Lecture 3 Radiation and Planetary Energy Balance

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Lecture 3Radiation and Planetary Energy Balance
(provide a review and add something new)
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Electromagnetic Radiation

• Oscillating electric and magnetic fields
  propagate through space
• Virtually all energy exchange between the Earth
  and the rest of the Universe is by
  electromagnetic radiation
• Most of what we perceive as temperature is also
  due to our radiative environment
• Dual properties may be described either as waves
  or as particles (photons)
• High energy photons short waves lower energy
  photons longer waves

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Electromagnetic Spectrum of the Sun
Visible light band, i.e. 0.40.7 µm, occupies 44
of total energy
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Spectrum of the sun compared with that of the
earth
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Blackbodies and Graybodies

• A blackbody is a hypothetical object that absorbs
  all of the radiation that strikes it. It also
  emits radiation at a maximum rate for its given
  temperature.
• Does not have to be black!
• A graybody absorbs radiation equally at all
  wavelengths, but at a certain fraction
  (absorptivity, emissivity) of the blackbody rate
• The energy emission rate is given by
• Plancks law (wavelength dependent emission)
• Stefan Boltzmann law (total energy)
• Wiens law (peak emission wavelength)

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Blackbody Radiation

• Plancks Law describes the rate of energy output
  of a blackbody as a function of wavelength
• Emission is a very sensitive function of
  wavelength
• Total emission is a strong function of
  temperature

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Total Blackbody Emission

• Integrating Planck's Law across all wavelengths,
  and all directions, we obtain an expression for
  the total rate of emission of radiant energy from
  a blackbody
• E sT4
• This is known as the Stefan-Boltzmann Law, and
  the constant s is the Stefan-Boltzmann constant
  (5.67 x 10-8 W m-2 K-4).
• Stefan-Boltzmann says that total emission
  strongly depends on temperature!
• Strictly, S-B Law is true only for a blackbody.
  For a gray body, E eE, where e is called the
  emissivity.
• In general, the emissivity depends on wavelength
  just as the absorptivity does, for the same
  reasons el El/El

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Red is Cool, Blue is Hot

• Take the derivative of the Planck function, set
  to zero, and solve for wavelength of maximum
  emission

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Solar and Planetary Radiation

• Earth receives energy from the sun at many
  wavelengths, but most is in visible wavelengths
• Earth emits energy back to space at much longer
  (thermal) wavelengths, infrared
• Because temperatures of the Earth and Sun are so
  different, it's convenient to divide atmospheric
  radiation into solar and planetary components

Overlapped band is trivial
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3 Ways to label radiation

• By its source
• Solar radiation - originating from the sun
• Terrestrial radiation - originating from the
  earth
• By its proper name
• ultra violet, visible, near infrared, infrared,
  microwave, etc.
• By its wavelength
• short wave radiation ? ? 3 micrometers
• long wave radiation ? gt 3 micrometers

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Molecular Absorbers/Emitters
facts

• Molecules of gas in the atmosphere interact with
  photons of electromagnetic radiation
• Different kinds of molecular transitions can
  absorb/emit very different wavelengths of
  radiation
• Some molecules are able to interact much more
  with photons than others
• Different molecular structures produce
  wavelength-dependent absorptivity/emissivity

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Molecular Absorbers/Emitters

• permanent dipole moment existence of dipole
  pole (e.g., H2O)
• 3 modes of motions in tri-atomic molecule
• Symmetric vibration
• Bending
• Anti-symmetric vibration

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Remarks

• Molecules containing two atoms of the same
  element such as N2 and O2 and monatomic molecules
  such as Ar have NO NET change in their dipole
  moment when they vibrate and hence almost do not
  interact with infrared photon.
• Although molecules containing two atoms of
  different elements such as carbon monoxide (CO)
  or hydrogen chloride (HCl) do absorb IR, they are
  short-lived in the atmosphere owing to their
  reactivity and solubility. As a consequence their
  greenhouse effect is neglected.

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How do greenhouse gases (GHGs) "work"?

• After GHGs absorb passing IR photons, the energy
  of the photon is converted into various excited
  vibration states.
• The IR spectrum spans a range of wavelengths with
  different energies. Different types of GHGs
  absorb different wavelengths of IR photons.
• Different vibrational modes allow GHGs to absorb
  IR photons in more than one wavelength. This in
  fact causes the uncertainty as to how much of the
  greenhouse effect each gas produces

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Remarks (cont.)

• Relative contributions of atmos. constitutes to
  the greenhouse effect
• water vapor, 3672 (discussed later)
• carbon dioxide, 926 (In fact, CO2 is NOT the
  BIG guy)
• methane, 49
• ozone, 37

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Conservation of Energy

• Incident radiation (Ei) upon a medium can be
• absorbed (Ea)
• Reflected (Er)
• Transmitted (Et)
• Ei Ea Er Et
• Define
• reflectance r Er/Ei
• absorptance a Ea/Ei
• transmittance t Et/Ei
• Conservation r a t 1
• Emissivity e of an object its absorptance a (it
  must!!)

