This lecture note is about the evaporation and evapotranspiration

1. E-mail: getachewtegegne21@gmail.com
Hydrology
Africa Center of Excellence for Water Management
Addis Ababa University
Getachew Tegegne (Ph.D.)
Hydrologic, Hydraulic and Water Resources Engineering

2. 3. Evaporation and Evapotranspiration
3.1 Factors controlling evaporation
3.2 Evaporation from free water surface
3.3 Estimation of evaporation and evapotranspiration

3. 3. Evaporation and Evapotranspiration
 Terminology
 Evaporation – the process through which water is transferred from the surface of
the Earth to the atmosphere
 Transpiration - the water loss from the plants, through the pores at the surface
of their leaves
 Evapotranspiration – Evaporation + Transpiration
 Evaporation is important in all areas of water resources because it affects:
 The capacity of the reservoir,
 The yield of river basin,
 The consumptive use of water

4.  It is the maximum amount of water that could be evapotranspirated at a site.
 Potential Evapotranspiration (PET):
 Index of dryness or aridity index (AI):
𝑃𝐸𝑇: mean annual potential evapotranspiration
𝑃: mean annual precipitation
𝐴𝐼 =
𝑃𝐸𝑇
𝑃

5. a) Meteorological factors
b) The nature of the evaporating surface
3.1 Factors controlling evaporation
a) Meteorological factors
 Solar radiation:
 Evaporation is a process of energy exchange.
 Solar radiation supply the energy necessary for the liquid water
molecules to evaporate.
 Relative humidity:
 As the humidity of air increases its ability to absorb more water
vapor decreases, and the rate of evaporation becomes slower.

6.  The temperature of air:
 Temperature increase saturation vapor pressure (increases saturation deficit),
high temperature implies that there is energy available for evaporation.
 Wind:
 As the liquid water vaporizes from a water body, the air adjacent to this body
will be saturated. For the continuation of evaporation, this saturated air should
be removed by wind.
 10% change in the wind speed  1-3% change in evaporation.

7. b) The nature of the evaporating surface
Temperature of liquid water:
 High liquid water temperature
High molecular motion in the water
The number of molecules leaving the water body will be high
 Salinity:
 Adversely affects evaporation
 1% increase in salt concentration  1% decrease in evaporation
 Reflection coefficient (albedo) of the surface:
 High albedo  Low evaporation from the surface

8.  In general, the two main factors that affect evaporation from an open water
surface are: the supply of energy (solar radiation) and the ability to transport the
vapor away from the evaporative surface (depends on the wind velocity).
 The potential evapotranspiration (PET) is the evapotranspiration that would occur
from a well vegetated surface when moisture supply is not limiting, and this is
calculated in a very similar to that for open water evaporation.
 Actual evapotranspiration drops below its potential level as the soil dries out.
Potential evapotranspiration (PET) is
defined as the amount of ET that would
occur if a sufficient water source were
available.
Actual ET (AET) is limited by the actual soil
moisture. It might be smaller than PET.

9.  Evaporation
 How to measure it?
 Mass Balance – account for all inflows, all
outflows
 Land Pan (4ft diameter, 10 inches deep
unpainted galvanized metal)
 Daily records of depth of water,
precipitation, replacement water and
wind record – empirical relationships

10.  Problems
o Averages (One daily/weekly/monthly vs.
Continuous)
o Highly variable depending on conditions
o What does a pan tell us about say something
the size of a lake?
o Empirical Corrections – EMPIRICAL!!
o Works well in lab where conditions are well
controlled, but real life is not so simple
o Penman Formula (Semi-Empirical)

11.  Transpiration
 Transpiration is the process by which moisture is
carried through plants from roots to small pores
on the underside of leaves, where it changes to
vapor and is released to the atmosphere.
 Transpiration is essentially evaporation of water
from plant leaves.
 Studies have revealed that about 10 percent of
the moisture found in the atmosphere is released
by plants through transpiration.

