Lecture 5 Abiol 574 Blackbody Radiation/ Planetary Energy Balance This material is from Ch. 3 of The Earth System, ed. 3, by Kump, Kasting, and Crane. The chapter is posted on the class website under Readings.

Solar Spectrum The sun emits radiation at all wavelengths Most of its energy is in the IR-VIS-UV portions of the spectrum ~50% of the energy is in the visible region ~40% in the near-IR ~10% in the UV

Wavelength (m)

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

Wikipedia Commons:

Basic Laws of Radiation 1)All objects emit radiant energy. 2)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 =  T 4 F = flux of energy (W/m 2 ) T = temperature (K)  = 5.67 x W/m 2 K 4 (a constant)

Basic Laws of Radiation 1)All objects emit radiant energy. 2)Hotter objects emit more energy than colder objects (per unit area). The amount of energy radiated is proportional to the temperature of the object. 3)The hotter the object, the shorter the wavelength ( ) of the peak in emitted energy.  This is Wien’s Law:

 Stefan-Boltzmann law F =  T 4 F = flux of energy (W/m 2 ) T = temperature (K)  = 5.67 x W/m 2 K 4 (a constant)  Wien’s law

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/m 2 ) Sun6000 Earth300

T (K) max (  m) region in spectrum F (W/m 2 ) Sun Earth30010

Electromagnetic Spectrum (  m) ultraviolet visible light infrared microwaves x-rays High Energy Low Energy

T (K) max (  m) region in spectrum F (W/m 2 ) Sun Visible (yellow?) Earth30010infrared

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) region in spectrum F (W/m 2 ) Sun Visible (green) Earth30010infrared

 Stefan-Boltzman law F =  T 4 F = flux of energy (W/m 2 ) T = temperature (K)  = 5.67 x W/m 2 /K 4 (a constant)

T (K) max (  m) region in spectrum F (W/m 2 ) Sun Visible (green) 7 x 10 7 Earth30010infrared460

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

The next part of this lecture (derivation of the planetary energy balance equation) will be done on the blackboard…

Putting numbers into the planetary energy balance equation yields the following results…

T 4 = S o (1-A) 4  For Earth: S o = 1370 W/m 2 A = 0.3  = 5.67 x T 4 = (1370 W/m 2 )(1-0.3) 4 (5.67 x W/m 2 K 4 ) T 4 = 4.23 x 10 9 (K 4 ) T = 255 K (= -18 o C)

Is the Earth’s surface really -18 o C?

NO. The actual temperature is warmer! The observed temperature (T obs ) is 15 o C, or about 59 o F.

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

In other words, the Earth is 33 o C 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 o C.

The concern is that the amount of greenhouse warming will increase with the rise of CO 2 due to human activity.