1. 1
First International Conference on Science & Environment,
Tsu City, Nov. 19-21, 2015, ISBN: 978-4-9905958-3-8 C3051
EXAMINING THE SIX WELL KNOWN EQUATIONS FOR
ESTIMATING REFERENCE EVAPOTRANSPIRATION IN
HERAT, AFGHANISTAN
Homayoon Ganji1 Takamitsu Kajisa1 Masaaki Kondo1 Behroze Rostami1
1Graduate School of Bioresources, Mie University, 514-8507 Kurima-machiya-cho 1577, Tsu, Japan
ABSTRACT
Herat province as a semi-arid area, having strong winds which are known as “120-day winds” needs to be
investigated with aim for discovering the best method for estimating the reference evapotranspiration (ET0)
which has the most accuracy and is adaptable in the area. In this research, an examining has been done between
six well known methods based on their performances under the given climatic condition in the Herat provinces.
Pan evaporation (Epan) is considered as indicator to compare with Penman-Monteith, which is the only method
that includes a variable of wind, Thornthwaite, and Hargreaves, and Hamon, Net radiation and solar radiation
methods. 8 years data from 2006 to 2013 is used to show the seasonal climatic variations as well the year 2009
data is used to compare the six methods between each other. The ET0 estimated values by six methods have been
correlated with Epan estimated value, using Pearson’s correlation (R) methods. Based on p-value, all of the six
methods are found significant to be used for measuring the ET0. The Penman-Monteith method is showing the
highest R. Hence, by considering the standard error estimation (SEE) calculation, the Penman-Monteith method
has the lowest value which suggests the best measuring of the ET0. The secondary smallest SEE was shown for
Hargreaves. The yearly ET0 of Hargreaves was larger than the Epan, while the yearly ET0 of Penman-Monteith
was smaller than Epan. Therefore, in a case the aim is not accuracy but design, the Hargreaves might not be
ignored.
Keyword: 120-day winds, Pan Evaporation, Reference Evapotranspiration,Herat, Afghanistan
INTRODUCTION
Evapotranspiration (ET) is defined as physical
processes whereby liquid water vaporized into the
atmosphere from evaporating surfaces [2], [11] and
[15]
ET is the most significant component of the
hydrologic budget, apart from precipitation [7].
Accordingly, in arid and semi-arid areas, ET is
important as well. The ET varies according to
weather and wind conditions. Because of this
variability, water managers who are responsible for
planning and adjudicating the distribution of water
resources need to have a thorough understanding of
the ET process, and knowledge about the spatial and
temporal rates of it.
ET is defined in different concepts as one of the
concepts is called potential or reference
evapotranspiration (ET0). The concept of the ET0 is
used to introduce the evaporative demand of the
atmosphere apart from the crop type, crop
development and management practice [2].
Many different methods for measuring the ET0
have been developed based on their daily
performances under the given climatic condition in
the world. In this study, only six models are selected
to estimate the ET0 for Herat, Afghanistan.
Penman-Monteith, the United Nations Food and
Agriculture Organization (FAO) has introduced a
model for estimating of the standard ET0 which is
known as Penman-Monteith model Eq. (1) Table 1
[2]. The accuracy of the FAO model is as high as
recommended sole method of calculating ET0, if the
requirement set of data are available [2]. The only
limitation to the Penman family of models, they
require many meteorological inputs, thereby limiting
their utility in data-sparse areas [7], [4].
Thornthwaite (1944) defines ET0 as “the water
loss which will occur if at no time there is a
deficiency of water in the soil for use of vegetation”
[16]. As this method requires only monthly average
temperature, is considered to be popular method [13]
According to the Mintz and Walker (1993), the
Thornthwaite method has been developed to
temperature measured under potential conditions and
in only overestimate the potential evaporation in arid
regions if air surface temperature is applied Eq. (2)
Table 1.
The Hargreaves-Samani (1985) is one of the
older ET models which are introduced by Allen and
2. First International Conference on Science & Environment,
Tsu City, Nov. 19-21, 2015, ISBN: 978-4-9905958-3-8 C3051
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Hargreaves Eq. (3) [9] Table 1. The requirement
component for this model is simpler than the
Penman-Monteith. The Hargreaves’s ET0 model
requires only measured temperature data. This
model is seen to be less impacted than Penman-type
methods when data are collected from arid or semi-
arid and non-irrigated sites.
