CIVL3101: Hydraulics and Hydrology
Evaporation & Evapotranspiration
Lecturer: Dr Fatemeh Salehi
Today’s topics
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Evaporation
Transpiration
Evapotranspiration
Estimation of evapotranspiration
• Recommended reading
✓ Section 5 of Handbook of Applied
Hydrology, Second Edition, by Singh
(2017).
Reminder from previous week
Reminder from previous week
Rainfall measurement
Processing rainfall data
• Scrutiny of rainfall data: Time series analysis
• Scrutiny of rainfall data: Statistical tests
• Scrutiny of rainfall data: Spatial consistency
• Spatial averaging of rainfall data
• Arithmetic average method
• Thiessen polygon method
• Isohyetal method
Evaporation, Transpiration & Evapotranspiration
Evaporation + Transpiration = Evapotranspiration!
https://svs.gsfc.nasa.gov/10926
Evaporation & Evapotranspiration
• Evaporation is the process by which liquid water from water bodies (rivers,
ponds, lakes) or soil is converted to vapor (often presented as mm/h).
• Crops and trees transpire large portions of water that is applied through
irrigation or is received through rainfall.
• Evaporation and transpiration together constitute what is called
evapotranspiration (ET).
• The importance of ET depends upon the time scale and the type of
hydrologic event.
• ET is an important process in the water cycle because it is responsible for
15% of the atmosphere’s water vapor
Evaporation process
Evaporation process
• The conversion of liquid water into water vapor requires energy.
• Evaporation involves the transfer of energy, and hence the molecules that
have energy to break all bonds with their neighbours and move into the air
will evaporate.
• Evaporation is high when the vapor pressure of air is low, which means that
the gradient between the vapor pressure of air and that of water is low.
• Heat energy, which is essential for evaporation, is derived generally from
solar radiation. The relative humidity of air and the wind velocity across the
water surface also influence the rate of evaporation.
Evaporation process
• Water molecules in a water body are tightly held by intermolecular forces. In
evaporation, energy is consumed to overcome these forces and move the
molecules away.
• The energy required to move to the vapor form is called the latent heat of
vaporization (λ), and is about 2.5 MJ/kg, depending on temperature:
𝝀 = 𝟐. 𝟓𝟎𝟏 − 𝟎. 𝟎𝟎𝟐𝟑𝟔𝑻
Atmosphere
Water vapor
Vaporization
T is the temperature of water in degrees Celsius
𝝀 is in MJ/kg
Water body, Temperature (T)
Condensation
Evaporation: Important factors
Temperature
Wind speed
Humidity
Soil type
Evaporation
Water
quality
Atmospheric
pressure
Radiation
Vapor
pressure
Evaporation: Important factors
Temperature
• Temperature is affected by geographical location altitude, season, and
distance from the sea or ocean.
• Temperature is influenced by the exchange of air masses and by cloudiness
and follows diurnal and seasonal cycles.
• Temperature falls with altitude at approximately 0.6°C/100 m rise in
elevation for moist air and 0.9°C/100 m for dry air. Hence, evaporation is less
at higher altitudes.
• The temperature variation near large water bodies, such as seas, is less due
to the moderating influence, and hence the annual and diurnal range is
smaller.
Evaporation: Important factors
Relative humidity
• Relative humidity typically expressed in percent, can be defined as the ratio
of the actual vapor pressure of air to the saturation vapor pressure at the
same pressure and temperature.
• Due to the availability of moisture, places close to the sea and large open
water bodies have higher RH and a smaller daily variation than the other
locations. RH does not vary rapidly with time.
Evaporation: Important factors
Wind speed
• The wind speed at a place is controlled by the pressure gradient, which
depends on temperature, topographic features, and land use/cover.
• Wind speed shows a wide variation with place and time.
Vapour pressure
• Because air is less dense at lower atmospheric pressures, the likelihood of
collision of water molecules escaping in the air with air molecules reduces
with atmospheric pressure. For this reason, evaporation is more when
atmospheric pressure is low.
• The vapor pressure of water is reduced when solids are dissolved in water.
• Pure water has a higher vapor pressure than saltwater.
Evaporation: Important factors
Soil type
• Because there is a wide range of purity of water present in nature, it is very
difficult to predict the effect of dissolved minerals in any given body of water
on evaporation.
