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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

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 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

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

Climate feedback mechanisms





Positions of the jet streams

Fig. 7-27, p. 191

Using total ozone measurements
Using Total Ozone measurements systems

  • 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, 1990 systemsSub-tropical = Blue, Polar = Red

Mean latitude of the sub tropical front
Mean latitude of the Sub-tropical front systems

Shift from 1980 to 2004 is 1.7 degrees

Mean latitude of the polar front
Mean Latitude of the Polar Front systems

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 systems

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

Observed vs predicted widening
Observed vs Predicted Widening systems

  • 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)

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