1. 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

2. 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

3. 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

4. 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)

5. 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

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

7. 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

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

9. 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

10. “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

11. 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)

12. Downward solar radiation (top of atmos. or TOA)
(Appendix D)
0 to 1367 W m-2
[W m2]
Determined by:
Radiation emitted by the sun
Distance of earth from the sun
Solar zenith angle
Number of daylight hours

13. See section 2.7 of Hartmann GPC

14. 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

15. 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)

17. 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)

18. 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
Cloud factor
Near-surface atmospheric values

19. - + - = 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)

20. 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 Rn separately
…or by measure net upward and downward total radiation (no filtering)

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

22. 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)

23. 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

24. Directly measuring sensible and latent heat fluxes
w= vertical wind speed 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

25. 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

26. 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 ):
cp=specific heat of air at constant pressure
=1.005x10-3MJ kg-1 K-1
water and heat transfer

27. Diurnal Variations in
Surface Energy Fluxes

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

29. (W m-2)

30. (W m-2)

31. (W m-2)

32. 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)= x10-3 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.