• Precipitation that is ponded on a drainage basin and intercepted
precipitation are evaporated rapidly after rainfall, when insolation provides
renewed heating. The effect of this heating is increased because dark soils
and other dark objects absorb incoming radiation and convert it to heat
more effectively than lighter-coloured soils and objects
Evaporation measurement
• The evaporation pan, a small, shallow vessel filled with water and placed in an open
area and exposed to weather, is the most widely used device to measure
evaporation.
• The water level in the pan is measured carefully to determine how much water
(measured in terms of depth) is lost by evaporation.
𝑬 = 𝑷 ∓ ∆𝒅
• 𝐸 is the amount of evaporation between two successive observations
[mm].
• 𝑃 is the depth of precipitation during the period between the two
measurements [mm].
• ∆𝑑 is the depth of water added to (+) or removed from (−) the pan [mm].
Evaporation measurement
Errors in the data may occur due to the following:
• The observer may overfill or underfill the pan on a
particular day.
• Leakage is the most serious problem, which occurs
usually at the joint between the pan base and side wall.
• Animals and birds may drink the pan water, especially if
the covering wire mesh is damaged.
•
Algae and dirt, if present in the water, reduce the rate of
evaporation.
Errors arise during periods of high rainfall when the depth
caught by the rain gauge is different from the rain falling in
the pan as a result of splashing or wind eddies.
Evaporation measurement for a lake
• Evaporation data from pans are commonly used to estimate evaporation from lakes
and reservoirs.
𝑬𝑹 = 𝑲𝑷 𝑬𝒑
• 𝐾𝑃 is the pan coefficient.
• 𝐸𝑅 is the depth of evaporation from the reservoir
[mm].
• 𝐸𝑃 is the pan evaporation [mm].
The value of 𝐾𝑃 depends on climate, geographical location, season, and size and depth of the water body. It generally
varies from 0.6 to 0.85 (annual scale) and from 0.3 to 1.7 (monthly scale). Lower values are typical of dry seasons and
arid climates, while higher values are for humid climates. In the absence of better estimates, a pan coefficient value of
0.7 may be used.
Example #1
The surface area of a lake is 500 ha. Compute the daily evaporation for the data provided
below. Assume the pan coefficient is 0.8.
Day
1
2
3
4
5
6
Pan Evaporation
(cm)
1.5
2.2
0.6
1.2
0.7
1.7
Evaporation from water bodies
• Evaporation from water surfaces can be determined by different approaches
• water budget
• energy budget
• mass transfer methods
• combination methods
• evaporation formulas
Evaporation from water bodies: Water budget
• The water budget is a method of determining long-term evaporation.
𝑬 = 𝑰 + 𝑷 − 𝑶 − 𝑶𝒔 + ∆𝑺
• 𝐸 is the evaporation (𝑚3 ).
• 𝐼 is the inflow (𝑚3 ).
• 𝑃 is the precipitation (𝑚3 ).
• 𝑂 is the outflow (𝑚3 ).
• 𝑂𝑠 is the seepage (𝑚3 ).
• ∆𝑆 is the change in storage (𝑚3 ).
Evaporation from water bodies: Aerodynamic method
• This method computes evaporation by considering the ability of the atmosphere to
transport water vapor away from the evaporating surface.
• Thus, evaporation is a function of the difference between the saturation vapor
pressure at the surface at the ambient temperature and the vapor pressure at a
height 𝑧2 (cm) above the water surface.
𝑬=
𝟎. 𝟏𝟎𝟐𝒖𝟐
𝐥𝐧
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𝒛𝟐
𝒛𝟎
𝟐
𝑒𝑎𝑠
(𝒆𝒂𝒔 − 𝒆𝒂 )
𝐸 is the evaporation rate [mm/day]
𝑢2 is the wind velocity in at height 𝑧2 [m/s]
𝑧0 is the roughness height of water surface [cm]
𝑇 is the mean daily temperature [°C]
𝑒𝑎𝑠 is the saturated vapor pressure [Pa]
𝑒𝑎 is the vapour pressure [Pa]
𝑅ℎ is the relative humidity [-].
