Radiation Parameterization
2 November 2012
Thematic Outline of Basic Concepts
• Why is radiation important?
• What are the fundamental processes that must be
represented by a radiation parameterization?
• How are radiative transfer processes handled within
a radiation parameterization?
• Where can more information be found regarding the
specifics of radiation parameterization?
Additional References
Fundamentals of Atmospheric Physics by Murry Salby
(Salby, M. L., 1996: Fundamentals of Atmospheric Physics. Academic Press, 627pp.)
“The Parameterization of Radiation for Numerical
Weather Prediction and Climate Models” by Graeme
Stephens
(Stephens, G. L., 1984: The parameterization of radiation for numerical weather
prediction and climate models. Mon. Wea. Rev., 112, 826-867.)
Why is Radiation Important?
• The sun is the primary source of energy for the Earth.
• Most of this energy comes in the form of radiation
energy, often referred to as insolation.
• Insolation, or more specifically spatial and temporal
variability thereof, drives atmospheric circulations!
– Hadley circulation; mid-latitude westerlies; tropics; etc.
– Moist convection; coastal circulations; inversions; etc.
Why is Radiation Important?
• Insolation is a function of many different things…
– Latitude and the seasonal cycle
– Angle at which insolation intersects the Earth
– Attenuation by the Earth’s atmosphere
• A model must be able to accurately simulate how
insolation interacts with land, oceans, vegetation,
clouds, air molecules, and aerosols.
– Implications: radiative heating and cooling of the Earth’s
surface and the atmosphere
Why is Radiation Important?
• These interactions are typically parameterized by
numerical models.
• Important radiative transfer processes (scattering,
absorption, etc.) occur on the molecular level.
• Radiative transfer is complex…
– Dependency upon a broad spectrum of wavelengths
– Dependency upon numerous atmospheric constituents
– Oftentimes considered over many distinct vertical layers,
involving numerous calculations per layer
Fundamentals of Radiation
• There are four important processes to consider when
attempting to describe radiative transfer…
– Absorption: radiation energy absorbed by the surface
and/or one or more atmospheric constituents
– Scattering: radiation energy reflected by the surface
and/or one or more atmospheric constituents
– Emission: radiation energy emitted by the surface and/or
by one or more atmospheric constituents
– Transmission: radiation energy that is transmitted from
space to the Earth’s surface (or vice versa)
Fundamentals of Radiation
• Energy transfer in the atmosphere involves radiation
in two distinct bands of wavelength…
– Shortwave: radiation emitted by the sun
– Longwave: radiation emitted by the Earth’s surface and
atmosphere
• Their wavelengths differ as a function of the
disparate temperatures of their respective emitters.
Electromagnetic Spectrum
(Image Source: Wikipedia)
Fundamentals of Radiation
• Relevant physics: Wien’s Displacement Law
– Derived from Planck’s law
– Relates the wavelength of maximum intensity to the
temperature of a (blackbody/perfect) emitter…
max
2897 m

