Space Science Atmosphere Part-5 Planck Radiation Law

Space Science : Atmosphere Part-5 Planck Radiation Law Local Thermodynamic Equilibrium: LET Radiative Transport Approximate Solution in Grey Atmosphere Skin Temperature Greenhouse Effect Radiative Balance Radiative Time Constant Reading Ionosphere for Previous part Radiation Transport Greenhouse Effect

Windows and Absorptions in the Solar Spectrum 0. 2 0. 6 1. 0 1. 4 1. 8 2. 2 2. 6 3. 0 m

Radiation: Solar and Earth Surface B (T) Fraction absorbed Atmosphere is mostly transparent in visible but opaque in UV and IR; IR window 8 -13 um

Before Discussing Radiation Define Solid Angle z d r d r sin d y x d r sin d

Planck’s Law for Thermal Emission of Photons

GREY ATMOSPHERE Chap 3 G+W , H p 10 -17 Gray vs. Black vs. Transparent Also, absorption independent of frequency over the range of relevant frequencies Processes Surface heated by visible Warm Surface emits IR ~ 3 – 100 mm peak ~ 15 mm IR absorbed by CO 2, O 3, H 2 O, etc. Remember why not O 2 and N 2 ?

Vibrational Bands CO 2 (IR active? ) Symmetric Stretch O C O Asymmetric Stretch 7. 46 mm (N) O C Bending O 4. 26 mm (Y) O O 15. 0 m (Y) C H 2 O Symmetric Stretch 2. 73 mm (Y) O H H Asymmetric Stretch O H H 2. 66 mm (Y) Bending O H H 6. 27 mm (Y) You can have combination bands or 2 vib. levels

IR Emission and Absorption Ground Emits Primarily Triatomc Molecules Absorb and Re-emit: vibrational and rotational states To determine T we assume excited molecules heat locally by collisions. CO 2(v=1) + M --> CO 2(v=0) + M + K. E.

Slab of Atmosphere Absorption I + d. I dz I

Solution: Absorption Only (did earlier; new notation)

What about EMISSION Slab of atmosphere has a T Þ emits IR Assume LTE ® Local Thermodynamic Equilibrium molecular motion and the population of the vibrational and rotational states are all described by Boltzmann distribution and photons by Planck’s law ---using the same T Kirchhoff’s Law In LTE the emissivity of a body (or surface) equals its absorptivity.

Radiative Transport with Emission + Absorption

Flux (cont) d. A = r 2 d r I

Radiative Transport (cont. ) include angles dz m = cos

Radiation Transport (cont. ) I and B are isotropic

Not Quite Isotropic t* » 5/3 t Use t* not t in transport eq. dz

Third Equation is the Heat Equation

Radiative Transport Solution (cont. ) Use Eqs. (1) and (2) with (3).

Radiative Transport Solution (cont. ) Use Eq. (3) and (4)

Radiative Transport: Solution use C 1 in (5) and (6)

Solution to the radiative transfer equations for a grey atmosphere * Optical Thickness in IR g * Radiative Transport Conductive Transport (Adiabatic Lapse Rate) Becomes radiative dominated near tropopause

Finally: we do not know Tg we know only Te for emission to space! This is the Green House Effect Ground T exceeds T for emission to space

A Real Green House IR Visible Outside Inside How do you get IR out equal to Visible light absorbed inside: RAISE T Note: For a real green house convection may be as important: i. e. glass a thermal barrier

Greenhouse Effect is Complex

PLANETARY ENERGY BALANCE G+W fig 3 -5 Incoming solar radiation IR Radiation To Space 67 mesopause 113 86 GROUND Convective 30

Radiation Transport (Review) dz IR Atmospheric Slab

Integrate (*) for upward moving and downward moving IR photons

(Review continued)

Ground T (review)

G + W (simple version; 4 layers) 0 1 2 F 1 F 2 F 3 F 1 F 2 3 4 Space FVIS=Fout F 4 F 3 Fg F 4 Ground

Earth tg » 2

VENUS (Problem for set 2) Te = 230 Therefore: Tg = 750 t g* = ? Therefore: Use cross section from previous slide, pure CO 2 N = ?

Top Why isn’t Te = T( ) at the top? Te 4(1 -e) e T 4 e=emissivety e T 4

Thermal Structure Tropopause to Mesopause

TIME CONSTANT FOR RADIATIVE EQUILIBRIUM

Carbon concentration vs. time

Carbon Concentration Long Term Later we will look at the carbon cycle

GREEN HOUSE EFFECT

However,

#4 Summary Things you should know Planck Radiation Law Local Thermodynamic Equilibrium: LET Radiative Transport Greenhouse Effect Surface temperature Skin Temperature Radiative Time Constant