Meteorology ENV 2A23 Radiation Lectures

How is energy transferred?

How is energy transferred?

Conduction Convection Radiation

Conduction Convection Radiation

Conduction Convection Radiation

How is energy transferred? 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 (mm), i.e. 0.1-10 x10-6 m

Electomagnetic radiation travels in packets (quanta), whose energy is given by E = hc/8, where 8 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 = FT4, where, F is flux density W m-2, T is temperature, F = 5.67x10-8 W m-2 K-4

Radiation flux density at the Earth sun rs rd earth F = FT4 per unit area So over sphere 4Brs2FT4 Hence at distance of earth (rd): 4Brs2FT4/ 4Brd2 i.e. S0 = rs2/rd2 FT4, an inverse square law

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 planet Energy 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:

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: Latitude Season Time of day

Distribution of Insolation The solar zenith angle (2s) 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: where S0 is the solar constant, and d is the sun-earth distance 2s earth

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

Distribution of Insolation

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

Energy balance 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

Energy balance at the top of the atmosphere Outgoing longwave radiation

Energy balance at the top of the atmosphere Net radiation The net radiation can be calculated from R = SWd – SWu + LWd – LWu , Where SW = shortwave (solar) radiation, LW = longwave (terrestrial radiation) => R = SWd(1-αp) –LWu at the top of the atmosphere, where αp is the planetary albedo.

Energy balance at the top of the atmosphere => R = SWd(1-αp) –LWu at the top of the atmosphere, where αp is the planetary albedo.

Energy balance at the top of the atmosphere 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 = BI For example: emission from a blackbody, emission from the atmosphere Animation…

What about the wavelength of the radiation? Planck’s Law i.e. B Bv(T) dv = FT4 In other words, radiation intensity depends on frequency (or equivalently wavelength) of emission.

What about the wavelength of the radiation? Wein’s Law Sun’s emission peaks ~ 4.8 microm Earth’s emission peaks ~ 10 microm Brightness 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 ?

Radiation in the atmosphere Difference is due to selective scattering, absorption and emission of radiation by the atmosphere. These depend upon the structure of the molecules present. sketch

Radiation in the atmosphere 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 mm 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 O - H H +

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 Natural broadening – associated with the finite time of photon emission and the uncertainty principle Pressure broadening (or collision broadening) – collisions between molecules supply or remove small amounts of energy during radiative transitions. - Primary mechanism in the troposphere (why?) 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 mm and 10-12 mm. 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 mm.

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, a = 0.9 Thin clouds (e.g. 100 m), e.g. stratus, a = 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