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Based on notes by Ashish Sharma, Ian Acworth Page 2-1
2 EVAPORATION AND EVAPOTRANSPIRATION
2.1 Introduction
Water is removed from the surface of the earth to the atmosphere
by two distinct mechanisms evaporation
and transpiration. Both describe a process whereby liquid water
is transformed to a gas (water vapour). This
requires large amounts of energy. Therefore driving force behind
all evaporation is the quantity of energy
received from the sun. This is why we have covered the energy
balance of the earth in detail in the previous
sections.
Evaporation can (somewhat obviously) only occur where and when
liquid water is available. It also requires
that the atmosphere is not saturated so that the water vapour
has somewhere to go once it leaves the surface.
This chapter discusses the mechanisms for evaporation and
evapotranspiration and methods for calculating its
contribution to the water cycle.
The importance of evaporation can be seen from the data in Table
2-1 which lists monthly average rainfall and
evaporation for Sydney. The two fluxes are very similar,
indicating that runoff and infiltration could be second
order processes.
Table 2-1 Mean monthly distribution of rainfall and pan
evaporation for Sydney (Australian Bureau of Meteorology, Stn
066062)
Month Mean Rainfall
(mm)
Mean Pan
Evaporation (mm)
January 101.1 142.6
February 118.0 109.2
March 129.7 96.1
April 127.1 78.0
May 119.9 58.9
June 132.0 36.0
July 97.4 46.5
August 80.7 58.9
September 68.3 75.0
October 76.9 102.3
November 83.9 129
December 77.6 136.4
Annual 1211.8 1058.5
Average annual precipitation and evaporation data for Australia
is shown in Figure 2-1 and Figure 2-2 sourced
from the Australian Bureau of Meteorology
(http://www.bom.gov.au/climate/averages/maps.shtml). It can be
seen that for many parts of Australia evaporation is much larger
than the rainfall.
The total evaporation from continental areas around the world is
approximately 70% of total precipitation
over the continents. In Australia the ratio is much larger with
evaporation accounting for approximately 90% of
the total rainfall that occurs over the continent.
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Evaporation is an important part of the water balance and has
large impacts on many water resources
systems. Evaporation losses from reservoirs are a substantial
percentage of the total storage capacity
(generally around 20% yield) and in some cases can exceed 50%.
Evaporation and evapotranspiration are also
important for agriculture. It is therefore vital that we
correctly measure or estimate evaporation.
Figure 2-1 Average annual rainfall for Australia for the period
1961-1990 (Australian Bureau of Meteorology Product Code
IDCJCM004)
Figure 2-2 Average annual pan evaporation for Australia for the
period 1975-2005 (Australian Bureau of Meteorology Product Code
IDCJCM0006)
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2.2 Important definitions
There are a number of key terms when thinking about evaporation
and evapotranspiration.
Evaporation: the amount of water that passes or could pass into
the atmosphere across a soil/air or water/air
interface
Transpiration: the process by which water is removed from
vegetation into the atmosphere by evaporation
from the plant stomates. Alternately, transpiration is the
transport of that water within the plant and its
subsequent release as a vapour into the atmosphere.
Evapotranspiration: the combined process of evaporation and
transpiration. It describes the amount of water
that passes into the atmosphere across the plant/air interface.
It is often used interchangeably with
evaporation. Commonly 'evaporation' refers to an open water
surface or bare soil and 'evapotranspiration' is
used when referring to soil surfaces with plants.
Potential evaporation/evapotranspiration (ET0): the maximum
amount of water that can evaporation or
transpire from a surface when water availability is not limiting
(i.e. a well-watered surface or an open water
body). Potential evaporation is limited by the amount of solar
radiation that is available and the capacity of the
air to receive more water.
Actual evaporation/evapotranspiration (ETa): the actual amount
of water that is evaporated into the air. It is
limited by the amount of water available in the soil for the
evaporation rather than the moisture holding
capacity of the air. Actual evaporation is always equal to or
less than potential evaporation.