17.27𝑇
= 611 × exp
237.3 + 𝑇
𝑒𝑎 = 𝑅ℎ × 𝑒𝑎𝑠
Example #2
At a given location, the net radiation on May 1 was 180 W/m2, the air temperature was 25
°C, the wind velocity at 2-m height was 2.5 m/s, and relative humidity was 70%. Use the
aerodynamic method to determine the open water evaporation rate if the roughness height
is 0.04 cm.
Evaporation from water bodies: Energy budget
• Assuming unlimited availability of water, the evaporation rate is chiefly governed by
the amount of available radiant energy.
• The net amount of radiation available at the Earth's surface is obtained using
• 𝑅𝑛 is the net amount of radiation (MJ m-2/day).
• 𝑆𝑛 is the solar (shortwave) radiation (MJ m-2/day)
𝑹𝒏 = 𝑺𝒏 + 𝑳𝒏
• 𝐿𝑛 is the long-wave radiation (MJ m-2/day)
• The net amount of radiation available at the Earth's surface is obtained using
• 𝐸 is evaporation rate (m/s)
• 𝑅𝑛 is the net amount of radiation (W/m2)
• 𝜌𝑤 is the density of water (kg/m3)
• 𝜆 is the latent heat of vaporization ( J/kg)
𝑬=
𝑹𝒏
𝝀𝝆𝒘
Transpiration
Stomata are small openings in plant leaves for the exchange of moisture and gases with
the atmosphere. The number of stomata on a plant leave varies with the plant species,
and their function is vital to plant metabolism
Transpiration
• Transpiration is the process by which plants use water for their metabolism and
growth.
• Plants extract water from the soil through their roots and transfer it to the
atmosphere as vapor through stomata.
• During daylight, stomata actively transpire water vapor to the atmosphere, but they
close after sunset, and then transpiration ceases.
• They allow carbon dioxide to enter the plant in the process of photosynthesis.
Evapotranspiration
• Evapotranspiration (ET) includes transpiration
of water by vegetation, as well as evaporation
from water surfaces, soil, snow, ice, and
vegetation.
• ET estimation is necessary in many studies,
such as catchment modelling, agricultural
water management, determination of water
balance, and assessment of the impact of land
use changes on the hydrologic response.
Evapotranspiration
Evapotranspiration (ET) estimation methods
FAO-56 PM
HargreavesSamani
Jensen-Haise
ET
estimation
Thornthwaite
PriestleyTaylor
ET estimation: FAO-56 Penman-Monteith method
• This method links the evaporation dynamics with the flux of net radiation and
aerodynamic transport characteristics of a natural surface.
𝟗𝟎𝟎
𝟎. 𝟒𝟎𝟖∆ 𝑹𝒏 − 𝑮 + 𝜸 𝑻 + 𝟐𝟕𝟑 𝒖𝟐 (𝒆𝒔 − 𝒆𝒂 )
𝑬𝑻𝟎 =
∆ + 𝜸(𝟏 + 𝟎. 𝟑𝟒𝒖𝟐 )
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𝐸𝑇0 is the grass reference ET [mm/day]
∆ is the slope of vapor pressure versus the temperature curve [kPa/°C]
𝑅𝑛 is the net radiation at the grass surface [MJ m−2 /day]
𝐺 is the soil heat flux density [MJ m−2 /day]
𝑇 is the mean daily air temperature at 2-m height [°C]
𝑢2 is the mean hourly wind speed at 2-m height [m/s]
𝑒𝑎 is the actual hourly vapor pressure [kPa]
𝑒𝑠 is the hourly saturation vapor pressure [kPa]
𝑔
𝛾 is the psychrometric constant [= 0.4 𝑘𝑔 /𝐾]
ET estimation: The Hargreaves-Samani method
• This method is based on temperature, day of year, and latitude to calculate
evapotranspiration.
𝑬𝑻𝟎 = 𝟎. 𝟎𝟏𝟑𝟓𝑲𝑻 (𝑻 + 𝟏𝟕. 𝟕𝟖) × 𝑹𝒂 (𝑻𝒎𝒂𝒙 − 𝑻𝒎𝒊𝒏 )𝟎.𝟓
• 𝐸𝑇0 is the grass reference ET [mm/day]
• 𝑅𝑎 is the mean extra-terrestrial radiation in term of water evaporation it is a function of
latitude [mm/day]
• 𝑇 is the mean daily temperature [°C]
• 𝑇𝑚𝑎𝑥 is the maximum daily temperature [°C]
• 𝑇𝑚𝑖𝑛 is the minimum daily temperature [°C]
• 𝐾𝑇 is a region dependent coefficient and can be generally taken as 0.162.
