Meteorology ENV 2A23 Radiation Lectures. How is energy transferred?

Meteorology ENV 2A23

Radiation Lectures

How is energy transferred?


• Conduction

• Convection

• Radiation

• Conduction• Convection• Radiation

• Conduction• Convection• Radiation


• Conduction – energy transfer from molecule to molecule

• Convection – spatial mixing of “air parcels” i.e. masses of air

• Radiation – primary source of energy for the Earth

Radiation imbalances drive the circulation of the atmosphere and ocean

• Electomagnetic radiation in the range 0.1 to 10 micrometres (m), i.e. 0.1-10 x10-6 m

• Electomagnetic radiation travels in packets (quanta), whose energy is given byE = hc/,

where is wavelength,

h is Planck’s constant (6.625x10-34 J s-1)

c is speed of light (3x108 m s-1)

The Sun

• Most solar radiation is emitted from the photosphere (T~6000 K)

• Sun powered by nuclear fusion, H to He

• Plasma ejected as “solar wind”

The Sun

• The sun’s radiative output is centred on visible wavelengths

The Sun

• The sun’s output is not constant

• Sunspot cycle ~11 years• Periods of high/low activity

Sun-Earth Geometry

• Axial tilt = 23.5o

• Eccentricty = 0.02• Aphelion = 1.50x108 km, 3 July• Perihelion = 1.45x108 km, 3 January

– SH receives more solar radiation in summer than NH– Is it warmer?

Sun-Earth Geometry

• Equinoxes = “equal” days and nights

Sun-Earth Geometry

• Solstice = “sun stands still”, longest/shortest days

Changes in orbital parameters result in changes in incoming solar radiation and distribution

(Milankovitch 1930)Orbital feature Range Period

(years)Radiation changes

Tilt 21.8o to 24.4o 40,000 Seasonal radiation balance only

Eccentricity 0 to 0.06 96,000 Seasonal balance and total radiation by ±15%

Precession of equinoxes

orbit 21,000 Seasonal affects

The Sun’s energy output

• The solar constant is the radiation flux density at the top of the atmosphere, for the mean sun-earth distance

• i.e. the amount of radiation falling on the top of the atmosphere (per unit area)

• S0 = 1360 W m-2

The Sun’s energy output

• The sun is an almost perfect emitter of radiation, i.e. emits maximum possible radiation for its temperature

• It is a blackbody emitter and so governed by Stephan-Boltzmann Law: F = T4, where, F is flux density W m-2,

T is temperature,

= 5.67x10-8 W m-2 K-4

Radiation flux density at the Earth

• F = T4 per unit area

• So over sphere 4rs2T4

• Hence at distance of earth (rd): 4rs2T4/ 4rd

2

• i.e. S0 = rs2/rd

2 T4, an inverse square law

sun

rs

rd

earth

Emission temperature of a planet

The emission temperature of a planet is the blackbody temperature with which it needs to emit radiation in order to achieve energy balance. To calculate this for the Earth, equate blackbody emission with amount of solar energy absorbed.

- see radiation practical

Emission temperature of a planetEnergy incident on planet = solar flux density x shadow area

But not all radiation is absorbed, some is reflected:albedo (α) = reflected/incident radiation

Absorbed solar radiation = S0(1- α)π re2 (W)

Absorbed solar radiation per unit area = S0(1- α)/4 (W m-2)

This must be balanced by terrestrial emission. If we approximated Fe as a blackbody:

FEarth = σTe4 , where Te is the blackbody emission temperature.

=> Te4 = S0(1- α)/σ4

For Earth, Te = 255 K.

Note this is well below the average surface air temperature of the Earth = 288 K.

Distribution of Insolation

• Seasonal & latitudinal variations in temperature are driven primarily by variations in insolation

• The amount of solar radiation incident on the top of the atmosphere depends on:


• Seasonal & latitudinal variations in temperature are driven primarily by variations in insolation

• The amount of solar radiation incident on the top of the atmosphere depends on:– Latitude– Season– Time of day


The solar zenith angle (s) is the angle between the local normal to the Earth’s surface & the line between the Earth’s surface & the sun

The (daily) solar flux per unit area can be calculated as:

sd

dSQ cos

2

0

where S0 is the solar constant, and d is the sun-earth distance

earth

s

Distribution of Insolation• The season ~ declination angle ,

– i.e. latitude on Earth’s surface directly under the sun at noon

- varies between 23.5 & -23.5o

• The time of day ~ hour angle h,– Longitude of subsolar point relative to its position at

noon

• Then cos θs = sinφ sinδ + cosφ cosδ cosh, for latitude φ


sd

dSQ cos

2

0


• Equator receives more solar radiation than the poles (at the top of the atmosphere)

• As well as the distribution of insolation, the amount of energy absorbed and emitted depends on atmospheric and surface conditions.

Energy balance at the top of the atmosphere


• albedo (α) = reflected/incident radiation


• Outgoing longwave radiation


The net radiation can be calculated from

R = SWd – SWu + LWd – LWu ,

WhereSW = shortwave (solar) radiation,LW = longwave (terrestrial

radiation)

=> R = SWd(1-αp) –LWu

at the top of the atmosphere, where αp is the planetary albedo.

Net radiation


=> R = SWd(1-αp) –LWu

at the top of the atmosphere,

where αp is the planetary

albedo.


There must be a poleward transport of energy to balance out the net gain at the equator and the net loss at the poles.

Radiation Flux and Radiation Intensity

The radiation flux density (or irradiance), F (units W m-2) is the radiant energy crossing a unit area in unit time. It does not discriminate between different directions.

