GGR203 - INTRODUCTION TO CLIMATOLOGY

2.0        Radiation

The radiation referred to here is the energy emitted by all matter warmer than 0 K in the form of electromagnetic (EM) waves.

2.1        What are EM waves?

They are coupled, oscillating, electric and magnetic fields that move out (at the speed of light) in all directions from an oscillating electric charge.

Speed of wave,  c = speed of individual crests and troughs

Frequency of wave, ν = number of crests or troughs that pass a given point per second

Wavelength,    λ  = distance between corresponding points on successive waves

Clearly,  c = λν

(because if, for example, we see 10 wave crests passing a point in one second and the wavelength is 10 cm, the furthest crest was 100 cm away at the start of the second)

For EM waves, c is fixed, so    λ  α   1/ν    (wavelength varies inversely with frequency)

Frequency of an electric scillator = number of up & down cycles it does per second Frequency of an EM wave = frequency of the oscillator that generated it.

THUS:  faster frequency oscillator  ↔ shorter wavelength of EM radiation

See Figure 2.1, illustrating the electromagnetic spectrum  - the division of radiation of all possible wavelengths into different categories. Visible light is one very small set of wavelengths within the spectrum, with different colours corresponding to different wavelengths (and hence, different frequencies)

(Note that violet is next to ultraviolet, and red next to infrared, with violet being of shorter wavelength and red longer wavelength).

When an EM wave encounters another charge, it tends to set that charge in motion – because the oscillating electric field causes an oscillatory force on the charge [force on charge = electric field x magnitude of charge]

Interaction of EM wave with a charge tends to set it oscillating at the same frequency as the   EM radiation (or not at all)

In so doing – the charge acquires energy

- the EM radiation is absorbed

To conserve energy, it must be that

- the EM radiation itself carries energy

- an oscillator loses energy when it emits EM radiation.

2.2    Emission of EM radiation

All matter contains electric charges (protons, electrons).

Although non-ionized atoms and molecules are electrically neutral (# protons = # electrons), the “centre of mass” of the positive and negative charges might not coincide. This gives an electric dipole.

Electric dipoles in atoms and molecules can arise in 3 ways:

1. From asymmetry of a molecule. Example: H2O:

-electrons are pulled toward the oxygen atom

2.From the presence of an electric field, which pushes electron and protons in opposite directions

3.From asymmetric vibrations. Example: CO2, a symmetric linear molecule        O=C=O

CO2 can vibrate symmetrically (both bonds being stretch at the sametime), asymmetrically in two ways: bending, or asymmetric bond stretching, where one bond shortens while the other lengthens, and viceversa

Heat is the random motion of molecules and atoms.

As all matter above 0 K is in thermal motion, and as all matter contains electric dipoles – all matter radiates EM radiation.

Consider a solidbody:

- At a given temperature, the atoms or molecules will oscillate at a given set of frequencies with a given set of amplitudes – to there will a range of wavelengths at which radiation is emitted, corresponding to the frequencies of the oscillators 

As T increases,

- more energy goes into existing oscillation frequencies by increasing the amplitudes of the oscillations

-  oscillations at higher frequencies (↔ shorter wavelengths) can occur

Hence, as T increases, more EM energy is radiated (emitted), and the emitted radiation shifts to shorter wavelengths.

The relationship between temperature and the maximum amount of radiation that can be emitted in a given wavelength interval is given by the Planck Function:

where c = speed of light = 2.998 x 108  m/s

h = Planck’s constant

k = Boltzman constant

B(λ,T) is the energy emitted perm2  of surface area per μm of wavelength interval.

The energy emitted in a λ interval of width Δλ and centred at λ is

B(λ,T)Δλ     W m-2

For example, to estimate the amount of radiation between wavelengths of 1.00 μm and 1.02 μm, calculate

B(λ,T) using λ in the centre of the interval (1.01 μm) and multiply by Δλ=0.02 μm.

Sum this approach over many small intervals:

We will designate the different intervals and the wavelength at the centre of each interval by the subscript i, where i=1 for the first interval, i=2 for the second interval and so on up to the last interval, n.