• The method is derived for semiarid conditions and does not explicitly account for
relative humidity. Hence, it may overestimate ET in humid regions.
ET estimation: The Thornthwaite method
• This method is based on monthly mean air temperature and heat index to calculate
evapotranspiration. Assuming that each month has 30 days, and each day has 12
hours of sunshine:
𝟏𝟎𝑻
𝑬𝑻 = 𝟏. 𝟔𝟐
𝑰
𝒂
12
𝑇𝑚
𝐼 = ෍ ( )1.51
5
𝑎 = 0.492 + 1792 × 10−5 𝐼 − 771 × 10−7 𝐼 2 + 675 × 10−9 𝐼 3
𝑚=1
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𝐸𝑇 is the potential evapotranspiration [cm/month]
𝐼 is the annual heat index obtained from monthly heat indices
𝑎 is an exponent as a function of the annual heat index
𝑇𝑚 is the mean monthly air temperature [°C]
• Under dry and arid conditions, it strongly underestimates ET - because it does
not consider the saturation deficit of air.
• At high altitudes, it also underestimates the effect of radiation.
Example #3
Using the Thornthwaite method, estimate the potential ET if mean monthly temperature is
25°C.
ET estimation: The Priestley-Taylor method
• This method is a simplified form of the Penman equation that needs only net
radiation and temperature to calculate evapotranspiration. This simplification is
based on the observation that ET is more dependent on radiation than on RH and
wind:
∆(𝑹𝒏 − 𝑮)
𝑬𝑻𝟎 = 𝜶
+𝜷
∆+𝜸
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𝐸𝑇0 is the grass reference ET [mm/day]
𝛼 and 𝛽 are calibration factors whose recommended values are 1.26 and 0, respectively
𝛾 is the psychrometric constant [kPa/°C]
∆ is the gradient of saturated vapor pressure (𝑘𝑃𝑎/°𝐶)
𝑅𝑛 is the net radiation at the grass surface [MJ m−2 /day]
𝐺 is the soil heat flux density [MJ m−2 /day]
• It underestimates ET in winters because net radiation is often negative in winters and
the method predicts dew formation, while the actual ET is positive.
ET estimation: The Jensen and Haise method
• Assuming that ET is more closely related to net radiation than other variables such
as air temperature and humidity, this method uses measured ET and solar radiation
data to derive the equation to estimate ET:
𝑬𝑻 =
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𝑪𝒕 𝑻 − 𝑻𝒙 𝑹𝒔
λ
𝐸𝑇 is the reference ET [mm/day]
𝐶𝑡 is the temperature coefficient [-]
𝑇 is the mean temperature for a 5-day period [°C]
𝑇𝑥 is the intercept of the temperature axis [°C]
λ is the latent heat of vaporization [MJ/kg]
𝑅𝑠 is the solar radiation received on the Earth's surface at a horizontal surface [MJ m−2 /day]
ET estimation: The Jensen and Haise method
• The temperature constant, 𝐶𝑡 , and the variable 𝑇𝑥 are given as:
1
𝐶𝑡 =
𝐶1 + 7.3𝐶𝐻
5
𝐶𝐻 =
𝑒2 −𝑒1
𝐶1 = 38 −
2ℎ
305
𝑇𝑥 = −2.5 − 0.14 𝑒2 −𝑒1 −
ℎ
550
• ℎ is the altitude of the location [m]
• 𝑒2 and 𝑒1 are the saturation vapor pressure at the mean maximum temperature and the mean
minimum temperature [kPa]
Example #4
Compute the ET using the Jensen-Haise method if the following data are available: the
mean air temperature = 25°C, latitude = 30°N, 𝑅𝑠 = 700 ly/day, the mean maximum
temperature of the warmest month = 30°C, the mean minimum temperature of the
warmest month = 20°C, and the elevation = 200 m.