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=  T 4 –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 Incoming shortwave + Incoming longwave = Reflected shortwave + Emitted longwave + Latent heat flux + Sensible heat flux + Emitted longwave + Latent heat flux + Sensible heat flux + Subsurface conduction

Surface energy balance dT/dt SWdn SWupLWdnLWupLHSH Fc Incoming shortwave + Incoming longwave = Reflected shortwave + Emitted longwave + 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/m 2  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 =  Tair 4 Surface emitted LW: LWup=  Ts 4

Net longwave radiation ( LWdn - Lwup =  Tair 4 -  Ts 4 ) 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 =  C d C p V (T surface - T air ) Where  is the air density, C d is flux transfer coefficient, C p 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, T surface is surface temperature, T air 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) C d needs to be measured from complicated eddy flux instrument

Latent heat flux LH =  C d L V (q surface - q air ) Where  is the air density, C d is flux transfer coefficient, L is latent heat of water vapor, V is surface wind speed, q surface is surface specific humidity, q air 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) C d 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 = C p (T surface - T air ) / L(q surface - q air ) 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 flux Fr = 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 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 dT/dt SWdn =Scos  SWup =SWdn  LWdn =  Tair 4 LWup =  Ts 4 LH=  C d LV(q surface - q air ) SH=  C d C p V(T surface - T air ) Fc = - dT/dz Incoming shortwave + Incoming longwave = Reflected shortwave + Emitted longwave + Latent heat flux + Sensible heat flux + Subsurface conduction  Bowen ratio B= SH/LH = C p (T surface - T air ) / L(q surface - q air ) 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 albedo.htmlhttp://nsidc.org/cryosphere/seaice/processes/ albedo.html