T
(where T is in Kelvin)
Fundamentals of Radiation
• Effective solar temperature: ~6000 K
– Wavelength of maximum intensity: 0.48 μm
– Visible spectrum, corresponding to blue light
• Solar radiation extends across the ultraviolet, visible,
and near-infrared portions of the spectrum.
– Peak between 0.36 – 0.75 μm
– Range from 0.15 – 3 μm
Fundamentals of Radiation
• Incoming shortwave radiation is attenuated by a
number of atmospheric constituents.
• Ultraviolet radiation (λ < 0.3 μm) is absorbed at high
levels associated with the photodissociation and
photoionization of O2 and O3.
• With the exception of narrow absorption bands of
CO2 and H2O, however, most other shortwave
radiation reaches the tropopause.
Fundamentals of Radiation
• In the troposphere, shortwave radiation (particularly
in the infrared) is substantially absorbed.
• Such absorption is primarily by H2O and CO2,
absolute concentrations of which are large in the
troposphere.
• Most shortwave radiation reaching the surface is
thus in the visible wavelengths, where the
atmosphere is mostly transparent.
Fundamentals of Radiation
Irradiance: a measure of radiation energy flux
(Salby, Figure 1.27)
Fundamentals of Radiation
• Mean temperature of Earth’s surface: 288 K
– Wavelength of maximum intensity: 10 μm
– In the infrared portion of the spectrum
• Terrestrial radiation extends across the far-infrared to
microwave portions of the spectrum.
– Peak around 10 μm
– Range from 5 – 100 μm
Fundamentals of Radiation
• Longwave radiation released by the Earth’s surface is
almost completely absorbed by the atmosphere.
– H2O, over a wide band centered at 6.3 μm
– CO2, over a band centered at 15 μm, or near the peak of
the longwave radiation emission spectrum
– Trace gases (O3, CH4, N2O) at specific wavelengths
• What is absorbed at some level is subsequently reemitted, with half directed upward and half directed
downward.
Fundamentals of Radiation
• Most longwave radiation emitted by the Earth’s
surface is absorbed in the troposphere.
• Only a small amount of longwave radiation reaches
beyond the tropopause.
– Atmospheric Window: 8-12 μm
– In this window, absorption is weak enough to permit
longwave radiation to be transmitted to space.
– Only notable absorber: O3, at 9.6 μm, in the stratosphere;
associated with the greenhouse effect.
Fundamentals of Radiation
Fundamentals of Radiation
• A couple of relevant definitions…
– Albedo: Fractional amount of incoming solar radiation that
is reflected and/or scattered back to space by the Earth’s
surface, atmosphere, and clouds.
– Emissivity: Fractional amount of radiation (per unit area
per unit time) emitted by some emitter such as the Sun or
the Earth’s surface.
• Larger values reflect greater reflection and greater
emission, respectively.
Global-Mean Energy Budget
(Salby, Figure 1.27)
Global-Mean Energy Budget
• The global-mean shortwave radiation flux at the top
of the atmosphere is approximately 343 W m-2.
–
–
–
–
20% is absorbed by the atmosphere.
49% (169 W m-2) is absorbed by the Earth’s surface.
26% is reflected by the atmosphere.
5% is reflected by the Earth’s surface.
• The 49% absorbed by the surface must be re-emitted
to maintain thermal equilibrium, however.
Global-Mean Energy Budget
• The Earth’s surface emits more energy as longwave
radiation than it absorbs as shortwave energy.
– Mean surface temperature: 288 K
– Stefan-Boltzmann law…
F  T
4
where ε = emissivity and σ = 5.67 x 10-8 W m-2 K-4
– For a blackbody emitter (ε = 1), F = 390 W m-2
Global-Mean Energy Budget
(Salby, Figure 1.27)
Global-Mean Energy Budget
• Of the 390 W m-2 emitted by the surface, 84% (323
W m-2) is ultimately reabsorbed by the surface.
• The balance between shortwave absorption and
longwave emission and absorption leads to a net
radiative heating of the surface of 106 W m-2.
• For equilibrium, this is balanced by transfers of
sensible and latent heat to the atmosphere.
– Sensible: conduction with the atmosphere
– Latent: evaporation off of the soils and oceans
Incident Radiation Variability
• There is substantial variability in the local shortwave
radiation flux incident at the top of the atmosphere.
– Latitude: highest at lower latitudes
– Season: highest in local summer
Incident Radiation Variability
• There is also substantial spatiotemporal variability in
the concentrations of atmospheric constituents that
influence radiative transfer.
– Concentrations of aerosols and other chemical compounds
– Presence (or lack thereof) of clouds, precipitation, etc.
• Furthermore, the Earth’s surface is non-uniform…
– Topography: less atmospheric influence at higher altitudes
– Land-surface: land vs. water, different soil types and land
uses, etc.
Radiation Parameterization
• A radiation parameterization must be able to address
such variability in the context of radiative transfer.
• It must be able to accurately describe how radiation
is absorbed, emitted, scattered, and transmitted
within the entire model atmosphere.
• Most radiation parameterizations will do this for
longwave or shortwave radiation in terms of a
radiation flux.
Radiation Definitions
• Intensity (Radiance): flow rate of energy in a given
direction per a unit area at a given wavelength.
• Flux (Irradiance): the amount of area-integrated
intensity that is fluxed across a planar surface.
• The total flux is the irradiance integrated over the
electromagnetic spectrum.
Absorption
• In the absence of scattering, the absorption of
radiation energy is expressed by Lambert’s Law:
dI
  a ds
I
Iλ = intensity at a given wavelength
ρ = mass per unit volume of the absorbing atmospheric constituent
σaλ = mass absorption coefficient
ds = an incremental distance
Absorption
• Integrating Lambert’s Law along the path that
radiation travels over a short distance, we obtain:
 s

