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Lecture 3 Radiation and Planetary Energy Balance


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Title: Lecture 3 Radiation and Planetary Energy Balance

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

Electromagnetic Spectrum of the Sun
Visible light band, i.e. 0.40.7 µm, occupies 44
of total energy
Spectrum of the sun compared with that of the
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
  • 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)

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
  • Total emission is a strong function of

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
  • In general, the emissivity depends on wavelength
    just as the absorptivity does, for the same
    reasons el El/El

Red is Cool, Blue is Hot
  • Take the derivative of the Planck function, set
    to zero, and solve for wavelength of maximum

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
3 Ways to label radiation
  • By its source
  • Solar radiation - originating from the sun
  • Terrestrial radiation - originating from the
  • 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

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

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

  • 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.

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

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

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

Greenhouse effect (actually, atmospheric effect
is a more proper term)
Heat balance of Solar-earth system
Heat flux coming from the sun heat loss of earth
Scenario 1 Simple heat balance of the Earth
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.
Scenario 2
with an atmosphere represented by a single layer,
which is totally transparent to solar radiation
but opaque to infrared radiations
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
Ts 303K (30C)
Scenario 3
Consider the fact that our atmosphere is not a
perfect blackbody but with the emissivity e lt 1,
a gray body
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
, and
  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.

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
Radiation-Convection balance model
(a)??????(100) ????16 ???
3 ???????? 6 ????20 ?????
4 ????51
(b) ????(??????) ????21 15?????,
6?????? ????38 ???26
???????? ?????, ?????, ????????? ?????????
(c) ????? ?? 16 3 15 34 ?? 38 26
64 ???? 30, lt ??????,????(23)????(7)??
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
  • dark shading gt 40 light shading lt 20

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
  6. Very strong maxima over deserts (hot surface,
    clear atmosphere)

dark shading lt 240 W m-2 light shading gt 280 W
TOA Net Incoming Radiation
Annual Mean
  1. Huge seasonal switch from north to south
  2. Tropics are always positive, poles always
  3. Western Pacific is a huge source of energy (warm
    ocean, cold cloud tops)
  4. Saharan atmosphere loses energy in the annual
  5. TOA net radiation must be compensated by lateral
    energy transport by oceans and atmosphere

dark shading lt 0 W m-2 light shading gt 80 W m-2
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
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.

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
  4. Ocean transport dominates in subtropics
  5. Atmospheric transport dominates in middle and
    high latitudes

End of Lecture 3
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