A method was described by Doorenbos and
Pruitt (1977) through which evaporation is
converted to ET0. This method described by Allen
et al. (1991), known as FAO 24 Pan Evaporation
(24PAN). In order to estimate ET0, the measured pan
evaporation is adjusted by a coefficient Kp Eq. (4).
This method is the basic form of the 24PAN model,
which is also described by Fontenot, R. L. (2004)
Table 1.
Homan Method is also known as one of the
simplest methods that are applicable for estimating
the ET0 in monthly base or yearly bases. According
to the Haith and Shoemaker (1987), this method
requires only average number of daylight hours per
day and saturated vapor pressure. The Eq. (5) is used
for this method which was given by [8] Table 1.
Finally, FAO-56PM was simplified by Irmak et
al. (2003) as expressing a multi-linear regression
function that only net radiation (Rn) and solar
radiation (Rs) are needed as requires input
parameters for estimation Eq. (6)-(7) Table 1.
Table 1 Deferent model’s equations
Model Equation No
FAO Penman-Monteith
(56PM) 𝐸𝑇0 =
0.408( 𝑅 𝑛 − 𝐺) +
900
𝑇 + 273
𝑢2 (𝑒𝑠 − 𝑒 𝑎 )
+ (1 + 0.34𝑢2
)
1
Thornthwaite
𝐸𝑇0 = 16 × (
10 𝑇𝑖
𝐼
)
𝑎
(
𝑁
12
) (
𝐼
30
)
𝐼 = ∑ (
𝑇𝑖
5
)
1.51412
𝑖 =1
𝑎 = (492390 + 17920𝐼 − 77.1I2
+ 0.675I3) × 10−6
2
Hargreaves-Samani 1985
(H-S)
𝐸𝑇0 = 0.0023 (𝑇 𝑚𝑒𝑎𝑛 + 17.8)(𝑇 𝑚𝑎𝑥 − 𝑇 𝑚𝑖𝑥 )0.5
𝑅 𝑎 3
Pan Evaporation 𝐸𝑇0 = 𝐾𝑝 × 𝐸𝑝𝑎𝑛 4
Homan Method
𝐸𝑇0 =
2.1 × 𝐻𝑡
2
𝑒𝑠
(𝑇 𝑚𝑒𝑎𝑛 + 273.3)
5
Net radiation (Rn) 𝐸𝑇0 = 0.489 + 0.289𝑅 𝑛 + 0.023𝑇 𝑚𝑒𝑎𝑛 6
Solar radiation (Rs) 𝐸𝑇0 = 0.611 + 0.149 𝑅𝑠 + 0.079𝑇 𝑚𝑒𝑎𝑛 7
Where:
ET0 is grass reference evapotranspiration (mm day-1),
Rn is net radiation (MJ m-2 day-1), G is soil heat flux
(MJ m-2 day-1), γ is the psychometric constant (kPa
°C-1), es is the saturation vapor pressure (kPa), ea is
the actual vapor pressure (kPa), ∆ is the slope of the
saturation vapor pressure - temperature curve (kPa
°C-1), T is the average daily air temperature (°C), u2
is the mean daily wind speed at 2 m (m s-1) [2]. Ti is
the mean monthly temperature (°C); N is the mean
monthly sunshine hour, Tmax is the daily
maximum temperature (°C), Tmin is the daily
minimum temperature (°C), Ra is the daily
extraterrestrial radiation (mm day-1), KP is the pan
coefficient, Epan is the pan evaporation (mm day-1),
Ht is average number of daylight hours per day [day],
Rs is solar shortwave radiation (MJ m-2 day-1).
