Chapter 3 Atmospheric Radiative
Transfer and Climate
授課: 3.8-3.12
自行閱讀: 3.1-3.7
3.8 Heuristic Model of Radiative Equilibrium
單層大氣
假設長波輻射全部被大氣吸收：
地表的輻射平衡：
Ts4 = S(1-A)/4+Te4
大氣的輻射平衡：
Ts4 = 2Te4  Ts = 21/4Te
如果Te = 255K  Ts = 303K
Te = 255 K
雙層大氣
Solution:
TOA:
Layer 1:
For n layers: (prove it!)
Layer 2:
Surface:
平流層
Tstra Emissivity: ε
地表大氣
Tsa Emissivity: ε
3.9 Cloud and Radiation
Low and high clouds in western Scotland, looking S from Ben Challum (1025 m asl.)
February 15, 2008. The linear high cloud are contrails from airplanes passing over UK.
www.climate4you.com/ClimateAndClouds.htm
Evaporation from the Barents Sea north of Norway produces linear cloud
systems drifting south, March 30, 2003. The clouds are seen to originate
shortly south of the sea ice limit in the upper part of the picture, where the
cold and dry Arctic air masses for the first time come into contact with the
warm sea water. The island Jan Mayen is seen near the southern tip of the
tongue of sea ice in the upper central part of the picture. Northern Norway,
Finland and part of Russia is seen snow covered in the lower right part of
the picture, which covers a distance of about 1000 km from south to north.
www.climate4you.com/ClimateAndClouds.htm
Space shuttle view of cloud systems forming by convection of air masses over the Pacific
Ocean. Evaporation consumes heat and leads to surface cooling. Higher up condensation of
the water vapour releases heat, which leads to warming of the atmosphere. By convection
both heat and water vapour is removed from the surface and are transported up into the
atmosphere. The picture covers an horizontal distance of about 40 km from left to right.
www.climate4you.com/ClimateAndClouds.htm
Cloud fraction January 2008. The cloud fraction expresses how much of the Earth is
covered by clouds. Imagery by Reto Stockli, NASA's Earth Observatory, using data
provided by the MODIS Atmosphere Science Team, NASA Goddard Space Flight
Center.
www.climate4you.com/ClimateAndClouds.htm
Clouds reflect and shade. Clouds usually have a high reflectivity, depending on
water droplet size, cloud thickness and the zenith angle of the sun. Low clouds
(stratocumulus) over the Barents Sea, August 18, 2003.
www.climate4you.com/ClimateAndClouds.htm
High clouds (cirrus) over Folldal, central Norway. September 22, 2006
www.climate4you.com/ClimateAndClouds.htm
Mid-level clouds (altostratus) over Nordmarka, South Norway, June 26, 2005.
www.climate4you.com/ClimateAndClouds.htm
Low clouds (stratocumulus) over Advent Bay, central Spitsbergen, Svalbard. July 31, 2003.
www.climate4you.com/ClimateAndClouds.htm
A thunderstorm with associated vertical cloud (cumulonimbus) developing
over southern Norway near Oslo. August 27, 2007.
www.climate4you.com/ClimateAndClouds.htm
Low and a few high clouds over Barents Sea, September 14, 2004. The
formation of clouds always occurs on a much smaller scale than can be
represented by grid size used by global climate models. In addition, clouds often
occur in several layers above each other, adding to the difficulty of modelling the
global cloud cover correctly.
www.climate4you.com/ClimateAndClouds.htm
If dropt size distribution and vertical distribution of humidity are
assumed, albedo and absorption depend on total liquid water content
and solar zenith angle.
1. How do liquid water content and
solar zenith angle affect cloud
albedo?
2. Why is albedo not sensitive to
zenith angle when liquid water
is large?
3. Why is albedo less sensitive to
liquid water content when zenith
angle is large?
1. How do liquid water content and
solar zenith angle affect cloud
absorption? Is it the same as in
albedo?
2. What is the difference between
overhead and near 90 degree
zenith angle? Why?
3. Why absorption decrease with
increasing zenith angle? Why is
it not sensitive when liquid water
content is small?
What is the relationship between albedo and drop size?
Why?
水滴與冰晶對長波的影響
1. What is the relationship between emissivity and water content?
2. Can cloud be treated as blackbody?
3.10 Radiative-Convective Equilibrium Temperature Profiles
Assuming 1-D radiative-convective equilibrium, one can
estimate equilibrium temperature profile due to the
balanced radiative forcing and convective adjustment.
What should be specified in the model?
• Gas concentrtation (what gases should we consider?)