Reference crop evapotranspiration (ETrc): the rate of
evapotranspiration from an idealised grass crop with an
assumed crop height (0.12 m), a fixed canopy resistance (70 s/m)
and albedo (0.23).
Crop coefficient (kc): the ratio of evapotranspiration of any
plant/crop compared to the reference crop defined
above.
2.3 Physics of evaporation
2.3.1 Introduction
The evaporation process is the result of an exchange of
molecules between water and the atmosphere. With
an increase in the water temperature, the kinetic energy of the
water molecule increases. This enables some
of them to escape from the surface. When in the vapour phase,
each molecule is separate from the others by a
large distance, and hence the hydrogen bonding properties of the
molecules are all but absent. Some of the
escaped molecules cool down and try to re-enter the water this
process is termed condensation. Evaporation
is the difference between the number of molecules leaving and
those re-entering the water body.
There is a very thin layer of saturated water just above the
water surface. This is formed due to the escape of
water molecules form the water surface and also the re-entry of
some molecules. When molecules escape this
layer to the air above, space is crated for more evaporation
from the water surface. This concept is
represented by Dalton's law:
( )as eeCE = 2-1 Where E is the evaporation, C is a coefficient
and es is the saturation vapour pressure (at the current air
temperature) and ea is the saturation vapour pressure at the dew
point temperature.
Remember that the saturation vapour pressure at the dew point
temperature (ed) is the same as the actual
vapour pressure at the present air temperature (e). This means
that in Equation 2-1 it is the difference
between the saturation vapour pressure and the actual vapour
pressure that drives evaporation. As the air
becomes more saturated, ea (or e) equals es and the evaporation
tends to zero. As the humidity in soils is often
close to 100% (i.e. es equals ea) there is little evaporation
from below the soil surface.
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Saturation vapour pressure is a function of the temperature. It
is low at low temperatures and increases at an
exponential rate from there as shown in Figure 2-3. Hence warm
air can hold a lot more water than cold air. An
approximate relationship for the saturation vapour pressure
is:
+=
TT
es 3.23727.17
exp6108.0 2-2
Where T is the air temperature in C and es is the saturation
vapour pressure in kPa.
Figure 2-3 Saturation vapour pressure relationship with air
temperature
2.3.2 Applications of evaporation in hydrology
Evaporation is important for the design and operation of water
storage reservoirs and for soil moisture. It
there has an impact on streamflows and catchment yields.
Evaporation is less important during storm events,
firstly because the actual vapour pressure is close to
saturation during precipitation and secondly because
storms do not usually have a very long duration.
Water resources managers can change the way that they operate
regulated river systems to ensure that the
evaporation losses are minimised. For example it is better to
release water from a dam in larger quantities less
frequently than to constantly release smaller amounts. This is
because the water depths in the river will be
shallower when smaller amounts are released so the surface area
to volume ratio will be higher and more
evaporation will result. An example is the management of
Menindee Lakes in western New South Wales where
operation of the lakes is being studied to minimise evaporation
losses http://www.water.nsw.gov.au/Water-
management/Water-recovery/Darling-Savings/Darling-water-saving
In some cases, evaporation can be suppressed by placing a thin
film of certain chemical (e.g. cetyl alcohol) that
spread over the water surface and can reduce evaporation by as
much as 70%. However the chemical layer can
be disrupted by wind and dust and can break up. This option is
therefore only practicable for small dams
where wind effects are minimal.
Groundwater storage dams have also been found to be effective in
some arid areas whereby the dam is filled
with sand or other relatively porous material. Water is stored
in the pore spaces and evaporation is reduced.
-10 0 10 20 30 40
12
34
56
7
Temperature (deg C)
Satu
rate
d Va
pou
r Pr
ess
ure
(kP
a)
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Knowledge of evaporative processes has also been used to dispose
of contaminated water by placing it is in
large evaporative ponds. This stops the contaminated water from
running off or entering groundwater. The
ponds are designed to be shallow to increase the evaporation
rate. Examples include brine from desalination
plants, waste water treatment plants or mine tailing water.
