Albedo

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Albedo

• Overall average reflection coefficient of an
  object
• Albedo of the Earth is about Albedo 0.3 which
  means that the Earth as a whole reflects 30 of
  solar radiation

http//www.latrobe.edu.au/crcss/view_earth.html
2
Total power of the incoming radiation Pin
(1-Albedo) Solar p REarth2
Example from Roland B. Stull, Meteorology for
Scientist and Engineers
3
External radiation

• Solar constant
• 1.4 kW/m2
• More accurately annual average solar constant
  Solar 1367 W/m2
• Variation between low and high solar activity 1
  W/m2
• Total power of the incoming radiation
• Pin (1-Albedo) Solar p REarth2 (Why?) 4
  1024

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Radiation of the Earth (assuming e1)

• Pout sSurface TEarth4
• Surface 4 p REarth2

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Greenhouse Effect

• http//phet.colorado.edu/web-pages/simulations-bas
  e.html

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From Perry J. Samson Professor University of
Michigan samson_at_umich.edu
Shortwave energy per square meter will decrease
at lower sun angles and shorter daylight periods.
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From Perry J. Samson Professor University of
Michigan samson_at_umich.edu
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(No Transcript)
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From Perry J. Samson Professor University of
Michigan samson_at_umich.edu
d is the day of the year (Jan 1 is day 1)
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From Perry J. Samson Professor University of
Michigan samson_at_umich.edu
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Earth Energy Balance

• Simple model
• Pin Pout
• Pin (1-Albedo) Solar p REarth2
• Pout 4p REarth2 s TEarth4
• T4Earth (1-Albedo) Solar p REarth2 / 4p REarth2
  s
• (1-Albedo) Solar /4 s
• (1- 0.3) 1367 W/m2/(45.6710-8 W/m2K4)
• TEarth 255 K -18 ºC
• Clearly something is wrong!

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Greenhouse Effect

• http//phet.colorado.edu/web-pages/simulations-bas
  e.html

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• We calculated the temperature as a whole
  including the atmosphere not the temperature of
  the surface of the Earth
• So we obtained a temperature of the Earth as seen
  from far away some combination of the
  temperature of the atmosphere and of the Earths
  surface
• Back to greenhouse effect!

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Earth Energy Balance

• Add atmosphere to the model.
• We will again make a very simple model but one
  which includes atmosphere modeled as a single
  layer

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Now the energy balance for the surface of the
Earth is

• Pin (1-Albedo) Solar p REarth2 s Te4 4p
  REarth2
• Pout s Ts4 4p REarth2

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Now the energy balance for the surface of the
Earth is

• (1-A) S p REarth2 s Te4 4 p REarth2 s Ts4 4p
  REarth2
• Ts4 (1-A) S / 4s Te4 2 Te4 (why?)
• Assuming Te 255 K
• We get Ts Te v2 303 K 30 ºC

4
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30 ºC

• Is it correct?
• Not really too hot!
• Whats wrong with our model
• Is atmosphere a thin layer?
• Is it totally absorbing in infrared?

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Atmospheric Absorption
1 0

• From http//www.everythingweather.com/atmospheric
  -radiation/absorption.shtml

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Lets have a closer look in infrared region.
We see plenty of holes.
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Lets correct the model once more

• What if the atmosphere only absorbs a fraction e
  of infrared? (e not equal 1)

sT4Earth
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• The atmosphere only absorbs a fraction e of
  infrared.
• The observer far away now sees the radiation
  both from the atmosphere and the surface of the
  Earth.
• We have to consider energy balance separately for
  the atmosphere and the surface

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• For the surface we have
• Pin (1-A) S p REarth2 e s Te4 4p REarth2
• Pout s Ts4 4p REarth2
• We know that
• (1-A) S p REarth2 s TEarth4 4p REarth2

s TEarth4 e s TA4 s Ts4
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• For the atmosphere we have
• Pout 2es Te4 4p REarth2
• Pin es Ts4 4p REarth2
• Te4 Ts4 /2

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• Combining these two equations
• s TEarth4 e s TA4 s Ts4
• TA4 Ts4 /2
• we have s TEarth4 e s Ts4/2 s Ts4
• Ts4 2TEarth4/(2-e)
• Analyzing the infrared absorption
• curve gives average e 0.9
• so we obtain
• Ts 23 ºC

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Earth Energy Balance

• The more complex models involving multilayer
  atmosphere partly transparent in infrared are
  coming up with proper average temperature of the
  surface of the Earth, which is about 15 ºC
• The process we followed is the process of
  consecutive approximation in modeling. Very often
  we start with a very simple model and progress to
  more complicated once getting (hopefully) closer
  and closer to reality.

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Different layers of the atmosphere
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Earth Energy Balance
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Atmospheric Absorption

• From http//www.everythingweather.com/atmospheric
  -radiation/absorption.shtml