1. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
ISSN 0976 – 6316(Online) Volume 5, Issue 2, February (2014), pp. 81-87 © IAEME
81
REFERENCE EVAPOTRANSPIRATION ESTIMATION BY RADIATION
BASED METHODS
K. Chandrasekhar Reddy
Professor and Principal, Department of Civil Engineering,
Siddharth Institute of Engineering & Technology, Puttur, Andhra Pradesh, India
ABSTRACT
Most of the studies have shown that the FAO-56 Penman-Monteith (PM) method gives very
accurate estimation of reference evapotranspiration(ET0) in different environments. However, under
limited climatic data availability conditions, the simple empirical methods yielding results
comparable with PM ET0 may be selected at regional level for reasonable estimation of ET0. This
study deals with the evaluation of monthly reference evapotranspiration(ET0) estimation using
radiation based methods of Priestley-Taylor(PT), FAO-24 Radiation(RA) and Makkink(MK) by
comparing their performance with that of PM method, developing relationships between PM and
other methods and recalibrating the methods with respect to PM method. Tirupati region of Andhra
Pradesh, India is selected as the study area and its meteorological data was collected from the India
Meteorological Department, Pune. It is observed that the RA method improved its performance
significantly on recalibration when compared to other two methods. Therefore, RA method may be
used for reasonable ET0 estimation in similar climatic regions as that of the study area.
Keywords: Radiation based methods, Penman-Monteith, Recalibration,
Reference evapotranspiration.
1. INTRODUCTION
Evapotranspiration(ET) is the loss of water into the atmosphere by the combined processes of
evaporation from the soil and plant surface and transpiration from plants.[1]
Field measurement of
evapotranspiration is rarely available and actual crop evapotranspiration(ETc) is usually calculated
from estimated reference crop evapotranspiration (ET0) using the crop factor method, which consists
of multiplying ET0 with crop coefficients (Kc) to obtain ETc (i.e., ETc = ET0 x Kc). Several reports on
the estimation of Kc are available in Doorenbos and Pruitt (1977)[5]
, Allen et al. (1998)[1]
. Doorenbos
and Kassam (1979)[4]
and Jensen et al. (1990) [8]
have reported crop coefficients for many crops.
These values are commonly used in places where the local data is not available.
Reference crop evapotranspiration or Reference evapotranspiration (ET0) is defined as the
rate of evapotranspiration from a hypothetical reference crop with an assumed crop height of 0.12 m,
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2. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
ISSN 0976 – 6316(Online) Volume 5, Issue 2, February (2014), pp. 81-87 © IAEME
82
a fixed surface resistance of 70 s m−1
, and an albedo of 0.23, closely resembling the evapotranspiration
from an extensive surface of green grass of uniform height, actively growing, completely shading the
ground, and not short of water.[1]
Its accurate estimation is vital in irrigation system design, crop yield
simulation and water resources planning and management. It is desirable to have a method that estimates
reasonably the reference Evapotranspiration (ET0).
The amount of ET0 is calculated by meteorological data based methods. However, choosing the
best method for ET0 estimation from the described methods is difficult. Therefore, the International
Commission for Irrigation and Drainage and the Food and Agriculture Organization of the United
Nations (FAO) Expert Consultation on revision of FAO methodologies for crop water requirements have
recommended the FAO56 Penman-Monteith (PM) equation, which was presented in FAO 56[1]
, to be
used as the standard method to estimate ET0. Many researchers thereafter took it as a standard to modify
other methods that required less input data.
Er-Raki et al. (2010)[6]
shown, under arid and semi-arid climates, radiation based models may
perform poorly. Bois et al. (2005)[2]
studied that use of locally calibrated equations can make them more
accurate than temperature based and even combination type ones. Denmirtas et al. (2007)[3]
developed
regional relationships between ET and that estimated by various climatological methods and concluded
that PM method gives the best results followed by Penman, Radiation and Blaney-Criddle methods.
Irmak et al. (2003)[7]
recommended solar radiation and net radiation based ET0 equations over the other
commonly used temperature and radiation based methods by comparing their performance with PM
method.
