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Vol 44, No. 7;Jul 2014
183 Pretoria, South Africa
Estimating reference evapotranspiration using modified
Blaney-Criddle equation in arid region
Mohamed H. Abd El-Wahed
1*
and Taia A. Abd El-Mageed
2
1
Soil and Water Dept. (Agric. Eng.), Fac. of Agric., Fayoum Univ., 63514-Fayoum,
Fayoum, Egypt
2
Soil and Water Dept, Fac. of Agric., Fayoum Univ., 63514-Fayoum, Fayoum, Egypt
*corresponding author
Tel +201067536208
Fax + 20 84 6334964
E-mail: abdelwahed_m64@yahoo.com
ABESTRACT
The estimation of reference evapotranspiration (ETo) is the most important step for
calculating crop water requirements. The Penman–Monteith equation (PM) is ranked as
the best equation for estimating ETo in all climates. The major limitation to PM is that it
requires many meteorological inputs. In Libya, there is a shortage in data or
unavailability. Alternatively, the Blaney-Criddle equation (BC) is a simpler method for
ETo estimation and it requires only air temperature as an input data. In this study, the BC
was modified based on the PM using the meteorological data of three stations (Obary,
Ghat and Ghadames station) in arid region of Libya. The modified BC equation (MBC)
used effective temperature instead of average temperature. The effective temperature can
be calculated based on the minimum and maximum temperature and a calibrated
coefficient (k).
In this study the variable k values (kv) and three constant k values (0.72, 0.69 and 0.64)
that suggested by other researchers were used to evaluate the MBC. The results showed
that the ETo values calculated based on the MBC which applied kv were better than the
results of ETo values calculated based on BC when compared with the ETo estimation
from the PM.
Key words: Penman-Monteith equation, Blaney-Criddle equation, evapotranspiration
INTRODUCTION
Currently about 70% of fresh water withdraw are used for agriculture (FAO, 2005). The
main user of fresh water is irrigation, and with the growing scarcity of this resource, it is
becoming increasingly important to maximize efficiency of water usage. Consequently, a
careful control of the fresh water used for irrigation is a key aspect to be considered in
order to ensure a proper distribution of the available resources between residential,
industrial and agricultural use. Several studies have shown that careful irrigation
management can considerably improve crops’ water use efficiency without causing yield
reduction (Du, et al., 2010, Hassanli, et al., 2010). One of the fundamental requirements
to estimate the amount of water necessary for optimal agricultural production is to
effectively understand the relationships between climatic conditions and
evapotranspiration (ETo). The estimation of ETo is the first and the most important step
towards designing, planning and managing different irrigation networks, water
distribution systems, water application, water balance, water management practices,
climatological and hydrological studies (Landeras et al, 2008 and Sentelhas et al. 2010).
Many equations based on meteorological data have already been developed to estimate
ETo in various climates. Among these equations, Penman–Monteith (PM) was introduced
Vol 44, No. 7;Jul 2014
184 Pretoria, South Africa
as a standard model to estimate ETo (Allen et al. 1998). PM is ranked as the best equation
for estimating daily and monthly ETo in all climates. This has been confirmed by many
researches in the last decade (Abdelhadi et al., 2000, Hargreaves and Allen 2003, Lopez-
Urrea et al., 2006, Gavilan et al., 2007, Trajkovic and Kolakovic 2009 and Martinez and
Thepadia, 2010).
The PM has two advantages over many other equations. First of all, it is a predominantly
physically based approach, indicating that the equation can be used globally without any
need for additional parameters' estimations. Secondly, the equation is well documented,
implemented in a wide range of software, and has been tested using a variety of lysimeters
(Irmak et al. 2003, Yoder et al. 2005, Suleiman and Hoogenboom 2007). Estimation of
ETo by PM requires the weather parameters like maximum and minimum temperature,
solar radiation, sunshine hours, wind speed and relative humidity. However, for many
locations, such meteorological variables are often incomplete and/or not available and/or
reliable where collecting wind speed, humidity, and radiation are limited and setting up a
new meteorological station for collecting required data costs a lot. The lack of
meteorological data from stations is a clear barrier to the proper management of water
resources in poor countries, increasing the risks of water scarcity and water conflicts
(Maeda et al. 2011 and Droogers and Allen 2002).
A much simpler alternative is the Blaney and Criddle equation (BC) since it is a
temperature-based method that requires only air temperature as input data. Air temperature
is available in the majority of metheorological stations all over the world. Although BC is
simple and old, the results of a study was carried out to estimate ETo for 16 Australian
locations indicated that the BC gave similar monthly ETo estimates as the PM (Chiew et al.,
1995). The results of another study in Saudi Arabia indicated that irrigation water
requirements for vegetables and perennial crops are close to the values estimated by the BC
(Abu Rizaiza and Al-Osaimy, 1996). Li et al. (2003) carried out a study at Naiman, Inner
Mongolia, China, and they found that the BC can be used instead of the PM equation for
estimating ETo. The results of another study to find the best alternative equation to estimate
ETo, found that BC was identified as the best equation among other climate based equations
used in the study when compared with PM for the Mahanadi Reservoir project at Raipur in
India (Chauhan and Shrivastava 2009).
