# Surface energy balance

```Surface energy balance (3)
Review: 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(TsurfaceTair)

dT/dt
Fc = -  dT/dz
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
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:
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(TsurfaceTair)

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)
• Factors affecting soil thermal conductivity
• Other heat sources: precipitation, biochemical, anthropogenic
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