1、Rec. ITU-R F.1333-1 1RECOMMENDATION ITU-R F.1333-1ESTIMATION OF THE ACTUAL ELEVATION ANGLE FROM A STATIONIN THE FIXED SERVICE TOWARDS A SPACE STATION TAKINGINTO ACCOUNT ATMOSPHERIC REFRACTION(Question ITU-R 163/9)(1997-1999)Rec. ITU-R F.1333-1The ITU Radiocommunication Assembly,consideringa) that in
2、 some frequency sharing studies between the fixed service and space radiocommunication services,including fixed-satellite, broadcasting-satellite and space science services, it is necessary to estimate various factorsrelated to propagation such as slant path attenuation by atmospheric gases and atte
3、nuation due to Fresnel zone blockage;b) that the above attenuation is a function of the actual elevation angle as seen from a station in the fixed servicetowards a space station (geostationary or non-geostationary);c) that it is necessary to establish a simplified calculation method to estimate the
4、actual elevation angle towards aspace station taking into account atmospheric refraction where the elevation angle of a space station is known only infree-space propagation conditions in vacuum;d) that it is generally appropriate to estimate the actual elevation angle of a space station under the co
5、ndition ofthe mean annual global reference atmosphere given in Recommendation ITU-R P.835,recommends1 that the method for estimating the actual elevation angle as seen from a station in the fixed service towards aspace station (geostationary or non-geostationary) under the condition of the mean annu
6、al global reference atmospherein Recommendation ITU-R P.835 as described in Annex 1 should be used where the elevation angle towards a spacestation is known only in free-space propagation conditions in vacuum (see Notes 1 and 2);2 that for an atmospheric refractivity model other than the mean annual
7、 global reference atmosphere as given inRecommendation ITU-R P.835, a different numerical formula should be derived corresponding to the specificatmospheric refractivity model (see Note 3).NOTE 1 This Recommendation can be used, for example, for estimation of slant path attenuation by atmospheric ga
8、sesand Fresnel zone blockage attenuation required in Recommendation ITU-R F.1249.NOTE 2 Annex 1 to Recommendation ITU-R F.1108 gives an example method for calculating the elevation angletowards a non-geostationary space station in free-space propagation conditions, and Annex 2 to Recommenda-tion ITU
9、-R F.1249 gives a method for calculating the elevation angle towards a geostationary space station in free-spacepropagation conditions.NOTE 3 Annex 2 to Recommendation ITU-R SF.765 (and also Annex 2 to Recommendation ITU-R F.1249) gives anexample of the numerical formulae for refraction corrections
10、corresponding to the exponential model of N0= 400 andD N = 68 (for maximum refraction correction) and the exponential model of N0= 250 and D N = 30 (for minimumrefraction correction), where N0is the sea-level radio refractivity and D N is the gradient (difference between sea leveland 1 km altitude),
11、 which are used for determination of the separation angle between the fixed service antenna mainbeam direction and the direction towards the geostationary-satellite orbit (GSO) (or a specific orbital location inthe GSO).Rec. ITU-R F.1333-12ANNEX 1Actual elevation angle where the elevation angle of a
12、 space stationis known only in free-space propagation conditions1 IntroductionIn some cases of sharing studies, the elevation angle of a space station (geostationary or non-geostationary), as seen froma fixed service station, is known only in free-space propagation conditions in vacuum. In such case
13、s, it is necessary toestimate the actual elevation angle taking account of atmospheric refraction. This annex gives a calculation method forsuch a need.2 Visibility of space stationUnder a quasi-exponential model of atmosphere for refraction, such as in Recommendation ITU-R P.835, the radio beamemit
14、ted from a fixed service station (h (km) altitude above sea level and q (degrees) elevation angle) is bent towards theEarth due to the effect of atmospheric refraction. This refraction correction, t (degrees), can be evaluated by thefollowing integral:tj=-nxnxxh()()tand (1)where j is determined as f
15、ollows on the basis of Snells law in polar coordinates:cos j = crxnx()()+ (2)c = (r + h) n(h) cos q (3)where:r : Earths radius (6 370 km).The function n(x) is the atmospheric refractive index at altitude x (km), and can be calculated by using the formula forthe radio refractive index in Recommendati
16、on ITU-R P.453 based on the mean annual global reference atmosphere inRecommendation ITU-R P.835. In addition, n(x) is the derivative of n(x).The values of t (h, q ) (degree) have been evaluated under the condition of the mean annual global reference atmosphereand it was found that the following num
17、erical formula gives a good approximation:t (h, q ) = 1 / 1.283 + 0.7491 q + 0.01986 q2+ h (0.3114 + 0.07020 q ) (4)The above formula has been derived as an approximation for 0 h 3 km and qm q 90, where qmis the angle atwhich the radio beam is just intercepted by the surface of the Earth and is give
18、n by:qm= arc cos ( )( )rrhnnh+0(5)or, approximately, qm= 0.875 h degrees.Rec. ITU-R F.1333-1 3Now, assume that the elevation angle of a space station is q0(degrees) under free-space propagation conditions. Theminimum elevation angle from a fixed service station for which the radio beam is not interc
19、epted by the surface of theEarth is qm. The refraction correction corresponding to qmis t (h, qm). Therefore, the space station is visible only whenthe following inequality holds:qm t (h, qm) q 0(6)3 Estimation of the actual elevation angleWhen the inequality in equation (6) holds, the actual elevat
20、ion angle, q (degrees), taking account of atmosphericrefraction can be calculated by solving the following equation:q t (h, q ) = q 0(7)We define that the solution of equation (7) is given as follows:q = q 0+ ts(h, q 0)(8)where the values of ts(h, q0) are identical with those of t (h, q ), but are e
21、xpressed as a function of q0.The function ts(h, q0) (degrees) can be closely approximated by the following numerical formula:ts(h, q0) = 1 / 1.712 + 0.5507 q0+ 0.03424 q02+ h (0.2584 + 0.07940 q0+ 0.01034 q02) (9)Now, the value of q calculated by equation (8) is the actual elevation angle to be used
22、 in the estimation of various factorssuch as slant path attenuation and attenuation due to Fresnel zone blockage.4 Summary of calculationsStep 1: The elevation angle of a space station in free-space propagation conditions in vacuum is designated as q0.Step 2: By using equations (4) and (5), examine
23、whether the inequality in equation (6) holds or not. If the answer isno, the satellite is not visible and, therefore, no further calculations are required.Step 3: If the answer in Step 2 is yes, calculate q by using equations (8) and (9). This is the actual elevation angle to beused for estimation of various factors such as slant path attenuation and attenuation due to Fresnel zone blockage.
