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Wavelength, (xm figure 4.9 (a) Solar spectral irradiance at the top of the atmosphere and at sea level. Shaded regions indicate the molecules responsible for absorption. Absorption spectra for (b) molecular oxygen and ozone, (c) water vapor, and (d) the atmosphere, expressed on a scale of 0-1.

Similar arguments hold for ozone; however, nitrogen and oxygen are symmetric and thus are not strongly affected by radiation above 400 nm. The C02 molecule is linear but can easily be bent, leading to an induced dipole moment. A transverse vibrational mode exists for C02 at 15 pm, just where the Earth emits most of its infrared radiation.

TABLE 4.2 Solar Spectral Irradiance, Normalized to a Solar Constant of 1367 ffm 2

m.

/o

m,

X, nm

W m 2 nm 1

Wnr2

X, nm

W m 2 nm '

Wra2

250.5

0.059

2.092

490.5

2.009

276.7

255.5

0.089

2.387

495.5

1.928

286.4

260.5

0.102

2.967

500.5

1.859

296.1

265.5

0.280

3.921

510.5

1.949

315.3

270.5

0.293

5.257

520.5

1.833

333.5

275.5

0.200

6.245

530.5

1.954

352.3

280.5

0.112

7.111

540.5

1.772

371.1

285.5

0.141

8.364

550.5

1.864

389.8

290.5

0.623

10.44

560.5

1.845

408.4

295.5

0.548

13.19

570.5

1.772

426.7

300.5

0.403

15.51

580.5

1.840

445.2

305.5

0.580

18.26

590.5

1.815

463.3

310.0

0.495

20.54

600.5

1.748

481.1

315.2

0.695

24.03

610.5

1.705

498.7

320.0

0.712

27.46

620.5

1.736

515.7

325.2

0.646

31.15

631.0

1.641

535.0

330.0

1.144

35.86

641.0

1.616

551.4

335.5

0.982

41.69

651.0

1.608

567.5

340.5

0.992

46.17

661.0

1.573

582.8

345.5

0.967

50.77

671.0

1.518

598.2

350.5

1.119

55.52

681.0

1.494

613.3

355.5

1.058

60.69

691.0

1.450

627.9

360.5

0.979

65.26

701.0

1.388

642.2

365.5

1.263

70.56

711.0

1.387

656.1

370.5

1.075

76.52

721.0

1.332

669.7

375.5

1.141

81.75

731.0

1.327

683.0

380.5

1.289

87.77

741.0

1.259

696.0

385.5

0.954

92.27

751.0

1.263

708.8

390.5

1.223

97.67

761.0

1.238

721.3

395.5

1.378

103.0

771.0

1.205

733.4

400.5

1.649

109.5

781.0

1.188

745.3

405.5

1.672

118.0

791.0

1.159

757.1

410.5

1.502

126.3

801.0

1.143

768.5

415.5

1.736

135.1

821.0

1.081

790.6

420.5

1.760

143.8

841.0

1.045

811.8

425.5

1.697

152.3

861.0

0.997

831.6

430.5

1.136

159.8

881.0

0.960

850.9

435.5

1.725

168.3

901.0

0.905

869.7

440.5

1.715

177.1

921.0

0.830

887.1

445.5

1.823

186.7

941.0

0.800

903.5

450.5

2.146

196.8

961.0

0.767

919.1

455.5

2.036

206.9

981.0

0.762

934.3

460.5

2.042

217.1

1002.5

0.745

952.8

465.5

2.044

227.3

1052.5

0.661

987.9

470.5

1.879

237.1

1102.5

0.608

1019

475.5

2.018

247.3

1152.5

0.545

1048

480.5

2.037

257.4

1202.5

0.496

1074

485.5

1.832

267.4

1252.5

0.474

1098 (Continued)

table 4.2 (Continued)

m,

m.

X, nm

Wm"2nm 1

W m~2

X,nm

Wm"Jnra 1

Wr!

1302.5

0.438

1120

2302.5

0.066

1313

1352.5

0.387

1140

2402.5

0.054

1319

1402.5

0.353

1159

2517.5

0.047

1325

1452.5

0.323

1176

2617.5

0.04 Î

1329

1502.5

0,296

1191

2702.5

0.036

1332

1552.5

0.273

1205

2832.5

0.03!