The available ET0 date with different
organization in Herat province is calculated through
software developed by FAO, called CLIMWAT and
CROPWAT software. Except that, there is no any
method has been recommended for estimating the
ET0 in Herat province yet, it means that, still no any
research has been done to compare different
3. First International Conference on Science & Environment,
Tsu City, Nov. 19-21, 2015, ISBN: 978-4-9905958-3-8 C3051
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methods in this regards so far. Thus, in order to
establish a common method which can provide a
more accurate ET0, this research has been done with
following hypothesis:
1) Epan can be a good indicator for ET0
estimation through different methods.
2) The ET0 estimation value is more accurate
with the methods those require wind factor than the
dose do not require wind factor.
ESTIMITION METHODS
For estimating the ET0 rate, six well known
methods are used as shown in Table 1. Climatic
parameters that is important for estimation of the six
different methods, shown in Table 2.
Table 2 Metrological parameters for different methods.
Methods
Variables
Temperature Humidity
Wind
speed
Radiation
No. of
Daylight hours
Saturated
vapourpressure
FAO56-PM necessary necessary necessary necessary necessary
Thornthwaite necessary - - necessary
Hargreaves necessary - - necessary - -
Hamon necessary - - necessary -
Rs- based
radiation
necessary necessary - necessary necessary -
Rn- based
radiation
necessary necessary - necessary necessary -
Due to lack of enough Epan data, only the data
from year 2009 is used to estimate the ET0.
Collecting the metrological data is still a
challenge in Afghanistan, but recently the ministry
of Agriculture and livestock with support of FAO
organization could reestablish the metrological
stations in each province of Afghanistan.
There is a metrological station in Herat province
which belongs to the department of Agriculture and
livestock. This station is called Urdu Khan Research
Center.
Urdu khan Regional Agricultural Research
Station with a total area of 225 hectares is located in
latitude of 39° 11' N and a longitude of 68° 13' E
with an elevation of 964 meters in Urdu khan village,
at 5.8 kilometers southeast of Herat city. The
maximum mean annual temperature is around
28.9°C and minimum mean temperature -0.6 °C.
Precipitation is reported 220 mm in average base
yearly. The first frost almost occurs around
November 4th whereas the last frost is seen about
March 28th. The total frost-free days are 226 day
during the summer season [14]. A strong wind
which is called the “120-day winds” persists from
early June until late September with a strong average
force (7.01 m/sec) [6].
RESULT AND DISCUSSION
Strong winds as a metrological factor, influences
the ET0 which is estimated by different methods.
The ET0 rate is shown different according to the
different methods because all applied methods
require different metrological factors in estimation
of the ET0.
Among the applied methods in this study,
Penman-Monteith is the only method which requires
wind factor directly for estimating the ET0 including
of the temperature, relative humidity and sun shine
hours. Epan which is measured directly from A-class
pan and Hargreaves methods, which requires
temperature only, are influenced by wind speed
whereas the other methods are seemed not
influenced by wind factor.
1. Daily difference among the metrological
variables is shown in Fig. 1. The monthly average
variation of temperature, wind speed, humidity, solar
radiation and net radiation which are necessary for
ET0 estimation has been measured for 8 years.
5. First International Conference on Science & Environment,
Tsu City, Nov. 19-21, 2015, ISBN: 978-4-9905958-3-8 C3051
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Humidity is seen high in the early spring, entire
the winter and late fall whereas the summer season
is characterized with low humidity, due to low
precipitation.
The entire of the summer season, wind speed is
seen faster, almost more than 5 m/s averagely than
the other seasons. Similarly, temperature is high in
the summer, but since early of fall the temperature
drops till medal of spring.
Net radiation is decreasing by early of fall and
again increasing from late winter on.
2. Compression of the daily average ET0 value,
estimated through the different six methods such as;
Thornthwaite, Hargreaves, Hamon, Solar radiation
and Net radiation, Epan and FAO-56PM between
each other is shown by (Fig. 2 to 7),using data of
year 2009. All methods show a higher rate of ET0
from the early summer until late fall.
The Penman-Monteith and Hargreaves methods
show closer ET0 value to the Epan entire of the year,
especially at early of summer until late fall seasons
(Fig 2 and 3). The reason might be referred to the
strong wind “120-day winds” which blows all the
summer season with high speed. This is why the ET0
estimated through penman-Monteith, which requires
wind velocity and Hargreaves method, which is
recommended at the arid area are closer in volume
with Epan.
