Reference standard atmospheres




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Rec. ITU-R P.835-3

RECOMMENDATION ITU-R P.835-3

REFERENCE STANDARD ATMOSPHERES

(Question ITU-R 201/3)

(1992-1994-1997-1999)

Rec. ITU-R P.835-3

The ITU Radiocommunication Assembly,



considering

a) the necessity for a reference standard atmosphere for use in calculating gaseous attenuation along an Earth space path,



recommends

1 that the standard atmospheres in Annex 1 be used to determine temperature, pressure and water-vapour pressure as a function of altitude, for calculating gaseous attenuation when more reliable local data are not available;

2 that the experimental data in Annex 2 be used for the locations of interest when seasonal and monthly variations are concerned.
ANNEX 1

1 Mean annual global reference atmosphere


The following reference standard atmosphere reflects the annual mean profiles when averaged across the globe.

1.1 Temperature and pressure


The reference standard atmosphere is based on the United States Standard Atmosphere, 1976, in which the atmosphere is divided into seven successive layers showing linear variation with temperature, as given in Fig. 1.

The temperature T at height h is given by:



T(h)  TiLi (hHi)               K (1)

where:


TiT(Hi) (2)

and Li is the temperature gradient starting at altitude Hi and is given in Table 1.

TABLE 1


Subscript, i

Altitude, Hi
(km)

Temperature gradient, Li
(K/km)

0

0

– 6.5

1

11

0.0

2

20

1.0

3

32

2.8

4

47

0.0

5

51

– 2.8

6

71

– 2.0

7

85






FIGURE 0835-01

When the temperature gradient Li  0, pressure is given by the equation:

               hPa (3)

and when the temperature gradient Li  0, pressure is obtained from the equation:

               hPa (4)

The ground-level standard temperature and pressure are:

(5)

Note that above about 85 km altitude, local thermodynamic equilibrium of the atmosphere starts to break down, and the hydrostatic equation, on which the above equations are based, is no longer valid.


1.2 Water-vapour pressure


The distribution of water vapour in the atmosphere is generally highly variable, but may be approximated by the equation:

(h)  0 exp (–h / h0)               g/m3 (6)

where the scale height h0  2 km, and the standard ground-level water-vapour density is:

0  7.5               g/m3 (7)

Vapour pressure is obtained from the density using the equation (see Recommendation ITU-R P.453):

               hPa (8)

Water-vapour density decreases exponentially with increasing altitude, up to an altitude where the mixing ratio e (h)/P(h)  2  10–6. Above this altitude, the mixing ratio is assumed to be constant.

1.3 Dry atmosphere for attenuation calculations


The profile of the density of atmospheric gases other than water vapour (the “dry atmosphere”) may be found from the temperature and pressure profiles given in § 1.1.

For attenuation calculations, this density profile may be approximated by an exponential profile according to equation (6) with:



h0  6 km (9)

2 Low-latitude annual reference atmosphere


For low latitudes (smaller than 22°) the seasonal variations are not very important and a single annual profile can be used.

The temperature T (K) at height h (km) is given by:



T(h)  300.4222 – 6.3533 h  0.005886 h2 for 0  h  17

T(h)  194  (h – 17) 2.533 for 17  h  47

T(h)  270 for 47  h  52

T(h)  270 – (h – 52) 3.0714 for 52  h  80

T(h)  184 for 80  h  100

while the pressure P (hPa):



P(h)  1012.0306 – 109.0338 h  3.6316 h2 for 0  h  10

P(h)  P10 exp [– 0.147 (h – 10)] for 10 = h = 72

P(h)  P72 exp [– 0.165 (h – 72)] for 72 = h = 100

where P10 and P72 are the pressures at 10 and 72 km respectively.

For water vapour (g/m3):

r(h)  19.6542 exp [– 0.2313 h – 0.1122 h2  0.01351 h3

– 0.0005923 h4] for 0  h  15



r(h)  0 for h  15

3 Mid-latitude reference atmosphere


For mid-latitudes (between 22 and 45) the following profiles may be used for the summer and winter.

3.1 Summer mid-latitude


The temperature T (K) at height h (km) is given by:

T(h)  294.9838 – 5.2159 h – 0.07109 h2 for 0  h  13

T(h)  215.5 for 13  h  17

T(h)  215.5 exp [(h – 17) 0.008128] for 17  h  47

T(h)  275 for 47  h  53

T(h)  275  {1– exp [(h – 53) 0.06] } 20 for 53  h  80

T(h)  175 for 80  h  100

while the pressure P (hPa):



P(h)  1012.8186 – 111.5569 h  3.8646 h2 for 0  h  10

P(h)  P10 exp [– 0.147 (h – 10)] for 10  h  72

P(h)  P72 exp [– 0.165 (h – 72)] for 72  h  100

where P10 and P72 are the pressures at 10 and 72 km respectively.

For water vapour (g/m3):

r(h)  14.3542 exp [– 0.4174 h – 0.02290 h2  0.001007 h3] for 0  h  10

r(h)  0 for h  10

3.2 Winter mid-latitude


The temperature T (K) at height h (km) is given by:

T(h)  272.7241 – 3.6217 h – 0.1759 h2 for 0  h  10

T(h)  218 for 10  h  33

T(h)  218  (h – 33) 3.3571 for 33  h  47

T(h)  265 for 47  h  53

T(h)  265 – (h – 53) 2.0370 for 53  h  80

T(h)  210 for 80  h  100

while the pressure P (hPa):



P(h)  1018.8627 – 124.2954 h  4.8307 h2 for 0  h  10

P(h)  P10 exp [– 0.147 (h – 10)] for 10  h  72

P(h)  P72 exp [– 0.155 (h – 72)] for 72  h  100

where P10 and P72 are the pressures at 10 and 72 km respectively.