2.4 Evaporation measurement
2.4.1 Evaporation pan
The Class A evaporation pan is probably the most widely used
instrument around the wold to measure
potential evaporation. The Class A pan is 120.7 cm in diameter
and 25 cm deep and is constructed from
galvanised metal. The plan is placed in an open area and fenced
to spot animals drinking from it. The water
level in the pan is maintained at a constant depth by adding or
subtracting water from the pan each day. The
evaporation is calculated by considering a simple water balance
by using the change in depth of the water in
the pan and the rainfall that has occurred in the previous 24
hours. The surface of the pan can either be left
open or a bird grill added. When grills were added to pans
around Australia, evaporation was decreased on
average by around 7%. Long term records have been homogenised to
account for this error. A Class A pan is
shown in Figure 2-4.
Figure 2-4 Class A evaporation pan in Townsville
(http://www.bom.gov.au/qld/townsville/images/Evap_Pan_650.jpg)
The pan heats up more rapidly than the ground around it and
there are also the side walls of the pan which
can receive some solar radiation. Therefore evaporation from a
pan will be higher than from the environment.
A correction factor is therefore normally used to convert the
pan evaporation measurement into true potential
evaporation. This pan factor is normally between 0.6 to 0.8 and
depends on the soil type, surrounding
vegetation and climatic conditions. The pan coefficient can be
calibrated for sites where enough data exists to
also directly calculated open water body evaporation using the
Penman equation. In the absence of a locally
calibrated value, a table of pan coefficients is provided by
Allen et al. [1998].
http://www.fao.org/docrep/X0490E/x0490e08.htm#pan%20evaporation%20method
Using this table and average wind speed (3.6 m/s) and relative
humidity (65%) for Sydney a pan coefficient of
0.7 would be chosen (assuming 10 m of short green grass adjacent
to the pan).
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Based on notes by Ashish Sharma, Ian Acworth Page 2-6
The equation to use the pan coefficient (kpan) is:
panpan EkET =0 2-3
2.4.2 Lysimeter
A lysimeter is a tank of soil which is planted with vegetation
and is hydrologically sealed so that the water
leakage from the system is negligible. It is used to measure
evapotranspiration in the field and for studying
soil-water-plan relationships under natural conditions. The
lysimeter should be representative of the
surrounding natural soil profile and vegetation types. The rate
of evapotranspiration from this instrument is
obtained by undertaking a soil water budget. The precipitation
on the lysimeter, the drainage through its
bottom, and the changes in soil moisture within the lysimeter
are all measured. The amount of
evapotranspiration is the amount necessary to complete the water
balance.
2.4.3 Eddy covariance measurement
If the energy fluxes at a site can be measured then evaporation
can be calculated directly. The vertical
fluctuations of the wind and water vapour are measured and then
their correlations calculated over some
averaging period (around 15 minutes to an hour). It is only in
the last 10 to 15 years that suitable
instrumentation has become commercially available. However the
instrumentation is expensive and requires
special skill to operated and therefore this method is only used
in research experiments. It is the preferred
micrometeorological technique on the grounds that it is a direct
measurement with minimum theoretical
assumptions. A map showing the locations of eddy covariance
stations in Australia is in Figure 2-5.
Figure 2-5 Network of meteorological flux stations in Australia
and New Zealand
(http://www.ozflux.org.au/monitoringsites/index.html)
2.5 Evaporation calculations
As can be seen from the methods above the measurement of
evaporation is labour intensive and expensive.
Therefore in most cases evaporation is calculated by considering
the physical relationship between different
climatic variables and the evaporation rate. There are a number
of different methods for calculating
evaporation/evapotranspiration and a comprehensive review of the
different methods is provided by
McMahon et al. [2013]. In general the methods can be classified
as:
temperature-based methods
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radiation-based methods
combination methods (resistance plus energy)
If all the required climatic data are available then the Penman
Monteith method (a combination approach) is
recommended as the most accurate approach. Details of this
method are provided in the next section.