12.  Evapotranspiration
 In the field it is next to impossible to
distinguish between evaporation and
transpiration so we lump them together.
 From a water budget perspective we
don’t care too much about the details
How to measure it?

13.  The estimation of evaporation from free water surfaces is necessary for mainly two
purposes:
3.2 Evaporation from free water surface
a) The determination of actual evaporation taking place from an existing
reservoir for an optimum operation of the reservoir.
b) The estimation of future evaporation from a reservoir to be constructed.
 The evaporation from free water surface can be estimated using evaporation pans

14.  Evaporation from water surfaces can be determined by:
1) Water budget
2) Energy budget
3) Mass transfer methods
4) Combination methods
5) Evaporation formulas
Water Budget?
 The water-budget equation for estimating evaporation can be written as:
𝐸 = 𝐼 + 𝑃 − 𝑂 − 𝑂𝑆 + ∆𝑆
Where, E =Evaporation, I = Inflow, P = Precipitation, O = Outflow, Os = Seepage
and ΔS = Change in storage

15.  Water budget (storage equation) approach
 This method consists of drawing up a balance sheet of all the water entering and
leaving a particular catchment or drainage basin.
 Continuity Equation:
where
∆S : change in storage (S2 – S1)
P: precipitation
QS: surface inflow
Q0: surface outflow
QSS: subsurface outflow (seepage)
∆t: week, month or year.

16.  Energy budget method
where
QN: net radiation absorbed by the water body
Qh: sensible heat transfer
Qe: energy used for evaporation
Q: increase in energy stored in the water body
QV: advected energy of inflow and outflow
𝑄𝑁 = 𝑄𝑠 − 𝑄𝑟 − 𝑄𝑏
𝑄𝑁 − 𝑄ℎ − 𝑄𝑒 = 𝑄𝜃 − 𝑄𝑉
where
Qs: shortwave solar radiation
Qr: shortwave reflected radiator
Qb: longwave radiation to atmosphere
where
ρ: density of water (gr/cm3)
Le: latent heat of vaporization (cal/gr)
R : ratio of heat loss by conduction to
that by evaporation
𝐸 =
𝑄𝑁 + 𝑄𝑉 − 𝑄𝜃
𝜌𝐿𝑒 1 + 𝑅
𝑅 = 𝛾
𝑇𝑠 − 𝑇𝑎
𝑒𝑠 − 𝑒𝑎
where
γ : Psychrometer constant = 0.66 mb/°C.
Ts: water surface temperature in °C.
Ta: air temperature in °C.
es: saturation vapor pressure in mb.
ea: vapor pressure of the air in mb

17.  The following empirical aerodynamic equation was proposed by Dalton to estimate
the evaporation of open water
𝐸𝑜 = 𝑓(𝑈)(𝑒𝑠 − 𝑒𝑑)
where f(U) is a function of the wind speed, es is the saturation vapor pressure
corresponding to the temperature Ts of the laminar sub-layer at the surface, ed is
the actual vapor pressure of the air at a standard height (usually 2 m).
 Some examples of the aerodynamic approach to compute Eo in mm/day are:
a) Ijssel Lake (the Netherlands)
𝐸𝑜 = 0.25(1 + 0.25𝑈6)(𝑒𝑤 − 𝑒𝑑)
b) Lake Hefner (USA)
𝐸𝑜 = 0.122𝑈4(𝑒𝑤 − 𝑒𝑑)
 Mass transfer method
c) General equation (Harbeck, 1962)
𝐸𝑜 = 0.291𝐴−0.05
𝑈2(𝑒𝑤 − 𝑒𝑑)
• A is the size of the Lake in Mm2, ew is the saturation
vapor pressure for the temperature of the water.

18.  Combined approach, the equation of Penman
 Using energy budget and mass transport methods, Penman (1956) proposed a
new equation which gives a good estimation of evaporation from lakes for
daily to monthly periods:
where
E0: evaporation from open water surface (mm/day)
Qn: net amount of radiation remaining at the free water surface (g.cal/cm/day = 59 mm/day)
Ea: evaporation due to mass transfer of vapor (mm/day)
∆ : gradient of saturation vapor pressure at air temperature t (oC).
: Psychrometer constant (=0.66 mb/oC or 0.49 mm Hg / oC)
𝐸0 =
∆𝑄𝑛 + 𝛾𝐸𝑎
𝛾 + ∆

19.  ∆ is determined as shown in the following figure.

