CENGR511 – Hydrology 1
MODULE NO.4
EVAPORATION
Learning Objectives:
1. Discuss the concept of Evaporation Process
2. Determine the types of Evaporimeters
3. Calculate evaporation rate
4. Discuss the methods of reservoir evaporation reduction
5. Solve evaporation problems
OVERVIEW
Evaporation is the by which water in its liquid or solid state is transformed into water vapor,
which mixes with the atmosphere. Evapotranspiration (ET) is considered separately as the combine
loss of water vapor from the surface of plants (transpiration) and the evaporation of moisture from
soil. Knowledge of evaporation processes is important in predicting water losses to evaporation
from the lake or reservoir. However, variations in evaporation across the continent can be very
large due to effects of solar input, location of mountains, and proximity to ocean.
In Engineering Hydrology, runoff due to storm event is often the major subject of study.
All abstractions from precipitation, those due to evaporation, transpiration. Infiltration, surface
detention and storage, are considered as losses in the production of runoff. Chief components of
abstractions from precipitation, knowledge of which are necessary in the analysis of various
hydrologic situations will be described in this module.
Evaporation from water bodies and soil masses together with transpiration from vegetation
is termed as evapotranspiration.
EVAPORATION PROCESS
Evaporation is the process in which a liquid change to the gaseous state at the free surface,
below the boiling point through the transfer of heat energy. Consider a body of water in a pond.
The molecules of water are in constant motion with a wide range of instantaneous velocities. An
addition of heat causes this range and average speed to increase. When some molecules possess
sufficient kinetic energy, they may cross over the water surface.
For the case of evaporation from a lake surface, water loss is a function of solar radiation,
temperature of the water and air, difference vapor pressure between water and the overlying air,
and wind speed across the lake. As evaporation proceeds in a closed – container system at a
constant temperature, pressure in the air space increases because of an increase in partial pressure
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of water vapor. Evaporation continues until vapor pressure of the overlying air equals the surface
vapor pressure; at this point the air space is said to be saturated at that temperature, and further
evaporation ceases. This state of equilibrium would not be reached if the container were open to
the atmosphere, in which case all water would eventually evaporate.
The rate of evaporation is dependent on (i) the vapor pressures at the water surface and in
air above, (ii) air and water temperatures, (iii) wind speed, (iv) atmospheric pressure, (v) quality
of water, and (vi) size of the water body.
Vapor Pressure
The rate of evaporation is proportional to the difference between the saturation vapor
pressure at the water temperature, ew , and the actual vapor pressure in the air, ea. Thus,
EL =C (ew - ea ) Eq.1
where:
EL = rate of evaporation (mm/day)
C = constant
ew and ea = are in mm of mercury
Eq. 1 is known as Dalton’s Law of Evaporation after John Dalton (1802) who first
recognized this law. Evaporation continues until ew = ea . If ew > ea , condensation takes place.
Temperature
Other factors remaining the same, the rate of evaporation increases with an increase in the
water temperature. Regarding air temperature, although there is a general increase in the
evaporation rate with increasing temperature, a high correlation between evaporation rate and air
temperature does not exist. Thus, for the same mean monthly temperature it is possible to have
evaporation to different degrees in a lake in different months.
Wind
Wind aids in removing the evaporated water vapor from the zone of evaporation and
consequently creates greater scope for evaporation. However, if the wind velocity is large enough
to remove all the evaporated water vapor, any further increase with the wind speeds up to a critical
speed beyond which any further increase in the wind speed has no influence on the evaporation
rate. This critical wind speed value is a function of the size of the water surface. For large water
bodies high-speed turbulent winds are needed to cause maximum rate of evaporation.
Atmospheric Pressure
Other factors remaining same, a decrease in the barometric pressure, as in high altitudes,
increase evaporation.
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Soluble Salts
When a solute is dissolved in water, the vapor pressure of the solution is less than that of
pure water and hence causes reduction in the rate of evaporation.
Heat Storage in Water Bodies
Deep water bodies have more heat storage than shallow ones.
EVAPORIMETERS
Estimation of evaporation is of utmost importance in many hydrologic problems associated
with planning and operation of reservoirs and irrigation systems. The amount of water evaporated
from a water surface is estimated by the following methods: (i) using evaporimeter data, (ii)
empirical evaporation equations, and (iii) analytical methods.
Types of Evaporimeters
Evaporimeters are water-containing pans which are exposed to the atmosphere and the loss
of water by evaporation measured in the, at regular intervals. Meteorological data, such a humidity,
wind movement, air and water temperatures and precipitation are also noted along with
evaporation measurement.
Many types of evaporimeters are in use and a few commonly used pans are described here.
a. Class A Evaporation Pan
It is a standard pan of 1210 mm diameter and 255 mm depth used by the US Weather
Bureau and is known as Class A Land Pan. The depth of water is maintained between 18 cm and
20 cm, Figure 1. The pan is normally made of unpainted galvanized iron sheet. Monel metal is
used where corrosion is a problem. The pan is placed on a wooden platform of 15 cm height above
the ground to allow free circulation of air below the pan. Evaporation measurements are made by
measuring the depth of water with a hook gauge in a stilling well.
