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