Outline of the course The Basics The global hydrological cycle Precipitation Soil water (lab work) Surface energy fluxes Evaporation and transpiration Snowpack Groundwater Streamflow Floods & Droughts Water management

Surface Energy Fluxes and Balance 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

Surface energy balance is coupled to evapotranspiration Describe the global water cycle, and then point out that my research covers many aspects of the global water cycle, such as the variability and long-term changes in atmospheric water vapor and clouds, precipitation, evaporation, streamflow, runoff, continental freshwater discharge, and soil moisture. When the water cycle is out of balance over a region on land, floods and droughts occur. This leads the topic of my talk Today – drought and how it responds to global warming. Trenberth et al. (2009, BAMS)

Major components of the surface energy budget Net radiation (Rn) 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 SH L S LH L G

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

Review of radiation All objects warmer than 0 Kelvin emit radiation, depending on their temperature shortwave longwave http://atoc.colorado.edu/wxlab/radiation/background.html

Blackbody radiation 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” : 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 (ελ): actual emitted radiation / blackbody emitted radiation with the same temperature Absorptivity : absorbed radiation / incoming radiation Reflectivity (αλ): reflected radiation / incoming radiation Transmissivity: transmitted radiation / incoming radiation These depend on the properties of the material Absorptivity = emissivity  surface emissivity ε = (1- α) For surface radiation balance we will use Surface emissivity (ε) : ελ integrated over all thermal wavelengths Surface albedo (α) : αλ integrated over all solar wavelengths

Surface radiation budget Consider four components: Solar (shortwave) down: Kd Solar (shortwave) up: Ku Thermal (terrestrial, longwave) up: Ld Thermal (terrestrial, longwave) down: Lu Rn= Kd – Ku + Ld - Lu Kd Ku Ld Lu Rn - + - = 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 http://en.wikipedia.org/w/index.php?title=File:Seasons1.svg&page=1 [W m2] Determined by: Radiation emitted by the sun Distance of earth from the sun Solar zenith angle Number of daylight hours

See section 2.7 of Hartmann GPC

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

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

Upward surface thermal radiation 180 to 550 W m-2 Determined by: Surface temperature Surface emissivity (εs) Lu= εs σ Ts4 + (1- εs) Ld T in Kelvin Shuttleworth (2012)

Downward surface thermal radiation 180 to 550 W m-2 Determined by: Profile of (lower) atmospheric temperatures Profile of (lower) atmospheric emissivity Determined by clouds and greenhouse gases (especially H2O) Both clouds and greenhouse gasses absorb and re-emit longwave radiation, resulting in larger Ld 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 Ld ≈ f εatm Tatm4 http://www.globalwarmingart.com/wiki/File:Atmospheric_Absorption_Bands_png Cloud factor Near-surface atmospheric values

- + - = Surface radiation budget: summary Rn = Kd – Ku + Ld - Lu Rn = Kd (1-) + εsLd – εsσTs4 Rn ≈ Kd (1- ) + εs σ f εatm Tatm4 – εsσTs4 All things we can easily measure or calculate Kd Ku Ld Lu Rn - + - = shortwave/solar (λ<2 μm) Longwave/terrestrial/Thermal/IR (λ>3 μm)

Measuring surface radiation http://en.wikipedia.org/wiki/Pyranometer 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. http://en.wikipedia.org/wiki/Pyrgeometer Thermal radiation measured with a “pyrgeometer”: Records flux of radiation First filters out the solar wavelengths Dome isolates sensor http://en.wikipedia.org/wiki/File:Hukseflux_netto_radiometer_nr01_photo.jpg Net radiation measured with a net radiometer: measure all 4 components of Rn separately …or by measure net upward and downward total radiation (no filtering)

Diurnal (daily) cycle of radiation (clear sky) At Bergen, Norway 13 April 1968 Shuttleworth (2012) 11 January 1968

Ground heat flux +/- 200 W m G(z) = -ksoil dTsoil/dz ks is thermal conductivity, measure of how easily heat moves through the ground Upwards (downwards) when temperature increases (decreases) with depth Shuttleworth (2012) 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 w= vertical wind speed http://joewheatley.net/flux-towers-part-i/ w units: [L / T] units: [W/ m2] LE = λv ρa E w units: [W/ m2] Specific heat of air Gas analyzer 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 http://en.wikipedia.org/wiki/File:Eddy_Covariance_IRGA_Sonic.jpg

Latent heat turbulent flux: 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 KE u(zm) [es – e(zm)] -- called bulk formula in climate modeling KE = water-vapor transfer coefficient (p.126, using Fick’s law and the universal u distribution): zm is the measurement height (e.g., 2m) v (x106J/kg) = 2.50 – 2.36 x 10-3 T (oC) w =1000kg/m3 water and heat transfer

Sensible heat turbulent flux: 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 = KH u(zm) [Ts – T(zm)] KH = sensible-heat transfer coefficient (pp. 127-128): cp=specific heat of air at constant pressure =1.005x10-3MJ kg-1 K-1 water and heat transfer

Diurnal Variations in Surface Energy Fluxes

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

(W m-2)

(W m-2)

(W m-2)

Surface Energy Balance: SH E G Aw 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)=2.50-2.36x10-3 T(oC) is latent heat SH = sensible heat flux (positive upward) G = downward heat flux through conduction (often small) Aw = 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.