Evapotranspiration
- Rate and amount of ET is the core information needed to design irrigation
projects, managing water quality, predicting flow yields, ground water recharge,
etc.
- Only occurs when there is a vapor pressure gradient between the evaporating
surface and the air
- esat high during warm periods and actual vapor pressure (e) in air is low when
air is dry. Evaporation increases with saturation deficit (esat-e) and stops when it
is zero
- Dalton’s Law never expressed mathematically by Dalton, but simply states that
if other factors remain constant, evaporation is proportional to the wind speed
and vapor pressure deficit
- evaporation from a particular surface is directly related to availability of water
at that surface, or the opportunity for evaporation (ranges from 100% at open
water surfaces to essentially 0 for very dry soils)
- Within about 1 mm of the surface, water molecule transfer is by molecular
diffusion, after that it is by turbulent eddy transfer (eddy diffusion)
- as heat is added to a water body the molecules become increasingly
energized and move more rapidly, increasing the distance between the
molecules, and weakening the hydrogen bond. At high temperatures more of
the water molecules will “fly off” into the adjacent layer of air
- condensation occurs at same time
Factors affecting Evaporation from an open water surface:
1. Meteorology
a) energy (mostly solar)
b) wind
c) temperature at the air-water interface
d) humidity in the overlying air
2. Geographical
a) Water quality
- saline water has a reduced vapor pressure, and therefore evaporation
decreases about 1% for every 1% increase in salinity. Normally a small
consideration
- turbidity of the water can affect the heat budget, but generally not considered
b) Depth of water body
- residence time and annual turnover
c) Size of the water surface (fetch)
Additional factors specific to soils:
a) Soil moisture content
- Soil is different than open water surface because opportunity for evaporation is not
always 100%, can be more or less
- evaporation decreases as the soil surface dries, therefore more rain is evaporated
in small frequent storms than in large infrequent storms
b) Soil capillary characteristics
- capillary rise is affected by soil texture. < in sandy soils > in clay soils
c) water table depth
d) soil colour - darker soils absorb more heat
e) presence of vegetation - shading effects
f) snow cover
Physics of Evapotranspiration
Fick’s 1st law of diffusion
“A diffusing substance moves from where its concentration is larger to where its
concentration is smaller at a rate that is proportional to the spatial gradient of
concentration”
dC( X )
FZ ( X )   DX
dz
where
Fz(X) is the rate of transfer of a constituent X in direction z per unit area
per unit time (the flux of X)
C(X) is the concentration of X
D(X) is the diffusivity of X in the fluid (also called diffusion coefficient)
Evaporation is a diffusive process which follows Fick’s first law of Diffusion
Vapor pressure relations review:
1.
2. Latent-Heat Exchange
Evaporation causes a reduction in surface temperature due to latent heat
exchange, which may or may not be balanced by transfer of radiative or
sensible heat from the air to the surface
rate of latent transfer is simply the rate of evaporation times the latent heat
of vaporization and the mass density of water
LE = ρwλvE
λv (latent heat of vaporization) decreases as the temperature of the
evaporating surface increases..
Sensible-Heat Exchange
Upward rate of sensible heat exchange is given by the finite-difference
equation:
H is the upward rate of sensible heat exchange by turbulent transfer
KH is a measure of the efficiency of vertical transport of sensible
heat by turbulent eddies..
Bowen Ratio
The ratio of sensible heat exchange to latent heat exchange is called the
Bowen Ratio
or combining the equations:
ca P(Ts  Ta )
B
0.622v ( es  ea )
ca is the heat capacity of air (1.005 J/g/°C)
P is atmospheric pressure..
Therefore the Bowen ratio depends on the ratio of surface-air temperature
difference to surface-air vapor pressure difference times the psychrometric
constant (γ)
- γ is sometimes entered into ET estimates as a separate term
- not strictly a constant because P and λv vary with altitude and
temperature..
Energy Balance for an evaporating surface
LE = K + L - G - H + Aw - ΔQ/Δt
LE through Aw are average energy fluxes (energy gained or released per unit
area per unit time) through:
LE
K
net shortwave radiation input
L
net longwave input
G
net output via conduction to ground
H
net output of sensible heat exchange with the atmosphere
Aw
water advected energy (from inflows and outflows)
The term ΔQ/Δt is the heat change in the evaporating body per unit area over
the given time period..