The energy emitted in each interval i is B(λi,T)Δλi, and the total energy emitted is the sum of the radiation emitted in all the intervals. That is

Total energy emitted = ∑1 B(λ i  , T)Δ λ i       ~ “Area” under that curve, where the “area” has units = units

of height x units of width of each rectangle.

(in the above, ∑1 xi  is the standard summation notation and means add all the values of xi  (whatever xi is) from x1 to xn)

As stated above, the Planck function gives the maximum amount of radiation that can be emitted in a given wavelength interval. An object that emits this amount at all wavelengths is called blackbody.

Layout calculations for Q2 of PS1 in columns:

2.3      Radiation Laws Derived From the Planck Function  (or: properties of blackbodies)

1.  The emission at all wavelengths increases as T increases

2. As Δλ i  → 0, ∑Ni=1B(λi, T)Δλi → ∫0 ∞ B(λ, T)dλ = σT4

Total radiation emitted by a blackbody, B(T) = σT4,

where σ = 5.673 x 10-8  W m-2  K-4  is the Stefan-Boltzman constant, and the equation is called the Stefan-Boltzman Law

3. Wavelength at which maximum emission occurs decreases as T increases.

λmax = 2898/T   Wien’s Displacement Law, T isin K and λ is in μm

At higher T, higher frequency oscillations – corresponding to shorter λ radiation – can be excited.

4. Almost all the radiation emitted by the Sun is at λ < 4.0 μm   Almost all the radiation emitted by the Earth is at λ > 4.0 μm

See Figure 2-2.

To recap – the Planck function gives the blackbody emission  - which is the maximum amount permitted at a given temperature. The ratio of actual emission (F(T)) to BB emission is called the emissivity, ε .

That is, ε = F(T)/σT4, so    11

F(T) = εσT4.   ε  ≤= 1 , ε = 1 for a BB

Emissivity at a particular wavelength is called the spectral emissivity, ελ .

The emission is F(λ,T) = ελB(λ,T)

2.4 Absorption of electromagnetic radiation

The fraction of total incident radiation absorbed by an object (or gas) is called the absorptivity, a.

The fraction of incident radiation at a specific wavelength absorbed is called the spectral absorptivity, aλ .

An oscillator will absorb a photon of a given frequency (wavelength) only if it can oscillate at that frequency. Likewise, it will emit at that frequency if it has enough energy (that is, if it is warm enough).

These ideas and others lead to Kirchoff’s Law:

a = ε,  absorptivity = emissivity

Also true at every wavelength:   aλ . = ελ .

If something is a good absorber at a given wavelength, it is potentially a good emitter too. For a BB, ε = 1 so a = 1. A blackbody absorbs all the radiation falling on it.

Although emissivity = absorptivity, this does not mean that emission = absorption

Absorbed energy = a I = ε I      … .. I depends on the temperature of the surroundings

Emitted energy   = εσT4                     … . depends on temperature of itself

2.5      Types of possible electric oscillators

As we have seen, emission and absorption of electromagnetic radiation involve oscillating electric charges or dipoles. These can arise in 3 ways:

-oscillation of electrons in their orbitals – v. high frequency, short λ radiation: 0.1-0.7 μm -vibration of dipole molecules – medium frequency, medium λ radiation: 0.8- 18 μm

-rotation of dipole molecules – low frequency, long λ rad’n mostly > 50 μm, some effects down to 12 μm The part of the electromagnetic spectrum of importance to climate is:

As electrons oscillate, or dipole molecules vibrate or rotate, they give offEM radiation but at the same time drop to lower energy levels.

Electron transitions/oscillations   - correspond to UV, Visible radiation

Vibrational transitions                 - correspond to NIR, IR

Rotational transitions                   - correspond to IR, far IR

Recall: a vibrating or rotating molecule will emit EM radiation only if it has a dipole (centre of positive charge distribution  ≠ centre of negative distribution)

2.6      Temperature

Temperature is a measure of the kinetic energy of atoms or molecules. This kinetic energy occurs as

-     Vibrations

-     Rotations

-     Translation = uniform. from one point to another

Only vibrational and rotational KE involves emission/absorption of EM radiation (and then, only if there is a dipole).

Conversely, if amolecule has a dipole but was simply moving at a uniform velocity (having translational kinetic energy only), it would not emit radiation.

Temperature is directly related to the translational KE but not the vibrational and rotational KE.