1. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
ISSN 0976 – 6316(Online) Volume 5, Issue 3, March (2014), pp. 178-186 © IAEME
178
RECALIBRATION OF REFERENCE EVAPOTRANSPIRATION
ESTIMATION METHODS
K. CHANDRASEKHAR REDDY
Professor, Department of Civil Engineering and Principal,
Siddharth Institute of Engineering & Technology, Puttur, Andhra Pradesh, India.
ABSTRACT
Reference evapotranspiration (ET0) estimates are often required in irrigation system design,
crop yield simulation and water resources planning and management. Many reference
evapotranspiration (ET0) estimation methods have been developed for different types of climatic
data, and the accuracy of these methods varies with climatic conditions. In this study, the weekly ET0
values estimated from nine different ET0 equations are evaluated with ET0 estimated by FAO-56
Penman-Monteith(PM) equation in order to select an appropriate ET0 equation for the semi-
aridNellore region of Andhra Pradesh, India. The evaluation is based on performance criteria
namely, Root Mean Square Error (RMSE), Coefficient of Determination (R2
) and Efficiency
Coefficient (EC). Then the ET0 equations were recalibrated with respect to PM method for
improving their weekly ET0 estimation capability in the region selected for the present study. The
recalibrated Modified Penman and Blaney-Criddle methods showed satisfactory performance in the
weekly ET0 estimation. However, the recalibrated Blaney-Criddle method can be adopted because of
its simpler data requirements with reasonable degree of accuracy.
Keywords: Reference Evapotranspiration, Recalibration, Performance Evaluation.
1. INTRODUCTION
Evapotranspiration (ET) is the loss of water to the atmosphere by the combined processes of
evaporation from soil and plant surfaces and transpiration from plants. It is one of the major
components of the hydrologic cycle and its accurate estimation is essential for many studies such as
hydrologic water balance, crop yield simulation, and water resources planning and management.
Field measurement of evapotranspiration is rarely available and actual crop evapotranspiration (ETc)
is generally calculated from reference 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. Allen et al., (1998)[2]
and Jensen et al. (1990)[5]
have
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2. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
ISSN 0976 – 6316(Online) Volume 5, Issue 3, March (2014), pp. 178-186 © IAEME
179
reported crop coefficients for many crops. These values are commonly used in places where the
local data is not readily available.
It is desirable to have a method that estimates reasonably the reference Evapotranspiration.
According to the Food and Agricultural Organization (FAO), FAO-56 Penman-Monteith (PM)
method, that requires numerous climatic parameters, achieves better agreement with the lysimeter
ET0 measurements compared to all other known methods. However, under limited climatic data
availability conditions, the simple empirical methods yielding results comparable with PM ET0 may
be selected for reasonable estimation of ET0.
Irmak et al.(2003)[4]
, Berengena and Gavilan(2005)[3]
, Alkaeed et al.(2006)[1]
, Suleiman and
Hoogenboom (2007)[8]
, Trajkovic and Stojnic (2008)[9]
have evaluated, compared and tested the
applicability of various ET0 equations for different regions.
The present study reports the performance evaluation of nine ET0 estimation methods based
on their accuracy of estimation and these methods are recalibrated with PM method for Nellore
region of Andhra Pradesh.
2. MATERIALS AND METHODS
Nellore region located in Nellore district of Andhra Pradesh, India, with global coordinates of
140
22’
N latitude and 790
59’
E longitudes, has been chosen as the study area. Meteorological data in
the study area for the period 1983-2003 was collected from India Meteorological Department (IMD),
Pune. A part of the data (1983-1997) was used for the purpose of developing recalibrated equations,
while the rest of the data (1998-2003) was used to verify the performance of the recalibrated
equations. The details of the methods selected for the present study are shown in Table 1.
Table 1: Details of reference evapotranspiration estimation methods
Method Equation
Input data
Primary Secondary
Temperature based
1. FAO-24Blaney-
Criddle(BC)
method
2. Jensen-Haise (JH)
method
3. FAO-56
Hargreaves
(HR) method
ET0 = a +b [p (0.46T + 8.13)]
Where
a = 0.0043 (RHmin) – n/N – 1.41
b = 0.82– 0.0041 (RHmin) + 1.07 (n/N)+ 0.066 (ud)
– 0.006 (RHmin) (n/N)–0.0006 (RHmin) (ud)
ET0 = Rs (0.025 Tmean + 0.08)
ET0 = 0.0023 Ra (Tmean + 17.8) x (TD) 0.5
Tmax, Tmin
Tmax, Tmin,
n
Tmax, Tmin,
n
RHmin, n, u2,
ud/un
---
---
Radiation based
1. Priestley-Taylor
(PT) method
2. FAO-24 Radiation
(RA) method
3.Makkink(MK)
method
ET0 = c (W.Rs)
Where
c = 1.066 – 0.00128 RHmean + 0.045 ud –
0.0002RHmeanud
+ 0.0000315 (RHmean) 2
– 0.00103 (ud)2
Tmax, Tmin,
n
Tmax, Tmin,
n
Tmax, Tmin,
n
---
RHmax,
RHmin, u2,
ud/un
---
0 Rs
γΔ
Δ
65.0ET
+
=
)GRn(26.1ET0 −
γ+∆
∆
=

3. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
ISSN 0976 – 6316(Online) Volume 5, Issue 3, March (2014), pp. 178-186 © IAEME
180
Physically based
1. FAO-24Modified-
Penman(MP)
method
2.FAO-56 Penman-
Monteith(PM)
method
ET0 = C x






−+
+∆
+
+∆
∆
))(01.00.1)(27.0( 2 asn eeUR
γ
γ
γ
Where
C = 0.68 + 0.0028 (RHmax) + 0.018 (Rs) – 0.068 (ud)
+ 0.013 (ud/un) + 0.0097 (ud )(ud/un)
+ 0.000043 (RHmax) (Rs) (ud)
ET0 =
)34.01(
)(
273
900
)(408.0
2
11
11
2
1111
u
eeu
T
GR as
mean
n
++∆
−
+
+−∆
γ
γ
Tmax, Tmin,
RHmax,
RHmin, n
Tmax, Tmin,
RHmax,
RHmin, u2, n
u2, ud/un
---
Pan Evaporation
based
1. FAO-56 Pan
Evaporation(PE)
method
2.Christiansen(CS)
method
ET0 = Kp Epan
where
Kp = 0.108 – 0.0286 u2 + 0.0422 ln(FET)
+ 0.1434 ln(RHmean) – 0.000631 [ln(FET)]2
ln(RHmean)
ET0 = 0.473 Ra CT CW CH CS CE CM
where
CT = 0.393 + 0.5592 (T/Tm) + 0.04756 (T/Tm)2
CW = 0.708 + 0.3276 (U2/U2m) – 0.036 (U2/U2m)2
CH = 1.25 – 0.212(RH/RHm) – 0.038(RH/RHm)5
CS = 0.542+0.64(sp/spm)–0.4992(sp/spm)2
+0.3174(sp/spm)3
CE = 0.970 + 0.030(E/Em)
CM = ranges from 0.9 to 1.1depending on the latitude
Epan
---
FET, RHmax,
RHmin, u2
Tmax, Tmin,
u2, RHmax,
RHmin, n, E
3. PERFORMANCE EVALUATION CRITERIA
The performance evaluation criteria used in the present study are, namely, 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
)
Coefficient of Determination 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.
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 3, March (2014), pp. 178-186 © IAEME
181
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)[10]
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( −
=
∑=
3.5 Efficiency Coefficient (EC)
It is used to assess the performance of different models (Nash and Sutcliffe, 1970)[7]
. It is a
better choice than RMSE statistic when the calibration and verification periods have different lengths
(Liang et al., 1994)[6]
. It measures directly the ability of the model to reproduce the observed values
and it 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
Reference evapotranspiration(ET0) was estimated using the climatic data for different
methods with original values of empirical coefficients. The mean weekly values were compared with
those estimated by PM method. The percentage deviations with respect to PM method are shown in
Table 2. The positive deviation represents overestimation and negative deviation indicates

5. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
ISSN 0976 – 6316(Online) Volume 5, Issue 3, March (2014), pp. 178-186 © IAEME
182
underestimation of ET0 values. It may be observed that the percentage deviation between PM method
and other methods varied between –14.9% and 55.3%. RA method estimated ET0 with largest
deviation followed by JH method and, HR, PT, CS, and BC methods with minimum deviation. The
performance indicators of the methods with original coefficients are presented in Table 3. The
relatively more unsystematic RMSE components with the ET0 estimation methods except MP and
BC methods indicate more noise level in the methods and scatter about the regression line.
The temperature, radiation, physically and pan evaporation based methods selected for the
present study were recalibrated with respect to PM method as presented in Table 4. The performance
indicators of these empirical models with original and recalibrated coefficients in the estimation of
ET0 are given in Table 5. The improved R2
, EC and reduced RMSE (Table 5) indicate the closeness
of estimated weekly ET0 values and thereby reflect the appropriateness of recalibration. Though an
improvement in the performance of ET0 estimation methods with recalibrated coefficients over these
methods with original coefficients, in general, has been observed (Table 5), a significant
improvement has been found in case of recalibrated MP and BC methods. However, out of these
methods, recalibrated BC method may be adopted in the reasonable weekly ET0 estimation in the
regions because of simpler data requirements. The scatter plots as shown in Figs.1 & 2 also depict
similar observations.
Table 2: Percentage deviations in the estimated mean weekly reference evapotranspiration
with original coefficients
Method PM BC JH HR PT RA MK MP PE CS
ET0
(mm)
4.7 4.5 6.3 4.7 4.8 7.3 4 6.0 4.2 4.8
Percentage
deviation
… -4.3 34.0 0.0 2.1 55.3 -14.9 27.7 -10.6 2.1
Table 3: Performance indicators of various methods with original coefficients against PMM
Method Slope(m) Intercept(c) R2
RMSE
(mm)
RMSES
(mm)
RMSEu
(mm)
EC
(%)
BC 0.9241 0.5012 0.9276 0.33 0.09 0.32 92.76
JH 0.7125 0.2030 0.7179 0.65 0.35 0.55 71.79
HR 0.9962 0.0369 0.7208 0.65 0.35 0.55 72.08
PT 1.0048 -0.1147 0.6270 0.75 0.46 0.60 62.70
RA 0.6193 0.1504 0.5384 0.83 0.57 0.62 53.84
MK 1.1337 0.1849 0.5434 0.83 0.57 0.62 54.34
MP 0.7606 0.0860 0.9673 0.22 0.04 0.22 96.73
PE 0.5933 2.1925 0.4745 0.89 0.65 0.61 47.45
CS 0.9184 0.2547 0.9024 0.38 0.12 0.36 90.24

6. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
ISSN 0976 – 6316(Online) Volume 5, Issue 3, March (2014), pp. 178-186 © IAEME
Table 4: ET0 estimation methods with original and recalibrated coefficients
Method Original equation Recalibrated equation
BC ET0 = a +b [p (0.46T + 8.13)]
where
a = 0.0043 (RHmin) – n/N – 1.41
b = 0.82 – 0.0041 (RHmin) + 1.07 (n/N)
+ 0.066 (ud) – 0.006 (RHmin) (n/N)
– 0.0006 (RHmin) (ud)
ET0 = a +b [p (0.46T + 8.13)]
where
a = – 0.0722 (RHmin) – 4.27 (n/N) + 4.70
b = – 0.36+ 0.0115 (RHmin) + 0.96 (n/N)
+ 0.215 (ud) + 0.004 (RHmin) (n/N)
– 0.0027 (RHmin) (ud)
JH ET0 = Rs (0.025 T + 0.08) ET0 = Rs (0.030 T – 0.29)
HR ET0 = 0.0023 Ra (T + 17.8) x (TD) 0.5
ET0 = 0.0024 Ra (T +14.9) x (TD) 0.5
PT
RA ET0 = c (W.Rs)
where
c = 1.066 – 0.00128 RH + 0.045 ud
– 0.0002 RH ud + 0.0000315 (RH) 2
– 0.00103 (ud)2
ET0 = c (W.Rs)
where
c = 0.554 + 0.00185 RH + 0.346 ud
– 0.0037 RH ud – 0.000015 (RH)2
– 0.00195 (ud)2
MK
MP ET0 = C






−+
+∆
+
+∆
∆
))(01.00.1)(27.0( 2 asn eeUR
γ
γ
γ
where
C = 0.68 + 0.0028 (RHmax) + 0.018 (Rs)
– 0.068 (ud) + 0.013 (ud / un)
+ 0.0097 (ud )(ud/un)
+ 0.000043 (RHmax) (Rs) (ud)
ET0 = C