Fig. 2 Daily average estimated ET0 through Epan
and Penman-Monteith methods
Fig. 3 Daily average estimated ET0 through
Epan and Hargreaves methods
It is shown in Fig. 2 that, there is deference
between Penman-Monteith ET0 value and Epan value
since early of summer until end of summer season;
as well, the deference is seen between Hargreaves
ET0 value and Epan value from January until June
shown in Fig. 3.
The other four methods show lower ET0 value
than the Epan, as there is a big deference between
each method and Epan, especially form around May
until late November (Fig. 4 to 7).
Fig. 4 Daily average estimated ET0 through
Epan and Hamon methods
Fig. 5 Daily average estimated ET0 through
Epan and Thornthwaite methods
Fig. 6 Daily average estimated ET0 through
Epan and Solar radiation methods
Fig. 7 Daily average estimated ET0 through Epan
and Net radiation methods
0
5
10
15
20
25
ET0(mm/day)
Epan Penman-Montieth
0
5
10
15
20
25
ET0(mm/day)
Epan Hargreaves
0
5
10
15
20
25
ET0(mm/day)
Epan Hamon
(C)
0
5
10
15
20
25
ET0(mm/day)
Epan Thoranthwait
0
5
10
15
20
25
ET0(mm/day)
Epan Solar radiation (Rs) based method
0
5
10
15
20
25
ET0(mm/day)
Epan Net radiation (Rn)based Method
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3. Yearly estimated ET0 value by using the six
well known methods is shown by Fig. 8. The
Hargreaves, Epan and Penman- Monteith show higher
total annual ET0 value than the four others.
Variations in the ET0 estimation reflect the
differences in the variables applied in each method.
According to the Fig. 8, Hargreaves shows the
highest total annual ET0 value that is 3500 mm/year,
whereas the Thornthwaite, Homan, Solar radiation
based method and Net radiation based methods show
the lower value of total annual ET0 of which
Thornthwaite method shows the lowest total annual
value that is 1000 mm/year.
Fig. 8 Total annual ET0 estimates given by different
methods covering 2009 year metrological data
As the Epan is considered as indicator, the
estimated ET0 through Penman-Monteith and
Hargreaves methods are closer to the Epan value.
Therefore, the Penman-Monteith methods can be
considered the most accurate method, whereas the
Hargreaves methods as the second accurate method
is useful to apply for designing of irrigation plan.
4. Brutsaert and Parlange (1998) indicated
that, Epan is often taken as a good indicator of ET0.
Therefore Fig. 4 shows a strong correlation between
penman-Monteith method and Epan. This correlation
is found by Zhang et al., 2007. Zhang considered
Epan as indicator for reference evapotranspiration and
potential evapotranspiration.
Fig. 9 Relationships between yearly Penman-
Monteith ET0 and evaporation Epan [17]
Therefore, The Hargreaves, Thornthwaite,
Hamon, solar radiation and net radiation-based
methods, Penman-Monteith are correlated with Epan
as the value of (R2), (a) coefficients and Total yearly
ET0 is shown by Table 4. By considering the (R2)
and (a) value, in a case if the (R2) value is the same
between two methods, the most accurate and
significant method is the one which has the (a)
nearest to the 1.
The Penman-Monteith method with having (R2 =
0.8817& a = 0.6962) is shown the highest
correlation with Epan as well as shows the closest ET0
value to the Epan.
Table 3 Correlated coefficient and standard error
estimation of six well known methods
Models
coefficients
SEE
P-
valueR2 a b n
Hargreaves 0.8 0.8 3.6 365 3.32 0.00
FAO-56PM 0.8 0.6 0.7 365 2.70 0.00
Solar-
radiation
0.8 0.2 1.4 365 5.70 0.00
Net radiation 0.6 0.2 1.9 365 6.11 0.00
Hamon 0.8 0.3 0.5 365 5.71 0.00
Thornthwaite 0.8 0.3 0.0 365 5.97 0.00
The relationship between the six methods is
shown in Fig. 5. Based on P-value all the methods
have significant correlation with Epan, but by
considering the (a) value, except the Hargreaves
which has (R2 = 0.8067 & a = 0.8037), all the others
have the low value of (a) coefficient. Furthermore,
Penman–Monteith requires the wind as a main factor
for estimating the ET0 and in other hand, Herat is
characterized with strong wind velocity, the
Penman–Monteith is recommended as the most
accurate model for estimating the ET0.
