Transcript Meteorology ENV 2A23 - University of East Anglia

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
rs
sun
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:
2
d 
Q  S0   cos s
d 
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
2
d 
Q  S0   cos s
d 
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
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
-2
Bυ(T) = (2hυ3/c2).1/(exp(hυ
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).
/
k
T
)
-
1
)
(
W
m
The Stephen-Boltzmann Law is an integral of Planck’s Laws over all frequencies and all angles in a
hemisphere.

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
We can differentiate Bυ(T) to give the frequency (or wavelength) of maximum emission:
dBυ/dυ
max = 2900/T μ
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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
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 infrared 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