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”

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

F X DdC X

dzZ X( )( )

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 is the heat capacity of air (1.005 J/g/°C)

P is atmospheric pressure..

Bc P T T

e ea s a

v s a

( )

. ( )0 622

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..