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## Surface energy balance (2)

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**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 • 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 • Blackbodies: purely hypothetical bodies that absorb and emit the maximum radiation at all wavelengths • The Earth and the sun are close to blackbodies. • The atmosphere is not close to blackbody, but it can served as the first order approximation**Stefan-Boltzmann Law**• States that radiation emitted from a blackbody is a function ONLY of temperature I=T4 where I is the intensity of the radiation, T is the temperature in K, and is the Stefan-Boltzmann constant, 5.67 x 10-8 W m-2 K-4) • So, hotter surface emit more energy than colder surface (double T, 16x more radiation) • Earth (290K)= 401 Wm-2, Sun (6000K) = 7.3 x 106 Wm-2. So ISun >> Iearth • 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 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 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**Other heat sources**• Precipitation: Rain water generally has a temperature lower than the surface temperature and therefore can cool down the surface • Biochemical heating: chemical reaction involving biomolecules may generate or consume heat • 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 =Tair4 LWup=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 SHand 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