This lack of data motivated Camargo et al. (1999) to develop a new approach to improve
the estimation of ETo calculating by Thornthwaite where using effective temperature
instead of average temperature. The effective temperature can be calculated using the
approach proposed by other investigators based on the minimum and maximum temperature
and a calibrated coefficient (k). Fooladmand and Ahmadi (2009) and Fooladmand (2011)
applied the T
eff
in the BC while Camargo et al. (1999), Pereira and Pruitt (2004), Dinpashoh
(2006) and Sepaskhah and Razzaghi (2009) applied the T
eff
in the Thornthwaite equation.
They reported its reliable performance compared with the PM in the estimation of ETo.
Some researchers suggested the constant value for calibrated coefficient (k); Camargo et al.
(1999) and Dinpashoh (2006) suggested the value to be 0.72, Pereira and Pruitt (2004)
suggested 0.69, Sepaskhah and Razzaghi (2009) suggested 0.64. However, Fooladmand and
Ahmadi (2009) and Fooladmand (2011) used variable k values.
Therefore, the objective of this study was to evaluate the accuracy of ETo estimation from
modified Blaney–Criddle (MBC) based on variable and constant of calibration coefficient
values compared with the ETo estimation from the PM in arid region of Libya.
Vol 44, No. 7;Jul 2014
185 Pretoria, South Africa
MATERIAL AND METHODS
Three stations in arid region of Libya (Fig. 1) applied modified Blaney–Criddle (MBC)
equation for estimating ETo based on PM equation. Details about the selected stations are
presented in Table 1. For each station, data were record during period 1996- 2006.
Fig. (1): Regional map of Libya and the selected stations in the study.
Table (1): The information about the selected stations.
station
Latitude
Longitude
Elevation (m)
Obary
26º 36ˋ
12º 47ˋ
463
Ghat
25º 08ˋ
10º 09ˋ
692
Ghadames
30º 06ˋ
09º 29ˋ
346
Mean monthly values for air temperature (T), relative humidity (RH), wind speed (U) and
sunshine hours (n) for the three stations are shown in Fig. 2.
Vol 44, No. 7;Jul 2014
186 Pretoria, South Africa
Fig. (2): Mean monthly values for air temperature (T), relative humidity (RH), wind speed (U) and
sunshine hours (n) for three stations.
In this study, the complete weather data in the three stations were used to calculate ETo
by PM. Sometimes, full meteorological data are not available or not reliable for
estimating the monthly ETo with the PM, alternatively, the modified BC (MBC) could be
used. The BC (Doorenbos and Pruitt 1984) is as follows:
According to (Frevert et al., 1983) b
can be calculated as follows:
Where:
)1(13.846.0
mean
TpbaETo
)2(41.10043.0
min
N
n
RHa
)3()()(0006.0
)()(006.0)(066.0)(07.1)(0041.082.0
min
minmin
URH
N
n
RHU
N
n
RHb
Vol 44, No. 7;Jul 2014
187 Pretoria, South Africa
ETo
is the reference evapotranspiration, mm d
-1
a and b
are the coefficients which depend on the U, RH
min
and n/N
P
is the mean annual percentage of daytime hours.
*T
mean
is mean air temperature at 2 m height,
0
C.
RH
min
is minimum relative humidity , %
n/N
is ratio of possible to actual sunshine hours,
U
is mean daytime wind speed at 2 m height, m s
-1
.
The first step to modify BC method, calculating k values (eq.4) for the three stations, in
this study k value was calculated as:
a) Constant value of 0.72, 0.69 and 0.64 will be presented by k0.72, k0.69 and
k0.64.
b) Variable values for different months and different stations, will be presented by
kv.
Therefore, four methods were used to calculate ETo with MBC.
The second step is calculate the effective temperature (T
eff
) as follows (Camargo et al.,
1999):
Where:
T
eff
effective monthly temperature (°C),
k
calibrated coefficient,
T
max
maximum monthly temperature (°C),
T
min
minimum monthly temperature (°C).