In a case if the requirement factors for penman-
Monteith is not available, the Hargreaves with (R2 =
0.8067 & a = 0.8037) method, which only requires
temperature and radiation for calculation, is
recommended for estimating the ET0 as it shows
high correlation with Epan .
0
500
1000
1500
2000
2500
3000
3500
4000
ET0 (mm/year)
ETpan (mm/y)
ET0(mm/y)
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Tsu City, Nov. 19-21, 2015, ISBN: 978-4-9905958-3-8 C3051
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Fig. 10 Relationships between daily average Epan
evaporation and Penman-Monteith methods
Fig. 11 Relationships between daily average Epan
evaporation and Hargreaves methods
Fig. 12 Relationships between daily average Epan
evaporation and Thornthwaite methods
Fig. 13 Relationships between daily average Epan
evaporation and Hamon methods
Fig. 14 Relationships between daily average Epan
evaporation and Solar-radiation methods
Fig. 15 Relationships between daily average Epan
evaporation and Net radiation Methods
CONCLUSION
In Herat province, the ET0 rate is shown different
according to the different methods because all
applied methods require different metrological
factors for estimation of the ET0. Among the applied
methods in this study, Penman-Monteith is the only
method which requires wind factor directly for
estimating the ET0 including the temperature,
relative humidity and sun shine hours.
Epan evaporation which is measured directly from
A-class pan and Hargreaves methods, which requires
temperature only, is also influenced by wind factor
whereas the othermethods are not influenced.
1. Humidity is high in the early spring, entire
the winter and late fall whereas the summer season
is characterized with low humidity due to low
precipitation.
The entire of the summer season, wind speed is
seen faster almost more than 5 m/s averagely than
the other seasons. Similarly, temperature also is high
in the summer, but since early of fall season the
temperature decreases till middle of spring.
Net radiation is decreasing by early of fall and
again increasing from late winter on.
2. All methods show a higher rate of ET0 from
the early summer until late fall. The Penman-
y = 0.6962x +0.7842
R² = 0.8817
0
5
10
15
20
25
0 5 10 15 20
Penman-Montieth(mm/day)
Epan (mm/day)
y = 0.8037x +3.6209
R² = 0.8067
0
5
10
15
20
25
0 5 10 15 20
Hargreaves(mm/day)
Epan (mm/day)
y = 0.3757x -0.0749
R² = 0.8177
0
5
10
15
20
25
0 5 10 15 20
Thoranthwait(mm/day)
Epan (mm/day)
y = 0.349x +0.5597
R² = 0.8306
0
5
10
15
20
25
0 5 10 15 20
Hamon(mm/day)
Epan (mm/day)
y = 0.2775x+ 1.4685
R² = 0.8256
0
5
10
15
20
25
0 5 10 15 20
Solarradiation(Rs)based
method(mm/day)
Epan (mm/day)
y = 0.201x+ 1.9272
R² = 0.6556
0
5
10
15
20
25
0 5 10 15 20
Netradiation(Rn)based
method(mm/day)
Epan (mm/day)
8. First International Conference on Science & Environment,
Tsu City, Nov. 19-21, 2015, ISBN: 978-4-9905958-3-8 C3051
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Monteith and Hargreaves show closer ET0 to the Epan
entire of the year, whereas the other four methods
are different especially at early of summer until late
fall seasons. The reason is referred to the strong
wind “120-day winds” which blows all the summer
season with high speed. This is why the estimated
ET0 through penman-Monteith, which requires wind
velocity and Hargreaves method, which is
recommended at the arid area, are closer to the
measured evaporation through Epan.
3. Hargreaves, Penman-Monteith and Epan
methods show the higher value of ET0 as the
Hargreaves shows the highest total annual value of
ET0 3500 mm/year, whereas the Thornthwaite,
Homan, Solar radiation based method and Net
radiation based methods, show the lower value of
ET0 as Thornthwaite has the lowest total annual
value of 1000 mm/year.
