1、 Recommendation ITU-R P.453-11 (07/2015) The radio refractive index: its formula and refractivity data P Series Radiowave propagation ii Rec. ITU-R P.453-11 Foreword The role of the Radiocommunication Sector is to ensure the rational, equitable, efficient and economical use of the radio-frequency sp
2、ectrum 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 Radiocommunicati
3、on Conferences 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 stat
4、ements 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
5、available 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 satel
6、lite 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 signa
7、ls and 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 m
8、eans whatsoever, without written permission of ITU. Rec. ITU-R P.453-11 1 RECOMMENDATION ITU-R P.453-11 The radio refractive index: its formula and refractivity data (Question ITU-R 201/3) (1970-1986-1990-1992-1994-1995-1997-1999-2001-2003-2012-2015) Scope Recommendation ITU-R P.453 provides methods
9、 to estimate the radio refractive index and its behaviour for locations worldwide; describes both surface and vertical profile characteristics; and provides global maps for the distribution of refractivity parameters and their statistical variation. The ITU Radiocommunication Assembly, considering a
10、) the necessity of using a single formula for calculation of the index of refraction of the atmosphere; b) the need for reference data on refractivity and refractivity gradients all over the world; c) the necessity to have a mathematical method to express the statistical distribution of refractivity
11、 gradients, recommends 1 that the atmospheric radio refractive index, n, be computed by means of the formula given in Annex 1; 2 that refractivity data given on world charts and global numerical maps in Annex 1 should be used, except if more reliable local data are available; 3 that the statistical
12、distribution of refractivity gradients be computed using the method given in Annex 1; 4 that in the absence of local data on temperature and relative humidity, the global numerical map of the wet term of the surface radio refractivity exceeded for 50% of the year described in Annex 1, 2.2 be used (s
13、ee Fig. 3). 2 Rec. ITU-R P.453-11 Annex 1 1 The formula for the radio refractive index The atmospheric radio refractive index, n, can be computed by the following formula: n 1 N 106 (1) where the radio refractivity, N, is: (N-units) (2) the dry term of the radio refractivity, Ndry, is: (3) and the w
14、et term of the radio refractivity, Nwet, is: (4) where: Pd: dry atmospheric pressure (hPa) P: total atmospheric pressure (hPa) e: water vapour pressure (hPa) T: absolute temperature (K) and (5) Since , equation (2) can be rewritten as: = 77.6 5.6 +3.75 x 105 2 (6) Equation (6) may be approximated wi
15、th reduced accuracy as: (7) Equation (7) yields values of N within 0.02 percent of the value obtained from equation (2) for the temperature range from 50oC to +40oC. For representative profiles of temperature, pressure and water vapour pressure, see Recommendation ITU-R P.835. For ready reference, t
16、he relationship between water vapour pressure e and relative humidity is given by: 100seHe (8) with: 251075.3726.77 T eTeTPN d TPN ddry 6.77251075.372 T eTeN w e t ePP d ePPd TePTN 48106.77Rec. ITU-R P.453-11 3 cttdtbaEFe s e x p (9) and: 274 109.500320.02.7101 tPEF w a t e r 274 104.600382.02.2101
17、tPEF i c e where: : temperature (oC) : pressure (hPa) H: relative humidity (%) es: saturation vapour pressure (hPa) at the temperature t (C) and the coefficients a, b, c and d are: for water for ice a 6.1121 a 6.1115 b 18.678 b 23.036 c 257.14 c 279.82 d = 234.5 d = 333.7 (valid between 40 to 50 (va
18、lid between 80 to 0 Vapour pressure e is obtained from the water vapour density using the equation: 7.216Te hPa (10) where is given in g/m3. Representative values of are given in Recommendation ITU-R P.836. 2 Surface refractivity and height dependence 2.1 Refractivity as a function of height It has
19、been found that the long-term mean dependence of the refractive index n upon the height h is well expressed by an exponential law: n(h) 1 N0 106 exp (h/h0) (11) where: N0: average value of atmospheric refractivity extrapolated to sea level h0: scale height (km). N0 and h0 can be determined statistic