The radiation intensity (or radiance), I, (units W m-2 steradians-1) includes information on directionality.

Special Case : Radiation intensity I is isotropic, Then F = IFor example: emission from a blackbody, emission from the atmosphere

Animation…

What about the wavelength of the radiation?

• In other words, radiation intensity depends on frequency (or equivalently wavelength) of emission.

Planck postulated that the energy of molecules is quantized. This lead to Planck’s law: A blackbody with temperature T emits radiation at frequency υ with an intensity given by Bυ(T) = (2hυ3/c2).1/(exp(hυ/kT)-1) (W m-2 steradians-1 s-1), where h = 6.625x10-34 J s Planck’s constant, k = 1.37x10-23 J K-1 Boltzmann’s constant, c = 3x108 m s-1 speed of light, υ is frequency of radiation s-1 and T is temperature). The Stephen-Boltzmann Law is an integral of Planck’s Laws over all frequencies and all angles in a hemisphere.

i.e. Bv(T) dv = T4

Planck’s Law

What about the wavelength of the radiation?

We can differentiate Bυ(T) to give the frequency (or wavelength) of maximum emission: dBυ/dυ = 0 => λmax = 2900/T μm. Knowing the emission spectrum, we can infer a ‘brightness temperature’

Wein’s Law

Sun’s emission peaks ~ 4.8 micromEarth’s emission peaks ~ 10 micromBrightness temperatures of the sun and Earth are ~6000 K and 255 K

What about the wavelength of the radiation? When an object is not a blackbody, then its radiation flux density can be written

F = eσT4, where e is the emissivity.

Usually eλ = e(λ) is a function of wavelength.

If we define absorptivity aλ as the fraction of incident radiation that is absorbed. It can be shown that

eλ = aλ , this is Kirchoff’s Law.i.e. an object emits radiation at each wavelength as efficiently as

it absorbs it.

Radiation in the atmosphere

• Earlier we found the blackbody emission temperature Te = 255 K, much colder than the observed Tsurface = 288 K.

• Why ?


• Difference is due to selective scattering, absorption and emission of radiation by the atmosphere.

• These depend upon the structure of the molecules present.

sketch


• Difference is due to selective scattering, absorption and emission of radiation by the atmosphere.

• These depend upon the structure of the molecules present.

Scattering• Scattering decreases the intensity of the solar beam. • It depends upon λ (wavelength) and d (particle size).• Three cases:

(1) Rayleigh Scattering occurs when d << λ

For example from O2 or N2, the major tropospheric gases, where d = 10-10 m and λ = 0.5x10-6 m.

Scatters equal amounts of radiation forward and backward

The amount of scattering strongly dependent on λ:the volume extinction coefficient is a function of 1/ λ4

Rayleigh scattering explains why the sky is blue and sunsets are red.

- blue (short λ) scattered more than red (long λ) light

(2) Diffuse scattering occurs when d >> λ

• Diffuse scattering occurs when d >> λ, for example from dust or cloud droplets

• Typically ~10 m

• Diffuse scattering is independent of λ.– Clouds appear white and polluted skies are pale

• Full consideration requires Mie theory.

(3) Complex Scattering occurs when d = λ

• Diffraction

Absorption• All gases absorb and re-radiate energy at

specific wavelengths depending on their molecular structure. – Electronic excitation – visible uv– Vibrational excitation – IR– Rotational excitation – thermal IR

• Molecules need a permanent electric dipole, e.g. H2O

H H

O

+

-

• Aborption occurs at specific wavelengths (lines) according to the excitational properties of the gas (or gases) involved.

• However these lines are broadened by various mechanisms into absorption bands.

Absorption line broadening

1. Natural broadening – associated with the finite time of photon emission and the uncertainty principle

2. Pressure broadening (or collision broadening) – collisions between molecules supply or remove small amounts of energy during radiative transitions.

- Primary mechanism in the troposphere (why?)

3. Doppler broadening – results from the movement of molecules relative to photons.

- dominant at higher altitudes

• Groups of lines within a frequency interval are termed absorption bands

• In the thermal infra-red there are important absorption bands due to H2O, CO2, O3, CH4, N2O, etc

• Bottom panel shows atmosphere is generally opaque to IR radiation

• There are important “windows” at 8-9 m and 10-12 m.

• It is through these “windows” that most passive satellite sensors observe radiation emissions

• For example, this geostationary Meteosat image shows radiation emitted in the IR at 10.5-12.5 m.

Clouds and radiation

• Clouds consist of liquid water droplets or ice particles suspended in the atmosphere

• The droplets or ice particles interact with both solar and terrestrial (IR) radiation, depending on their size and shape.

• i.e. the cloud albedo is a function of total liquid water content and solar zenith angle.

• Thick clouds (e.g. 1 km), e.g. cumulus, = 0.9• Thin clouds (e.g. 100 m), e.g. stratus, = 0.7• Very important for planetary albedo

Global (1 dimensional) Energy Balance

• Observations from the ground & space of emitted radiation, combined with climatological surface energy flux observations have allowed an average (1D) picture of energy transfer through the Earth’s atmosphere to be estimated.

SH = sensible heat fluxes, LE = latent heat fluxes

• Solar: 100 units incoming, 70 absorbed, 30 reflected or scattered• Terrestrial 110 emitted from surface!• The strong downward LW emission (89) is responsible for modulating the diurnal

cycle

Further reading:

• Chapters 2 and 3 Ahrens

Documents

Meteorology ENV 2A23 Radiation Lectures. How is energy transferred?