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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 - PowerPoint PPT Presentation
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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 Incoming shortwave + Incoming longwave = Reflected
shortwave shortwave
+ Emitted longwave + Latent heat flux + Sensible heat flux + Emitted longwave + Latent heat flux + Sensible heat flux
+ Subsurface conduction
Surface energy balance
dT/dt
SWdnSWup LWdn LWup LH SH
Fc
Incoming shortwave + Incoming longwave = Reflected shortwave + Emitted Incoming shortwave + Incoming longwave = Reflected shortwave + Emitted longwavelongwave
+ Latent heat flux + Sensible heat flux + Subsurface conduction+ Latent heat flux + Sensible heat flux + Subsurface conduction
Incoming solar radiation
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
SWdn = S cos
Reflected solar radiation
where is albedo, which is the ratio of reflected flux density to incident flux density, referenced to some surface.
SWup = SWdn
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
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
dT/dt
Net radiative fluxFr = SWdn - SWup + LWdn - LWup
Net turbulent flux Ft = LH + SH
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
Bowen ratio
Latent heat flux
Subsurface conductionFourier’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
dT/dt
SWdn =Scos
SWup =SWdn
LWdn =Tair4
LWup=Ts4
LH=CdLV(qsurface- qair)
SH=CdCpV(Tsurface- Tair)
Fc = - dT/dz
Incoming shortwave + Incoming longwave = Reflected shortwave + Emitted longwave
+ Latent heat flux + Sensible heat flux + Subsurface conduction
• 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
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