20、ally for different climates. For reference purposes a global mean of the height profile of refractivity may be defined by: N0 315 h0 7.35 km 4 Rec. ITU-R P.453-11 These numerical values apply only for terrestrial paths. This reference profile may be used to compute the value of refractivity Ns at th
21、e Earths surface from N0 as follows: Ns N0 exp (hs/h0) (12) where: hs: height of the Earths surface above sea level (km). It is to be noted, however, that the contours of Figs. 1 and 2 were derived using a value of h0 equal to 9.5 km. Figures 1 and 2 were derived from a 5-year data set (1955-1959) f
22、rom about 1 000 surface stations. (Figures 1 and 2 are not available in numerical form.) For Earth-satellite paths, the refractive index at any height is obtained using equations (1), (2) and (10) above, together with the appropriate values for the parameters given in Recommendation ITU-R P.835, Ann
23、ex 1. The refractive indices thus obtained may then be used for numerical modelling of ray paths through the atmosphere. (Note that the exponential profile in equation (12) may also be used for quick and approximate estimates of refractivity gradient near the Earths surface and of the apparent bores
24、ight angle, as given in 4.3 of Recommendation ITU-R P.834.) 2.2 Wet term of the surface refractivity Figure 3 shows for easy reference the median value (50%) of the wet term of the surface refractivity exceeded for the average year. Data file ESANWET.TXT contains the numerical data. The wet term of
25、the surface refractivity was derived from two years (1992-1993) of initialization data of the numerical weather forecast of the European Centre for Medium-range Weather Forecast (ECMWF). NOTE 1 The data file ESANWET.TXT has a resolution of 1.5 in both latitude and longitude. The companion data files
26、 ESALAT.TXT and ESALON.TXT contain respectively the latitudes and longitudes of the corresponding entries (gridpoints) in data file ESANWET.TXT. The data range from 0 to 360 in longitude and from +90 to 90 in latitude. For a location different from the gridpoints, the wet term of the refractivity at
27、 the desired location can be derived by performing a bi-linear interpolation on the values at the four closest gridpoints. The data files can be obtained from the Radiocommunication Bureau (BR). Rec. ITU-R P.453-11 5 FIGURE 1 Monthly mean values of N0: February P .04 53 -01 6 Rec. ITU-R P.453-11 FIG
28、URE 2 Monthly mean values of N0: August P .0453-02 Rec. ITU-R P.453-11 7 FIGURE 3 Wet term of the surface refractivity (ppm) exceeded for 50% of the year P.0453-031501005005010015080604020020406080Longitude(degrees)Latitude (degrees)8 Rec. ITU-R P.453-11 3 Vertical refractivity gradients The statist
29、ics of the vertical gradient of radio refractivity in the lowest layer of the atmosphere are important parameters for the estimation of path clearance and propagation associated effects such as ducting on transhorizon paths, surface reflection and multipath fading and distortion on terrestrial line-
30、of-sight links. 3.1 In the first kilometre of the atmosphere Figures 4 to 7 present isopleths of monthly mean decrease (i.e. lapse) in radio refractivity over a 1 km layer from the surface. The change in radio refractivity, N, was calculated from: N Ns N1 (13) where N1 is the radio refractivity at a
31、 height of 1 km above the surface of the Earth. The N values were not reduced to a reference surface. Figures 4 to 7 were derived from a 5-year data set (1955-1959) from 99 radiosonde sites. (Figures 4 to 7 are not available in numerical form.). In addition, the annual values of N, exceeded for 0.1,
32、 0.2, 0.5, 1, 2, 5, 10, 20, 30, 40, 50, 60, 70, 80, 90, 95, 98, 99, 99.5, 99.8, 99.9 of an average year are an integral part of this Recommendation and are available in the form of digital maps and are provided in the file R-REC-P.453-11-201404-I!ZIP-E. The monthly values of N, exceeded for 0.1, 0.2
33、, 0.5, 1, 2, 5, 10, 20, 30, 40, 50, 60, 70, 80, 90, 95, 98, 99, 99.5, 99.8, 99.9 of an average month are an integral part of this Recommendation and are available in the form of digital maps and are provided in the file R-REC-P.453-11-201404-I!ZIP-E. R-REC-P.453-11-201404-I!ZIP-E.zip3.2 In the lowes
34、t atmospheric layer Refractivity gradient statistics for the lowest 100 m from the surface of the Earth are used to estimate the probability of occurrence of ducting and multipath conditions. Where more reliable local data are not available, the charts in Figs. 8 to 11 give such statistics for the w