Then, applying the T
eff
instead of the Tmean, therefor Eq. 1 can be rewritten as
Eq. 5, this is called the modified Blaney–Criddle equation (MBC):
Under the three stations the final step will consider, each ETo values that estimated with
MBC by four methods to be compared with ETo values calculating from PM to identify
the method of k that gave the best estimate for ETo. The performance of the four methods
of k applied in MBC was evaluated for two years under the three stations. For this
)5()46.0()13.8(
eff
TpbpbaETo
)4(
2
)3(
minmax
TTk
T
eff
2
minmax
TT
T
mean
Vol 44, No. 7;Jul 2014
188 Pretoria, South Africa
purpose, 1999 and 2005 were selected randomly. ETo values obtained using MBC for
two years selected and three stations were compared with ETo values obtained using PM.
Statistical analyses:
The ETo was calculated with BC and MBC that applied four methods under the three
stations and two years compared with ETo calculated with PM to evaluate the accuracy of
the values of k. The statistical analyses were:
1- Root mean square error (RMSE)
The RMSE value was calculated as follows:
Where:
RMSE
is root mean square error (mm d
-1
),
Yi
is the calculated ETo with BC and MBC under four condition,
Xi
is the calculated ETo with PM,
n
is the number of sample.
2- Mean bias error (MBE)
3- Coefficient of determination (R2)
Coefficient of determination (R
2
) is a measure of the fraction of the variation in the
dependent variable that can be explained by the independent variable.
4- Percentage error of estimates (PE)
The estimated PE was calculated by divided ETo calculated with BC and MBC
under four condition by ETo calculated with PM.
The condition that has the lowest RMSE and MBE, the PE value is closest to 100 and the
highest (R
2
) (Parmele and McGuinness 1974) is the best.
Results and Discussions
Under different stations' conditions, the mean monthly weather data was used to calculate
kv. The kv values calculated based on the PM method and BC for all stations and months
are shown in Table 2.
)6(
5.0
1
2
n
XY
RMSE
n
i
ii
)7(
1
n
XY
MBE
n
i
ii
)8(100
and
PMbyvalueETo
MBCBCbyvalueETo
PE
Vol 44, No. 7;Jul 2014
189 Pretoria, South Africa
Table (2): The kv values for all stations and months.
Months
Obary
Ghat
Ghadames
Jan
0.41
0.44
0.51
Feb
0.44
0.49
0.56
Mar
0.46
0.54
0.58
Apr
0.51
0.60
0.61
May
0.51
0.58
0.64
Jun
0.46
0.55
0.62
Jul
0.44
0.52
0.58
Aug
0.44
0.53
0.61
Sep
0.49
0.56
0.67
Oct
0.49
0.55
0.61
Nov
0.42
0.48
0.56
Dec
0.40
0.45
0.53
As presented in Table 2, the kv values are changed according to the different months and
stations. This result is in full agreement with obtained results from Ahmadi and
Fooladmand (2008) and Fooladmand (2011), who reported that the k value will be
changed for different months and stations.
The performance of ETo calculated by BC and different methods (Kv, K0.72, K0.69 and
K0.64) were evaluated for two years under the three stations. ETo estimated by the PM
against BC and different methods for each of the three stations and for two years are
plotted in Fig. 3. As shown in Fig.3, there are some differences in the ETo values
estimated by the different methods in each station and among stations. This finding is in
agreement with those reported by Al-Ghobari (2000) who showed that the variation of
ETo increased or decreased between the methods depending on the accuracy method
used. Also, there is a variation between the values of ETo estimated by the different
methods when compared among stations that can be attributed to the accuracy method
used and to the natural variation in climatic conditions influencing ETo occurring in each
station.
In general, it can be seen that the ETo calculated by kv are more related to ETo calculated
by PM when compared by other methods.
Vol 44, No. 7;Jul 2014
190 Pretoria, South Africa
Fig. 3: ETo calculated by PM against BC and different methods in three stations and two years.
Generally, Table 3 shows that the mean RMSE values ranged between 0.29 and 1.59 mm
day
–1
. This result takes the same line obtained by Mahmood and Hubbard (2005) and
Gavilan et al. (2006), who found that the RMSE ranged between 0.92–1.31 and 0.46–1.65
mm day
–1
, respectively.
In Obary station Table 3, the mean RMSE values of Bc, kv, k0.72, k0.69 and k0.64 were
1.38, 0.26, 2.08, 1.83 and 1.41mm d
-1
, respectively. As shown, the mean RMSE values of
BC and all methods were more than 1 mm d
-1
except for kv which was lower than 1 mm
d
-1
. However, the best condition was using kv value (0.26 mm d
-1
). Regarding Ghat, the
mean RMSE values of BC, kv, k0.72, k0.69 and k0.64 were 1.18, 0.29, 1.58, 1.33 and
0.92 mm d
-1
respectively. The mean RMSE values of kv and k0.64 were lower than 1 mm
d
-1
. But the best condition was using kv value where the kv values (0.29 mm d
-1
) lower
than the k0.64 (0.92 mm d
-1
). Concerning Ghadames, the mean RMSE values of BC, kv,
k0.72, k0.69 and k0.64 were 0.68, 0.33, 1.12, 0.88 and 0.52 mm d
-1
, respectively. The
mean RMSE values of all methods were lower than 1 mm d
-1
except for k0.72 which was
more than 1 mm d
-1
. Therefore, all methods except k0.72 can be used, but the best
condition was using kv value where this value was lower than other methods.
