ATM 301 Lecture #9 (6.1, Appendix D) Surface Energy Fluxes and Balance Major Surface Energy Fluxes Review of Radiation Solar Radiation Thermal Radiation Ground heat flux LH and SH fluxes

Why study surface energy fluxes in this course? ET is directly coupled to surface energy balance Surface energy balance is commonly used to estimate ET Surface energy fluxes are a major topic of Hydrometeorology

3 Trenberth et al. (2009, BAMS) Surface energy balance is coupled to evapotranspiration

Major components of the surface energy budget Net radiation (R n ) Downward solar (or shortwave) radiation (S  or K  ) Upward solar radiation (S  or K  ) Downward thermal (or infrared or longwave) radiation ( L  ) Upward thermal radiation ( L  ) Latent heat flux (LH= E, associated with ET) Sensible heat flux (SH) Ground heat flux (G) Storage (U) SS SS LL LL G SH LH

λ=c/f (wavelength= speed of light / frequency ) 1  m (micrometer) = 1x10 -6 m Review of radiation (see Appendix D1) Earth Sun

Review of radiation Electromagnetic waves can interact with matter in the following ways Radiation is emitted by all matter, depending on temperature and “emissivity” of the material Radiation can be absorbed by a material, with its energy going into changing the material’s temperature Radiation can be transmitted through a medium without loss of amplitude Radiation can be reflected or scattered, bouncing off in a different direction

All objects warmer than 0 Kelvin emit radiation, depending on their temperature Review of radiation longwave shortwave

Radiation Plays a Key Role in Earth’s Climate Trenberth et al. (2009).

A blackbody is an idealization: a substance that emits radiation in all direction at the maximum rate (for its temperature) and absorbs all incoming radiation For a blackbody, “spectral flux” : Blackbody radiation For a blackbody, total flux (all wavelengths): Stephan-Boltzman Law σ = 5.67x10 -8 W m -2 K -4 T in Kelvin

“Gray” radiation Real substances do not emit and absorb perfectly like a blackbody. As a result they are sometimes called “gray” Departure from blackbody behavior is characterized by: Emissivity (ε λ ): actual emitted radiation / blackbody emitted radiation with the same temperature Absorptivity : absorbed radiation / incoming radiation Reflectivity (α λ ): reflected radiation / incoming radiation Transmissivity: transmitted radiation / incoming radiation These depend on the properties of the material Absorptivity = emissivity For surface radiation balance we will use Surface emissivity (ε) : ε λ integrated over all thermal wavelengths Surface albedo (α) : α λ integrated over all solar wavelengths

Surface radiation budget Consider four components: Solar (shortwave) down: K d Solar (shortwave) up: K u Thermal (terrestrial, longwave) up: L d Thermal (terrestrial, longwave) down: L u R n = K d – K u + L d - L u KdKd KuKu LuLu LdLd -+ - = RnRn shortwave/solar (λ<2 μm) Longwave/terrestrial/Thermal/IR (λ>3 μm)

Downward solar radiation ( top of atmos. or TOA ) (Appendix D) 0 to 1367 W m -2 [W m 2 ] Determined by: 1.Radiation emitted by the sun 2.Distance of earth from the sun 3.Solar zenith angle 4.Number of daylight hours

See section 2.7 of Hartmann GPC

5.Reduced by absorption of sunlight by gasses and aerosols 6.Reduced by reflection of sunlight by aerosols and clouds 7.Reduced by topography, vegetation, buildings 8.Terrain slope Downward surface solar radiation Capturing these effects requires detailed mathematical models of “radiative transfer” Can be crudely estimated using surface humidity & fractional cloud cover 0 to  1000 W m -2

Upward (reflected) surface solar radiation Albedo depends on solar angle & surface properties 0 to  800 W m -2 Determined by: 1.Downward solar radiation 2.Surface albedo K u =  K d Shuttleworth (2012) (angle from the horizon)

Upward surface thermal radiation  180 to  550 W m -2 Determined by: 1.Surface temperature 2.Surface emissivity L u = ε s σ T s 4 T in Kelvin Shuttleworth (2012)