35、orld which were derived from a 5-year data set (1955-1959) from 99 radiosonde sites. (Figures 8 to 11 are not available in numerical form.) In addition the following parameters are an integral part of this Recommendation and are available in the form of digital maps and are provided in the file R-RE
36、C-P.453-11-201404-I!ZIP-E: The annual values of the refractivity gradient in the lowest 65 m from the surface of the Earth, N65m, exceeded for 0.1, 0.2, 0.5, 1, 2, 5, 10, 20, 30, 40, 50, 60, 70, 80, 90, 95, 98, 99, 99.5, 99.8, 99.9 of an average year. The monthly values of the refractivity gradient
37、in the lowest 65 m from the surface of the Earth, N65m, exceeded for 0.1, 0.2, 0.5, 1, 2, 5, 10, 20, 30, 40, 50, 60, 70, 80, 90, 95, 98, 99, 99.5, 99.8, 99.9 of an average month. The percentage of annual and monthly times for which refractivity gradient, N over 100 m is lower than 100 N-unit/km, (%)
38、. The data range from 0 to 360 in longitude and from +90 to 90 in latitude. For a location different from the gridpoints, the refractivity gradient at the desired location can be derived by performing a bi-linear interpolation on the values at the four closest gridpoints as described in Recommendati
39、on ITU-R P.1144. Rec. ITU-R P.453-11 9 FIGURE 4 Monthly mean values of N: February P .0453-04 FIGURE 5 Monthly mean values of N: May P .04 53 -05 10 Rec. ITU-R P.453-11 FIGURE 6 Monthly mean values of N: August P .04 53 -06 FIGURE 7 Monthly mean values of N: November P .04 53 -07 Rec. ITU-R P.453-11
40、 11 FIGURE 8 Percentage of time gradient 100 (N-units/km): February P .04 53 -08 FIGURE 9 Percentage of time gradient 100 (N-units/km): May P .04 53 -09 12 Rec. ITU-R P.453-11 FIGURE 10 Percentage of time gradient 100 (N-units/km): August P .04 53 -10 FIGURE 11 Percentage of time gradient 100 (N-uni
41、ts/km): November P .04 53 -11 Rec. ITU-R P.453-11 13 4 Statistical distribution of refractivity gradients It is possible to estimate the complete statistical distribution of refractivity gradients near the surface of the Earth over the lowest 100 m of the atmosphere from the median value Med of the
42、refractivity gradient and the ground level refractivity value, Ns, for the location being considered. The median value, Med, of the refractivity gradient distribution may be computed from the probability, P0, that the refractivity gradient is lower than or equal to Dn using the following expression:
43、 1/10 1 0)1/1( kP kDM e d En (14) where: E0 log10 ( | Dn | ) k1 30. Equation (14) is valid for the interval 300 N-units/km Dn 40 N-units/km. If this probability P0 corresponding to any given Dn value of refractivity gradient is not known for the location under study, it is possible to derive P0 from
44、 the world maps in Figs. 8 to 11 which give the percentage of time during which the refractivity gradient over the lowest 100 m of the atmosphere is less than or equal to 100 N-units/km. Where more reliable local data are not available, Ns may be derived from the global sea level refractivity N0 map
45、s of Figs. 1 and 2 and equation (12). For Dn Med, the cumulative probability P1 of Dn may be obtained from: 132111En kkBM e dDP (15) where: 2 2103.0 sNM e dB)1(log101 FE 16725.6 BM edDF n 1206.12 Bk Bk 1203 14 Rec. ITU-R P.453-11 Equation (15) is valid for values of Med 120 N-units/km and for the in
46、terval 300 N-units/km Dn 50 N-units/km. For Dn Med, the cumulative probability P2 of Dn is computed from: 1422111EnkkB M e dDP (16) where: 2 2103.0 sNM e dB)1(log101 FE 16725.6 BM edDF n 4.24 100 BkEquation (16) is valid for values of Med 120 N-units/km and for the interval 300 N-units/km Dn 50 N-un
47、its/km. 5 Surface and elevated ducts Atmospheric ducts may cause deep slow fading, strong signal enhancement, and multipath fading on terrestrial line-of-sight links and may also be the cause of significant interference on transhorizon paths. It is therefore of interest to describe the occurrence of
48、 ducts and their structure. This section gives statistics derived from 20 years (1977-1996) of radiosonde observations from 661 sites. Ducts are described in terms of modified refractivity defined as: M(h) = N(h) + 157h (M-units) (17) where h (km) is the height. Rec. ITU-R P.453-11 15 Figure 12 illustrates the modified refractivity as a function of height above ground and the definitions of duct types. Ducts can be of three types: surface based, elevated-surface, and elevated ducts. Due to rather few cases of elevated-surface ducts in comp