I  s   I  0  exp    a ds' 
 0

Iλ = intensity at a given wavelength (at s = 0 and s = 0)
• The optical path length, or weighted dimensionless
distance traveled by radiation, is given by:
s
u s     a ds '
0
Absorption
• In the absence of scattering and emission, the
transmissivity and absorptivity of a medium are
related to the optical path length by:
 s   e u  s 
a s   1  e u  s 
transmissivity
absorptivity
Emission
• To maintain thermal equilibrium, a substance that
absorbs radiation energy must also emit it.
• The basis for describing thermal emission is the
theory of blackbody radiation, where…
– The emitted radiation is uniquely a function of the
emitter’s temperature.
– For a given temperature, the emitted radiation is the
maximum possible at all wavelengths (perfect emitter).
– Emitted radiation is isotropic, such that its intensity is
independent of the direction of emission.
Emission
• The spectrum of intensity emitted by an absorbing
medium is given by Planck’s Law:
B T  
2hc2
 KhcT

  e  1


5
Bλ(T) = spectrum of emitted intensity
h = Planck’s constant (6.6261 x 10-34 J s-1)
K = Boltzmann constant (1.381 x 10-23 J K-1)
c = speed of light
Emission
• The wavelength of maximum intensity is given by
Wien’s Displacement Law, described earlier.
• The total flux emitted by a blackbody follows by
integrating Planck’s law over the entire spectrum, as
expressed by the Stefan-Boltzmann Law.
• For a non-blackbody emitter, Kirchhoff’s Law applies,
where emissivity is equal to the absorptivity.
Scattering
• Scattering refers to the extraction and subsequent
reemission of energy by matter.
• Scattering is generally non-isotropic; radiation energy
is scattered in wavelengths and directions different
than those of the incident radiation.
• Definition: mass scattering coefficient (σsλ), or the
amount of radiation lost due to scattering.
Scattering
• A total mass extinction coefficient, combining the
effects of absorption and scattering, can be defined:
k   a   s
• The extinction coefficient follows, i.e.,
e  k
• Lambert’s Law then holds with kλ in place of σaλ.
– In reality, however, the non-isotropic nature of scattering
makes things a bit more complex than the above.
Radiative Transfer Equation
• The general form of the radiative transfer equation
is given by:
dI
 I  J 
k ds
k λ = mass extinction coefficient
I λ = intensity at a given wavelength
Jλ = source function for intensity (equal to Planck’s Law)
ρ = mass per unit volume of the absorbing atmospheric constituent(s)
• This is integrated over many layers of incremental
geometric thickness ds to assess radiative transfer.
Radiation Parameterization
• The aforementioned radiative processes are
accounted for in calculations of the vertical fluxes of
longwave and shortwave radiation at each grid point.
• The vertical convergence of these fluxes is then
employed in the thermodynamic equation, where…
T
1 
FD  FU 

t
cP z
FD = downward flux of radiation energy
FU = upward flux of radiation energy
Radiation Parameterization
• This is computed over all wavelengths at both the
model surface and at all model atmospheric levels.
• The challenge in radiation parameterization is a
classic one: accuracy versus efficiency.
– A radiation parameterization is generally not called each
model time step because it is computationally intensive.
– Accuracy is also strongly influenced by the coupled nature
of atmospheric processes to radiation effects.
Radiation Parameterization
• Radiation parameterization requires accurate
knowledge of both atmospheric state and nonroutinely observed molecular constituent fields.
– Atmospheric state: temperature (Planck’s Law, Wien’s
Displacement), water vapor concentration (H2O), etc.
– Molecular constituents: particularly natural and
anthropogenic aerosols (CO2, O3, CH4 etc.)
• This poses particular challenges to climate models…
– Accurate representation of aerosol radiative effects
– Accurate knowledge of future aerosol concentrations
Radiation Parameterization
• Approximations to the radiative transfer equation for
longwave and shortwave radiation are described in
Sections 4.5.3 and 4.5.4 of the text, respectively.
• These represent primarily empirical applications of
the principles outlined earlier in this lecture.
• For a more comprehensive description of radiation
parameterization, see Stephens (1984, MWR).