Blackbody Radiation/ Planetary Energy Balance

Electromagnetic Spectrum visible light 1000 100 10 1 0.1 0.01 0.7 to 0.4 m  (m)

Electromagnetic Spectrum visible light ultraviolet 1000 100 10 1 0.1 0.01  (m)

Electromagnetic Spectrum visible light infrared ultraviolet 1000 100 10 1 0.1 0.01  (m)

Electromagnetic Spectrum visible light microwaves infrared ultraviolet x-rays 1000 100 10 1 0.1 0.01  (m)

Electromagnetic Spectrum visible light microwaves infrared ultraviolet x-rays 1000 100 10 1 0.1 0.01 Low Energy High Energy  (m)

Blackbody Radiation Blackbody radiation—radiation emitted by a body that emits (or absorbs) equally well at all wavelengths

The Planck Function Blackbody radiation follows the Planck function

Basic Laws of Radiation All objects emit radiant energy.

Basic Laws of Radiation All objects emit radiant energy. Hotter objects emit more energy than colder objects.

Basic Laws of Radiation All objects emit radiant energy. Hotter objects emit more energy than colder objects. The amount of energy radiated is proportional to the temperature of the object.

Basic Laws of Radiation All objects emit radiant energy. Hotter objects emit more energy than colder objects. The amount of energy radiated is proportional to the temperature of the object raised to the fourth power.  This is the Stefan Boltzmann Law F =  T4 F = flux of energy (W/m2) T = temperature (K)  = 5.67 x 10-8 W/m2K4 (a constant)

Basic Laws of Radiation All objects emit radiant energy. Hotter objects emit more energy than colder objects (per unit area). The amount of energy radiated is proportional to the temperature of the object. The hotter the object, the shorter the wavelength () of emitted energy.

T(K) Basic Laws of Radiation All objects emit radiant energy. Hotter objects emit more energy than colder objects (per unit area). The amount of energy radiated is proportional to the temperature of the object. The hotter the object, the shorter the wavelength () of emitted energy. This is Wien’s Law max  3000 m T(K)

max  3000 m T(K)  Stefan Boltzmann Law. F =  T4 F = flux of energy (W/m2) T = temperature (K)  = 5.67 x 10-8 W/m2K4 (a constant)  Wien’s Law max  3000 m T(K)

We can use these equations to calculate properties of energy radiating from the Sun and the Earth. 6,000 K 300 K

T (K) max (m) region in spectrum F (W/m2) Sun 6000 Earth 300

T (K) max (m) region in spectrum F (W/m2) Sun 6000 0.5 Earth 300 10

Electromagnetic Spectrum visible light microwaves infrared ultraviolet x-rays 1000 100 10 1 0.1 0.01 Low Energy High Energy  (m)

T (K) max (m) F (W/m2) Sun 6000 0.5 Visible Earth 300 10 infrared region in spectrum F (W/m2) Sun 6000 0.5 Visible (yellow?) Earth 300 10 infrared

Blue light from the Sun is removed from the beam by Rayleigh scattering, so the Sun appears yellow when viewed from Earth’s surface even though its radiation peaks in the green

T (K) max (m) F (W/m2) Sun 6000 0.5 Visible Earth 300 10 infrared region in spectrum F (W/m2) Sun 6000 0.5 Visible (green) Earth 300 10 infrared

 Stefan Boltzman Law. F =  T4 F = flux of energy (W/m2) T = temperature (K)  = 5.67 x 10-8 W/m2K4 (a constant)

T (K) max (m) F (W/m2) Sun 6000 0.5 Visible 7 x 107 Earth 300 10 region in spectrum F (W/m2) Sun 6000 0.5 Visible (green) 7 x 107 Earth 300 10 infrared 460

Solar Radiation and Earth’s Energy Balance

Planetary Energy Balance We can use the concepts learned so far to calculate the radiation balance of the Earth

Some Basic Information: Area of a circle =  r2 Area of a sphere = 4  r2

Energy Balance: The amount of energy delivered to the Earth is equal to the energy lost from the Earth. Otherwise, the Earth’s temperature would continually rise (or fall).

Energy Balance: Incoming energy = outgoing energy Ein = Eout Eout Ein

(The rest of this derivation will be done on the board. However, I will leave these slides in here in case anyone wants to look at them.)

How much solar energy reaches the Earth?

How much solar energy reaches the Earth? As energy moves away from the sun, it is spread over a greater and greater area.

How much solar energy reaches the Earth? As energy moves away from the sun, it is spread over a greater and greater area.  This is the Inverse Square Law

So = L / area of sphere

So is the solar constant for Earth So = L / (4  rs-e2) = 3.9 x 1026 W = 1370 W/m2 4 x  x (1.5 x 1011m)2 So is the solar constant for Earth

So is the solar constant for Earth So = L / (4  rs-e2) = 3.9 x 1026 W = 1370 W/m2 4 x  x (1.5 x 1011m)2 So is the solar constant for Earth It is determined by the distance between Earth (rs-e) and the Sun and the Sun’ luminosity.

