Lecture 1: Introduction to the planetary energy balance

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Lecture 1 Introduction to the planetary energy
balance

• Keith P Shine,
• Dept of Meteorology,The University of Reading
• k.p.shine_at_reading.ac.uk

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Structure

• The solar constant how much solar radiation
  is absorbed by the Earth
• The effective emitting temperature of the Earth
• Spectral variation of emission by the Sun and the
  Earth
• A simple illustration of the energy balance and
  the greenhouse effect, including the stratosphere
• A more realistic view of the energy balance
• A few problems

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• Almost the only essential physics you will need
  to know ...... a black body (i.e. a perfect
  emitter/ absorber of radiation) emits a flux
  density (irradiance) ?T4 (in Wm-2) into the
  hemisphere above it, averaged over all
  wavelengths. ? is the Stefan-Boltzmann constant
  (5.67x10-8 Wm-2K-4) and T is the temperature in
  Kelvin.

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The Solar Constant (1)

• Solar Constant somewhat dated term (now often
  referred to, more accurately, as the Total Solar
  Irradiance) which is defined as the number of
  Watts incident on a unit area perpendicular to a
  line joining the centres of the Earth and the
  Sun, at the mean Sun-Earth distance.
• Measured So (from satellites) is about 1370 Wm-2
  implies Sun is emitting as a black body at a
  temperature, TSun, of about 5800 K.
• Energy intercepted by Earth is So ? re2 where re
  is Earths radius .... but Earth has surface area
  of 4?re2 ... Therefore ..

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The Solar Constant (2)

• Average solar irradiance incident on Earth is
• But .... fraction of this incident radiation
  reflected back to space (by clouds, gases,
  aerosols and the surface)....this fraction is
  called the planetary albedo, ?p. Observations
  from satellites indicate that the value of ?p is
  about 0.3.
• Hence, the total (rate of) solar energy absorbed
  by the Earth-atmosphere system is

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Effective Emitting Temperature of the Earth (1)

• At the top of the atmosphere there must be a long
  term balance between the energy absorbed from
  the Sun and the energy emitted to space by the
  Earth-atmosphere system.
• Assume (but only for now!) that the Earth emits
  as a black body to space at a temperature Te
  (where the e could stand for Earth, or
  emitting, or effective!). In balance

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Effective Emitting Temperature of the Earth (2)

• Note that Te is much less than the global average
  surface temperature, TS (about 288 K).
• Now have two characteristic temperatures ..
  TSun5800 K, and Te255 K can derive the
  variation of emitted radiation with wavelength
  from the Planck Function available in all good
  physics texts.
• Consequence is that, after diluting the emitted
  solar radiation as it spreads out from Sun, the
  solar radiation and the Earth emitted radiation
  (coincidentally!) are in separate wavelength
  regions separated at about 4 ?m see Figure.

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fig
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Simple model of greenhouse effect (1)

• Difference between Ts and Te is because of the
  greenhouse effect water vapour, carbon dioxide,
  ozone, and clouds absorb and emit thermal
  infrared radiation (i.e. at ? gt 4?m). Simple
  illustration using single layer model of the
  atmosphere following approximations
• Atmosphere does not absorb any solar radiation
  all is absorbed at the Earths surface.
• The atmosphere emits thermal infrared radiation
  as a grey body it emits ??T4 upwards and
  downwards, where ? is the emittance (? 1).
  Ability to emit and absorb are related so
  emittance absorptance and transmittance 1
  absorptance. (e.g. for a black body
  ?absorptance1, transmittance0).
• The surface is a black body in the thermal IR.

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Simple model of greenhouse effect (2)

• Can show that
• Note that if ?0 (no absorbing atmosphere) then
  we get the earlier equation
• Pluck a number from the air ?0.6, gives
  Ts278 K i.e. nearer observations. Increasing ?
  (e.g. more CO2) increases Ts.
• This simple equation encapsulates many of the
  externally forced climate change mechanisms ..
  changes in So, ? and ? can all cause climate
  change.

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Why the stratosphere is different

• In the simple model above, the atmosphere is
  essentially heated from below as this is where
  the suns energy is deposited.
• The stratosphere is different it is heated from
  within, partly by absorption of solar radiation,
  ast, by ozone. A simple model of its energy
  balance is then

Notice that an increase in ?st (e.g. by
increasing CO2) now leads to a cooling of the
stratosphere, as is found in more sophisticated
models
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A more realistic energy budget

• energy exchanges in the atmosphere are not solely
  radiative surface fluxes of latent and sensible
  heat , vertical fluxes of latent and sensible
  heat by convection, fronts etc
• the atmosphere does absorb some solar radiation
• the value of ? chosen earlier is entirely
  arbitrary in reality the atmosphere is not a
  grey absorber it absorbs well at some
  wavelengths, poorly at others (see next lecture).

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Modern (global and annual averaged!) Earth energy
budget from Kiehl and Trenberth (1997)

• FURTHER (INTRODUCTORY) READING
• Hartmann D.L. (1994) Global Physical Climatology,
  Academic Press
• Kiehl J.T. and K.E.Trenberth (1997), Earths
  Annual Global Mean Energy Budget. Bulletin of the
  American Meteorological Society, vol 78, 197-208.