ATM 301 Lecture #11 (sections ) E from water surface and bare soil

Homework #4 (on ET, due 11/03) 1. Ex. 1a on p. 307 (part a only). (5%) 2. Ex. 2 on p. 307 (12%) 3. Ex. 3 on p. 308 (20%) 4. Ex. 9 on 309 (Correction: use Eq. (5.57), not (5.56); use a shelter factor k s =0.5; the symbol C* stom in the table should be C* leaf ) (18%) 5. In your own words, describe the basic processes involved in a) evaporation over a water surface, b) transpiration by plants, and c) interception loss. (15%) 6. What are the main controls on evaporation and how do they affect evaporation over a) a free-water surface, b) bare soil, and c) a vegetated area? (10%) 7. What are the common methods used to estimate the evaporation rate from a free-water surface? (10%) 8. What are the difference and the relationship between the potential evapotranspiration and the actual evapotranspiration? (10%)

E over free-water surface (such as lakes) and wet soils is energy-limited E over dry soil is water-limited Evaporation from free-water surface and bare soil

Free-water or Potential Evaporation (E o ) : Is the rate of evaporation that would occur from an extended open-water surface under current meteorological conditions without heat-storage or water-advected-energy effects, i.e., the G, A w and dU/dt terms are zero in the surface energy eq.: E = R n – SH – G + A w – dU/dt = R n - SH E o is a theoretical concept for developing methods for estimating E over free-water surface. It represents atmospheric demand for moisture from the surface under a given meteorological condition. PET is the evaporation with unlimited water supply, such as that over a wet surface. Lake Evaporation: actual E over a lake is the rate of evaporation over a lake surface. It can be determined by adjusting the free- water E o to account for the advection and heat-storage effects. Actual Evaporation (E) is the rate of evaporation over an actual surface. Direct measurements are for actual E E is often water-limited over most land areas E is energy-limited at high latitudes

1. 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

2. Mass transfer method (based on the 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 K E u(z m ) [e s – e(z m )], E = K E u(z m ) [e s – e(z m )] 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, p is air pressure in kPa (=101.3kPa at sea level), A L is lake area in km 2. One empirical form: E (mm/day) = 1.5 u(2m) [e s – e(2m)] where u= 2m wind speed in m/s, e s and e(2m) are surface saturation and 2m vapor pressure in kPa Need measurements of 2m wind speed and vapor pressure and surface temperature for e s (Ts).

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. Recall: 3. Surface Energy Balance: S L SH E G AwAw SH = K H u(z m ) [T s – T(z m )]

3. The Bowen Ratio Method for Estimating actual E: The Bowen ratio is the ratio of the sensible to latent heat fluxes: B  SH/LH where is the psychrometric constant E can be estimated using surface energy balance eq.: Requires accurate estimates of R n, G, and B. G is often assumed to be small over ground.

4. The Combined Method – the Penman Equation for E o : Combine the bulk formula for SH and LH, and use the sfc. energy balance and the slope  =de s /dT to remove “T s -T(z m )” from the eqs., one can derive the Penman Eq. (see Box 6.3 on p. 265): SH = K H u(z m ) [T s – T(z m )], E =  w v K E u(z m ) [e s – e(z m )],  = [e s –e s (z m )] / [T s -T(z m )] z m = measurement height (e.g., 2m) for wind speed (u) and relative humidity (RH) R n = net surface radiation. Need estimates of R n, RH, u, RH and T. Net heating Dryness of air Resistance

Penman E o Compares Well with Obs. It is the standard method for estimating free-water E Penman E o Compares Well with Obs. It is the standard method for estimating free-water E Penman Obs.

5. Pan Evaporation (E pan ) – An approximation of PET Pan evaporation is the evaporation rate from a shallow pan of water exposed to the atmosphere, estimated by the water balance: where P = precipitation over the measurement time period (often a day) S 1 and S 2 is the water volume in the pan at the start and end of the period. Many U.S. weather stations make E pan Practical issues: Heat conduction can affect E pan Water depth may affect E pan “Class A” pan is standard for US National Weather Service

Pan Evaporation vs. Free-water Evaporation: A pan of water differs from free water in a lake (e.g., lower heat storage capacity, etc.), which generally leads to higher evaporation from a pan than from a lake. Pan coefficient: the ratio of lake evaporation to pan evaporation. About 0.7 for the U.S. but varies with season. E pan can be adjusted to represent the “free-water” E at the same location (see p. 268): E o  0.7 E pan Heat storage in a lake causes lake water temperatures to lower in Spring and higher in Fall than those of pans, causing the seasonal variations in the pan coeff.

U.S. Annual Pan Evaporation (in inches)

6. Water-balance Approach: The water balance equation can be used to estimate the actual evaporation over a region (e.g., a lake or reservoir): where P = precipitation, Q in and Q out are the inflows and outflows of surface water, and GW in and GW out are the inflows and outflows of ground water, and  S is the water storage change. Practical issues: Difficult to estimate the GW, Q,  S, and even P terms Often with large uncertainties

Summary of Evaporation Estimates over Free Water: There are a number of studies comparing the various methods to estimate E over a lake or reservoir; Near-surface net radiation, air temperature, wind speed, and relative humidity are found to be important for estimating E; Energy storage in a water body needs to be considered; The Penman method and energy balance methods seem to perform well.

Example Calculations of Free-Water Evaporation:

H = K H u(z m ) [T s – T(z m )] R n = K + L = K d (1-  ) + ε s L d – ε s σT s 4 ε s = 1 - 

What does this negative B mean?

- Penman Eq:

Method

Evaporation over Bare Soil (a.k.a. Exfiltration): Over one-third of global land surface has little or no vegetation Agricultural lands have little vegetation cover over much of the time Thus, bare-soil evaporation is important for global land and for agriculture

Evaporation over Bare Soil: Following infiltration due to rain, snowmelt or irrigation, evaporation from a wet bare soil occurs in two stages: Stage 1: Atmosphere-controlled E rate (E 1 ) depends on surface energy balance and mass transfer (wind and humidity) E 1 is close to E o over free-water surface Soil water moves to the surface by capillary action The Penman eq. for E o can be used to estimate E 1

Evaporation over Bare Soil: Transition Period: As the soil dries, the menisci began to detach from the surface to form a dry front (Fig. 6.9a) The depth of this dry front is typical 3-14mm, and is larger for clays than for sands. The E 1 decreases to approach a constant rate during this period The transition period may last for several days as the dry font descends

Evaporation over Bare Soil: Stage 2: Soil-Controlled Evaporation rate (E 2 ) is nearly constant E 2 is around 0.7 (for sand) to 3.5 (for clay) mm/day, much lower than E 1 E 2 is controlled by soil’s physical properties, not by surface atmospheric conditions Vapor diffusion rate through the dry layer is critical

Evaporation over Bare Soil: Estimate of Stage 2 Evaporation Rate E 2 Soil dries up by both gravity-induced drainage and evaporation loss Assuming drainage rate is larger than evaporation, E 2 during the transition period and Stage 2 can be estimated as How does this estimate compare with observations?

Bare-soil Evaporation: Obs (  ) vs. calculated (line) Good match after t 1 t 1 is associated with large albedo increases