Evaporation

Transpiration

Topics Evaporation from water, bare soil and transpiration from

plants

Calculation of ET with use of water budget and energy budget

Potential vs actual ET

Based on:

Chow: Applied hydrology; van Dam: Transport in the Atmosphere -Vegetation - Soil Continuum; Maidment: Handbook of Hydrology; Fares: Handouts on Watershed Hydrology;

Moene and van Dam: Transport in the Atmosphere – Vegetation – Soil Continuum; Kramer and Boyen: Water Relations of Plants and Soils

Evaporation, evapotranspiration

Usgs.gov

…when liquid water is converted into water vapor

ET

- evaporation (E): direct transfer of water from open water bodies or soil surfaces

- transpiration (T): indirect transfer of water from root-stomatal system

Potential evaporation Evaporated water from an idealized free water surface under

given atmospheric conditions

Reference crop evapotranspiration …from an idealized grass crop with height of 0.12 m, an albedo

of 0.23.

Crop completely shades the ground and is not short of water

Three main factors affect E or T from evaporating & transpiring surfaces:

Supply of energy to provide the latent heat of evaporation (solar radiation)

Ability to transport the vapor away from the evaporative surface (wind and humidity gradient)

Supply of water at the evaporative surface

CondensationVaporization

Air is saturated when condensation = vaporization -> reached at saturated vapor pressure (temp dependent)

Sensible heat – energy warming up the air at the ground which is then moving upwards

Energy budget

G

H lE

Rn

Rn … net radiant energylE … energy as evaporation (latent)H … sensible heat fluxG … heat conduction into soilS … stored energy (usually neglected)P … absorbed energy by plants (~2%)Ad … loss due to horizontal air

movement (neglected)

P

SAi

dA0

d

lE + H = Rn – G – S – P - Ad (MJ M-2 day-1)

Vapor Diffusion

Molecular diffusion

Controlled by boundary layer resistance

Most important on plant leaves –stomata

Turbulent diffusion

Primer process

Wind

Effect depends on aerodynamic resistance of the canopy

Water movement in plants -Evapotranspiration

Illustration of the energy differentials which drive the water movement from the soil, into the roots, up the stalk, into the leaves and out into the atmosphere. The water moves from a less negative soil moisture tension to a more negative tension in the atmosphere.

Evaporation calculation Aerodynamic method (Thornthwaite – Holzman)

Use of measurement towers (eddy correlation) Humidity gradient + wind speed - > vapor flux

Combination methods Bowen Penman

Suited for small areas with decent climatological data Usual data: net radiation, air temperature, humidity, wind speed,

air pressure

Evaporation calculation Penman-Monteith

Available energy A = evaporation E + sensible heat H Canopy represented by “one big leaf” in a reference height Calculated from meteorological variables: (reference evapotranspiration)

𝐸𝑟𝑐 =∆

∆ + 𝛾∗(𝑅𝑛−𝐺) +

𝛾

∆ + 𝛾∗900

𝑇 + 275𝑈2𝐷

Psychrometric constant 𝛾 = 0.0016286𝑃

𝜆… P is atmospheric pressure

𝛾∗ = 𝛾 (1 + 0.33𝑈2)Rn … net radiation exchange for the crop coverG … soil heat fluxU2 … wind speed at 2 mD … vapor pressure deficit (es – e)T … temperature at 2 m

Saturated water pressure 𝑒𝑠 = 0.6108𝑒17.27𝑇

237.3+𝑇

Vapor Pressure gradient Δ =4098 𝑒𝑠

(237.3+𝑇)2

Latent heat 𝜆 = 2.501 − 2.361 𝑇𝑠

Evapotranspiration Calculated based on the same methods as from open

water Reference crop evapotranspiration (Er)

…from an idealized grass crop with height of 0.12 m, an albedo of 0.23.

Crop completely shades the ground and is not short of water

Potential evapotranspiration Crop coefficient kc (0.2 < kc < 1.3)

𝐸𝑝 = 𝑘𝑐𝐸𝑟

Actual evapotranspiration Soil coefficient a (0 < a < 1)

𝐸𝑎 = a 𝑘𝑐𝐸𝑟

Potential ET

Actual ET (according to Feddes)

Root water uptake distribution

Evaporation calculation From an open water surface (energy balance method)

𝐸 =𝑅𝑛

𝜆𝜌𝑤Latent heat 𝜆 = 2.501 − 0.002361 𝑇 (𝑀𝐽 𝑘𝑔

− 1)

Water density = 997 kg/m3

lE + H = Rn – G – S – P - Ad

Er … evaporation rate from previous example

Saturated water pressure 𝑒𝑠 = 0.6108𝑒17.27𝑇

237.3+𝑇

Pressure gradient Δ =4098 𝑒𝑠

(237.3+𝑇)2

Latent heat 𝜆 = 2.501 − 0.002361 𝑇

𝛾 = 0.0016286𝑃

𝜆, where atm. pressure = 101.3 kPa