The present study reports the performance evaluation of commonly used radiation based ET0
estimation methods based on their accuracy of estimation and development of inter-relationships between
the PM and the other climatological variables. And also, these methods are recalibrated with reference to
PM method for Tirupati region of Andhra Pradesh, India.
2. MATERIALS AND METHODS
Tirupati region, located in Chittoor district of Andhra Pradesh, India, with global coordinates of
130
05’N latitude and 790
05’
E longitudes, has been chosen as the study area. The meteorological data of
the study area for the period 1992-2001 was collected from IMD, Pune. Data from 1992 to 1998 is used
for the purpose of training the model and that of 1999 to 2001 for testing the model. The details of the
methods selected for the present study are presented in Table 1.
Table1: Details of reference evapotranspiration estimation methods
Method Basic
reference
Equation Input data
Primary Secondary
FAO 56 Penman-
Monteith (PM)
Method
Allen et al.,
(1998)[1]
ET0 =
)34.01(
)(
273
900
)(408.0
2
''
''
2
''''
u
eeu
T
GR as
mean
n
++∆
−
+
+−∆
γ
γ
Tmax, Tmin,
RHmax,
RHmin, u2, n
….
Radiation based methods
1.Priestley-
Taylor (PT)
Priestley-
Taylor
(1972)[12]
( )G−
+
= n0 R
γ∆
∆
26.1ET
Tmax, Tmin, n ---
2.FAO-24
Radiation (RA)
Doorenbos
and Pruitt
(1977)[5]
ET0 = c (W.Rs)
Where
c = 1.066 – 0.00128 RHmean
+ 0.045 ud – 0.0002 RHmean ud
+ 0.0000315 (RHmean) 2
– 0.00103 (ud)2
Tmax, Tmin, n RHmax, RHmin,
u2, ud/un
3.Makkink(MK) Makkink
(1957)[10]
Tmax, Tmin, n ---
Rs
γΔ
Δ
65.0ET0
+
=

3. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
ISSN 0976 – 6316(Online) Volume 5, Issue 2, February (2014), pp. 81-87 © IAEME
83
3. PERFORMANCE EVALUATION CRITERIA
The performance evaluation criteria used in the present study are the coefficient of
determination (R2
), the root mean square error (RMSE), systematic RMSE, unsystematic RMSE and
the efficiency coefficient (EC).
3.1 Coefficient of Determination (R2
)
It is the square of the correlation coefficient (R) and the correlation coefficient is expressed as
Where O and P are observed and estimated values, O and P are the means of observed and
estimated values and n is the number of observations. It measures the degree of association between
the observed and estimated values and indicates the relative assessment of the model performance in
dimensionless measure.
3.2 Root Mean Square Error (RMSE)
It yields the residual error in terms of the mean square error and is expressed as
(Yu et al., 1994)[13]
n
op
RMSE
ii
n
i
2
1
)( −
=
∑=
3.3 Systematic RMSE (RMSEs)
It measures the room available for local adjustment. It is expressed as
n
op
RMSE
ii
n
i
s
2
1
)ˆ( −
=
∑=
Where ii boap +=ˆ
, a and b are the liner regression coefficients
3.4 Unsystematic RMSE (RMSEu)
It shows the noise level in the model and is a measure of scatter about the
regression line and potential accuracy. It is expressed as
n
pp
RMSE
ii
n
i
u
2
1
)ˆ( −
=
∑=
2/1
1
2
1
2
1
)()(
))((




∑ −∑ −
−−∑
=
==
=
n
i
i
n
i
i
ii
n
i
ppoo
ppoo
R

4. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
ISSN 0976 – 6316(Online) Volume 5, Issue 2, February (2014), pp. 81-87 © IAEME
84
3.5 Efficiency Coefficient (EC)
It is used to assess the performance of different models (Nash and Sutcliffe, 1970)[11]
. It is a
better choice than RMSE statistic when the calibration and verification periods have different lengths
(Liang et al., 1994)[9]
. It measures directly the ability of the model to reproduce the observed values
and is expressed as
( )
( )∑
∑
=
=
−
−
−= n
i
i
n
i
ii
oo
po
EC
1
2
1
2
1
A value of EC of 90% generally indicates a very satisfactory model performance while a
value in the range 80-90%, a fairly good model. Values of EC in the range 60-80% would indicate an
unsatisfactory model fit.