2.5.1 Energy balance to drive evaporation
As discussed above evaporation is driven by energy allowing
water molecules to escape from the water
surface. Therefore the general principle of calculating
evaporation is to use consider the energy budget.
The available energy A is the energy balance:
= 2-4
Where
A is Available Energy
Rn is Net Incoming Radiation (i.e. considering the solar and
longwave radiation components and
directions)
G is the outgoing heat conduction into the soil
Under most conditions the terms S, P and Ad are neglected. The
temporary soil volume energy (S) needs to be
considered when the energy balance is over a forest. Over the
course of a day G is approximately equal to zero
so can also generally be neglected if daily evaporation
estimates are required. Therefore the available energy
can be approximated as the net radiation.
As shown in Equation 2-5, the available energy A can be
partitioned into two components sensible heat H
and latent energy E (i.e. the outgoing energy in the form of
evaporation)
= + 2-5
Thus if there is limited water available for evaporation, the
sensible heat partition will become larger and the
air temperatures will be higher. The ratio between sensible heat
and latent heat is called the Bowen Ratio and
can be used to summarise the aridity of a location.
= / 2-6
Table 2-2 lists Bowen ratios for a number of different climatic
conditions.
Table 2-2 Typical values of the Bowen ration [Ladson, 2008]
Conditions Bowen ratio
Arid conditions (hot deserts) 10
Semi-arid regions 2-6
Temperate forests and grass lands 0.4-0.8
Tropical rain forests 0.2
Tropical oceans 0.1
Well watered short vegetation with no wind and low
temperatures
(i.e. close to zero sensible heat flux)
~ 0
Well watered vegetation with low humidity. In this case the
leaf
temperature can be less than the air temperature because of
evaporative cooling so the sensible heat is providing
additional
energy for evaporation i.e. the Bowen ratio can be negative
< 0
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Based on notes by Ashish Sharma, Ian Acworth Page 2-8
2.5.2 Available energy
If we assume that the energy loss to the ground is zero
(reasonable assumption over the course of a day or
longer), then the available energy is just the energy balance
between the incoming and outgoing shortwave
and longwave radiation.
nlnsn RRRA == 2-7
Where Rn is the net incoming radiation, Rns is the net shortwave
radiation (incoming outgoing) and Rnl is the
net outgoing radiation (incoming outgoing).
Although over the earth as a whole, the net radiation is in
balance at any one point and any one time, there
will be an energy inbalance and if the energy inbalance is
positive it will lead to evaporation and/or heating.
We therefore need to be able to calculate the energy inbalance
at any location and for any time of year by
finding the shortwave and longwave radiation.
Shortwave (solar) radiation
The extraterrestrial solar radiation is the radiation received
at the top of the earth's atmosphere on a
horizontal surface. It changes throughout the year due to
changes in the position of the sun and the length of
the day. It is therefore a function of the latitude, date and
time of day. These values can be substituted into
the following equation to calculate the extraterrestrial solar
radiation Ra (MJ m-2
day-1
).
( )ssr
da
R pi
sincoscossinsin1.118 += 2-8
where s represents the sunset hour angle:
)tantanarccos( =s
2-9
and is the latitude for the site (negative for Southern
Hemisphere) with the solar declination (in radians), given as:
= 405.1
3652
sin4093.0 Jpi 2-10
and J is the Julian day number (day number from start of
year).
The relative distance between the earth and sun is calculated
as:
+= J
rd
3652
cos033.01 pi 2-11
Not all the energy at the top of the atmosphere reaches the
earth's surface and therefore solar radiation (Rs)
at the surface will be less than extraterrestrial solar
radiation. On a cloudless day clear sky solar radiation (Rso)
is approximately 75% of the extraterrestrial radiation. When
there are clouds the solar radiation will be even
lower.
