BuT buTByTTB bcT bcTsTsT n

Table 4.2 The terrestrial infra-red region divided into spectral intervals with centres w cm-1 and width Aw within which there are important overlapping bands of water-vapour, carbon dioxide, methane and ammonia. (Vardavas and Carver 1984)

UJi

A uji

Absorbers and Bands

1

20

40

H20 rot 12 pm)

2

100

120

H2O rot 12 pm)

3

220

120

H2O rot (~ 12 pm)

4

330

100

H2O rot (~ 12 pm)

5

440

120

H2O rot (~ 12 pm)

6

525

50

H2O rot-cont (16.7-20.8 pm)

T

6T5

250

H2O rot-cont, CO2 (15 pm), NH3 (10.5 pm)

S

S50

100

H2O rot, H2O cont (8-13 pm), CO2 (15 pm)

CO2 (10.4 pm), NH3 (10.5 pm)

9

950

100

H2O rot, H2O cont (8-13 pm), CO2 (10.4 pm)

NH3 (10.5 pm)

10

1040

S0

H2O cont (8-13 pm), CO2 (10.4 pm), CO2 (9.4 pm),

O3 (9.6 pm), NH3 (10.5 pm)

11

1110

60

H2O cont (8-13 pm), CO2 (9.4 pm), NH3 (10.5 pm)

12

11T0

60

H2O cont (8-13 pm), NH3 (10.5 pm), CH4 (7.66 pm)

13

12T5

150

H2O vib-rot (6.3 pm), CH4 (7.66 pm)

14

1400

100

H2O vib-rot (6.3 pm),CH4 (7.66 pm),NH3 (6.14 pm)

15

1500

100

H2O vib-rot (6.3 pm), CH4 (7.66 pm),NH3 (6.14 pm)

16

1600

100

H2O vib-rot (6.3 pm), NH3 (6.14 pm)

1T

1T00

100

H2O vib-rot (6.3 pm), NH3 (6.14 pm)

1S

1S00

100

H2O vib-rot (6.3 pm), NH3 (6.14 pm)

19

1900

100

H2O vib-rot (6.3 pm), NH3 (6.14 pm)

20

2000

100

H2O vib-rot (6.3 pm)

21

2125

150

H2O vib-rot (6.3 pm)

22

>2200

TO

see Table 6.1

will consider in more detail in Chapter 6, because of their importance to near-infrared (0.85 to 5 ¡m) solar radiation absorption. There are also very weak bands between 16.7 and 20.8 ¡m, and between 0.4 and 0.75 ¡m. Details on how to obtain an estimate of the absorption of the near-infra-red bands can be found in Vardavas and Carver (1984).

4.6.3 Carbon dioxide

Carbon dioxide is the second most important greenhouse gas. Carbon dioxide has a strong fundamental band, at least three isotopic bands and at least ten hot bands that are centred near 15 ¡m, which overlap each other over the spectral interval 550 to 800 cm-1. The fundamental band absorptance for collisionally broadened lines, at 300 K and a pressure of 1 atm, can be estimated from the band-absorptance formulation, eqn (4.79), by setting Ao = 25 cm-1, d = 1.56 cm-1, bc = 0.065p cm-1, and k = 194 cm-2 atm-1. These values give u = 7.76X

and ¡3 = 0.17p where X is the CO2 amount in atm cm and p is the pressure in atm. One can then use the temperature dependence of k, 3 and bc to evaluate the absorptance at different temperatures, pressures and amounts. The mean transmission of the fundamental band can then be obtained using an effective width of about 235 cm-1. Carbon dioxide has two hot weak bands centred at 10.4 ¡m and 9.4 ¡m. The former band overlaps the interval 800-1000 cm-1, while the latter band overlaps the interval 1080-1140 cm-1. A table of total band absorptance for the CO2 total band absorptance for the CO2 15 ¡m bands as a function of amount and pressure is given in Vardavas and Carver (1984), where simple expressions for the transmittance for the weak hot bands are also given.

4.6.4 Ozone

Ozone is a strong absorber near 9.6 ¡m. There are two fundamental bands, a very strong band at 1042.1 cm-1 and a weaker one at 1103.16 cm-1, and at least three hot bands and three isotopic bands of the strong band. An estimate of the strong band absorptance for collisionally broadened lines, at 300 K and 1 atm, can also be obtained from eqn (4.79), using Ao = 30 cm-1, bc = 0.078 cm-1, k = 376 atm-1 cm-2, d = 0.1 cm-1. These values give u = 12.5X, 3 = 3.12p, where X is the ozone amount in atm cm and p in atm. The mean transmission can then be obtained using an effective bandwidth of about 100 cm-1. A table of total band absorptance for the O3 9.6 ¡m bands as a function of amount and pressure is given in Vardavas and Carver (1984).

4.6.5 Methane, ammonia and N2O

Methane absorbs strongly in the region 1100-1750 cm-1 centred at 7.66 ¡m. From measurements of band absorptance, an estimate of the mean transmission, t = 1 — A/wes = exp(—r), of this band can be obtained using a mean optical depth, r = 8.22X~0'54 with X = XQpv and XQ the methane amount in g cm~2, p in atmospheres, n = 0.5 and weff = 300 cm-1. Methane also has a near-infra-red band at 3.31 /xm, with r = 9.97X0'61, r/ = 0.45 and weB = 600 cm"1.

Ammonia is a very strong absorber in the regions 660-1300 cm-1, the 10.5 ¡m band, and 1300-2000 cm-1, the 6.14 ¡im bands. For the 10.5 ¡im band r = 21.2X0'604 with n = 0.7 and weff = 500 cm-1, while for the 6.14 ¡m bands t = 38.1X0 74 with n = 0.6 and weff = 400 cm-1. Ammonia has also a near-

infra-red bands near 3.03 ¡im with r = 32.68X0'822, r] = 0.3 and weg = 400 cm- 1 .

Another molecule that contributes to atmospheric absorption is nitrous oxide, N2O, with bands near 7.8 ¡m and 17 ¡m. Line strengths and absorption cross-sections for N2O are given in the next section for the 7.8 ¡m band using the HITRAN database.

4.7 The HITRAN database

The HITRAN database, originally developed by the US Air Force, provides a valuable source of spectroscopic parameters for the theoretical calculation of molecular transmittances. Here we shall give parameter symbols, nomenclature and units as close as possible to those given in the HITRAN database, and hence different from those used in the preceding sections of this chapter. For a given molecule, the database contains information for all the known energy transitions, including transitions due to isotopes. The parameters necessary for the calculation of a molecule's absorption coefficient are:

1. The position of each transition, in wave number wiu (cm"1), that corresponds to the energy of the photon emitted or absorbed by the molecule in the transition between two energy states.

2. The spectral line intensity of the transition, denoted in the database by Slu in units cm"1/(molecule cm"2), [cf. eqn (4.31)]. The line intensity for a rotational-vibrational transition is given in the form

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