Week 3: Earth's Atmosphere and Greenhouse Effect

How is matter bound together?

• Electric fields

• Atoms bound by sharing electrons

• Atoms aggregated into gases, liquids/ solids bound by electric forces

Why is it important for the climate that ice is less dense than water?

• if water froze and it sunk instead of sitting on top of the water

• lower albedo of earth as albedo of ice is very high

How can the state of matter be changed?

Only if EM of the right frequency interacts with it

The Molecular Absorption Spectra

• Molecules absorb at more frequencies than atoms

• Various processes broaden the absorption spectra of molecules

  • collisions/ pressure broadening

  • doppler shift

What makes a molecule a good absorber of EM radiation?

• Molecules with an electric dipole

• Symmetric electrical fields e.g N₂ and O₂ don’t absorb IR

• CO₂ is symmetric but can produce an electric dipole if distorted → IR absorption for vibrations

• H₂O has a dipole in resting state → IR absorption for vibrations and rotations

What does Planck’s Law give?

• the intensity of black-body radiation as a function of wavelength and temperature, i.e. the shapes of the black-body radiation curves

• Planck’s law is an idealisation → real bodies don’t absorb or emit all wavelengths of light

How can you calculate thermal emission from real bodies?

Product of Planck’s Law and the Body’s Emissivity

Bλ (λ,T) × ε(λ

• both functions of wavelength

• Planck’s law sets the maximum thermal emission for the body.

• The emissivity sets the fraction of this maximum that is realized at each frequency / wavelength, i.e. the efficiency with which it emits

What is Kirchoff’s Law?

Absorptivity (aλ ) = emissivity (ελ )

Things are as good at absorbing EM radiation of a specific wavelength as they are at emitting it → absorption lines = emission lines

How are emissivity and absorptivity measured?

• As a fraction

• Range between 0 and 1

How are concentrations of gases in the atmosphere expressed?

parts per million by volume (ppmv)

Which gases in the atmosphere have a significant radiative effect?

• CO₂ (~410 ppmv), Methane (1.9 ppmv), Water Vapour

• ^ have 3 or more parts and so more complex vibrations

What is the dominant greenhouse gas in the Earth’s atmosphere?

• Water Vapour

• Absorbs strongly in many bands

• Weakly absorbing in atmospheric window

Where is the atmospheric window?

• Between ~8 and ~14 μm

• Around the peak of Earth’s black-body spectrum

Why does CO₂ have a greater greenhouse effect than H₂O?

• CO2 absorbs over a narrower range of frequencies than water but it has a strong absorption band in the atmospheric window

• Gases which absorb wavelengths in the atmospheric window can have a greenhouse effect

• Greenhouse gases (GHGs) are most effective if they absorb frequencies that other GHGs don’t.

• If they were all absorbing the same frequencing→ less of the spectrum in total absorbed

Absorption of light by the atmosphere

Some frequencies of incoming light are absorbed by the atmosphere

• Water vapour absorbs some bands of the near-infrared

• Ozone absorbs UV strongly

Where does the blackbody spectrum show emission from?

• Reflects the temperature and altitude of the last layer which emitted it

• The Earth’s longwave spectrum follows the black-body spectrum for the surface where it is transparent and the cooler upper atmosphere where it is strongly absorbing

What is radiative forcing?

measure of the influence a factor has in altering the balance of incoming and outgoing energy in the Earth system.

Units of radiative forcing

Wm^-2

What effect does a positive radiative forcing have?

• A positive radiative forcing will cause the Earth to absorb more energy and warm.

• As it warms it will emit more longwave radiation (Stefan-Boltzmann law) and eventually a new equilibrium temperature will be reached when incoming and outgoing energy balances again

As you increase the amount of CO₂ in the atmosphere, what effect does it have on outgoing longwave radiation

0 → 10 ppmv takes a big bite out of the spectrum and has a large radiative forcing

400 → 410 ppmv has a tiny radiative forcing.

What does band saturation do?

• At current CO₂ conc. → increasing conc. leads to diminishing increases in radiative forcing due to band saturation

• Frequencies most effectively absorbed have all been absorbed

• Increasing CO2 increases absorption at tails of distribution

• CO2 radiative forcing does not increase linearly with CO2 concentration

• CO2 absorbs all long-wave emitted from the surface around its peak absorption frequency, and exponentially weakly away from this peak.

Radiative Forcing of CO₂

proportional to the number of doublings of the CO2 concentration, i.e., it follows a logarithmic function:

RF_CO2 = 3.71 x ln(C/ C₀) / ln (2) Wm^-2

• This is because of band saturation

Ideal gas assumptions

• Molecules are point particles (imagined as tiny balls)

• Have elastic interactions (don’t lose energy after collision)

When do assumptions about ideal gases break down?

• At very high pressure and low temperature

• Assumption works well for atmospheric conditions

Equation showing the relationship between kinetic energy of an ideal gas and its temperature

E_K = 3/2 nRT

n = number of moles

R= ideal gas constant

T= temperature in Kelvin

Force =

Mass x Acceleration

Unit of force

1 Newton (N) = 1 kg ms^-2

Pressure =

force/ area

Units of Pressure

1 Pascal (Pa)= 1 Nm^-2

What is pressure against a box determined by?

• Number of collisions over area

• Kinetic energy of colliding particles

Ideal Gas Law

PV = nRT

What does pressure in the ocean depend on?

• Function of depth

Water:

• Is effectively incompressible.

• Pressure is proportional to depth as the weight of water above you increases monotonically

• Every 10m deeper, pressure rises by 1 atmosphere (atm)

What does pressure in the atmosphere depend on?

• Pressure as a function of altitude

Air:

• Is compressible

• Air at the bottom is compressed by the weight of air above.

• Pressure falls exponentially with altitude

What is the scale height of the earth?

8 km

What is the air pressure at sea level?

1 atm

What is the air pressure at 8 km?

• e^-1

• e-folding height

• every 8 km it falls by the same fraction

• Most of the mass of the atmosphere is below 8 km