20.  Evaporation pans
 At many meteorological stations the evaporation from a small water body (evaporation
pan) is usually monitored.
 Evaporation is recorded from water level changes, corrected by rainfall depths.
 Annual evaporation from a nearby lake is approximately 0.7 times the observation from
a pan.
 This factor 0.7 is known as the pan coefficient and usually varied between 0.67 to 0.87.
 The FAO uses pan evaporation data Epan to estimate the reference evaporation ETref as
follows:
ETref = kpan Epan
• Kpan is the pan coefficient usually vary between 0.35 to 0.85

21. • Surface area is 1m2 and water depth of 25cm
• The pan is filled with water to a depth of 20cm
• The decrease of water is measured by a point gage, which is
an evaporation rate.
• The pan is placed 15cm above the ground.
• Everyday water is added so that water surface is 5-8 cm
below the upper rim of the pan.
• Evaporation is the difference between the observed levels
• It is measured daily.
What is pan coefficient?
 Pan evaporation
rates are higher than
actual values. That’s
why they have to be
adjusted with a
coefficient as 0.7
 Evaporation pans

22. 3.3 Estimation of evaporation and evapotranspiration
 Methods to estimate evaporation:
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23.  Methods to estimate evapotranspiration:
 Energy Methods (use parameters such as
solar radiation, soil heat flux, etc.)
 Penman-Monteith equation
 FAO56-Penman-Monteith method
 Evaporation pans
 Empirical Methods
 Blaney-Criddle
 Turc (1961)
 Thornthwaite method
1) Potential evapotranspiration
 Remote Sensing (satellite data)
 Turc (1954)
 Coutagne
 Crop-coefficient method
(based on vegetation type,
albedo, surface resistance)
2) Actual evapotranspiration

24.  Evaporation pan
 Provide a direct measure of evaporation in the field
 Pans measure the integrated effect of radiation, wind, temperature and humidity,
on the evaporation from open water surfaces
 Water should be regularly renewed (at least once a week)
 Water depth should be greater than 20 cm
 Evaporation rates are sensitive to the size of the pan – small pans yield higher
evaporation rates
 Typical Class A Pan  120.7 cm in diameter and 25 cm deep.
a) Potential evapotranspiration estimation

25. Class A evaporation pan.
 Pan evaporation generally represent the evaporation
in the edges of large water bodies
 Pans may also absorb radiation providing greater
energy for evaporation
 Pan evaporation models (which take into account
radiation, wind speed, and relative humidity) have
been developed for interpolation of pan data
 Evapotranspiration can be estimated from standard Class-A Pans by multiplying
by a pan coefficient:
𝑃𝐸𝑇 = 𝐾𝑝𝐸𝑝
𝑃𝐸𝑇 = Potential Evapotranspiration
Kp= Pan coefficient
Ep= measured pan evaporation

26.  FAO Penman-Monteith Method
 The FAO Penman-Monteith method is used to estimate reference
evapotranspiration. The equation is:
𝐸𝑇𝑟𝑒𝑓 =
0.408∆ 𝑅𝑛 − 𝐺 + 𝛾 900
𝑇+273𝑢2 𝑒𝑠−𝑒𝑎
∆ + 𝛾 1 + 0.34𝑢2
ETref = reference evapotranspiration [mm day-1]
Rn = net radiation at the crop surface [MJ m-2 day-1]
T = mean daily air temperature at 2 m height [°C]
u2 = wind speed at 2 m height [m/s]
es = saturation vapour pressure [kPa]
ea = actual vapour pressure [kPa]
es - ea = saturation vapour pressure deficit [kPa]
Δ = slope of vapour pressure curve [kPa°C-1]
Υ = psychometric constant [kPa°C-1]