4. As the Epan is considered as indicator, the
estimated ET0 through Penman-Monteith and
Hargreaves methods are closer to the Epan value.
Therefore, those methods are applicable than the
other four methods in Herat, Afghanistan.
ACKNOWLEDGEMENT
REFERENCES
[1] Allen, Richard G., and William O. Pruitt.
"FAO-24 reference evapotranspiration factors."
J. of irrigation and drainage engineering, Vol.
117(5), Sep. 1991, pp. 758-773.
[2] Allen, Richard G., et al. "Crop
evapotranspiration-Guidelines for computing
crop water requirements-FAO Irrigation and
drainage paper 56" FAO, Rome , Vol. 300(9),
year 1998.
[3] Brutsaert, W., and M. B. Parlange. "Hydrologic
cycle explains the evaporation paradox", J. of
Nature, Vol. 396.6706, Nov. 1998, pp. 30-30.
[4] Dingman, S.L.1994. Physical Hydrology. Upper
Saddle River, NJ: Prentice Hall
[5] Fontenot, R. L., An evaluation of reference
evapotranspiration models in Louisiana. Diss.
Faculty of the Louisiana State University and
Agricultural and Mechanical College in partial
fulfillment of the requirements for the degree of
Master of Natural Sciences In The
Interdepartmental Program of Natural Sciences
by Royce Landon Fontenot BS, Louisiana State
University, 2004.
[6] Ganji H, Rahmany Ab. S, Kajisa T, Kondo M,
Hajime N, “Comparison of the Crop Water
Need between Actual Wind Condition and Zero
Wind Simulation; Wind Velocity within 24-
Hour Interval in Herat, Afghanistan”. In Tokyo
University of Agriculture. 20th Int. Conf. on
ISSAAS, 2014, pp. 91.
[7] Hanson, Ronald L. "Evapotranspiration and
droughts." Paulson, RW, Chase, EB, Roberts,
RS, and Moody, DW, Compilers, National
Water Summary (1988), pp. 99-104.
[8] Haith, Douglas A., and Leslie L. Shoenaker.
"Generalized Watershed Loading Functions for
Stream Flow Nutrients1", J. JAWRA, Vol.
23(3), Jun. 1987, pp. 471-478.
[9] Hargreaves, George H., and Richard G. Allen.
"History and evaluation of Hargreaves
evapotranspiration equation." J. of Irrigation
and Drainage Engineering, Vol. 129(1), Feb.
2003, pp. 53-63.
[10] Irmak, S., et al. "Solar and net radiation-based
equations to estimate reference
evapotranspiration in humid climates", J. of
irrigation and drainage engineering, Vol. 129(5),
Oct. 2003, pp. 336-347.
[11] Li, F., Lyons, T.J., 1999. Estimation of regional
evapotranspiration through remote sensing. J.
Appl. Meteorol.38, 1644-1654.
[12] Mintz, Y., and Walker, G. K. “Global fields of
soil moisture and land surface
evapotranspiration derived from observed
precipitation and surface air temperature.” J. of
Meteorology, Vol. 32, Aug. 1993, pp. 1305-
12334.
[13] O. Alkaeed, C. Flores, K. Jinno and A.
Tsutsumi. 2006. Comparison of Several
Reference Evapotranspiration Methods for
Itoshima Peninsula Area, Fukuoka, Japan.
Kyushu University, Vol. 66, No.1.
[14] Osmanzai, M. 2009. Annual Report. CIMMYT,
Afghanistan.
[15] Penman, H.L. 1948. Natural evapotranspiration
from open-water, bare soil and grass. Proc. R.
Soc. Acad., 193: 120-145.
[16] Thornthwaite, C. W. 1948. “An approach
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[17] Zhang, Yongqiang, et al. "Trends in pan
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112.D12. Jun. 2007.
