Lecture 5 -- Blackbody Radiation/Planetary Energy Balance: Lecture 5 -- Blackbody Radiation/ Planetary Energy Balance Abiol 574
Slide2: Electromagnetic Spectrum (m) visible
light 0.7 to 0.4 m
Slide3: Electromagnetic Spectrum (m) ultraviolet visible
light
Slide4: Electromagnetic Spectrum (m) ultraviolet visible
light infrared
Slide5: Electromagnetic Spectrum (m) ultraviolet visible
light infrared microwaves x-rays
Slide6: Electromagnetic Spectrum (m) ultraviolet visible
light infrared microwaves x-rays High
Energy Low
Energy
Blackbody Radiation: Blackbody Radiation Blackbody radiation—radiation emitted by a body that
emits (or absorbs) equally well at all wavelengths
The Planck Function: The Planck Function Blackbody radiation follows the Planck function
Slide9: Basic Laws of Radiation
All objects emit radiant energy.
Slide10: Basic Laws of Radiation
All objects emit radiant energy.
Hotter objects emit more energy than colder objects.
Slide11: 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.
Slide12: 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)
Slide13: 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.
Slide14: 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)
Slide15: 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)
Slide16: We can use these equations to calculate properties of energy radiating from the Sun and the Earth. 6,000 K 300 K
Slide19: Electromagnetic Spectrum (m) ultraviolet visible
light infrared microwaves x-rays High
Energy Low
Energy
Slide21: 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
Slide23: Stefan Boltzman Law.
F = T4
F = flux of energy (W/m2)
T = temperature (K)
= 5.67 x 10-8 W/m2K4 (a constant)
Slide25: Solar Radiation and Earth’s Energy Balance
Planetary Energy Balance: Planetary Energy Balance We can use the concepts learned so far to calculate the radiation balance of the Earth
Slide27: Some Basic Information:
Area of a circle = r2
Area of a sphere = 4 r2
Slide28: 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).
Slide29: Energy Balance:
Incoming energy = outgoing energy
Ein = Eout Ein Eout
Slide30: (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.)
Slide31: How much solar energy reaches the Earth?
Slide32: How much solar energy reaches the Earth?
As energy moves away from the sun, it is spread over a greater and greater area.
Slide33: 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
Slide34:
So = L / area of sphere
Slide35: 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
Slide36: 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.
Slide37: Each planet has its own solar constant…
Slide38: 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
Slide39: 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
Slide40: How much energy does the Earth emit?
300 K
Slide41: How much energy does the Earth emit?
Eout = F x (area of the Earth)
Slide42: How much energy does the Earth emit?
Eout = F x (area of the Earth)
F = T4
Area = 4 re2
Slide43: How much energy does the Earth emit?
Eout = F x (area of the Earth)
F = T4
Area = 4 re2
Eout = ( T4) x (4 re2)
Slide44: (m) Earth Sun Hotter objects emit more energy than colder objects
Slide45: (m) Earth Sun Hotter objects emit more energy than colder objects
F = T4
Slide46: (m) Earth Sun Hotter objects emit at shorter wavelengths.
max = 3000/T
Hotter objects emit more energy than colder objects
F = T4
Slide47: How much energy does the Earth emit?
Eout = F x (area of the Earth)
Slide48: How much energy does the Earth emit?
Eout = F x (area of the Earth)
F = T4
Area = 4 re2
Eout = ( T4) x (4 re2)
Slide49: How much solar energy reaches the Earth? Ein
Slide50: 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
Slide51: 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
Slide52: 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. Remember…
Slide53: 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
Slide54: How much solar energy reaches the Earth?
Ein = So re2
BUT THIS IS NOT QUITE CORRECT!
**Some energy is reflected away**
Ein re
Slide55: How much solar energy reaches the Earth?
Albedo (A) = % energy reflected away
Ein = So re2 (1-A)
Ein re
Slide56: 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
Slide57: Energy Balance:
Incoming energy = outgoing energy
Ein = Eout Eout Ein
Slide58: Energy Balance:
Ein = Eout
Ein = So re2 (1-A)
Ein
Slide59: Energy Balance:
Ein = Eout
Ein = So re2 (1-A)
Eout = T4(4 re2)
Ein
Slide60: Energy Balance:
Ein = Eout
So re2 (1-A) = T4 (4 re2)
Ein
Slide61: Energy Balance:
Ein = Eout
So re2 (1-A) = T4 (4 re2)
Ein
Slide62: Energy Balance:
Ein = Eout
So (1-A) = T4 (4)
Ein
Slide63: Energy Balance:
Ein = Eout
So (1-A) = T4 (4)
T4 = So(1-A)
4
Ein
Slide64:
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.
Slide65:
T4 = So(1-A)
4
For Earth:
So = 1370 W/m2
A = 0.3
= 5.67 x 10-8 W/m2K4
Slide66:
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)
Slide67:
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
Slide68: Expected Temperature:
Texp = 255 K
(oC) = (K) - 273
Slide69: Expected Temperature:
Texp = 255 K
(oC) = (K) - 273
So….
Texp = (255 - 273) = -18 oC
(which is about 0 oF)
Slide70: Is the Earth’s surface really -18 oC?
Slide71: 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.
Slide72: 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
Slide73: 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.
Slide74: 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.
Slide75: 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.
Slide76: The greenhouse effect:
Heat is absorbed or “trapped” by gases in the atmosphere.
Earth naturally has a greenhouse effect of +33 oC.
Slide77: The concern is that the amount of greenhouse warming will increase with the rise of CO2 due to human activity.