AOS 100: Weather and Climate

Instructor: Nick BassillClass TA: Courtney Obergfell

Miscellaneous

• Homework Reminder• Exam Reminder

Review of September 17th: Radiation

• Radiation is the one form of heat transfer that does not require a medium (air, water, etc.)

• The energy of radiation is carried in the form of electromagnetic waves

• All objects emit/receive radiation• As objects emit radiation, they lose energy

and cool (unless they are gaining more radiation from absorption or some other process)

Review Continued• Wien’s Law: the wavelength of radiation an

object emits depends on its temperature• The peak wavelength (λ) of emission is

approximately ~ 2897/ T• Stefan-Boltzmann Law: warmer objects emit

more energetic radiation than do colder objects, by E=σ*T4

• Shorter wavelengths carry more energy• The albedo of an object is a measure of the

amount of sunlight it reflects• The Earth’s average albedo is .3, meaning it

reflects 30% of incoming solar radiation on average

A Comparison of Emittances

From:www.csulb.edu/~rodrigue/geog140/sunwavelength.gif

• The atmosphere absorbs some radiation

• However, this doesn’t happen uniformly for all wavelengths

• Since the Sun’s radiation and the Earth’s radiation are almost completely separate wavelengths, these variations are important!

• Much more of the Earth’s radiation is absorbed by the atmosphere than the Sun’s

Kirchoff’s Law• Kirchoff’s Law: The efficiency of absorption at a certain

wavelength of energy is exactly equal to the efficiency of emission in the same wavelength

• For example, snow is very good at absorbing IR radiation, which means it is also very good at emitting IR radiation

• If something is perfect at absorbing all wavelengths of radiation (and thus perfect at emitting all wavelengths), then we call it a blackbody

• The Earth is a close approximation to a blackbody (for a given temperature, it will emit as much radiation as possible for that temperature)

• This means Wien’s Law and Stefan-Boltzmann’s Law can be used with good accuracy for the Earth

Stefan-Boltzmann Law Revisited

• Energy=σT4

• Let’s compare the Earth and Sun:

The Earth’s temperature is ~288 K

E=5.67*10-8*(288)4

E=390 Watts/m2

The Sun’s temperature is ~6000 K

E=5.67*10-8*(6000)4

E=73,483,200 Watts/m2

This means the Sun’s surface emits roughly 190,000 times more energy from every square meter than the Earth does

The Earth’s Energy Balance

• Of the radiation emitted from the Sun, the amount that makes it to the Earth is approximately 342 W/m2 at any given spot at the top of the atmosphere

• But remember we need to factor in the albedo, which is .3, so 30% of this is reflected to space

342*.7 = 239.2 W/m2

Using E=σ*T4, we get

239.2 = 5.67x10-8 * T4

Solving for T gets about 255 K

Energy Balance Continued

• This calculation gives us an average surface temperature of 255 K

• 255 K is equal to about -18 ºC, or about 0 ºF• But we know our Earth’s temperature is much

warmer!• (more than 50 ºF warmer!)• What’s going on then?

We have an atmosphere!• Our atmosphere absorbs more longwave radiation

(the kind that the Earth emits) than it does shortwave radiation (the kind the Sun emits)

Energy Balance Continued• Our atmosphere emits the absorbed radiation in

all directions• Therefore, half of it goes back towards the

surface and half goes out to space• So the extra bit that the atmosphere is

continuously sending the surface keeps it warmer

• The actual average temperature is about 288 K (about 15 ºC or 59 ºF)

• Radiative equilibrium: the state where the rate an object emits radiation is equal to the rate the object absorbs radiation

• Due to the Earth’s tilt, different locations receive different intensities of sunlight

• This leads to both differing daytime temperatures and the different seasons

The Seasons (Intro)

Diurnal Temperature Change• Obviously, the Earth is only receiving

(shortwave) solar radiation when the Sun is above

• However, the Earth is always transmitting (longwave) radiation

• This means that the surface is often losing energy at nighttime, and gaining it during the daytime

• This is largely what causes temperature changes from day to night, in addition to other things such as warm or cold air advection

What can modify this?