Solar radiation (Rs) can be calculated using the Angstrom
formula:
+=
Nn
aR
sR 5.025.0 2-12
Where n is the actual duration of sunshine (hours) and N is the
maximum possible duration of sunshine or
daylight hours (hours) calculated as:
sN
pi
24= 2-13
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Based on notes by Ashish Sharma, Ian Acworth Page 2-9
The constants in the Angstrom formula can vary depending on
location but the above values are
recommended by Allen et al. [1998] in the absence of local
data.
The net solar radiation (Rns) is the balance between the
incoming and reflected solar radiation which is
controlled by the albedo ().
)1( =s
Rns
R 2-14
An albedo of 0.23 is assumed for the reference crop (discussed
below).
Longwave (terrestrial) radiation
The longwave energy is described by the Stefan-Boltzmann law
which states that the energy emission is
proportional to the absolute temperature of the surface raised
to the fourth power. Clouds, water vapour,
carbon dioxide and dust can absorb the emitted longwave
radiation and re-emit towards earth. Therefore net
outgoing longwave radiation will be smaller when there is higher
cloudiness or humidity. This relationship is
shown in the following equation:
( )
+= 35.035.114.034.0
2
4min,
4max,
so
sa
KK
RR
eTT
nlR 2-15
Where:
Rnl is the net outgoing longwave radiation (MJ m-2
day-1
)
is the Stefan Boltzmann constant = 4.903 x 10-9
MJ m-2
K-4
day-1
Tmax,K and Tmin,K are the maximum and minimum daily air
temperature (K)
ea is the actual vapour pressure (kPa)
and Rso is found using:
( )za
Rso
R 510275.0 += 2-16
Where z is the station elevation (m above sea level). Once again
the constants in this equation can be locally
calibrated. More details are provided in Allen et al.
[1998].
Net radiation
Net radiation is simply the difference between incoming net
shortwave radiation and outgoing net longwave
radiation:
nlnsn RRR = 2-17
Other heat fluxes (if significant) are subtracted from the net
radiation in Equation 2-17 to arrive at the
available energy (Equation 2-4). Note that the above estimate is
in MJ m-2
day-1
which can be converted to mm
units by dividing it by the latent heat of vaporisation of
water. The following conversion may be used to
convert energy to other units:
1 MJ m-2
day-1
= 11.57 W m-2
= 0.408 mm day-1
(at 20C) 2-18
2.5.3 Penman-Monteith equation
Penman [1948] combined the energy balance with the mass transfer
method and derived an equation to
compute the evaporation from an open water surface from standard
climatological records of sunshine,
temperature, humidity and wind speed. This so-called combination
method was further developed by many
researchers and extended to cropped surfaces by introducing
resistance factors.
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Based on notes by Ashish Sharma, Ian Acworth Page 2-10
As was shown in Equation 2-1, evaporation is controlled by the
difference between the saturated vapour
pressure es and actual vapour pressure ea (equivalent to
saturation vapour pressure at the dew point
temperature). The vapour pressure deficit is normally denoted as
D such that:
as eeD = 2-19
The Penman-Monteith approach is called a combination approach
because it calculates evaporation as the
weighted combination of the available energy and the vapour
pressure deficit. The general form for the
equation is therefore:
( )asa
p
rr
rDcA
E++
+=
1
2-20
Where:
E is the latent heat flux of evaporation (kJ m-2
s-1
)
E is the evaporation rate (m s-1
)
is the latent heat of vapourisation (MJ kg-1
)
is the slope of the saturated vapour pressure temperature curve
which was shown in Figure 2-3
A is the available energy (kJ m-2
s-1
)
D is the vapour pressure deficit (kPa)
is the density of air (kg m-3
)
cp is the specific heat of moist air (kJ kg-1
C-1
) and is equal to 1.013
rs is the surface resistance (s m-1
)
ra is the aerodynamic resistance (s m-1
)
is the psychometric constant (kPa C-1
)
The slope of the saturation vapour pressure relationship with
respect to temperature is:
( )23.2374098
T
es
+= 2-21
The latent heat of vapourisation () can be calculated using
Equation 2-22 if the surface temperature of the
water surface (Ts) in C is known
sT002361.0501.2 = 2-22
Finally the psychometric constant () is defined as:
P00163.0= 2-23
Where P is the atmospheric pressure (kPa). In the absence of
data on atmospheric pressure an estimate can be
made using the site elevation (z) in units of metres:
26.5
2930065.02933.101
=
zP 2-24
The combination approach can be seen more clearly if Equation
2-20 is split into two components:
aerorad ETETET +=0 2-25
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Where ET0 is the potential evapotranspiration and ETrad is the
contribution from radiation energy input (i.e.