Figure 1. U.S. Class A Evaporation Pan
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b. ISI Standard Pan
Also known as modified Class A Pan, consists of a pan 1220 mm in diameter with 255 mm
of depth. The pan is made of copper sheet of 0.9 mm thickness tinned inside, Figure 2. A fixed-
point gauge indicates the level of water. A calibrated cylindrical measure is used to add or remove
water maintaining the water level in the pan to a fixed mark. The top of pan is covered fully with
a hexagonal wire netting of galvanized iron to protect the water temperature more uniform during
day and night. The evaporation from this pan is found to be less by about 14% compared to that
from unscreened pan. The pan is placed over a square wooden platform of 1225 mm width and
100 mm height to enable circulation of air underneath the pan.
Figure 2. ISI Evaporation Pan
c. Colorado Sunken Pan
This pan, 920 mm square and 460 mm deep is made up of unpainted galvanized iron sheet
and buried into the ground within 100 mm of the top, Figure 3. The chief advantage of the sunken
pan is that radiation and aerodynamic characteristics are similar to those of a lake. However, it has
the following disadvantages: 9i) difficult to detect leaks, (ii) extra care is needed to keep the
surrounding area free from tall grass, dust, etc., and (iii) expensive to install.
Figure 3. Colorado Evaporation Pan
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d. US Geological Survey Floating Pan
With a view to stimulate the characteristics of a large body of water. This square pan (900
mm side and 450 mm depth) supported by drum floats in the middle of a raft (4.25 m x 4.87 m) is
set afloat in a lake. The water level in the pan is kept at the same level as the lake leaving a rim of
75 mm. Diagonal baffles provided in the pan reduce the surging in the pan due to wave action. Its
high cost of installation and maintenance together with the difficulty involved in performing
measurements are its main disadvantages.
e. Pan Coefficient Cp
Evaporation pans are not exact models of large reservoirs and have the following principal
drawbacks:
1. they differ in the heat-storing capacity and heat transfer from the sides and bottom. The
sunken pan and floating pan aim to reduce this deficiency. As a result of this factor the
evaporation from a pan depends to a certain extent on its size. While a pan of 3 m diameter
is known to give a value, which is about the same as from a neighboring large lake, a pan
of size 1.0 m diameter indicates about 20% excess evaporation than hat of the 3m diameter
pan.
2. The height of the rim in an evaporation pan effects the wind action over the surface.
Also, it casts a shadow of variable magnitude over the water surface.
3. The heat-transfer characteristics of the pan material is different from that of the reservoir.
In view of the above, the evaporation observed from a pan has to be corrected to get the
evaporation from a lake under similar climatic and exposure conditions. Thus, a coefficient
is introduced as
Lake Evaporation = Cp x Pan Evaporation Eq.2
where:
Cp = pan coefficient (given in Table 1)
Table 1. Values of Pan Coefficient Cp
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f. Evaporation Stations
It is usual to install evaporation pans in such locations where other meteorological data are
also simultaneously collected. A typical hydrometeorological station contains the following:
Ordinary raingauge; recording raingauge; Steven Box with maximum and minimum thermometer
and dry and wet bulb thermometers; wind anemometer, wind direction indicator, sunshine
recorder, thermohydrograph and pan evaporimeter.
EMPIRICAL EVAPORATION EQUATIONS
A large number of empirical equations are available to estimate lake evaporation using
commonly available meteorological data. Most formulae are based on the Dalton-type equation
and can be expressed in the general form
EL =K f(u)(ew - ea ) Eq.3
where:
EL = lake evaporation in mm/day
ew = saturated vapor pressure at the water surface
temperature in mm of mercury
ea = actual vapor pressure of over0lying air at a specified height in mm of
mercury
f(u) = wind-speed correction function
K = a coefficient
Two commonly used empirical evaporation formulae are:
1. Meyer’s Formula (1915)
u
EL =KM (ew - ea ) (1+ 169) Eq.4
where:
u9 = monthly mean wind velocity in km/h at about 9 m above
KM = coefficient accounting for various other factors with a value of 0.36 for large
deep waters and 0.50 for small, shallow waters
K = a coefficient
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2. Rohwer’s Formula (1931)
Rohwer’s formula considers a correction for the effect of pressure in addition to the wind-
speed effect and is given by
EL =0.771 (1.465 - 0.000732 pa )(0.44 + 0.0733 uo )(ew - ea ) Eq.5
where:
pa = mean barometric reading in mm of mercury
uo = mean wind velocity in km/h at ground level, which can be taken to be the
velocity at 0.6 m height above ground.
These empirical formulae are simple to use and permit the use of standard meteorological
data. However, in view of the various limitations of the formulae, they can at best be expected to
give an approximate magnitude of the evaporation.
