9/7/2010
Lecture 5: Surface
Energy Balance
Professor Noah Molotch
September 7, 2010
Energy
Budget
by Latitude
Figure 4.13
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Energy Pathways
INCIDENT ENERGY FROM SUN
Atmosphere
Reflectance
If scatter back to
space we call that
reflectance
Reflectance is also
called albedo.
Albedo =
reflected Shortwave
incoming Shortwave
In atmosphere it is
dominated by clouds.
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Refraction
Figure 4.4
Absorption
absorption can be
considered as extinction of
light as it passes through a
medium.
Amount of extinction
varies with distance
travelled.
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Surface Energy Balance
Radiative Fluxes
Shortwave Radiation
Longwave Radiation
Turbulent Fluxes
Latent heat flux (e.g. evaporation)
Sensible heat flux (heating surface)
Earth Energy Balance
Turbulent fluxes
Radiative Fluxes
Figure 4.12
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Surface Energy Balance
Two major fluxes are “radiative” flux and
“turbulent” flux.
Radiative fluxes are associated with shortwave
radiation incoming from the sun and reflected
by Earth’s surface and longwave radiation
emitted by Earth’s surface and radiated toward
the surface by the atmosphere.
Turbulent fluxes are associated with heating of
the Earth’s surface and phase changes of water
(e.g. evaporation) – these are driven by wind
and hence the word “turbulent”.
Surface Energy Balance
We can express this mathematically:
Radiative Fluxes = Turbulent Fluxes
or
Rnet - G = H + LE
Here: Rnet is the net radiation
G is the ground heat flux
H is the sensible heat flux
LE is the latent heat flux
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Earth Energy Balance
Radiative Fluxes
Turbulent fluxes
Figure 4.12
Radiative Fluxes
Radiative flux is summarized using the term
“net radiation”. It is equal to the balance of
incoming and outgoing shortwave and
longwave radiation:
Rnet = S↓ - S↑ + L↓ - L↑
Where S is shortwave from the sun and L is
longwave radiation emitted by earth
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Radiative Flux
Rnet = S↓ - S↑ + L↓ - L↑
Figure 4.1
Insolation at Earth’s Surface
Figure 4.2
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Animation of Insolation
Albedo
Figure 4.5
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Animation of Albedo
Longwave Radiation
Figure 4.1
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Longwave Radiation
100000000
10000000
Sun (5800K)
Scaled for Earth-Sun distance
Earth (288K)
1000000
10000
1000
Longwave emitted by Earth
100
10
1
0.1
0.1
1
10
100
wavelength (µm)
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Longwave Radiation
Emission of radiation
from a perfect emitter
(i.e. black body) at a
given wavelenght is
given by Planck’s
Law.
All of the energy
emitted across all
wavelengths is the
longwave emission.
100000000
10000000
Sun (5800K)
Scaled for Earth-Sun distance
Earth (288K)
1000000
100000
radiance
radiance
100000
10000
Longwave
1000
100
10
1
0.1
0.1
1
10
100
wavelength (µm)
All energy is the area under this curve
2
0
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Longwave Radiation
We estimate the total emission from a
black body using Stefan-Boltzmann’s Law:
L = σT4
c
h
k

speed of light
Planck’s constant
Boltzmann’s constant
Stefan-Boltzmann constant
3.00108 ms–1
6.6310–34Js
1.3810–23JK–1
5.6710–8Wm–2K–4
T = temperature in Kelvin
(Kelvin is degrees Celsius + 273.15 (thus 0 *C = 273.15 K)
Longwave Radiation
In reality objects are not perfect black
bodies. Meaning they are not perfect
emitters. Thus we introduce the term
emissivity (ε).
L = εσT4
T = temperature in Kelvin
(Kelvin is degrees Celsius + 273.15 (thus 0 *C = 273.15 K)
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Longwave Radiation and Emissivity
The emissivity of a material (ε) is the
relative ability of its surface to emit heat by
radiation.
ε is the ratio of energy radiated by an
object and the energy radiated by a black
body at the same temperature.
A true black body would have an emissivity of 1
while any real object would have an emissivity
less than 1. Aluminum emissivity = 0.04; Cast
iron = 0.65; water = 0.95.
Longwave Radiation
Earth’s surface emits longwave radiation as
a function of the surface temperature and
emissivity.
The atmosphere emits longwave radiation
back toward the Earth surface (e.g.
Greenhouse effect). This also varies with
atmospheric emissivity and temperature.
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Net Longwave Radiation
Earth Energy Balance: Turbulent Fluxes
Turbulent fluxes
Figure 4.12
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Turbulent Fluxes
As implied by word “turbulent”, these fluxes are
largely driven by wind.
Sensible heat fluxes (associated with convection)
driven by difference in temperature between
surface and the atmosphere.
Latent heat fluxes (e.g. evaporation) driven by
difference in vapor pressure between surface and
atmosphere.
Both sensible and latent heat fluxes are driven by
turbulence as air at the surface-atmosphere
interface is replenished by wind.
Turbulent Fluxes
Recall our energy balance equation:
Rnet - G = H + LE
The left side of the equation is often referred to as “available
energy”.
If surface moisture is limiting then
we can not expend energy to
evaporate water and LE will be
low. As a result we heat the
surface and H must be high.
Remember the natural grass VS
Astroturf example.
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Turbulent Fluxes
Rnet - G = H + LE
↓ LE then ↑ H
↑ H = heating
Also note available energy
increases because:
- asphalt has low albedo
- atmosphere heats up and reradiates longwave energy back to
surface
Turbulent Fluxes
Rnet - G = H + LE
↑ LE = ↓ H
↓ H = cooling
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Turbulent Fluxes
Rnet - G = H + LE
↓ LE then ↑ H
↑ H = heating
Turbulent Flux Animations
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Simplified Surface Energy Balance
NET R =
+SW (insolation)
–SW (reflection)
+LW (infrared)
–LW (infrared)
Figure 4.16
Daily Radiation Curves
Figure 4.14
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Radiation Budgets
El Mirage,
CA
Pitt Meadows,
BC
Figure 4.20
Summary
Radiative Fluxes
Shortwave Radiation (controlled by sun and albedo)
Longwave Radiation (controlled by emissivity and
temperature of surface and atmosphere)
Turbulent Fluxes
Latent heat flux (controlled by moisture availability and
wind speed)
Sensible heat flux (controlled by temperature and wind
speed)
Partitioning between sensible and latent heat fluxes
controls surface temperature – largely driven by land
cover (e.g. urbanization).
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