1. METO 621 Lesson 19

2. Role of radiation in Climate We will focus on the radiative aspects of climate and climate change We will use a globally averaged one dimensional radiative-convective approximation. First we will assume that the atmosphere has negligible absorption for visible radiation Then we will add visible absorption

3. Radiative Equilibrium with Zero Visible Opacity The surface is assumed to be reflective in the visible and black in the IR. Thus the surface is heated by incoming solar radiation and by downwelling IR radiation from the atmosphere The atmosphere is heated by IR radiation from the surface and the surrounding atmospheric layers. This will set up a diffusive-like temperature gradient throughout the optically thick region. At the upper ‘edge’, when the optical depth drops to 1 the atmosphere radiates to space, at a globally averaged effective temperature, T e,determined by the overall energy balance Also assume that the optical depth is independent of frequency – the gray approximation.

4. Zero Visible Opacity

6. In radiative equilibrium the net flux F  is equal to the net outgoing flux, σ B T e 4, which is constant for all . If we integrate the equation 1 over solid angles then we get In radiative equilibrium, the source function is equal to the mean intensity.

7. Zero Visible Opacity

11. Greenhouse effect - one atmospheric layer model Є is the fraction of the IR radiation absorbed by the atmosphere

12. Zero Visible Opacity

14. Finite Visible Opacity Any realistic atmosphere absorbs radiation at both IR and UV/visible wavelengths. The procedure to solve this problem is similar to that for the case of no visible opacity. I will give only the solutions, using the two stream approximation.

15. Finite Visible Opacity

16. This is the strong greenhouse limit where the solar radiation penetrates deeply into the atmosphere, In the deep atmosphere, the greenhouse enhancement “saturates” to the constant value G(  →∞) = (1+  )/2 The asymptotic temperature is This solution resembles that for Venus, which has a surface temperature of 800 K. It does not apply to the Earth or Mars, because of the importance of the surface in the radiative transfer, and the neglect of convection. Finite Visible Opacity

17. For this case  This represents an isothermal situation where the solar heating exactly balances the IR escape.

18. Finite Visible Opacity For the case  1 or k IR <<k V This represents the anti-greenhouse case. This is relevant to numerous phenomena in the solar system An inverted temperature structure characterizes the Earth’s upper atmosphere, where high middle-UV opacity due to ozone absorption gives rise to a temperature inversion. This scenario may have happened in the Earth’s history. Worldwide cooling causing mass extinction as the result of an injection of massive quantities of dust (meteoroid impact) Stratospheric aerosols (  up to 10), from Mt Toba eruption some 70,000 years ago may have been responsible for a subsequent cooling of the Earth for a period of 200 years.