1336

1602.5

0.247

1218

3025.0

0.024

1342

1652.5

0.234

1230

3235.0

0.019

1346

1702.5

0.217

1241

3425.0

0.015

1349

1752.5

0.187

¡25!

3665.0

0.012

1353

1802.5

0.169

1260

3855.0

0.010

1355

1852.5

0.148

1267

4085,0

0,008

1357

1902.5

0.133

1274

4575.0

0,005

1360

! 952.5

0.126

1281

5085.0

0,003

1362

2002.5

0.116

1287

5925.0

0.002

1364

2107.5

0.093

1298

7785.0

0.001

1366

2212.5

0,075

1307

10075.0

0.000

1367

Source: Fröhlich and London < 1986).

Source: Fröhlich and London < 1986).

Table 4.2 tabulates the solar spectral irradiance, normalized to a solar constant of I367Wm~2. Solar spectral actinic llux at the surface (Okm), 20, 30, 40, and 50km is shown in Figure 4.11.

CO2 Absorption in the Atmosphere The spectral region from about 7 to 13 pm is a window region: nearly 80% of the radiation emitted by the Earth in this region escapes to space. Most of the non-C02 greenhouse gases, including Os, CH4, N20, and the chloro 11 uorocarbons, all have strong absorption bands in this window region. For this reason, relatively small changes in the concentrations of these gases can produce a significant change in the net radiative flux. As the concentration of a greenhouse gas continues to increase, it can absorb more of the radiation in its energy bands. Once an absorption wavelength becomes saturated, further increases in the concentration of the gas have iess and less effect on radiative flux. This is called the band saturation effect. For CO?, for example, the 15-|rm band is already close to saturated. In addition, if a gas absorbs at wavelengths that are also absorbed by other gases, then the effect of increasing concentrations on radiative flux is less than in the absence of band overlap. For example, there is significant overlap between some of the absorption bands of CH4 and N20; this overlap must be carefully accounted for when calculating the effect of these gases on radiative fluxes.

Even with the band saturation effect, it is incorrect to conclude that because there is already so much C02 in the atmosphere, more CO2 can have no additional effect on absorption of outgoing radiation. When gases are present in small concentrations, doubling the concentration of the gas will approximately double its absorption. When

Wavelength, jim

100 40

Net Irradiance _ at Tropopause

Wavelength, jim

100 40

Net Irradiance _ at Tropopause

2000

2000

500 1000

Wavenumber.

Effect on Tropopause -Irradiance of Increasing Carbon Dioxide from ■ 1980 to 1990 Values

1500

2000

cm ri

FIGURE 4.10 Effect of C02: (a) net infrared irradiance (Wm 3 (cm" ')"1) at the tropopause; (b) representation of the strength of the spectral lines of CO? in the thermal infrared (note the logarithmic scale); (c) change in net irradiance at the tropopause as a result of increasing the C02 concentration from its 1980-1990 levels, holding all other parameters fixed (IPCC 1995).

an absorbing gas is present in high concentration the effect of further addition is not one-to-one but it is not zero, either. For example, doubling the concentration of C02 from its present-day value leads to a 10-20% increase in its total greenhouse effect. Where this increase comes from can be explained as follows. The top frame of Figure 4.10 shows the spectral variation in the infrared radiance at the tropopause, in Wm": (cm"1) \ The Planck function (4.2) determines the shape of the upper envelope of the curve, the maximum energy that can be emitted at a given wavelength and temperature. At typical atmospheric temperatures the maximum lies between 10 and 15 pm. The notches in the spectrum result from the presence of greenhouse gases and clouds. If the atmosphere were transparent to infrared radiation, the irradiance reaching the tropopause would be the same as that leaving the surface.

The middle frame of Figure 4.10 shows the C02 absorption spectrum. As noted earlier, a strong absorption band exists near 15 pm. The bottom frame shows the modeled effect of an instantaneous change in C02 abundance (change in concentration from 1980 to 1990) with all other factors, such as cloudiness, held fixed. At the center of the 15-|im band, the increase in C02 concentration has almost no effect; the C02 absorption is indeed saturated in this portion of the spectrum.