For water vapour (g/m3):

r(h)  3.4742 exp [– 0.2697 h – 0.03604 h2  0.0004489 h3] for 0  h  10

r(h)  0 for h  10

4 High latitude reference atmosphere


For high latitudes (higher than 45) the following profiles may be used for the summer and winter.

4.1 Summer high latitude


The temperature T (K) at height h (km) is given by:

T(h)  286.8374 – 4.7805 h – 0.1402 h2 for 0  h  10

T(h)  225 for 10  h  23

T(h)  225 exp [(h – 23) 0.008317] for 23  h  48

T(h)  277 for 48  h  53

T(h)  277 – (h – 53) 4.0769 for 53  h  79

T(h)  171 for 79  h  100

while the pressure P (hPa):



P(h)  1008.0278 – 113.2494 h  3.9408 h2 for 0  h  10

P(h)  P10 exp [–0.140 (h – 10)] for 10  h  72

P(h)  P72 exp [–0.165 (h – 72)] for 72  h  100

where P10 and P72 are the pressures at 10 and 72 km respectively.

For water vapour (g/m3):

r(h)  8.988 exp [– 0.3614 h – 0.005402 h2 – 0.001955 h3] for 0  h  15

r(h)  0 for h  15

4.2 Winter high latitude


The temperature T (K) at height h (km) is given by:

T(h)  257.4345  2.3474 h – 1.5479 h2  0.08473 h3 for 0   h  8.5

T(h)  217.5 for 8.5  h  30

T(h)  217.5  (h – 30) 2.125 for 30   h  50

T(h)  260 for 50   h  54

T(h)  260 – (h – 54) 1.667 for 54   h  100

while the pressure P (hPa):



P(h)  1010.8828 – 122.2411 h  4.554 h2 for 0  h  10

P(h)  P10 exp [–0.147 (h – 10)] for 10  h  72

P(h)  P72 exp [–0.150 (h – 72)] for 72  h  100

where P10 and P72 are the pressures at 10 and 72 km respectively.

For water vapour (g/m3):

r(h)  1.2319 exp [0.07481 h – 0.0981 h2  0.00281 h3] for 0  h  10

r(h)  0 for h  10
BIBLIOGRAPHY

BRUSSAARD, G., DAMOSSO, E. and STOLA, L. [October, 1983] Characterisation of the 50-70 GHz band for space communications. CSELT Rapporti Tecnici, Vol. XI, No. 5.


ANNEX 2

1 Experimental data of atmospheric vertical profiles


Monthly averages of vertical profiles of temperature, pressure and relative humidity were calculated for 353 locations over the world, using 10 years (1980-1989) of radiosonde observations. This dataset (DST.STD) is available from ITU/BR and contains the mean monthly vertical profiles, for both 00.00 UTC and 12.00 UTC, of pressure, temperature and relative humidity. These profiles, calculated in the absence of rain, range from 0 to 16 km with a step of 500 m. An example of one profile is given in Table 2.

Above that altitude, extrapolation can be performed by using the reference profiles given in Annex 1. To translate the relative humidity into absolute values of water vapour density, the formulae contained in Recommendation ITU-R P.453 should be used.

TABLE 2

DST.STD data format – Example of month average profile


NNNNNMMT NL
01384111 33

Press(hPa)


Z(km)

Temp(K)

RH(%/100)



  .000

 .00

273.16

.000E+00

950.734

 .50

273.14

.730E+00

892.926

 1.00

271.16

.672E+00

837.925

 1.50

269.03

.581E+00

786.709

 2.00

266.60

.516E+00

737.580

 2.50

264.01

.467E+00

691.017

 3.00

261.18

.445E+00

647.037

 3.50

258.14

.427E+00

605.609

 4.00

255.07

.413E+00

566.371

 4.50

251.86

.402E+00

528.962

 5.00

248.62

.400E+00

493.406

 5.50

245.34

.362E+00

460.513

 6.00

241.99

.329E+00

429.041

 6.50

238.62

.297E+00

398.949

 7.00

235.19

.275E+00

371.513

 7.50

231.82

.237E+00

345.238

 8.00

228.65

.179E+00

319.967

 8.50

225.70

.139E+00

296.107

 9.00

223.06

.107E+00

271.381

 9.50

221.51

.943E-01

250.931

10.00

219.68

.815E-01

232.328

10.50

218.39

.723E-01

214.863

11.00

217.63

.642E-01

196.348

11.50

217.70

.539E-01

181.888

12.00

217.56

.477E-01

167.454

12.50

217.86

.421E-01

153.456

13.00

218.37

.366E-01

140.897

13.50

218.51

.317E-01

129.541

14.00

218.67

.272E-01

120.027

14.50

218.27

.253E-01

110.853

15.00

217.74

.235E-01

101.978

15.50

217.22

.220E-01

 91.925

16.00

217.89

.196E-01




Legend

NNNNN = WMO Station Number: 01384 MM = Month: 11

T = Launch time: 1 (1 = 00.00 UTC, 2 = 12.00 UTC) NL = Fixed number of profile levels: 33

Press(hPa) = Atmospheric Pressure Z(km) = Height above sea level

Temp(K) = Air Temperature RH(%/100) = Relative Humidity (as a fraction)

NOTE 1 – The first level (at surface) may be set to zero if unrecorded.





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