![1
First International Conference on Science & Environment,
Tsu City, Nov. 19-21, 2015, ISBN: 978-4-9905958-3-8 C3051
EXAMINING THE SIX WELL KNOWN EQUATIONS FOR
ESTIMATING REFERENCE EVAPOTRANSPIRATION IN
HERAT, AFGHANISTAN
Homayoon Ganji1 Takamitsu Kajisa1 Masaaki Kondo1 Behroze Rostami1
1Graduate School of Bioresources, Mie University, 514-8507 Kurima-machiya-cho 1577, Tsu, Japan
ABSTRACT
Herat province as a semi-arid area, having strong winds which are known as “120-day winds” needs to be
investigated with aim for discovering the best method for estimating the reference evapotranspiration (ET0)
which has the most accuracy and is adaptable in the area. In this research, an examining has been done between
six well known methods based on their performances under the given climatic condition in the Herat provinces.
Pan evaporation (Epan) is considered as indicator to compare with Penman-Monteith, which is the only method
that includes a variable of wind, Thornthwaite, and Hargreaves, and Hamon, Net radiation and solar radiation
methods. 8 years data from 2006 to 2013 is used to show the seasonal climatic variations as well the year 2009
data is used to compare the six methods between each other. The ET0 estimated values by six methods have been
correlated with Epan estimated value, using Pearson’s correlation (R) methods. Based on p-value, all of the six
methods are found significant to be used for measuring the ET0. The Penman-Monteith method is showing the
highest R. Hence, by considering the standard error estimation (SEE) calculation, the Penman-Monteith method
has the lowest value which suggests the best measuring of the ET0. The secondary smallest SEE was shown for
Hargreaves. The yearly ET0 of Hargreaves was larger than the Epan, while the yearly ET0 of Penman-Monteith
was smaller than Epan. Therefore, in a case the aim is not accuracy but design, the Hargreaves might not be
ignored.
Keyword: 120-day winds, Pan Evaporation, Reference Evapotranspiration,Herat, Afghanistan
INTRODUCTION
Evapotranspiration (ET) is defined as physical
processes whereby liquid water vaporized into the
atmosphere from evaporating surfaces [2], [11] and
[15]
ET is the most significant component of the
hydrologic budget, apart from precipitation [7].
Accordingly, in arid and semi-arid areas, ET is
important as well. The ET varies according to
weather and wind conditions. Because of this
variability, water managers who are responsible for
planning and adjudicating the distribution of water
resources need to have a thorough understanding of
the ET process, and knowledge about the spatial and
temporal rates of it.
ET is defined in different concepts as one of the
concepts is called potential or reference
evapotranspiration (ET0). The concept of the ET0 is
used to introduce the evaporative demand of the
atmosphere apart from the crop type, crop
development and management practice [2].
Many different methods for measuring the ET0
have been developed based on their daily
performances under the given climatic condition in
the world. In this study, only six models are selected
to estimate the ET0 for Herat, Afghanistan.
Penman-Monteith, the United Nations Food and
Agriculture Organization (FAO) has introduced a
model for estimating of the standard ET0 which is
known as Penman-Monteith model Eq. (1) Table 1
[2]. The accuracy of the FAO model is as high as
recommended sole method of calculating ET0, if the
requirement set of data are available [2]. The only
limitation to the Penman family of models, they
require many meteorological inputs, thereby limiting
their utility in data-sparse areas [7], [4].
Thornthwaite (1944) defines ET0 as “the water
loss which will occur if at no time there is a
deficiency of water in the soil for use of vegetation”
[16]. As this method requires only monthly average
temperature, is considered to be popular method [13]
According to the Mintz and Walker (1993), the
Thornthwaite method has been developed to
temperature measured under potential conditions and
in only overestimate the potential evaporation in arid
regions if air surface temperature is applied Eq. (2)
Table 1.
The Hargreaves-Samani (1985) is one of the
older ET models which are introduced by Allen and](https://image.slidesharecdn.com/7faed851-b439-4bfc-855a-c7fcddd9cce8-150701101119-lva1-app6891/85/Paper-SEE-1-320.jpg)
![First International Conference on Science & Environment,
Tsu City, Nov. 19-21, 2015, ISBN: 978-4-9905958-3-8 C3051
2
Hargreaves Eq. (3) [9] Table 1. The requirement
component for this model is simpler than the
Penman-Monteith. The Hargreaves’s ET0 model
requires only measured temperature data. This
model is seen to be less impacted than Penman-type
methods when data are collected from arid or semi-
arid and non-irrigated sites.