Downward surface thermal radiation Determined by: 1.Profile of (lower) atmospheric temperatures 2.Profile of (lower) atmospheric emissivity Determined by clouds and greenhouse gases (especially H 2 O) Both clouds and greenhouse gasses absorb and re-emit longwave radiation, resulting in larger L d 3.near-surface air T, humidity and cloud fraction These effects are often crudely estimated from: fractional cloud cover near-surface temp. near-surface humidity Wavelength (μm) % absorbed  180 to  550 W m -2 Cloud factor Near-surface atmospheric values Ld ≈ f ε atm T atm 4

Surface radiation budget: summary R n = K d – K u + L d - L u R n = K d (1-  ) + L d – ε s σT s 4 R n ≈ K d (1-  ) + f ε atm T atm 4 – ε s σT s 4 KdKd KuKu LuLu LdLd -+ - = RnRn shortwave/solar (λ<2 μm) Longwave/terrestrial/Thermal/IR (λ>3 μm) All things we can easily measure or calculate

Measuring surface radiation Solar radiation measured with a “pyranometer”: Records flux of radiation First filters out all but the solar wavelengths. Dome isolates sensor from sensible and latent heat fluxes. Thermal radiation measured with a “pyrgeometer”: Records flux of radiation First filters out the solar wavelengths Dome isolates sensor Net radiation measured with a net radiometer: measure all 4 components of R n separately …or by measure net upward and downward total radiation (no filtering) ometer_nr01_photo.jpg

Diurnal (daily) cycle of radiation (clear sky) At Bergen, Norway Shuttleworth (2012) 13 April January 1968

Ground heat flux +/-  200 W m G(z) = -k soil dT soil /dz k s is thermal conductivity, measure of how easily heat moves through the ground Upwards (downwards) when temperature increases (decreases) with depth Shuttleworth (2012)

Measuring Ground heat flux Measure temperature difference across a thin plate with similar properties to the soil Doesn’t work right at the surface, so use temperature measurements above to make a correction Shuttleworth (2012)

Major components of the surface energy budget Net radiation Downward solar Upward solar Downward thermal Upward thermal Ground heat flux Latent heat flux Sensible heat flux Storage

Directly measuring sensible and latent heat fluxes Eddy covariance Measure fluctuations of wind, temperature, and humidity (w’, T’, q’) Need time resolution  20Hz = 20 times per second! Wind is measured with ultra-sonic anemometer Water vapor measured with infrared gas analyzer Temperature measured with a high speed sensor Sensors require careful calibration and maintenance Expensive: cost  $30k ultra-sonic anemometer Gas analyzer units: [L / T] units: [W/ m 2 ] LE = λ v ρ a E units: [W/ m 2 ] w w w= vertical wind speed Specific heat of air

Latent heat turbulent flux: water and heat transfer Latent heat flux is E, where E is proportional to the product of near-surface wind speed and surface-air vapor pressure difference: E =  w v K E u(z m ) [e s – e(z m )] -- called bulk formula in climate modeling K E = water-vapor transfer coefficient (p.126, using Fick’s law and the universal u distribution): z m is the measurement height (e.g., 2m) v (x10 6 J/kg) = 2.50 – 2.36 x T ( o C)  w =1000kg/m 3

Sensible heat turbulent flux: water and heat transfer Sensible heat flux (SH) is proportional to the product of near-surface wind speed and surface- air temperature difference (following Fick’s law of diffusion): SH = K H u(z m ) [T s – T(z m )] K H = sensible-heat transfer coefficient (pp ): c p =specific heat of air at constant pressure =1.005x10 -3 MJ kg -1 K -1

Diurnal Variations in Surface Energy Fluxes

SH dominates over dry regions (i.e. Bo >1)

(W m -2 )

where  U/  t = energy storage change within the surface layer S = net shortwave (i.e. solar) radiation into the layer (positive down) L = net longwave (i.e. infrared) radiation into the layer (positive down) E = latent heat flux (positive upward), v (MJ/kg)= x10 -3 T( o C) is latent heat SH = sensible heat flux (positive upward) G = downward heat flux through conduction (often small) A w = net energy input associated with inflows and outflows of water (often  0) Thus, evaporation is constrained by and can be derived using the surface energy balance. Surface Energy Balance: S L SH E G AwAw