Vol 44, No. 7;Jul 2014
191 Pretoria, South Africa
The results showed that using kv values was better than using constant values. The
obtained results were in agreement with those reported by (Camargo et al., 1999, Pereira
and Pruitt, 2004 and Fooladmand, 2011).
Based on the MBE and PE, the kv method has the lowest MBE and PE (0.03 mm d
-1
and
PE = 99.43 %, respectively) and ranked first, but other methods ranked in decreasing
order; BC, k0.64, k0.69 and k0.72 (Table, 3).
Table (3) The RMSE (mm day
–1
), MBE (mm day
–1
) and P (%) calculated based on the
BC and different methods against the PM for all stations and years.
1999
2005
Obary
S. P.*
BC
Kv
K 0.72
K 0.69
K 0.64
BC
Kv
K 0.72
K 0.69
K 0.64
RMSE
1.32
0.29
2.02
1.76
1.34
1.43
0.23
2.13
1.89
1.49
MBE
-0.97
0.22
-1.89
-1.64
-1.23
-1.15
-0.03
-2.01
-1.78
-1.39
PE
118.11
95.89
135.18
130.60
122.98
124.39
100.66
142.42
137.56
129.44
Ghat
BC
Kv
K 0.72
K 0.69
K 0.64
BC
Kv
K 0.72
K 0.69
K 0.64
RMSE
1.39
0.25
1.68
1.42
0.98
0.97
0.33
1.49
1.24
0.85
MBE
-1.03
-0.03
-1.61
-1.36
-0.93
-0.62
0.10
-1.41
-1.17
-0.76
PE
117.05
100.56
126.60
122.39
115.37
110.54
98.32
124.16
120.00
113.06
Ghadames
BC
Kv
K 0.72
K 0.69
K 0.64
BC
Kv
K 0.72
K 0.69
K 0.64
RMSE
0.65
0.28
1.08
0.83
0.45
0.72
0.38
1.16
0.93
0.58
MBE
-0.22
-0.01
-0.93
-0.69
-0.30
-0.13
-0.05
-0.92
-0.70
-0.32
PE
103.56
100.20
114.98
111.14
104.74
102.29
100.92
115.80
111.93
105.48
* S. P.: Statistical parameters
The small value of MBE and PE resulted from kv means showed better performance of
the ETo estimation. So, it is concluded that the kv was more reliable than the BC and
different methods due to the very low values of MBE and PE.
Linear regression analyses were carried out between average ETo calculated by BC and
MBC which applied kv against PM at the three stations Fig. (4). Based on the results in
Fig. (4), the intercept values when applying kv were close to zero (0.0589, 0.2533 and
0.4504 for Obary, Ghat and Ghadames, respectively) and the slope values were close to 1
(0.9929, 1.0372 and 1.0801 for Obary, Ghat and Ghadames, respectively). Also, the R
2
values were high and closes to 1.0 (R
2
> 0.99) for the three stations. The close intercept
values to zero, close slope values to 1 and high R
2
values revealed that there is a reliable
and close relationship between the ETo calculated by MBC which applied kv and PM.
This means that the kv values are suitable and ranked first for calculating the ETo for the
three stations.
Vol 44, No. 7;Jul 2014
192 Pretoria, South Africa
Fig.4:Regression analysis of ETo estimated by PM against that estimated
by the BC and kv in three stations.
CONCLUSIONS
Calculating ETo is important in some applications such as irrigation design, irrigation
scheduling and water resource management. The Penman–Monteith equation (PM) is
ranked as the best equation for estimating ETo. The major limitation to PM is that it
Vol 44, No. 7;Jul 2014
193 Pretoria, South Africa
requires many meteorological inputs. However, for many stations in Libya the data are
incomplete or not available. Alternatively, the Blaney and Criddle equation (BC) which
requires only air temperature as input data will be applied.
However, BC often need to be calibrated to individual stations. In this study, a new
technique of the BC called the modified Blaney and Criddle equation (MBC) was
introduced. The MBC used effective temperature instead of average temperature. The
effective temperature can be calculated based on the minimum and maximum temperature
and a calibrated coefficient (k). The variable k values (kv) and the three constant k values
(0.72, 0.69 and 0.64) were used to evaluate the MBC.
The MBC was evaluated based on the PM through performing statistical analysis.
Statistical analysis indicated that the ETo calculated by using the MBC which applied kv
were more accurate than the ETo calculated based on BC and MBC which applied
constant values when compared with the ETo estimation from the PM.
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