available energy) and ETaero is the contribution from the
aerodynamic component (driven by the vapour
pressure deficit and advection from wind).
Alternatively we can write the equation as:
DFAFET DA +=0 2-26
In this form the weighting factors FA and FD depend on whether
evapotranspiration or open water body
evaporation is being calculated. Firstly we will look at the
estimate for the reference crop evapotranspiration,
and then with open water body evaporation.
2.5.4 Penman-Monteith reference crop evapotranspiration
As described in the section on resistance above, aerodynamic
resistance will vary according to the plant type.
Therefore to standardise the estimates from the Penman-Monteith
equation, a reference crop has been
defined by Allen et al. [1998] which has a surface resistance
rcrc
= 70 s m-1
. The reference crop is defined as a
hypothetical crop with a height of 0.12 m and an albedo of 0.23.
The reference surface is assumed to be of
green grass of uniform height which is actively growing.
Importantly the crop is completely shading the ground
and has adequate water so that it is forms potential
evapotranspiration conditions. The requirements that the
grass surface should be extensive and uniform result from the
assumption that all fluxes are one-dimensional
upwards [Allen et al., 1998].
Using Equation 2-20 and standard meteorological observations and
the information on the reference crop, the
reference crop evapotranspiration is estimated as:
( )22
34.01273
900408.0
u
DuT
AETrc ++
++
=
2-27
u2 is the wind speed at 2 m height (m s-1
)
T is air temperature at 2 m height (C)
ETrc is reference crop evapotranspiration (mm day-1
)
The units for A should be MJ m-2
day-1
and D in kPa to give the evapotranspiration in units of mm
day-1
. Note
that the constant of 900 has units of kJ-1
kg K.
In practice actual vapour pressure may not be available (if dew
point temperature has not been recorded) and
therefore it may need to be calculated from relative humidity
measurements. Because the saturated vapour
pressure curve is non-linear, average saturated vapour pressure
cannot be calculated using average
temperature. Therefore average saturated vapour pressure needs
to be calculated using the minimum and
maximum temperatures. Allen et al. [1998] recommends the
following procedures to estimate daily average
saturated and actual vapour pressure (es and ea
respectively)
( ) ( )( )maxmin5.0 TeTee oos += 2-28 Where e
o(T) is the saturated vapour pressure calculated at a specific
temperature (T) using Equation 2-2 and
Tmin and Tmax are the daily minimum and maximum temperatures for
which the vapour pressures are
calculated.
If maximum and minimum relative humidity data is available then
the actual vapour pressure (ea) is calculated
as:
( ) ( )( )minmaxmaxmin5.0 RHTeRHTee ooa += 2-29 Where RHmax and
RHmin are the maximum and minimum relative humidites (in %) for the
day. The idea is that
the maximum relative humidity generally occurs in the morning
when temperatures are lowest and the lowest
relative humidity occurs in the afternoon when temperatures are
highest.
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CVEN3501 Water Resources Engineering Fiona Johnson
[email protected]
Based on notes by Ashish Sharma, Ian Acworth Page 2-12
Refer to Allen et al. [1998] for details of other methods to
calculate actual vapour pressure in the absence of
minimum and/or maximum relative humidity measurements.