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Greenhouse effect(actually, atmospheric effect
is a more proper term)
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Heat balance of Solar-earth system
Heat flux coming from the sun heat loss of earth
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Scenario 1 Simple heat balance of the Earth
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Scenario 1
Absorbed solar radiation emitted terrestrial
radiation This leads to and finally to
This corresponds to Te255 K
( -18C). NOT Realistic!!
factor 1/4 arises from the spherical geometry of
the Earth, because only part of the Earths
surface receives solar radiation directly.
the temperature (-18C) that would occur on the
Earths surface if it were a perfect black body,
there were no atmosphere, and the temperature was
the same at every point.
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Scenario 2
with an atmosphere represented by a single layer,
which is totally transparent to solar radiation
but opaque to infrared radiations
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Scenario 2
Heat balance at the top of atmosphere (TOA)
Heat balance at the surface
energy emitted by the surface incoming solar
fluxes infra-red flux coming from the atmosphere
Combining two formula
NOT Realistic!! Much higher than the observed
15C
Ts 303K (30C)
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Scenario 3
Consider the fact that our atmosphere is not a
perfect blackbody but with the emissivity e lt 1,
a gray body
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Scenario 3
Heat balance at the surface is rewritten as
energy emitted by the surface incoming solar
fluxes infra-red flux coming from the
graybody atmosphere
Heat balance at TOA becomes (note transmittance
is not zero, but equals to 1- e in this scenario)
From surface
Combining above two formula
bonus
, and
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Discussions

1. For e0, corresponding to an atmosphere totally
   transparent to infra-red radiations (as if there
   exists no atmosphere),Ts Te, we go back to
   scenario 1.
2. For a perfect black body, e1, we go back to
   scenario 2.

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Discussions (cont.)

• A typical e value 0.97 for the atmosphere,
• gt Ts 1.18Te 301 K (28C), and
• gt Ta 255.1 K -18.1C

Fxxx, the ground is too warm and the air
is too cold!
Conclusion Our simple radiation balance model has
deficiencies
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Radiation-Convection balance model
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(a)??????(100) ????16 ???
3 ???????? 6 ????20 ?????
4 ????51
(b) ????(??????) ????21 15?????,
6?????? ????38 ???26
??????
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???????? ?????, ?????, ????????? ?????????
(c) ????? ?? 16 3 15 34 ?? 38 26
64 ???? 30, lt ??????,????(23)????(7)??
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Planetary Albedo
Annual Mean

• Global mean 30
• Not the same as surface albedo (clouds, aerosol,
  solar geometry)
• Increases with latitude
• Lower over subtropical highs
• Higher over land than oceans
• Bright spots over tropical continents
• Strong seasonality clouds, sea ice and snow
  cover
• dark shading gt 40light shading lt 20

JJA
DJF
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TOA Outgoing Longwave Radiation
Annual Mean

1. Given by esT4 (which T?)
2. Combined surface and atmosphere effects
3. Decreases with latitude
4. Maxima over subtropical highs (clear air neither
   absorbs or emits much)
5. Minima over tropical continents (cold high
   clouds)
6. Very strong maxima over deserts (hot surface,
   clear atmosphere)

JJA
DJF
dark shading lt 240 W m-2 light shading gt 280 W
m-2
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TOA Net Incoming Radiation
Annual Mean

1. Huge seasonal switch from north to south
2. Tropics are always positive, poles always
   negative
3. Western Pacific is a huge source of energy (warm
   ocean, cold cloud tops)
4. Saharan atmosphere loses energy in the annual
   mean!
5. TOA net radiation must be compensated by lateral
   energy transport by oceans and atmosphere

JJA
DJF
dark shading lt 0 W m-2 light shading gt 80 W m-2
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Energy Surplus and Deficit

1. Absorbed solar more strongly peaked than the
   emitted longwave
2. OLR depression at Equator due to high clouds
   along ITCZ
3. Subtropical maxima in OLR associated with clear
   air over deserts and subtropical highs

Annual Mean Zonal Mean TOA Fluxes
TOA net radiation surplus in tropics and deficits
at high latitudes must be compensated by
horizontal energy transports in oceans and
atmosphere
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Energy Budget Cross-Section

1. Excess or deficit of TOA net radiation can be
   expressed as a trend in the total energy of the
   underlying atmosphere ocean land surface, or
   as a divergence of the horizontal flux of energy
   in the atmosphere ocean
2. Cant have a trend for too long. Transport of
   RTOA will eventually adjust to balance trends.

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Energy Transports in the Ocean and Atmosphere

1. Northward energy transports in petawatts (1015 W)
   
2. Radiative forcing is cumulative integral of
   RTOA starting at zero at the pole
3. Slope of forcing curve is excess or deficit of
   RTOA
4. Ocean transport dominates in subtropics
5. Atmospheric transport dominates in middle and
   high latitudes

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End of Lecture 3