Away from this band, however, where C02 is less strongly absorbing, the increase in C02 does have an effect. As more and more C02 is added to the atmosphere, more of its spectrum will become saturated, but there will always be regions of the spectrum that remain unsaturated and thus capable of continuing to absorb infrared radiation. For example, the 10-jim absorption band is about 106 times weaker than the peak of the 15 pm band, but its contribution to the irradiance change in the lower frame is important. And as C02 concentrations increase, the importance of the lOfim band will continue to increase relative to the 15-)im band.

4.7 ABSORPTION BY 02 AND 03

For wavelengths below about 1000 nm (1 |im), the predominant absorbing species in the atmosphere are 02 and 03 (Figure 4.9). The spectral solar actinic flux at various altitudes, as shown in Figure 4,11, can, therefore, be computed fairly accurately by considering only the absorption by 02 and 03. The absorption cross sections of 02 and 03 are shown in Figures 4.12 and 4.13. All the absorption shown in Figure 4.12 and 4.13 leads to dissociation.

It) f i—i—i—i—|—i—i—i—i—|—i—p—i—i—|—i—i—i—i—|—i—i—i—r—;

It) f i—i—i—i—|—i—i—i—i—|—i—p—i—i—|—i—i—i—i—|—i—i—i—r—;

150 200 250 300 350 400

Wavelength, nm

FIGURE 4.11 Solar spectral actinic flux (photons cm 2 s 1 nm 1) at various altitudes and at the Earth's surface (DeMore et al, 1994).

150 200 250 300 350 400

Wavelength, nm

FIGURE 4.11 Solar spectral actinic flux (photons cm 2 s 1 nm 1) at various altitudes and at the Earth's surface (DeMore et al, 1994).

FIGURE 4.12 Absorption cross section of 02 (Brasseur and Solomon 1984). (With kind permission of Springer Science and Business Media.)

Wavelength, nm

FIGURE 4.12 Absorption cross section of 02 (Brasseur and Solomon 1984). (With kind permission of Springer Science and Business Media.)

The attenuation of radiation from the top of the atmosphere (TOA) to any altitude z is described by the Beer-Lambert Law (4.24),

FIGURE 4.13 Absorption cross section of 03. [Reprinted from Burrows et al. (1999), with permission from Elsevier.]

Wavelength, nm

FIGURE 4.13 Absorption cross section of 03. [Reprinted from Burrows et al. (1999), with permission from Elsevier.]

The optical depth of the atmosphere at the surface as a result of absorption by species A is given by (4.29)

rzTO A

Jo where m — sec 0o and where aA [T(z), X] is the absorption cross section of molecule A at temperature T(at altitude z). Here, the species of interest are 02 and O3. The total optical depth at the surface is then the sum of those attributable to 02 and 03:

To estimate x(0,A,) for 02 and 03, we neglect the temperature dependence of the absorption cross sections. Then (4.29) becomes for 02 and 03

i" "TOA

Jo rZTOA

The integrals in (4.42) and (4.43) are just the total column abundances (molecules cm-2) of 02 and 03, respectively.

Let us first estimate the transmittance of the atmosphere at the surface resulting from the absorption of solar radiation by 02. In (4.42), we need the total column abundance of 02 (molecules cm-2). From Chapter 1, estimation of the number concentration of air molecules at any altitude can be based on the scale height of the atmosphere

where H is the scale height (= 7.4km) and «a¡r(0) = 2.55 x 1019 molecules cm-3. Then

The column abundance of 02 is (0.21)(2.6 x 1019)(7.4 x 105) 9ï 4.0 x 1024 molecules cm"2.

In order to obtain an estimate of the atmospheric transmittance as a result of absorption by 02

Ftoa(X)

we can characterize each of the three absorption bands for 02 in Figure 4.12 by its maximum cross section. For this calculation, let us take m = 1 (overhead sun). The result

is tabulated here:

Absorption Band

cm2

xo.

