METO621
Lesson 18
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
F   (1  N ) F0  NFc
• 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 e, then N is
replaced by eN. Fc is still the flux for an opaque cloud.
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.


0

c
F  (1  N ) F  N F
*
*
• In the figures that follow the symbol a is the aspect ratio of
the cloud, i.e. height/radius.
Effective cloud fraction for isothermal cylinders
Effective cloud fraction for very tall non-isothermal cylinders
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-1correspond to the 15m band of CO2 and the 9.6
m band of O3.
• At the center of the CO2 bands, the atmosphere is opaque up to
about 5 km, hence the emission is from the troposphere.
• At the very center of the CO2 and O3 bands the intensity
increases because of emission from the stratosphere.
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 6.3m 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.
Upwelling intensities at 66 km, clear sky
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 CO2 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.
Homogeneous clear and black cloud condition
Homogeneous clear and black cloud condition
Intensity Calculations for the Thermal Infra-red
• The angular variation of the intensity integrated over the
intervals 12-20 ( the CO2 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.
Longwave radiation as a function of nadir angle and pressure
Longwave radiation as a function of nadir angle and pressure
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.
Profiles of clear sky upward and downward fluxes
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.
Profiles for cloudy skies of clear upward and downward
fluxes
Clear and cloudy sky heating rate profiles
Spectral contributions to the cooling rate – tropical atmopshere
Spectral contributions to the longwave cooling rate
Vertical profile of total longwave cooling