−+
+∆
+
+∆
∆
))(01.00.1)(27.0( 2 asn eeUR
γ
γ
γ
Where
C = 0.63+ 0.0012 (RHmax) + 0.011 (Rs)
– 0.010 (ud) + 0.013 (ud / un)
+ 0.0097 (ud )(ud/un)
– 0.000039 (RHmax) (Rs) (ud)
PE ET0 = Kp Epan
where
Kp = 0.108 – 0.0286 u2 + 0.0422 ln(FET)
+ 0.1434 ln(RH)
– 0.000631[ln(FET)]2
ln(RH)
ET0 = Kp Epan
where
Kp = – 2.896 + 0.1260 u2 + 0.0422 ln(FET)
+ 0.8127 ln(RH)
– 0.000631[ln(FET)]2
ln(RH)
CS ET0 = 0.473 Ra CT CW CH CS CE CM
where
CT = 0.393 + 0.02796 T + 0.0001189 (T)2
CW = 0.708 + 0.00339 W – 0.0000038
(W)2
CH = 1.25 – 0.00369 RH – 6.1x10-11
(RH)5
CS = 0.542 + 0.80 sp – 0.78 (sp)2
+ 0.62
(sp)3
CE = 0.970 + 0.0000984 E
CM = ranges from 0.9 to 1.1depending on
the latitude
ET0 = 2.45 Ra CT CW CH CS CE CM
where
CT = 1.06 – 0.06791 T + 0.001343 (T)2
CW = 0.819 + 0.002999 W – 0.0000024 (W)2
CH = 1.01 – 0.00684 RH – 29.68x10-11
(RH)5
CS = 0.847 – 0.40 sp + 2.06 (sp)2
– 1.51 (sp)3
CE = 0.970 + 0.0000984 E
CM = ranges from 0.9 to 1.1depending on the
Latitude
)GR(26.1ET n0 −
γ+∆
∆
=
s0 R
γΔ
Δ
76.0ET
+
=s0 R
γΔ
Δ
65.0ET
+
=
)GR(23.1ET n0 −
γ+∆
∆
=

7. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
ISSN 0976 – 6316(Online) Volume 5, Issue 3, March (2014), pp. 178-186 © IAEME
184
Table 5: Performance evaluation of ET0 estimation methods with original and
recalibrated coefficients against PM method
Method
Slope (m) Intercept (c) R2 RMSE
(mm)
EC
(%)
Original
recalibrated
Original
recalibrated
Original
recalibrated
Origina
l
recalibrated
Original
recalibrated
training testing training testing training testing training testing training testing
BC 0.9241 0.9999 1.0112 0.5012 0.0004 -0.0764 0.9276 0.9824 0.9882 0.33 0.15 0.15 92.76 98.24 98.82
JH 0.7125 0.8220 0.9462 0.2030 0.8726 0.2645 0.7179 0.7552 0.9132 0.65 0.57 0.42 71.79 75.52 91.32
HR 0.9962 0.9290 1.1888 0.0369 0.3448 -0.6678 0.7208 0.6977 0.8212 0.65 0.64 0.60 72.08 69.77 82.12
PT 1.0048 0.9473 1.2879 -0.1147 0.2409 -1.2627 0.6270 0.5793 0.7788 0.75 0.75 0.67 62.70 57.93 77.88
RA 0.6193 0.8238 0.7765 0.1504 0.7530 0.8841 0.5384 0.9221 0.9688 0.83 0.32 0.25 53.84 92.21 96.88
MK 1.1337 0.8745 1.2695 0.1849 0.6091 -1.2098 0.5434 0.4774 0.7476 0.83 0.84 0.71 54.34 47.74 74.76
MP 0.7606 1.0075 1.0141 0.0860 -0.0366 -0.0861 0.9673 0.9961 0.9967 0.22 0.07 0.08 96.73 99.61 99.67
PE 0.5933 0.5629 0.9029 2.1925 1.9086 1.1276 0.4745 0.5415 0.7645 0.89 0.78 0.69 47.45 54.15 76.45
CS 0.9184 0.6584 0.6254 0.2547 1.7254 1.8174 0.9024 0.8931 0.8674 0.38 0.38 0.48 90.24 89.31 86.74
Fig. 1: Scatter plots of weekly ET0 estimated by various methods with original
coefficients against ET0 estimated using PM method

8. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
ISSN 0976 – 6316(Online) Volume 5, Issue 3, March (2014), pp. 178-186 © IAEME
185
Fig. 2 Scatter plots of weekly ET0 estimated by various methods with recalibrated coefficients
against ET0 estimated using PM method during testing period
CONCLUSIONS
The BC, JH and HR (temperature based), PT, RA and MK (radiation based), MP(physically
based), PE and CS (pan evaporation based) reference evapotranspiration estimation methods have
been recalibrated with respect to FAO-56 Penman-Monteith (PM) method and their performance in
the weekly ET0 estimation was evaluated based on the performance criteria(R2
, RMSE and EC). All
these ET0 estimation methods, in general, showed an improved performance with recalibrated
coefficients. The recalibrated MP method and BC method have performed well in the weekly ET0
estimation. However, recalibrated Blaney-Criddle (BC) method may be applied for the reasonable
estimation of weekly reference evapotranspiration (ET0) in the region because of simpler data
requirements.

9. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
ISSN 0976 – 6316(Online) Volume 5, Issue 3, March (2014), pp. 178-186 © IAEME
186
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