1. METO621 Lesson 18

2. Thermal Emission in the Atmosphere – Treatment of clouds Scattering by cloud particles is usually ignored in the longwave spectrum (thermal emission) We have already treated the effect of full cloud cover when discussing the heating rates. A common approximation to account for partial clouds is to assume Where N is the cloud fraction. Note that this equation is only strictly true if the clouds are very thin (in dimension) and randomly distributed. If the clouds are not black, but have emissivity , then N is replaced by  N. F c is still the flux for an opaque cloud.

3. Treatment of clouds As clouds grow in the vertical, the sides of the clouds obscure portions of the sky, and the effective cloud fraction grows as an observer looks at angles away from the vertical For these cases the equation for the fluxes has the form. In the figures that follow the symbol  is the aspect ratio of the cloud, i.e. height/radius.

4. Effective cloud fraction for isothermal cylinders

5. Effective cloud fraction for very tall non-isothermal cylinders

6. Intensity Calculations for the Thermal Infra-red The next 12 figures show the calculated spectrum of intensity, fluxes and heating rates by Ellingson and Serafino (1984). The model employs the Goody random band model. Because of the quasi-isotropic nature of the radiation field (the source is blackbody radiation) the spectra shown apply equally well to the flux. The next figure shows the intensity seen at the top of the atmosphere. The two large holes between 500-800 cm -1 and 1000-1100 cm -1 correspond to the 15  band of CO 2 and the 9.6  band of O 3. At the center of the CO 2 bands, the atmosphere is opaque up to about 5 km, hence the emission is from the troposphere. At the very center of the CO 2 and O 3 bands the intensity increases because of emission from the stratosphere.

7. Intensity Calculations for the Thermal Infra-red The 800-1200 cm -1 region is known as the window region. The atmosphere absorbs only weakly, and the intensity is representative of Blackbody radiation from the surface. The intensities in the pure rotational water vapor band (0-600 cm -1 ) and the  vibration/rotation band (wavenumbers > 1200 cm -1 ), are representative of temperatures at the middle and upper troposphere. The atmosphere is opaque to radiation from the surface, and the intensity is due to emission from water vapor in the troposphere.

8. Upwelling intensities at 66 km, clear sky

9. Intensity Calculations for the Thermal Infra-red Downwelling Radiation The region of large upwelling intensity at the top of the atmosphere between 800 and 1200 cm-1 has a very low downwelling intensity at the surface. The downwelling radiation in the CO 2 and water vapor bands is characteristic of an altitude of about 2 km, due to the opaque nature of the absorption. The ozone band shows a much lower temperature, indicating that the emission is from a higher altitude, close to the tropopause.

11. Homogeneous clear and black cloud condition

13. Intensity Calculations for the Thermal Infra-red The angular variation of the intensity integrated over the intervals 12-20 ( the CO 2 band) and 10-12 micron (800-1000 cm-1) (the window region) is shown in the next two slides. In these figures a nadir angle of 0-90 corresponds to upwelling radiation and a nadir angle of >90 corresponds to downwelling. The upwelling radiance shows little variation with angle, whereas the downwelling radiance increases dramatically near the horizon (90 degrees) because of the longer path length. Note that the upwelling radiance is almost isotropic (no change with angle). Hence the mean angle used in the two stream approximation does not need to be specified exactly.

14. Longwave radiation as a function of nadir angle and pressure

16. Flux and Heating Rate Calculations The next two slides present examples of observed and calculated profiles of upward and downward longwave fluxes for clear and cloudy skies. Note that both the upward and downward fluxes decrease with increasing, but at different rates. The upward flux decrease because the principle source of heating is the radiation from the ground, and this is attenuated with height. The downward radiation fluxes increase towards the surface because the increasingly opaque atmosphere is emitting at progressively warmer temperatures.

17. Profiles of clear sky upward and downward fluxes

18. Flux and Heating Rate Calculations For cloudy conditions, the downward flux decreases with increasing altitude, but the decrease is slower than for clear skies due to the contribution from the nearly black cloud. The upward flux decreases rapidly in the lower portion of the cloud layer to a value approximately equal to the emission from a blackbody. That is the cloud absorbs the incident radiation, and replaces it with radiation at the cloud temperature. Near the top of the cloud, the downward flux decreases rapidly to the clear sky value, whereas the upward flux changes little from the value inside the cloud because there is little attenuation of the emission by the gases above the cloud.

19. Profiles for cloudy skies of clear upward and downward fluxes

20. Clear and cloudy sky heating rate profiles

21. Spectral contributions to the cooling rate – tropical atmopshere

22. Spectral contributions to the longwave cooling rate

23. Vertical profile of total longwave cooling