27.  Potential evapotranspiration can be calculated with the Penman-Monteith
equation which is the one step method
 The two-step approach is at the present the most popular. It computes the
potential evapotranspiration of the crop from the equation
𝑃𝐸𝑇. = 𝑘𝑐𝐸𝑇𝑟𝑒𝑓
 Where kc is a crop factor and ETref is the reference evaporation.
 The reference evaporation is often taken as the evaporation of an open water
surface (Eo)
 The Netherlands potential evapotranspiration of grass can be estimated from
𝑃𝐸𝑇. = 0.8𝐸0 for summer period,
𝑃𝐸𝑇. = 0.7𝐸0 for winter period

28. where
𝑃𝐸𝑇 = Potential Evapotranspiration (mm/day)
𝑝 = percentage of annual daylight hours (monthly in %)
Tavg=Average of daily maximum and minimum temperatures (monthly in ◦C)
 Empirical Methods for Potential Evapotranspiration
 Empirical models generally involve the application of linear regression techniques
between evapotranspiration and several climatic variables
 Since many climatic variables are interdependent, the most efficient regression
model is the one with the least number of climatic parameters
 Blaney-Criddle (1962)
𝑃𝐸𝑇 = 𝑝(0.46𝑇𝑎𝑣𝑔 + 8.13)

29.  Turc (1961)
where
𝑃𝐸𝑇 = Potential Evapotranspiration (mm/day)
Tmean = Mean air temperature (daily) (in ◦C)
Rs=Total incoming solar radiation (MJ/m2d)
𝑅𝐻 = Relative humidity (%)

30.  Thornthwaite Method
 Thornthwaite method is based on the assumption of an exponential relationship
between mean monthly temperature and mean monthly consumptive use.
𝑃𝐸𝑇 = 1.6 Τ
10𝑡 𝐼 𝑎
where
PET = unadjusted PET (cm per month),
t = mean air temperature (°C)
I = annual or seasonal heat index, the summation of 12 values of monthly heat
indices (i) when, 𝑖 = Τ
𝑡 5 1.514
𝑎 = 0.0000006751𝐼3 − 0.000071𝐼2 + 0.017921𝐼 + 0.49239

31.  Hargreaves’ Method
 Hargreaves based on his work on data from grass lysimeter, proposed the
following relationship to estimate ET,
𝑃𝐸𝑇 = 0.0135 𝑡 + 17.78 𝑅𝑠
where,
PET = reference crop potential consumptive use
t = mean daily temperature (°C)
Rs = incident solar radiation in langlay/day, it can be calculated using the
following relationship
𝑅𝑠 = 0.10𝑅𝑠𝑜𝑆 Τ
1 2
where,
S is the percent possible sunshine hour and Rso is the clear day solar radiation.

32.  Turc (1954):
where
𝐸𝑇 = Actual Evapotranspiration (mm/yr)
P = Precipitation (mm/yr)
T =Temperature (oC)
b) Actual evapotranspiration
 Coutagne:

33.  Soil water budget method
 The water balance of the root zone may be written as
𝐼 + 𝑃𝑆 + 𝐺 = 𝐸 + 𝐷 + 𝑄𝑆 + ∆𝑆/∆𝑡
• where I is irrigation, PS is precipitation minus interception, G is groundwater
contribution through capillary rise, E is evapotranspiration, D is percolation from
the root zone to the groundwater system, and QS is surface runoff.
 The boundary conditions for applying
the water balance equation are much
better defined with the use of a
lysimeter which is a closed container in
the soil from which the outflow
(drainage) can be measured.

34.  Lysimeter
 A lysimeter is a measuring device which can be used to measure the amount of actual
evapotranspiration which is released by plants, usually crops or trees.
 By recording the amount of precipitation that an area receives and the amount lost
through the soil, the amount of water lost to evapotranspiration can be calculated.
 Lysimeters are a tool for water balance studies and solute transport determination.
 Lysimeter – a large container holding
soil and plants.