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Lesson 2. AOSC 621. Radiative equilibrium. Where S is the solar constant. The earth reflects some of this radiation . Let the albedo be ρ , then the energy absorbed by the earth is (1- ρ ) F s. The thermal energy emitted by the earth is σ B T e 4. Hence we get. Radiative equilibrium.

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Lesson 2

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Lesson 2

Lesson 2

AOSC 621


Radiative equilibrium

Radiative equilibrium

Where S is the solar constant. The earth reflects some of this radiation . Let the albedo be ρ, then the energy absorbed by the earth is (1-ρ)Fs.

The thermal energy emitted by the earth is σBTe4

Hence we get


Radiative equilibrium1

Radiative equilibrium

  • The spherical albedo of the earth is about 30%. This gives an effective temperature of 255 K. This is considerably lower than the measured average temperature at the surface Ts of about 288 K.

  • The fact that Ts>Te is seen in all of the terrestrial planets with substantial atmospheres. It is due to the fact that whereas the planets are relatively transparent in the visible part of the spectrum, they are relatively opaque in the infra-red.

  • A portion of the IR emitted by the surface and atmosphere is absorbed by polyatomic gases and re-emitted in all directions – including back to the earth.


Greenhouse effect one atmospheric layer model

Greenhouse effect - one atmospheric layer model

  •  is the fraction of the IR radiation absorbed by the atmosphere


Greenhouse effect

Greenhouse effect


Greenhouse effect1

Greenhouse effect

  • An examination of the previous equation shows that as e increases the ground temperature increases.

  • This is what is referred to as greenhouse warming.

  • As we shall show later, not all of the additional energy trapped by the additional absorption goes inot heating the surface. Some , for example goes into evaporation of water - which stores energy in the atmosphere as additional latent heat.

  • So one should view the inference of the equation with some caution.

  • This issue will be discussed later when climate feedback is addressed.


Radiative equilibrium2

Radiative equilibrium

  • First Law of Thermodynamics - the time rate of change of the column energy is

  • Where N is calledthe radiative forcing

  • and

Where Teff is the effective transmission of the atmosphere to thermal radiation ( (1-e) in the simple model)


Perturbation to the radiative forcing

Perturbation to the radiative forcing

  • What happens if N(TS) is changed byΔ N(TS)

  • Assume that the atmosphere moves to a new equilibrium temperature, then we can write

We define the climate sensitivity α as


Climate sensitivity

Climate sensitivity


Co 2 doubling

CO2 doubling

  • The calculated radiative forcing from doubling CO2 is ~4 Wm-2

  • Assuming that the solar flux is constant we get

  • FTOA= 240 Wm-2 and Ts = 288 K, hence α=0.3 Wm-2K-1

  • Hence the increase in surface temperature is 1.2 K


Change in the solar constant

Change in the solar constant

  • Suppose the solar constant were to decrease by 1%

  • Assume no feedbacks other than the reduced thermal emission. If there is no albedo change due to the decreased solar flux then the second term in the climate sensitivity is zero. Hence we get:


Change in the solar constant 2

Change in the solar constant 2

  • Substituting for FTOA

  • Change in temperature is -0.72 K


General expression for

General expression for α

  • Consider a parameter Q ( such as albedo) that depends on the surface temperature

  • The direct forcing ΔN is augmented by a term

  • Solving for the climate sensitivity we find


General expression for1

General expression for α

  • If we have an arbitrary number of forcings Q then one can derive a general expression for the climate sensitivity

  • It should be noted that the above equation assumes that the individual forcings are independent of one another


Radiative forcing of greenhouse gases

Radiative forcing of greenhouse gases


Radiative forcing

Radiative forcing


Negative feedback

Negative feedback


Positive feedback

Positive feedback


Polar ice coverage positive feedback

Polar ice coverage - positive feedback


Climate feedback mechanisms

CLIMATE FEEDBACK MECHANISMS

  • ·POSITIVE AND NEGATIVE FEEDBACKS

  • ·WATER VAPOR - POSITIVE

  • ·ICE COVER - POSITIVE

  • .CLOUDS - POSITIVE AND NEGATIVE - MAINLY NEGATIVE


Lesson 2 3214860

Positions of the jet streams

Fig. 7-27, p. 191


Lesson 2 3214860

Relation between jet stream and high and low pressure systems

Fig. 8-30, p. 231


Using total ozone measurements

Using Total Ozone measurements

  • Contributions to the column ozone amount (total ozone) come mainly from the lower stratosphere. In this altitude region ozone has a long chemical lifetime compared to its dynamic lifetime. Hence one can treat Total Ozone acts as a dynamic tracer.

  • The subtropical and polar fronts correspond to a rapid change in the tropopause height, and total ozone shows abrupt changes.

  • Hudson et. al, 2003, 2006 developed a method to determine the position of the fronts (jet streams) from satellite total ozone data.


Jet streams on march 11 1990 sub tropical blue polar red

Jet Streams on March 11, 1990Sub-tropical = Blue, Polar = Red


Mean latitude of the sub tropical front

Mean latitude of the Sub-tropical front

Shift from 1980 to 2004 is 1.7 degrees


Mean latitude of the polar front

Mean Latitude of the Polar Front

Shift from 1980 to 2004 is 3.1 degrees


Summary of values of the tropical belt expansion

Summary of values of the tropical belt expansion

  • Zonal mean stream function study gives values from 2.5 to 3.1 degrees

  • Tropopause analysis gives values of 5-8 degrees

  • OLR study gives values from 2.3 to 4.5

  • Ozone gives value for the Northern Hemisphere only of 1.7 degrees

  • All over the period 1979 to 2005


21 st century predicted widening ensemble mean 2 deg latitude lu et al 2007

21st Century Predicted WideningEnsemble mean ~2 deg. latitude Lu et al. (2007)


Observed vs predicted widening

Observed vs Predicted Widening

  • Observed: ~2-5°latitude 1979-2005

  • Modeled (A2 scenario): ~2°lat over 21st century

  • Modeled 25-yr trends during 21st century

    • 40 100-yr projections →

    • Mean 0.5°

    • >2.0° in only 3% of cases

    • Max 2.75°

    • (Celeste Johanson, Univ. of Washington)


Temperature deviation giss versus latitude

Temperature deviation (GISS) versus latitude


Number of tropical pixels versus time for longitude 80 to 60

Number of tropical pixels versus time for longitude -80 to -60

38 to 42 latitude

28 to 32 latitude

48 to 52 latitude

58 to 62 latitude


Number of tropical pixels for 58 to 62 latitude vs longitude

Number of tropical pixels for 58 to 62 latitude vs longitude


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