EVAPORATION GEOG 405

Tom Giambelluca

1 Evaporation

The change of phase of water from liquid to gas; the net vertical transport of water vapor from the surface to the atmosphere.

2 Definitions • Evaporation: (specific) flux of water vapor from open water surface, wet vegetation, or wet soil; (general) total flux of water vapor from the surface to the atmosphere. • Transpiration: water vapor transfer to the atmosphere occurring primarily through the stomata of living plants. • Evapotranspiration (ET): total flux of water vapor from the surface to the atmosphere (same as the general use of “evaporation”). • Potential Evapotranspiration (PE): the environmental demand for evaporation; the

evaporation rate if moisture is not limiting. 3 ET and Hydrological Cycle

ET is one of the primary links in the hydrological cycle. 4 What Controls Evaporation?

For a water surface, the net rate of liquid-to-gas transition depends on:

• Humidity of the air (vapor pressure)

• Temperature of the water surface (saturation vapor pressure)

5 Evaporation

Aerodynamic issues • The humidity gradient (vapor pressure gradient) near a moisture source controls the rate of evaporation. • The mean vapor pressure gradient over a complex vegetated surface is impossible to measure. • Turbulent exchange influences the vapor pressure gradient by transporting humid air away from the evaporating surface and replacing it with drier air. • Wind speed, the vertical temperature gradient, and the roughness of the surface influence the vapor pressure gradient by controlling the amount of turbulence. • Temperature influences the vapor pressure gradient by controlling the saturation value. 6 Evaporation

Energy balance issues • Evaporation requires energy. • If no energy is added to the evaporating surface, via radiation or advection, the surface will cool, causing evaporation to be reduced or stopped. • To maintain evaporation at a certain rate, the net energy input must be sufficient. • By accounting for all the other inputs and outputs of energy to the surface, the amount of energy used for evaporation (latent energy) can be estimated.

7 NET RADIATION

Rnet = K ↓ −K ↑ +A ↓ −L ↑ where :

Rnet = net radiation A ↓= downward longwave radiation absorbed by the surface L ↑= upward longwave radiation emitted by the surface

GEOG 402: Radiation Balance 8 NET RADIATION

Rnet = K ↓ −K ↑ +A ↓ −L ↑ 4 Rnet = (1−α)K ↓ +A ↓ −ε sσTs 4 Rnet = (1−α)K ↓ +ε s (L↓ −σTs ) where α = albedo

ε s = surface emissivity

Ts = surface temperature L↓ = downward longwave radiation from atmosphere

GEOG 402: Radiation Balance 9 Latent Heat of Vaporization

λ = 2.454 x 106 J kg-1 at 20ºC -1 -1 The specific heat of water (Cw) = 4186 J kg K . Thus, it takes about 586 times as much energy to evaporate a kg of water as it does to raise its temperature by 1º. Example: Typical summer evaporation rate: 5 mm day-1 (mm per day) Water density: 1000 kg m-3 5 mm = 5 kg per square meter

Energy used to kg Convert1 d daysay to Multiply by latent heatJ of W evaporate 5 mm 5 2 × seconds ×vaporization24540 0of 0water =142 2 m day 86400 s kg of waterm Latent Heat of Vaporization λ = 2.454 x 106 J kg-1 at 20ºC Another way of stating the latent heat of vaporization: The amount of latent heat flux per mm/day of evaporation:

Examples: (a) E = 5 mm per day: λE = 5 mm day-1 x 28.4 W m-2 per mm day-1 = 142 W m-2

(b) λE = 110 W m-2 : E = 110 W m-2 / 28.4 W m-2 per mm day-1 = 3.88 mm day-1

Evaporation Estimation approaches Direct water loss measurements • Evaporation pans • Lysimeters • Soil water balance Soil water balance modeling • Potential evaporation: Penman, Priestley-Taylor, Penman-Monteith Meteorological Methods • Profile method • Penman-Montieth equation • Bowen ratio-energy balance • Resistance-energy balance • Temperature variance-energy balance • Scintillometer-energy balance

• Eddy covariance 12 Evaporation Pan

13 Weighing Lysimeter

14 Soil Water Balance

RF Irr ET Measure: RF RO Irr ΔSM ΔSM Estimate: RO GWR GWR Get ET by difference 15

Soil Water Balance Modeling

Measure: RF Irr ET RF, Irr RO Rn, T, RH, U Estimate: ΔSM PE RO Use water balance to get GWR ET GWR

ΔSM 16 Meteorological Approaches The evaporation rate can also be understood in terms of an Ohm’s Law analogue. R

In this case, the evaporation rate is driven by the vapor pressure gradient and limited by resistance to transfer of water vapor molecules away from the surface:

ρCp (e s[Tsurface ] − e) λE = γ rW ρ = air density (kg m-3 ) C ⋅ P γ = psychrometric "constant" = p ε ⋅ λ -1 -1 Cp = specific heat of air at constant pressure = 1005 J kg K λ = latent heat of vaporization (MJ kg−1)

rW = resistance to transfer of water vapor from the surface; 17 depends on wind speed and surface aerodynamic characteristics Meteorological Approaches

e s[Tsurface ] − e

Note that the vapor pressure gradient is sometimes approximated (using the saturation vapor pressure of the air rather than that of the water surface) as the vapor pressure deficit:

VPD = es - e

18 Potential Evapotranspiration Penman Equation:

ΔH +γE E = a 0 Δ +γ where:

E0 = open water evaporation (pan evaporation; potential evaporation)

Δ = slope of the saturation vapor pressure vs. temperature curve at Ta H = net radiation in evaporation units (Rnet/28.4) γ = psychrometric constant

Ea = aerodynamic term aerodynamic term is an empirical function of wind speed and vapor pressure defi19ci t Parameter Estimation

• Δ = 4096*(0.6108*exp(17.27*T/(T+237.3)))/((T+237.3)^2) • γ = Cp*P/(λ*0.622) • λ = (2500.8-2.36*T+0.0016*T^2-0.00006*T^3)/1000

Constant: -1 -1 Cp = 0.001013 specific heat of air at constant press. (MJ kg K )

Variables: T = air temperature (°C) P = air pressure (kPa)

20 Potential Evapotranspiration

Priestley-Taylor Equation:

21 Penman-Monteith Equation

22 Bowen Ratio H Bowen Ratio : β = or H = β ⋅ LE LE

Energy Balance: Rnet − G = H + LE R − G Combining, we get : LE = net β +1 Need independent estimate of β :

c p ΔT β = λ Δq where : β = the Bowen ratio c p = specific heat of air at constant pressure λ = latent heat of vaporization ΔT = vertical temperature gradient

Δq = vertical humidity gradient 23 Bowen Ratio

24 Resistance Method

25 Other Methods of Estimating H

Temperature Variance Method: based on rapid fluctuations in air temperature g p ⎜⎛ ⎟⎞ 1.5 H = hσρC z -d σT ⎝ ⎠ T

Scintillation Method: based on optical disturbance of air by thermally-induced density differences

26 Scintillometer

27 Eddy Covariance

Method based on correlation of a scalar (e.g. temperature, humidity, carbon dioxide concentration) fluctuations with vertical wind speed variations.

LE = Lvρv' w'

H = CpρT'w'

28 Eddy Covariance

29 Eddy Covariance

30 Eddy Covariance

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