cven3501 week 2 notes

CVEN3501 Water Resources Engineering Fiona Johnson

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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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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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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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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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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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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.

cven3501 week 2 notes

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