Surface energy balance (2)

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Surface energy balance (2)
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Review of last lecture

• What is energy? 3 methods of energy transfer
• The names of the 6 wavelength categories in the
  electromagnetic radiation spectrum. The
  wavelength range of Sun (shortwave) and Earth
  (longwave) radition
• Earths energy balance at the top of the
  atmosphere.
• Incoming shortwave Reflected
  Shortwave  Emitted longwave
• Earths energy balance at the surface.
• Incoming shortwave Incoming longwave
  Reflected shortwave
• Emitted longwave Latent heat flux
  Sensible heat flux
• Subsurface conduction

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Surface energy balance
Incoming shortwave Incoming longwave
Reflected shortwave Emitted longwave
Latent heat flux
Sensible heat flux Subsurface conduction
SWdn
SWup
LWdn
LWup
LH
SH
dT/dt
Fc
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Incoming solar radiation
SWdn S cos?

• where
• S is solar constant S1366 Watts/m2
• ? is solar zenith angle, which is the angle
  between the local zenith and the line of line of
  sight to the sun

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Reflected solar radiation
SWup SWdn ?

• where ? is albedo, which is the ratio of
  reflected flux density to incident flux density,
  referenced to some surface.

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Global map of surface albedo ?
Typical albedo of various surfaces
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Incoming and surface emitted longwave radiation

• Can be estimated using the blackbody
  approximation
• Blackbodies purely hypothetical bodies that
  absorb and emit the maximum radiation at all
  wavelengths
• The Earth and the sun are close to blackbodies.
• The atmosphere is not close to blackbody, but it
  can served as the first order approximation

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Stefan-Boltzmann Law

• States that radiation emitted from a blackbody is
  a function ONLY of temperature
• I?T4
• where I is the intensity of the radiation, T
  is the temperature in K, and ? is the
  Stefan-Boltzmann constant, 5.67 x 10-8 W m-2 K-4)
• So, hotter surface emit more energy than colder
  surface (double T, 16x more radiation)
• Earth (290K) 401 Wm-2, Sun (6000K) 7.3 x 106
  Wm-2. So ISun gtgt Iearth
• Incoming LW (air-emitted) LWdn ?Tair4
• Surface emitted LW LWup?Ts4

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Net longwave radiation ( LWdn - Lwup ?Tair4 -
?Ts4 )

• Is generally small because air temperature is
  often close to surface temperature
• Is generally smaller than net shortwave radiation
  even when air temperature is not close to surface
  temperature
• Important during the night when there is no
  shortwave radiation

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Sensible heat flux

• Sensible heat heat energy which is readily
  detected
• Sensible heat flux
• SH ? Cd Cp V (Tsurface -
  Tair)
• Where ? is the air density, Cd is flux transfer
  coefficient, Cp is specific heat of air (the
  amount of energy needed to increase the
  temperature by 1 degree for 1 kg of air), V is
  surface wind speed, Tsurface is surface
  temperature, Tair is air temperature
• Magnitude is related surface wind speed
• Stronger winds cause larger flux
• Sensible heat transfer occurs from warmer to
  cooler areas (i.e., from ground upward)
• Cd needs to be measured from complicated eddy
  flux instrument

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Latent heat flux

• LH ? Cd L V (qsurface - qair)
• Where ? is the air density, Cd is flux transfer
  coefficient, L is latent heat of water vapor, V
  is surface wind speed, qsurface is surface
  specific humidity, qair is surface air specific
  humidity
• Magnitude is related surface wind speed
• Stronger winds cause larger flux
• Latent heat transfer occurs from wetter to drier
  areas (i.e., from ground upward)
• Cd needs to be measured from complicated eddy
  flux instrument

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Bowen ratio

• The ratio of sensible heat flux to latent heat
  flux
• B SH/LH
• Where SH is sensible heat flux, LH is latent heat
  flux
• B Cp(Tsurface - Tair) / L(qsurface - qair) can
  be measured using simple weather station.
  Together with radiation measurements (easier than
  measurements of turbulent fluxes), we can get an
  estimate of LH and SH

Net radiative flux Fr SWdn - SWup LWdn - LWup
Net turbulent flux Ft LH SH
dT/dt
Fd neglected
From surface energy balance Ft Fr (i.e. LHSH
Fr) With the help of SHB LH, we get LHFr/(B1),
SHFr B/(B1)
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Bowen ratio (cont.)

• When surface is wet, energy tends to be released
  as LH rather than SH. So LH is large while SH is
  small, then B is small.
• Typical values of B
• Semiarid regions 5
• Grasslands and forests 0.5
• Irrigated orchards and grass 0.2
• Sea 0.1
• Some advective situations (e.g. oasis)
  negative

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Map of Bowen ratio for Texas (By Prof.
Maidment, U of Texas)
River flow
Latent heat flux
Bowen ratio
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Subsurface conductionFouriers Law

• The law of heat conduction, also known as the
  Fouriers law, states that the heat flux due to
  conduction is proportional to the negative
  gradient in temperature.
• In upper ocean, soil and sea ice, the temperature
  gradient is mainly in the vertical direction. So
  the heat flux due to conduction Fc is
• Fc - ? dT/dz
• where ? is thermal conductivity in the unit of
  W/(m K)
• Note that Fc is often much smaller than the other
  terms in surface energy balance and can be
  neglected

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Other heat sources

• Precipitation Rain water generally has a
  temperature lower than the surface temperature
  and therefore can cool down the surface
• Biochemical heating chemical reaction involving
  biomolecules may generate or consume heat
• Anthropogenic heat Fossil fuel combustion,
  Electrical systems

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Summary Surface energy balance
Incoming shortwave Incoming longwave
Reflected shortwave Emitted longwave
Latent heat flux
Sensible heat flux Subsurface conduction
SWdn Scos?
SWup SWdn ?
LWdn ?Tair4
LWup?Ts4
LH?CdLV(qsurface- qair)
SH?CdCpV(Tsurface- Tair)
?
dT/dt
Fc - ? dT/dz

• Bowen ratio B SH/LH Cp(Tsurface - Tair) /
  L(qsurface - qair) provides a simple way for
  estimating SH and LH when the net radiative flux
  Fr is available LHFr/(B1), SHFr B/(B1)
• Subsurface conduction Fouriers law
• Other heat sources precipitation, biochemical,
  anthropogenic

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Works cited

• http//nsidc.org/cryosphere/seaice/processes/albed
  o.html