A method was described by Doorenbos and
Pruitt (1977) through which evaporation is
converted to ET0. This method described by Allen
et al. (1991), known as FAO 24 Pan Evaporation
(24PAN). In order to estimate ET0, the measured pan
evaporation is adjusted by a coefficient Kp Eq. (4).
This method is the basic form of the 24PAN model,
which is also described by Fontenot, R. L. (2004)
Table 1.
Homan Method is also known as one of the
simplest methods that are applicable for estimating
the ET0 in monthly base or yearly bases. According
to the Haith and Shoemaker (1987), this method
requires only average number of daylight hours per
day and saturated vapor pressure. The Eq. (5) is used
for this method which was given by [8] Table 1.
Finally, FAO-56PM was simplified by Irmak et
al. (2003) as expressing a multi-linear regression
function that only net radiation (Rn) and solar
radiation (Rs) are needed as requires input
parameters for estimation Eq. (6)-(7) Table 1.
Table 1 Deferent model’s equations
Model Equation No
FAO Penman-Monteith
(56PM) 𝐸𝑇0 =
0.408( 𝑅 𝑛 − 𝐺) +
900
𝑇 + 273
𝑢2 (𝑒𝑠 − 𝑒 𝑎 )
+ (1 + 0.34𝑢2
)
1
Thornthwaite
𝐸𝑇0 = 16 × (
10 𝑇𝑖
𝐼
)
𝑎
(
𝑁
12
) (
𝐼
30
)
𝐼 = ∑ (
𝑇𝑖
5
)
1.51412
𝑖 =1
𝑎 = (492390 + 17920𝐼 − 77.1I2
+ 0.675I3) × 10−6
2
Hargreaves-Samani 1985
(H-S)
𝐸𝑇0 = 0.0023 (𝑇 𝑚𝑒𝑎𝑛 + 17.8)(𝑇 𝑚𝑎𝑥 − 𝑇 𝑚𝑖𝑥 )0.5
𝑅 𝑎 3
Pan Evaporation 𝐸𝑇0 = 𝐾𝑝 × 𝐸𝑝𝑎𝑛 4
Homan Method
𝐸𝑇0 =
2.1 × 𝐻𝑡
2
𝑒𝑠
(𝑇 𝑚𝑒𝑎𝑛 + 273.3)
5
Net radiation (Rn) 𝐸𝑇0 = 0.489 + 0.289𝑅 𝑛 + 0.023𝑇 𝑚𝑒𝑎𝑛 6
Solar radiation (Rs) 𝐸𝑇0 = 0.611 + 0.149 𝑅𝑠 + 0.079𝑇 𝑚𝑒𝑎𝑛 7
Where:
ET0 is grass reference evapotranspiration (mm day-1),
Rn is net radiation (MJ m-2 day-1), G is soil heat flux
(MJ m-2 day-1), γ is the psychometric constant (kPa
°C-1), es is the saturation vapor pressure (kPa), ea is
the actual vapor pressure (kPa), ∆ is the slope of the
saturation vapor pressure - temperature curve (kPa
°C-1), T is the average daily air temperature (°C), u2
is the mean daily wind speed at 2 m (m s-1) [2]. Ti is
the mean monthly temperature (°C); N is the mean
monthly sunshine hour, Tmax is the daily
maximum temperature (°C), Tmin is the daily
minimum temperature (°C), Ra is the daily
extraterrestrial radiation (mm day-1), KP is the pan
coefficient, Epan is the pan evaporation (mm day-1),
Ht is average number of daylight hours per day [day],
Rs is solar shortwave radiation (MJ m-2 day-1).
The available ET0 date with different
organization in Herat province is calculated through
software developed by FAO, called CLIMWAT and
CROPWAT software. Except that, there is no any
method has been recommended for estimating the
ET0 in Herat province yet, it means that, still no any
research has been done to compare different](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)