F(0,X) / Ftoa(X)

Schumann-Runge continuum

10-

-17

4 x 107

~0

Schumann-Runge bands (175-205 nm)

10-

-20

4 x 104

~0

Herzberg continuum (185-242 nm)

10"

-23

40

~0

Since F(0,X)/FtoaP-) is effectively zero for each of these bands, which extend up to 242 nm, we see that atmospheric 02 completely removes all radiation below X = 242 nm from reaching the Earth's surface. [In such a case, the species is called optically thick in the region; conversely, for a species for which exp(—x) = 1, the species is optically thin.]

To estimate the transmittance resulting from 03 absorption, the cross section of which is shown in Figure 4.13, we follow the same procedure as for 02, in which we approximate the cross section of each band by its maximum value. Assuming a column abundance of 03 of 300 DU (recall 1DU = 2.69 x 1016 molecules cm"2), the result is

Absorption Band CTnlax, cm2 xo3 F{0,X)/Fjo\(X)

Hartley (220-280nm) 10"17 80 ~0

Huggins (310-330 nm) 10"19 0.8 0.15

At wavelengths X > 242 nm, the atmosphere is transparent with respect to 02. Ozone is the dominant absorber in the range 240-320 nm. Table 4.3 gives estimated surface-level spectral actinic flux at 40°N latitude on January 1 and July 1.

TABLE 4.3 Estimated Ground-Level Actinic Flux I(X) at 40° N Latitude

AX, nm

I(X) x 10"

14 (photons cm 2 s ')

Noon January 1

Noon July 1

290-295

0.0

0.0

295-300

0.0

0.031

300-305

0.021

0.335

305-310

0.196

1.25

310-315

0.777

2.87

315-320

1.45

4.02

320-325

2.16

5.08

325-330

3.44

7.34

330-335

3.90

7.79

335-340

4.04

7.72

340-345

4.51

8.33

345-350

4.62

8.33

350-355

5.36

9.45

355-360

5.04

8.71

360-365

5.70

9.65

Source: Finlayson-Pitts and Pitts (1986).

Source: Finlayson-Pitts and Pitts (1986).

A Somewhat More Accurate Estimate of Absorption of Solar Radiation by ()2

and O3 We calculate the reduction in solar radiation at the Earth's surface as a result of 02 and 03 absorption in the wavelength range from 200 to 320 nm at a solar zenith angle of 45°. The approximate column abundances are

02 4x I024 molecules cm

O^ 8 x 101S molecules cm'2 (300DU)

Absorption cross sections for CK and Oj, as well as the solar flux at the lop of the atmosphere, in 20nm increments arc

X, nm

a0;,cnr

<7o,, cm2

Fjoa , photons cm 2 s 1

200

9 x 10 24

3,2 x 10"19

1.5 x 1013

220

4.7 x 10~24

1.8 x 10"ia

9.6 x 1013

240

1.2 x 10 24

8.2 x 10"IR

1.0 x I014

260

0

1.1 x 10"17

2.6 x 1014

280

0

3.9 x i0"ls

4.2 x 1014

300

0

3.2 x 10"19

1.6 x 1015

320

0

2.2 x KT'9

2.4 x !01S

For solar zenith angle = 45°, m = sec 45° = 1.414.

The total transmittancc of the atmosphere is defined as the ratio F(z,X)/Fto.\ = exp [—(to2 + T03}] = exp (—Toj) exp (—To,), which is the product of the individual transmittances of 02 and 03. We obtain

o2

O3

Total

F(0,X),

X, nm

Transmittance

Transmit tance

Transmit tance

photons cm"

200

7.8 x 10"23

2.6 x 10~2

2.0 x 10"24

3.0 x 10"u

220

2.8 X lO"12

1.2 x 10"9

3.4 x I0~21

3.3 x 10~7

240

1.1 X 10 3

2.3 x 10 41

2.6 x 10 44

2.6 x 10"30

260

1.0

3.0 x lO"55

3.0 x 10"55

7.8 x 10"41

280

1.0

4.7 x 10"20

4.7 x 10 20

2.0 x 10"5

300

1.0

2,6 x lO'2

2.6 x 10 2

4.2 x 1013

320

1.0

8.1 x 10~2

8.1 x 10"2

2.0 x 10'4

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