1、 Recommendation ITU-R P.453-13 (12/2017) The radio refractive index: its formula and refractivity data P Series Radiowave propagation ii Rec. ITU-R P.453-13 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, 2017 ITU 2017 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.453-13 1 RECOMMENDATION ITU-R P.453-13 The radio refractive index: its formula and refractivity data (Question ITU-R 201/3) (1970-1986-1990-1992-1994-1995-1997-1999-2001-2003-2012-2015-2016-2017) Scope Recommendation ITU-R P.453 provid
9、es methods 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. Keywords Radio refractive index, surface
10、, vertical profile, refractivity parameters, statistical variation The ITU Radiocommunication Assembly, considering a) 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 o
11、ver the world; c) the necessity to have a mathematical method to express the statistical distribution of refractivity 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 globa
12、l numerical maps in Annex 1 should be used, except if more reliable local data are available; 3 that the statistical 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 ma
13、p of the wet term of the surface radio refractivity exceeded for 50% of the year described in Annex 1, 2.2 be used (see Fig. 3). 2 Rec. ITU-R P.453-13 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 (
14、1) where the radio refractivity, N, is: (N-units) (2) the dry term of the radio refractivity, Ndry, is: (3) and the wet 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 (
15、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 with 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 representativ
16、e profiles of temperature, pressure and water vapour pressure, see Recommendation ITU-R P.835. For ready reference, the 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 48
17、106.77Rec. ITU-R P.453-13 3 cttdtbaEFe s e x p (9) and: 264 109.50320.02.7101 tPEF w a t e r 264 104.60383.02.2101 tPEF i c e where: : temperature (oC) : total atmospheric pressure (hPa) H: relative humidity (%) es: saturation vapour pressure (hPa) at the temperature t (C) and the coefficients a, b,
18、 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 (valid between 80 to 0 While is defined as the total atmospheric pressure, the dry atmospheric pressure can be used with insignificant loss of prediction accuracy. Vapour
19、 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 been found that the long-t
20、erm 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 statistically for different climate
21、s. For reference purposes a global mean of the height profile of refractivity may be defined by: N0 315 4 Rec. ITU-R P.453-13 h0 7.35 km These numerical values apply only for terrestrial paths. This reference profile may be used to compute the value of refractivity Ns at the Earths surface from N0 a
22、s 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) from about 1 000 surface sta
23、tions. (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, Annex 1. The refractive indice
24、s 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 boresight angle, as given in 4.3
25、 of Recommendation ITU-R P.834.) 2.2 Wet term of the surface refractivity The annual and monthly values of the wet term of the surface refractivity, Nwet (ppm), exceeded for 0.1, 0.2, 0.3, 0.5, 1, 2, 3, 5, 10, 20, 30, 50, 60, 70, 80, 90, 95 and 99% respectively of an average year and an average mont
26、h are an integral part of this Recommendation. They are available in the form of digital maps and provided in the Supplement R-Rec. P.453-13-201712-I!ZIP-E.zip. The data is from 180 to 180 in longitude and from 90 to 90 in latitude, with a resolution of 0.75 in both latitude and longitude. The wet t
27、erm of the surface refractivity at any desired location on the surface of the Earth can be derived by the following interpolation method: a) determine the two probabilities, pabove and pbelow, above and below the desired probability, p, from the set: 0.1, 0.2, 0.3, 0.5, 1, 2, 3, 5, 10, 20, 30, 50, 6
28、0, 70, 80, 90, 95 and 99%; b) for the two probabilities, pabove and pbelow, determine the wet term of the surface refractivity, Nwet1, Nwet2, Nwet3, and, Nwet4 at the four closest grid points; c) determine the wet term of the surface refractivity, Nwetabove and Nwetbelow, at the probabilities, pabov
29、e and pbelow, by performing a bi-linear interpolation of the four values of the wet term of the surface refractivity, Nwet1, Nwet2, Nwet3, and, Nwet4 at the four grid points, as described in Recommendation ITU-R P.1144; d) determine the wet term of the surface refractivity, Nwet, at the desired prob
30、ability, p, by interpolating Nwetabove and Nwetbelow vs. pabove and pbelow to p on a linear Nwet vs. log p scale. The monthly and annual wet term of the surface refractivity have been derived from 36 years (1979-2014) of European Centre of Medium-range Weather Forecast (ECMWF) ERA Interim data. For
31、easy reference, Fig. 3 shows the median value (50%) of the wet term of the surface refractivity exceeded for the average year. Rec. ITU-R P.453-13 5 FIGURE 1 Monthly mean values of N0: February P .04 53 -01 6 Rec. ITU-R P.453-13 FIGURE 2 Monthly mean values of N0: August P .0453-02 Rec. ITU-R P.453-
32、13 7 FIGURE 3 Wet term of the surface refractivity (ppm) exceeded for 50% of the year P.0453-03150090606010215009600330 06090Longitude(degrees),ELatitude (degrees) , N1081020330901081501251007550250MedianannualNwet3 Vertical refractivity gradients The statistics of the vertical gradient of radio ref
33、ractivity 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-of-sight links. 8 Rec. ITU-R P.453-13 3.1
34、 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 height of 1 km abo
35、ve the surface of the Earth. The N values were not reduced to a reference surface. Figures 4 to 7 were derived from a five-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, 0.2, 0.5, 1, 2,
36、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 Supplement. The monthly values of N, exceeded for 0.1, 0.2, 0.5, 1, 2, 5, 10, 20, 30, 40, 50, 60, 7
37、0, 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 Supplement. 3.2 In the lowest atmospheric layer Refractivity gradient statistics for the lowest 100 m from the surface of the
38、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 world which were derived from a 5-year data set (1955-1959) from 99 radiosonde sites. (Figures 8 to
39、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 Supplement: The annual values of the refractivity gradient in the lowest 65 m from the surface of the Earth,
40、 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 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
41、, 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, (%). The data range from 0 to 360 in longitude and from +90 to 90 in latitude. For a location different from the gridpoints, t
42、he 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 Recommendation ITU-R P.1144. Rec. ITU-R P.453-13 9 FIGURE 4 Monthly mean values of N: February P .0453-04 FIGURE 5 Monthly mean values
43、of N: May P .04 53 -05 10 Rec. ITU-R P.453-13 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.453-13 11 FIGURE 8 Percentage of time gradient 100 (N-units/km): February P .04 53 -08 FIGURE 9 Percentage of time gradient 100 (
44、N-units/km): May P .04 53 -09 12 Rec. ITU-R P.453-13 FIGURE 10 Percentage of time gradient 100 (N-units/km): August P .04 53 -10 FIGURE 11 Percentage of time gradient 100 (N-units/km): November P .04 53 -11 Rec. ITU-R P.453-13 13 4 Statistical distribution of refractivity gradients It is possible to
45、 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 refractivity gradient and the ground level refractivity value, Ns, for the location being considered. The median value, Med
46、, 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: 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
47、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 the world maps in Figs. 8 to 11 which give the percentage of time during which the refractivity gradient over the lowest 1
48、00 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 maps of Figs. 1 and 2 and equation (12). For Dn Med, the cumulative probability P1 of Dn may be obtained from: 132111En kkBM e
49、 dDP (15) where: 2 2103.0 sNM e dB)1(log101 FE 16725.6 BM edDF n 1206.12 Bk Bk 1203 Equation (15) is valid for values of Med 120 N-units/km and for the interval 300 N-units/km Dn 50 N-units/km. 14 Rec. ITU-R P.453-13 For Dn Med, the cumulative probability P2 of Dn is computed from: 1422111EnkkB M e d