4. RESULTS AND DISCUSSION
The percentage deviations of ET0 values estimated by PT, RA and MK methods with
reference to PM method are presented in Table 2. It may be observed that the deviations are
significant for all the methods. Fig.1 showing the comparison of ET0 estimates with those of PM ET0
also exhibit similar observations.
Table 2 Percentage deviations in the monthly average ET0 values estimated by
radiation based methods with PM method
Percentage deviation
PT RA MK
-39.4 to 13.4 -11.6 to 75.6 -51.6 to -2.6
Fig.1 Comparison of monthly average ET0 values estimated by radiation based
methods with PM method
4.1 Development of inter-relationships between PM method and radiation based methods
The ET0 values estimated using PT, RA and MK methods plotted against PM ET0 are shown
in Fig.2 for study area. The performance indicators of the relationships developed between PM
method and these methods are presented in Table 3. The large deviations of the slope from one and
intercept from zero can be observed from the scatter plots. Low values of R2
& EC and high values
of RMSE indicate unsatisfactory performance of the relationship. High values of systematic RMSE
and unsystematic RMSE represent the scope for recalibration. It indicates the unsatisfactory
performance of relationships between PM and radiation based methods. Therefore, it may be tried to
improve these methods’ performance by suitably recalibrating them against PM method using the
observed climatic data.
Tirupati
0
1
2
3
4
5
6
7
8
9
10
11
1 11 21 31 41 51 61 71 81 91 101
Months
ETo(mm/day)
PM PT RA MK

5. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
ISSN 0976 – 6316(Online) Volume 5, Issue 2, February (2014), pp. 81-87 © IAEME
85
Fig.2 Scatter plots of monthly average ET0 values estimated by radiation based
methods against PM method
Table 3 Performance indicators of radiation based methods with reference to PM method
Method Relationship R2
RMSE
(mm)
RMSES
(mm)
RMSEU
(mm)
EC
(%)
PT PM = 1.4215 PT – 1.0428 0.5980 0.86 0.55 0.67 59.80
RA PM = 0.8174 RA – 0.4955 0.5164 0.95 0.66 0.68 51.64
MK PM = 1.3083 MK + 0.1970 0.4610 1.00 0.73 0.68 46.10
4.2 Recalibration of radiation based ET0 estimation methods
It has been emphasized in the above section that radiation based methods selected for the
present study have not performed satisfactorily in the regional ET0 estimation. The relationships
developed between PM method and these methods to estimate ET0 comparable with PM method in
the region as presented in the above section also showed unsatisfactory performances, though there
was an improvement over the original methods. Therefore, before applying these methods to other
regions, it is necessary to recalibrate them based on the locally collected lysimeter measured ET0
data accompanied by meteorological data such that they can be used in the region of the study area
for reliable ET0 estimation. However, in the absence of lysimeter data, the competent PM method is
usually adopted as the standard method of comparison for recalibration of the other methods. Since
lysimeter measured ET0 data is not available in most of the regions, the methods were recalibrated
with respect to PM method.
The PT, RA and MK methods selected for the present study were recalibrated with reference
to PM method. The recalibrated equations derived for the study area are presented along with
original equation in Table 4. The performance indicators of recalibrated equations in the estimation
of ET0 for both training and testing periods are given in Table 5. The scatter and comparison plots of
ET0 values estimated by these methods with those of PM ET0 during the testing period are shown in
Fig.3 and Fig.4 respectively.
It may be observed from Table 5 that the RA method yielded the least RMSE and high R2
&
EC values resulting in ET0 comparable with that from PM method. The RA method outperformed
these methods in terms of performance evaluation criteria which may be due to the fact that the
method takes into account not only the effects of humidity and wind velocity in the form of
secondary input in addition to the primary input of radiation but also adjusts on recalibration over the
other methods. The slope and intercept respectively close to one and zero also indicate an improved
performance of the method with recalibrated coefficients.