In using the empirical equations, the saturated vapor pressure at a given temperature (ew )
is found from a table of ew vs temperature in °C, Table 2. Often, the wind-velocity data would be
available at an elevation other than that needed in the [articular equation. However, it is known
that in the lower part of the atmosphere, up to a height of about 500 m above the ground level, the
wind velocity can be assumed to follow the 1/7 power law as
uh = Ch1/7 Eq.6
where:
uh = wind velocity at a height h above the ground
C = constant
This equation can be used to determine the velocity at any desired level if uh is known.
Table 2. Saturation Vapor Pressure of Water
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Sample Problem
1.A reservoir with a surface area of 250 hectares had the following average values of climate
parameters during a week:
Water temperature = 20°C
Relative Humidity = 40%
Wind velocity at 1.0 m above ground surface = 16 km/h
Estimate the average daily evaporation from the lake by using Meyer’s formula.
2. An IS Standard evaporation pan at the site indicated a pan coefficient of 0.80 on the basis of
calibration against controlled water budgeting method. If this pan indicated an evaporation of 72
mm in the week under question
(i) estimate the accuracy if Meyer’s method relative to the pan evaporation measurements.
(ii) Also, estimate the volume of water evaporated from the lake in that week.
ANALYTICAL METHODS OF EVAPORATION ESTIMATION
The analytical methods of determination of lake evaporation can be broadly classified into
three categories as:
1. Water-Budget Method
2. Energy-Balanced Method
3. Mass-Transfer Method
1. Water-Budget Method
The water-budget method is the simplest of the three analytical methods and is also the
least reliable. It involves writing the hydrological continuity equation for the lake and determining
the evaporation from a knowledge or estimation of other variables. Thus, considering the daily
average values for a lake, the continuity equation is written as
P + Vis + Vig = Vos +Vog + EL + ΔS + TL Eq. 7
where:
P = daily precipitation
Vis = daily surface inflow into the lake
Vig = daily groundwater inflow
Vos = daily surface inflow into the lake
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Vog = daily groundwater inflow
EL = daily lake evaporation
ΔS = increase in lake storage in a day
TL = daily transpiration loss
All quantities are in units of volume (m³) or depth (mm) over a reference area. Equation 7
can be written as
EL = P + (Vis - Vos ) + (Vig - Vog) - ΔS - TL Eq.8
2. Energy-Budget Method
The energy-budget method is an application of the law of conservation of energy. The
energy available for evaporation is determined by considering the incoming energy., outgoing
energy and energy stored in the water body over a known time interval.
Considering the water body as in Figure 4, the energy balance to the evaporating surface
in a period of one day is given by
Hn = H a + He + Hg + Hs + Hi Eq.9
where:
Hn = net heat energy received by the water surface
= Hc (1 - r)- Hb
Hc (1 - r) = incoming solar radiation into a surface of reflection coefficient
(albedo) r
Hb = back radiation (long wave) from water body
Ha = sensible heat transfer from water surface to air
He = heat energy used up in evaporation
= ρLEL
ρ = density of water
L = latent heat of evaporation
EL = evaporation in mm
Hg = heat flux in the ground
Hs = heat stored in water body
Hi = net heat conducted out of the system by water flow (advected
energy)
Estimation of evaporation in a lake by the energy balance method has been found to give
satisfactory results, with errors of the order of 5% when applied to periods less than a week.
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3. Mass-Transfer Method
This method is based on theories of turbulent mass transfer in boundary layer to calculate
the mass water vapor transfer from the surface to the surrounding atmosphere.
RESERVOIR EVAPORATION AND METHODS FOR ITS REDUCTION
Any of the methods mentioned above may be used for the estimation of reservoir
evaporation. Although analytical methods provide better results, they involve parameters that are
difficult to assess or expensive t obtain. Empirical equations can at best give approximate values
of the correct order of magnitude. Therefore, the pan measurements find general acceptance for
practical application. The water volume lost due to evaporation from a reservoir in a month is
calculated as
VE = A Epm Cp Eq.10
where:
VE = volume of water lost in evaporation in a month (m³)
A = average reservoir area during the month (m²)
Epm = pan evaporation loss in meters in a month (m)
= EL in mm/day x No. of days in the month x 10−3
Cp = relevant pan coefficient
Methods to Reduce Evaporation Losses
Various methods available for reduction of evaporation losses can be considered in three
categories:
a. Reduction of Surface Area
Since the volume of water lost by evaporation is directly proportional to the surface area
of the water body, the reduction of surface area wherever feasible reduces evaporation losses.
Measures like having deep reservoirs in place of wider ones and elimination of shallow areas can
be considered under this category.
b. Mechanical Covers
Permanent roofs over the reservoir, temporary roofs and floating roofs such as rafts and
light-weight floating particles can be adopted wherever feasible. Obviously, these measures are
limited to very small water bodies such as ponds, etc.
c. Chemical Films
this method consists of applying a thin chemical film on the water surface to reduce
evaporation. Currently this is the only feasible method available for reduction of evaporation or
reservoirs up to moderate size.