Each planet has its own solar constant…

How much solar energy reaches the Earth? Assuming solar radiation covers the area of a circle defined by the radius of the Earth (re) Ein re

How much solar energy reaches the Earth? Assuming solar radiation covers the area of a circle defined by the radius of the Earth (re) Ein = So (W/m2) x  re2 (m2) Ein re

How much energy does the Earth emit? 300 K

How much energy does the Earth emit? Eout = F x (area of the Earth)

How much energy does the Earth emit? Eout = F x (area of the Earth) F =  T4 Area = 4  re2

How much energy does the Earth emit? Eout = F x (area of the Earth) F =  T4 Area = 4  re2 Eout = ( T4) x (4  re2)

 (m) Sun Earth Hotter objects emit more energy than colder objects 1000 100 10 1 0.1 0.01 Hotter objects emit more energy than colder objects  (m)

 (m) Sun Earth Hotter objects emit more energy than colder objects 1000 100 10 1 0.1 0.01 Hotter objects emit more energy than colder objects F =  T4  (m)

Hotter objects emit at shorter wavelengths. max = 3000/T Sun Earth 1000 100 10 1 0.1 0.01 Hotter objects emit more energy than colder objects F =  T4  (m)

How much energy does the Earth emit? Eout = F x (area of the Earth) Eout

How much energy does the Earth emit? Eout = F x (area of the Earth) F =  T4 Area = 4  re2 Eout = ( T4) x (4  re2) Eout

How much solar energy reaches the Earth? Ein

How much solar energy reaches the Earth? We can assume solar radiation covers the area of a circle defined by the radius of the Earth (re). Ein re

How much solar energy reaches the Earth? We can assume solar radiation covers the area of a circle defined by the radius of the Earth (re). Ein = So x (area of circle) Ein re

So is the solar constant for Earth Remember… So = L / (4  rs-e2) = 3.9 x 1026 W = 1370 W/m2 4 x  x (1.5 x 1011m)2 So is the solar constant for Earth It is determined by the distance between Earth (rs-e) and the Sun and the Sun’s luminosity.

How much solar energy reaches the Earth? We can assume solar radiation covers the area of a circle defined by the radius of the Earth (re). Ein = So x (area of circle) Ein = So (W/m2) x  re2 (m2) Ein re

**Some energy is reflected away** How much solar energy reaches the Earth? Ein = So  re2 BUT THIS IS NOT QUITE CORRECT! **Some energy is reflected away** Ein re

How much solar energy reaches the Earth? Albedo (A) = % energy reflected away Ein = So  re2 (1-A) Ein re

How much solar energy reaches the Earth? Albedo (A) = % energy reflected away A= 0.3 today Ein = So  re2 (1-A) Ein = So  re2 (0.7) re Ein

Energy Balance: Incoming energy = outgoing energy Ein = Eout Eout Ein

Energy Balance: Ein = Eout Ein = So  re2 (1-A) Eout Ein

Ein = Eout Energy Balance: Ein = So  re2 (1-A) Eout =  T4(4  re2)

Energy Balance: Ein = Eout So  re2 (1-A) =  T4 (4  re2) Eout Ein

Energy Balance: Ein = Eout So  re2 (1-A) =  T4 (4  re2) Eout Ein

Energy Balance: Ein = Eout So (1-A) =  T4 (4) Eout Ein

Ein = Eout Energy Balance: So (1-A) =  T4 (4) T4 = So(1-A) 4 Eout

T4 = So(1-A) 4 If we know So and A, we can calculate the temperature of the Earth. We call this the expected temperature (Texp). It is the temperature we would expect if Earth behaves like a blackbody. This calculation can be done for any planet, provided we know its solar constant and albedo.

T4 = So(1-A) 4 For Earth: So = 1370 W/m2 A = 0.3  = 5.67 x 10-8 W/m2K4

T4 = So(1-A) 4 For Earth: So = 1370 W/m2 A = 0.3  = 5.67 x 10-8 T4 = (1370 W/m2)(1-0.3) 4 (5.67 x 10-8 W/m2K4)

T4 = So(1-A) 4 For Earth: So = 1370 W/m2 A = 0.3  = 5.67 x 10-8 T4 = (1370 W/m2)(1-0.3) 4 (5.67 x 10-8 W/m2K4) T4 = 4.23 x 109 (K4) T = 255 K

Expected Temperature: Texp = 255 K (oC) = (K) - 273

Expected Temperature: Texp = 255 K (oC) = (K) - 273 So…. Texp = (255 - 273) = -18 oC (which is about 0 oF)

Is the Earth’s surface really -18 oC?

Is the Earth’s surface really -18 oC? NO. The actual temperature is warmer! The observed temperature (Tobs) is 15 oC, or about 59 oF.

Is the Earth’s surface really -18 oC? NO. The actual temperature is warmer! The observed temperature (Tobs) is 15 oC, or about 59 oF. The difference between observed and expected temperatures (T): T = Tobs - Texp T = 15 - (-18) T = + 33 oC

T = + 33 oC In other words, the Earth is 33 oC warmer than expected based on black body calculations and the known input of solar energy.

T = + 33 oC In other words, the Earth is 33 oC warmer than expected based on black body calculations and the known input of solar energy. This extra warmth is what we call the GREENHOUSE EFFECT.

T = + 33 oC In other words, the Earth is 33 oC warmer than expected based on black body calculations and the known input of solar energy. This extra warmth is what we call the GREENHOUSE EFFECT. It is a result of warming of the Earth’s surface by the absorption of radiation by molecules in the atmosphere.

The greenhouse effect: Heat is absorbed or “trapped” by gases in the atmosphere. Earth naturally has a greenhouse effect of +33 oC.

The concern is that the amount of greenhouse warming will increase with the rise of CO2 due to human activity.