Surface energy balance (2)
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
–
–
Intensity of radiation (Stefan-Boltzman law): I=T4
Wavelength of radiation (Wein’s law): max = b/T
–
Earth’s energy balance at the top of the atmosphere.
Incoming shortwave = Reflected Shortwave + Emitted longwave
–
Earth’s energy balance at the surface.
Incoming shortwave + Incoming longwave = Reflected shortwave
+ Emitted longwave + Latent heat flux + Sensible heat flux
+ Subsurface conduction
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
Incoming solar radiation
SWdn = S cos
where
S is solar constant S=1366 Watts/m2
 is solar zenith angle, which is the angle between the
local zenith and the line of line of sight to the sun
Reflected solar radiation
SWup = SWdn 
where  is albedo, which is the
ratio of reflected flux density to incident
flux density, referenced to some surface.
Global map of surface albedo 
Typical albedo of various surfaces
Incoming and surface emitted
longwave radiation
• Can be estimated using the blackbody
approximation
• Incoming LW (air-emitted):
LWdn = Tair4
• Surface emitted LW:
LWup=Ts4
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
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
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
Video: Eddy Flux Tower
• https://www.youtube.com/watch?v=OfvPoP_xx
4Y
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. LH+SH = Fr)
With the help of SH=B LH, we get LH=Fr/(B+1), SH=Fr B/(B+1)
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
Map of Bowen ratio for Texas
(By Prof. Maidment, U of Texas)
River flow
Latent
heat flux
Bowen ratio
Subsurface conduction
Fourier’s Law
• The law of heat conduction, also known as the
Fourier’s 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
Factors affecting the thermal
conductivity of soil
(Key: conduction requires medium)
• Moisture content: wetter soil has a
larger thermal conductivity
• Dry density: denser soil has a larger
thermal conductivity
• Porosity
• Chemical composition. For example,
sands with a high quartz content
generally have a high thermal
conductivity
• Biomass
Other heat sources I:
Precipitation
• Rain water generally
has a temperature
lower than the surface
temperature and
therefore can cool down
the surface
• This term is generally
smaller than LH and
SH
Other heat sources II:
Biochemical heating
• Biochemical processes (any
chemical reaction involving
biomolecules is called a
biochemical process) may
generate or consume heat
• Examples: carbon and
nitrogen transformation by
microbial biomass
Other heat sources III:
Anthropogenic heat
• Fossil fuel combustion
• Electrical systems
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
LWup
=Tair4 =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
LH=Fr/(B+1), SH=Fr B/(B+1)
• Subsurface conduction: Fourier’s law
• Other heat sources: precipitation, biochemical, anthropogenic
Works cited
• http://nsidc.org/cryosphere/seaice/processes/
albedo.html