The Greenhouse Effect Solar Radiation, Earth's Atmosphere, and the Greenhouse Effect. Martin Visbeck DEES, Lamont-Doherty Earth Observatory

Elements of the Climate system

Outline Review of radiation lecture  Black body radiation  Wien's Law  Stefan Bolzmann Law The effective temperature of a planet The greenhouse effect

Black Body Emission T(sun) = 5780 K T(earth) = 288 K

Black Body Emission Wien's law states that:   max = a / T where max is given in  m, T is in units of K, and a is a constant equal 2897  m K. The Stefan-Boltzman law states that: I =  T 4 where I is in units of W/m 2, T is in units of K, and  (the Greek letter sigma) is a constant equal to  5.67 x with units of W m -2 K -4. Area ~ Energy (integrate over log of wavelength)

Temperature Scales Always use °K (Kelvin) in Radiation calculations 0 °K = -273 °C

Solar Constant I 2 = I 1 ( r 2 2 / r 1 2 ) I0I0 I1I1 I2I2 r0r0 r2r2 r1r1 I = I 0 (at the source) r (source) 2 / r 2

Solar Constant I = I 0 (at the source) r (source) 2 / r 2 I 0 =  T 4 (Stephan-Boltzmann Law) I 0 = W/m 2 (Sun T=5780K) I (at Earth) = I 0 r sun 2 / r 2 = 1367 W/m 2 (r sun = m)

Three Aspects of Radiation interacting with matter

Interaction of Energy from the Sun with Earth’s Atmosphere The energy that drives the climate system comes from the Sun. When the Sun energy reaches the Earth it is partially absorbed in different parts of the climate system. The absorbed energy is converted back to heat which causes the Earth to warm up and makes it habitable.

The Earth Radiation Budget

Emission Temperature of a Planet Conservation of Energy Solar radiation absorbed = planetary radiation emitted

Emission Temperature of a Planet I in = S (1-A)  R 2 S : Solar flux (W/m 2 ) A: albedo of the planet R: radius of the planet Solar radiation absorbed

Emission Temperature of a Planet I out =  T 4 4  R 2  : Steph.-Boltz. Const. T: Temperature of planet R: radius of the planet Planetary radiation emitted

Emission Temperature of a Planet Solar radiation absorbed = planetary radiation emitted I in = I out = S (1-A)  R 2 =  T 4 4  R 2

Emission Temperature of a Planet Solar radiation absorbed = planetary radiation emitted I in = I out = S (1-A)  R 2 =  T 4 4  R 2 => S (1-A) = 4  T 4 T 4 = S (1-A) / (4 

Emission Temperature of a Planet Solar radiation absorbed = planetary radiation emitted I in = I out = S (1-A)  R 2 =  T 4 4  R 2 => S (1-A) = 4  T 4 T 4 = S (1-A) / (4  We can now compute the emission temperature for each planet…. Lets do the Earth here...

Emission Temperature of a Planet Solar radiation absorbed = planetary radiation emitted I in = I out = S (1-A)  R 2 =  T 4 4  R 2 T 4 = S (1-A) / (4  T ~ 255 °K ~ -18 °C is that an reasonable answer? using: A = 0.3; S = 1370 W/m 2 ;  = W/m 2 /K 4

The Greenhouse Effect Composition of the Atmosphere Here is how the greenhouse effect works: The Earth's atmosphere contains many trace (or minor) components

Greenhouse Effect The Earth's atmosphere contains many trace (or minor) components. While the major atmospheric components (Nitrogen and Oxygen) absorb little or no radiation, some of the minor components are effective absorbers. Particularly effective is water vapor, which absorb effectively in the IR wavelength range.

Greenhouse Effect absorption by trace gases

Absorption by trace gases influences the atmosphere’s temperature O 2 + ultraviolet light = O + O O + O 2 = O 3 Emission Temperature O 3 + ultraviolet light = O 2 + O

Greenhouse Effect How big is the greenhouse effect on our planet ? Lets do a simple calculation...

Greenhouse Effect Ta Te The simple model has one layer of greenhouse gases that are transparent to short wave radiation but absorb all long wave radiation. The temperature of the absorbing layer is Ta The temperature at the surface is Te

Greenhouse Effect Solar radiation absorbed = planetary radiation emitted Top of the atmosphere balance Ta Te Energy conservation !

Greenhouse Effect Solar radiation absorbed = planetary radiation emitted S (1-A)  R 2 =  Ta 4 4  R 2 Ta 4 = S (1-A) / (4  (S(1-A) = H) Ta Te Energy conservation !

Greenhouse Effect Earth radiation absorbed = layer radiation emitted S (1-A)  R 2 =  Ta 4 4  R 2 Ta 4 = S (1-A) / (4  (S(1-A) = H) Ta Te Energy conservation ! IR absorbing layer

Greenhouse Effect Short wave radiation absorbed + layer radiation emitted = Earth radiation emitted S (1-A)  R 2 =  Ta 4 4  R 2 Ta 4 = S (1-A) / (4  (S(1-A) = H) Ta  Ta 4 =  Te 4 (H + H = G) Te Earth Surface budget

Greenhouse Effect S (1-A)  R 2 =  Ta 4 4  R 2 Ta 4 = S (1-A) / (4  (S(1-A) = H) Ta  Ta 4 =  Te 4 (H + H = G) Te S (1-A)/4 +  Ta 4 =  Te 4 Te = 2 (1/4) Ta  (S(1-A)+H =G)

Greenhouse Effect Bottom line Te = 2 (1/4) Ta = 1.19 Ta Substituting previous results Ta Te

Emission Temperature of a Planet Solar radiation absorbed = planetary radiation emitted Ta 4 = S (1-A) / (4  Ta ~ 255 K ~ -18 C using: A = 0.3; S = 1370 W/m 2 ;  = W/m 2 /K 4

Greenhouse Effect Bottom line Te = 2 (1/4) Ta = 1.19 Ta Substituting previous results Ta 4 = S (1-A) / (4   using: A = 0.3; S = 1370 W/m 2 Ta ~ 255 K ~ -18 C Te ~ 1.2*Ta ~ 303 K ~ 30 C very warm Earth ! Ta Te

Greenhouse Effect

Atmospheric Dynamic Processes