If wind measurements at a height of 2m are not available, the
following equation may be used to convert
measurements from a height zm to corresponding values for a
height of 2m:
)0023.0/ln()0023.0/2ln(
2m
zz
uu = 2-30
where uz is the wind speed measured at a height of zm. Commonly
wind speed measurements are made at a
height of 10 m.
2.5.5 Penman open water body evaporation
For open water body evaporation the surface resistance can be
neglected (rs = 0) in Equation 2-20 and thus the
form for the equation using standard meteorological variables
is:
( )( )
+
++=
DuAET 2053.0143.6
2-31
As for the reference crop, the units for A should be MJ m-2
day-1
and D in kPa to give the evaporation in units of
mm day-1
2.5.6 Other methods
Radiation based equations
The Priestley Taylor equation [Priestley and Taylor, 1972] is a
simpler relationship between reference crop
evaporation and the available energy, leaving out the vapour
pressure deficit part of the Penman Monteith
equation, on the basis that the first term usually exceeds the
second by a factor of four [Shuttleworth, 1993].
This is given as:
+
=
AETrc 2-32
where has been empirically estimated as 1.74 for arid climates
with relative humidity less than 60% in the
month with peak evaporation and 1.26 for humid climates.
Empirical equations
There are a number of empirically based equations, particularly
based on temperature, that are widely
referenced or have been commonly used in the past [McMahon et
al., 2013]. The physical basis for estimating
evaporation using temperature alone is that both radiation and
vapour pressure deficit are likely to have some
relationship with temperature. In general the only justification
of using estimation equations of this type is
that temperature is the only available variable that has been
measured. In this case it is unwise to make
evaporation estimates for less than a monthly averaging period
[Shuttleworth, 1993]. McMahon et al. [2013]
also recommend the use of physically based equations (such as
the Penman-Montheith method) should be
preferred compared to the empirical relationships particularly
for areas where the empirical coefficients
were not derived.
The Thornthwaite method [Shaw, 1994] provides estimates of
potential evapotranspiration using only mean
monthly temperature data. The estimates are based on
climatological average temperatures and therefore
provide a climatological estimate of evaporation rather than
true evaporation for any particular day or month.
a
o ITET
=
1016 2-33
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Where I is a heat index computed using all monthly average
temperatures as:
=
=
12
1
514.1
5jjTI 2-34
And a is:
49239.010792.11071.71075.6 22537 ++= IIIa 2-35
2.5.7 Calculating actual evapotranspiration
The water status of the soil is very important in estimating the
actual evapotranspiration compared to the
potential evapotranspiration. This relationship is shown
below:
oa ETfET )(= 2-36 A typical relationship for the soil moisture
extraction function is shown in Equation x.
=
wpfcwpff
)( 2-37
Where fc is the field capacity and wp is the wilting point.
2.6 References
Allen, R. G., L. S. Pereira, D. Raes, and M. Smith (1998), Crop
evapotranspiration - Guidelines for computing
crop water requirements, FAO - Food and Agriculture Organization
of the United Names, Rome.
Ladson, A. R. (2008), Hydrology: an Australian introduction,
Oxford university press.
McMahon, T., M. Peel, L. Lowe, R. Srikanthan, and T. McVicar
(2013), Estimating actual, potential, reference
crop and pan evaporation using standard meteorological data: a
pragmatic synthesis, Hydrology and Earth
System Sciences, 17(4), 1331-1363.
Penman, H. L. (1948), Natural Evaporation from Open Water, Bare
Soil and Grass, Proceeding of the Royal
Society of London, Series A, Mathematical and Physical Sciences,
193(1032), 120-145.
Priestley, C. H., and R. J. Taylor (1972), Assessment of Surface
Heat-Flux and Evaporation Using Large-Scale
Parameters, Monthly Weather Review, 100(2), 81-92.
Shaw, E. M. (1994), Hydrology in Practice, Chapman & Hall,
London.
Shuttleworth, W. J. (1993), Evaporation, in Handbook of
Hydrology, edited by D. R. Maidment, McGraw-Hill
Inc, New York.