From the above discussion, it may be concluded that the RA method with recalibrated
coefficients may be used for reasonable ET0 estimation in the study area.
Tirupati
0
1
2
3
4
5
6
7
8
9
10
11
0 1 2 3 4 5 6 7 8 9 10 11
ETo by PT, mm/day
ETobyPM,mm/day
Ideal line
Best fit line
Tirupati
0
1
2
3
4
5
6
7
8
9
10
11
0 1 2 3 4 5 6 7 8 9 10 11
ETo by RA, mm/day
ETobyPM,mm/day
Tirupati
0
1
2
3
4
5
6
7
8
9
10
11
0 1 2 3 4 5 6 7 8 9 10 11
ETo by MK, mm/day
ETobyPM,mm/day

6. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
ISSN 0976 – 6316(Online) Volume 5, Issue 2, February (2014), pp. 81-87 © IAEME
86
Table 4 Recalibrated radiation based ET0 equations
Method Original Equation Recalibrated Equation
1.Priestley-
Taylor (PT)
2.FAO-24
Radiation(RA)
ET0 = c (W.Rs)
Where
c = 1.066 – 0.00128 RHmean
+ 0.045 ud – 0.0002 RHmean ud
+ 0.0000315 (RHmean) 2
– 0.00103 (ud)2
ET0 = c (W.Rs)
Where
c = 0.325 + 0.00198 RHmean
+ 0.303 ud – 0.0026 RHmean ud
+ 0.000007 (RHmean) 2
– 0.000034 (ud)2
3.Makkink(MK)
Table 5 Performance indices of recalibrated radiation based ET0 methods
Method
Slope of the
scatter plots
Intercept of the
scatter plots
R2 RMSE
(mm)
EC
(%)
Training
Period
Testing
period
Training
period
Testing
period
Training
period
Testing
period
Training
Period
Testing
period
Training
period
Testing
period
PT 1.1933 1.1260 -0.8720 0.1894 0.6082 0.5668 0.85 0.88 60.82 56.68
RA 0.9390 1.0087 0.3052 0.1894 0.9528 0.9610 0.30 0.26 95.28 96.10
MK 0.9468 0.9445 0.2995 0.1501 0.4582 0.4459 1.00 0.99 45.82 44.59
Fig.3 Scatter plots of monthly average ET0 values estimated by recalibrated radiation based
methods against PM ET0 values during testing period
Fig.4 Comparison of monthly average ET0 values estimated by recalibrated radiation based
methods with those estimated by PM method during testing period
Tirupati
0
1
2
3
4
5
6
7
8
9
10
11
0 1 2 3 4 5 6 7 8 9 10 11
ETo by PT, mm/day
ETobyPM,mm/day
Ideal line
Best fit line
Tirupati
0
1
2
3
4
5
6
7
8
9
10
11
0 1 2 3 4 5 6 7 8 9 10 11
ETo by RA, mm/day
ETobyPM,mm/day
Tirupati
0
1
2
3
4
5
6
7
8
9
10
11
0 1 2 3 4 5 6 7 8 9 10 11
ETo by MK, mm/day
ETobyPM,mm/day
Tirupati
0
1
2
3
4
5
6
7
8
9
10
11
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37
Months
ETo(mm/day)
PM PT RA MK
Rs
γΔ
Δ
89.0ET0
+
=Rs
γΔ
Δ
65.0ET0
+
=
)GRn(52.1ET0 −
γ+∆
∆
=)GRn(26.1ET0 −
γ+∆
∆
=

7. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
ISSN 0976 – 6316(Online) Volume 5, Issue 2, February (2014), pp. 81-87 © IAEME
87
5. CONCLUSION
The percentage deviations of ET0 values estimated by PT, RA and MK methods with
reference to PM method are significant. The PT and MK methods underestimated and RA method
overestimated ET0 even after developing inter-relationships with PM methods, which is
unsatisfactory. The RA method improved its performance significantly on recalibration over the
other methods. Hence, the recalibrated RA method may be recommended for reasonable ET0
estimation in the study area.
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