoastaI areas (islands, or locations less than 10 km away from 1 sea shore) 5.5 10-4 TABLE 2 2.91 x Non-coastal equatorial areas All other areas 6.5 x 10-4 2.73 x 7.3 x 10-4 2.35 x To compute t
25、he corrective factor k of equation (6), an exponential variation with height h of the atmospheric refractivity N is assumed: N(h) = N, exp (4 / ho) (9) where N, is the average value of refractivity at the Earth?s surface (see Recommendation ITU-R PN.453) and ho is given by: k is then computed from t
26、he following expression: where n, and n (ho) are the values of the refractive index at the Earth?s surface and at height ho (given by equation (10) respectively, and r, and r(h0) are the corresponding distances to the centre of the Earth. 7. Propagation in ducting layers Ducts exist whenever the ver
27、tical refractivity gradient at a given height and location is less than -157 km-?. The existence of ducts is important because they can give rise to anomalous radiowave propagation, particularly on terrestrial or very low angle Earth-space links. Ducts provide a mechanism for radiowave signals of su
28、fficiently high frequencies to propagate far beyond their normal line-of-sight range, giving rise to potential interference with other services (see Recommendation IT-R PN.452). They also play an important role in the occurrence of multipath interference (see Recommendation ITU-R PN.530) although th
29、ey are neither necessary nor sufficient for multipath propagation to occur on any particular link. 7.1 Influence of elevation angle When a transmitting antenna is situated within a horizontally stratified radio duct, rays that are launched at very shallow elevation angles can become ?trapped? within
30、 the boundaries of the duct. For the simplified case of a ?normal? refractivity profile above a surface duct having a fixed refractivity gradient, the critical elevation angle a (radian) for rays to be trapped is given by the expression where dMldh is the vertical gradient of modified refractivity (
31、z O) and bh is the thickness of the duct which is the height of duct top above transmitter antenna. Figure 2 gives the maximum angle of elevation for rays to be ?trapped? within the duct. The maximum trapping angle increases rapidly for decreasing refractivity gradients below -157 km-? (Le., increas
32、ing lapse rates) and for increasing duct thickness. P v E o M C m - M C .- p: t! e ITU-R RECMN*RN- 834-1 94 E 4855212 0523965 026 E Rec. ITU-R PN.834-1 FIGURE 2 Maximum trapping angle for a surface duct of constant refractivity gradient over a spherical Earth 5.0 4.0 3.0 2.0 1 .o 0.0 - 100 - 200 - 3
33、00 Refractivity gradient (N/km) - 400 ?. ;w: 219 0.25 o. 20 0.15 0.10 0.05 0.00 - Lu o .- .- e U 7.2 Minimum trapping frequency The existence of a duct, even if suitably situated, does not necessarily imply that energy will be efficiently coupled into the duct in such a way that long-range propagati
34、on will occur. In addition to satisfying the maximum elevation angle condition above, the frequency of the wave must be above a critical value determined by the physical depth of the duct and by the refractivity profile. Below this minimum trapping frequency, ever-increasing amounts of energy will “
35、leak” through the duct boundaries. The minimum frequency for a wave to be trapped within a tropospheric duct can be estimated using a phase integral approach. Figure 3 shows the minimum trapping frequency for surface ducts (solid curves) where a constant (negative) refractivity gradient is assumed t
36、o extend from the surface to a given height, with a “standard” profile above this height. For the frequencies used in terrestrial systems (typically 8-16 GHt), a ducting layer of about 5 m to 15 m minimum thickness is required and in these instances the minimum trapping frequency,f,i, is a strong fu
37、nction of both the duct thickness and the refractive index gradient. In the case of elevated ducts an additional parameter is involved even for the simple,case of a linear refractivity profile. That parameter relates to the shape of the refractive index profile lying below the ducting gradient. The
38、dashed curves in Fig. 3 show the minimum trapping frequency for a constant gradient ducting layer lying above a surface layer having a standard refractivity gradient of -40 N/km. 220 25 20 h z c3, A 15 3 Lti bD C a a .- E - 10 .- z c: .- E 5 O O Rec. ITU-R PN.834-1 FIGURE 3 Minimum frequency for “tr
39、apping” in atmospheric radio ducts of constant refractivity gradients 10 20 30 Layer thickness (m) Surface-based ducts Elevated ducts above standard refractive profile - 40 For layers having lapse rates that are only slightly greater than the minimum required for ducting to occur, the minimum trapping frequency is actually increased over the equivalent surface-duct case. For very intense ducting gradients, however, trapping by an elevated duct requires a much thinner layer than a surface duct of equal gradient for any given frequency.