• Surface albedo
• Cloud type and fraction
• Lapse rate
氧化亞氮
甲烷
吸
收
率
氧與臭氧
水氣
二氧化碳
大氣的所有氣體
大氣不同氣體的輻射吸收帶 (圖片來源：Ahrens，p.38，
Fig. 2.11)
實際上能量的平衡，除了輻射能量以外，還有其他因素
地球-大氣間的能量平衡示意圖
(圖片來源：Ahrens，p.41，Fig. 2.13)
Syukuro “Suki” Manabe
(真鍋淑郎)
水氣+二氧化碳
水氣
水氣+二氧化碳+臭氧
水氣是最重要的溫室氣體！
S O3 ~ L CO2
L H2O: cooling
S H2O ~ L CO2
3.11 A Simple Model for the Net Radiative
Effect of Cloudiness
Energy balance at TOA
Difference between clear and cloudy sky
Difference in absorbed solar radiation
Difference in OLR
Or, if the top of cloud is above most of gaseous absorber
of longwave radiation (H20)
Change in net radiation at TOA
Cloud radiative forcing depends on
• the change in albedo, and
• the temperature at the cloud top
(qualitatively correct if cloud tops above 4 or 5 km)
assume
Solar constant: 1367
Clear-sky OLR: 265
Surface temp.: 288K
Lapse rate: 6.5
Cloud fraction
Cloud radiative forcing
The shortwave rays from
the Sun are scattered in
a cloud. Many of the
rays return to space. The
resulting "cloud albedo
forcing," taken by itself,
tends to cause a cooling
of the Earth.
Longwave rays emitted by the Earth
are absorbed and reemitted by a
cloud, with some rays going to the
surface. Thicker arrows indicate more
energy. The resulting "cloud
greenhouse forcing," taken by itself,
tends to cause a warming of the Earth.
earthobservatory.nasa.gov/Features/Clouds/
High cloud’s radiative effect
The high, thin cirrus clouds in the Earth's atmosphere
act in a way similar to clear air because they are
highly transparent to shortwave radiation (their cloud
albedo forcing is small), but they readily absorb the
outgoing longwave radiation. Like clear air, cirrus
clouds absorb the Earth's radiation and then emit
longwave, infrared radiation both out to space and
back to the Earth's surface. Because cirrus clouds are
high, and therefore cold, the energy radiated to outer
space is lower than it would be without the cloud (the
cloud greenhouse forcing is large). The portion of the
radiation thus trapped and sent back to the Earth's
surface adds to the shortwave energy from the sun
and the longwave energy from the air already
reaching the surface. The additional energy causes a
warming of the surface and atmosphere. The overall
effect of the high thin cirrus clouds then is to enhance
atmospheric greenhouse warming.
earthobservatory.nasa.gov/Features/Clouds/
In contrast to the warming effect of the higher clouds,
low stratocumulus clouds act to cool the Earth
system. Because lower clouds are much thicker than
high cirrus clouds, they are not as transparent: they
do not let as much solar energy reach the Earth's
surface. Instead, they reflect much of the solar
energy back to space (their cloud albedo forcing is
large). Although stratocumulus clouds also emit
longwave radiation out to space and toward the
Earth's surface, they are near the surface and at
almost the same temperature as the surface. Thus,
they radiate at nearly the same intensity as the
surface and do not greatly affect the infrared
radiation emitted to space (their cloud greenhouse
forcing on a planetary scale is small). On the other
hand, the longwave radiation emitted downward
from the base of a stratocumulus cloud does tend to
warm the surface and the thin layer of air in between,
but the preponderant cloud albedo forcing shields
the surface from enough solar radiation that the net
effect of these clouds is to cool the surface.
In contrast to both of the cloud categories
previously discussed are deep convective clouds,
typified by cumulonimbus clouds. A
cumulonimbus cloud can be many kilometers
thick, with a base near the Earth's surface and a
top frequently reaching an altitude of 10 km
(33,000 feet), and sometimes much higher.
Because cumulonimbus cloud tops are high and
cold, the energy radiated to outer space is lower
than it would be without the cloud (the cloud
greenhouse forcing is large). But because they
also are very thick, they reflect much of the solar
energy back to space (their cloud albedo forcing
is also large); hence, with the reduced shortwave
radiation to be absorbed, there is essentially no
excess radiation to be trapped. As a consequence,
overall, the cloud greenhouse and albedo
forcings almost balance, and the overall effect of
cumulonimbus clouds is neutral-neither warming
nor cooling.
Annual average net radiation determined from 1985 to 1986.
Annual average net cloud radiative forcing from 1985 to 1986.
Overall, clouds have the effect of lessening the amount of heating
that would otherwise be experienced at Earth's surface.
Annual Mean (March 2000 to February 2001)