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International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –
6480(Print), ISSN 0976 – 6499(Online) Volume 5, Issue 3, March (2014), pp. 183-190, © IAEME
183
GENERALIZATION OF PAN EVAPORATION BASED METHODS FOR
ESTIMATING REFERENCE EVAPOTRANSPIRATION
K. CHANDRASEKHAR REDDY
Professor, Department of Civil Engineering and Principal,
Siddharth Institute of Engineering & Technology, Puttur, Andhra Pradesh, India.
ABSTRACT
The main objective of this study is evaluation and generalization of the pan evaporation based
methods of FAO-56 Pan Evaporation (PE) method and Christiansen (CS) method with reference to
the standard FAO-56 Penman-Monteith (PM) method in Tirupati region of Andhra Pradesh, India for
estimating monthly reference evapotranspiration (ET0). Meteorological data observed in Tirupati
region was collected from the India Meteorological Department (IMD), Pune. The evaluation is
based on performance criteria namely, Root Mean Square Error (RMSE), Coefficient of
Determination (R2
) and Efficiency Coefficient (EC). The relationships between PM method and the
other methods were developed to obtain monthly ET0 estimates comparable with PM method. The
ET0 equations were then generalized (recalibrated) with respect to PM method for improving their
monthly ET0 estimation capability in the region selected for the present study. The recalibrated FAO-
56 Pan Evaporation (PE) method performed satisfactorily in the monthly ET0 estimation. So, it may
be adopted for the study area because of its simpler data requirements with reasonable degree of
accuracy.
Keywords: Reference Evapotranspiration, Recalibration, Penman-Monteith, Pan Evaporation Based
Methods.
1. INTRODUCTION
A reliable estimation of Evapotranspiration (ET) is of critical importance in irrigation system
design, crop yield simulation and water resources planning and management. Field measurement of
evapotranspiration is rarely available and actual crop evapotranspiration (ETc) is usually 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)[1]
and Jensen et al. (1990)[6]
have reported crop coefficients
for many crops. These values are commonly used in places where the local data is not available.
INTERNATIONAL JOURNAL OF ADVANCED RESEARCH IN ENGINEERING
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ISSN 0976 - 6480 (Print)
ISSN 0976 - 6499 (Online)
Volume 5, Issue 3, March (2014), pp. 183-190
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184
It is desirable to have a method that estimates judicially the reference Evapotranspiration
(ET0). 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, the simple empirical
methods for yielding results comparable with PM ET0 may be selected at regional level for
reasonable estimation of ET0 under limited climatic data availability conditions
Grismer et al. (2002)[4]
evaluated the use of FAO-24 table values of pan coefficients (Kp) and
six different Kp equations. Use of Kp table slightly underestimated measured ET0 at coastal sites,
while the Cuenca, Allen-Pruitt and Synder Kp equations most closely approximated the average
measured ET0 at all other sites.
Irmak et al. (2002)[5]
evaluated the Kp equation developed by Frevert et al. (1983)[3]
and
Synder (1992)[9]
using a 23 year climatic data of Gainesville, Florida to estimate ET0. The ET0
values estimated using Frevert et al.’s pan coefficients were in good agreement with FAO 56 PM
method compared to Snyder’s equation.
The present study reports the performance evaluation of commonly used pan evaporation
based ET0 estimation methods based on their accuracy of estimation and development of inter-
relationships with PM method. And also, these methods are recalibrated with PM method for
Tirupati region of Andhra Pradesh.
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 at the region for the period 1992-2001 were collected from IMD, Pune. For the purpose of
training the model, data from 1992 to 1998 is used and from 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)
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
---
Pan evaporation based methods
1.FAO-56 Pan
Evaporation
(PE)
Allen et al.
(1998)[1]
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)
Epan
FET,
RHmax,
RHmin, u2
2.Christiansen
(CS)
Christiansen
(1968)[2]
ET0 = 0.473 Ra CT CW CH CS CE CM
where
CT = 0.393 + 0.02796 T + 0.0001189 (T)2
CW = 0.708 + 0.003393 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
---
Tmax, Tmin,
u2, RHmax,
RHmin, n, E

185
3. PERFORMANCE EVALUATION CRITERIA
The performance evaluation criteria used in the 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 it 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 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 it 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 and 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 (RMSE u)
It shows the noise level in the model and it is a measure of scatter about the regression line
and potential accuracy. It is expressed as
2/1
1
2
1
2
1
)()(
))((










−−
−−
=
∑∑
∑
==
=
n
i
i
n
i
i
ii
n
i
ppoo
ppoo
R

186
n
pp
RMSE
ii
n
i
u
2
1
)ˆ( −
=
∑=
3.5 Efficiency Coefficient (EC)
Efficiency Coefficient is used to assess the performance of different models (Nash and
Sutcliffe, 1970)[8]
and it is a better choice than RMSE statistic when the calibration and verification
periods have different lengths (Liang et al., 1994)[7]
. 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 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 pan evaporation based methods with
reference to PM method are presented in Table 2. It may be observed that the deviations are
significant for both the methods. PE method underestimated ET0 for most of the period. The
performance of CS method is better. Further, both CS and PM methods consider similar climatic
parameters; the significant deviations in CS ET0 may be due to inapplicability of the coefficients in
the equation for the study area. Fig.1 shows 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 pan evaporation
based methods with PM method
Percentage deviation
PE CS
- 42.3 to 2.9 -19.0 to 16.2
Fig.1: Comparison of monthly average ET0 values estimated by pan evaporation based methods with
PM method
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 PE CS

187
4.1 Development of inter-relationships between PM method and pan evaporation based
methods
The ET0 values estimated using PE and CS methods plotted against PM ET0 are shown in
Fig.2 for the study area. The performance indicators of the relationships developed between PM
method and these methods are presented in Table 3.
It may be observed from the scatter plots and performance indices that both the methods have
improved their performance. The results are fairly comparable with PM method.
However, the high values of unsystematic RMSE indicate more scatter about the regression line and
considerably high values of systematic RMSE indicate the room for local adjustment of the
coefficients for improving their performance.
Fig.2: Scatter plots of monthly average ET0 values estimated by pan evaporation based methods
against PM method
Table 3: Performance indicators of pan evaporation based methods with reference to PM method
Method Relationship R2 RMSE
(mm)
RMSES
(mm)
RMSEU
(mm)
EC
(%)
PE PM = 1.1804 PE + 0.4006 0.9211 0.38 0.11 0.37 92.11
CS PM = 0.9617 CS + 0.1254 0.8457 0.54 0.21 0.49 84.57
4.2 Recalibration of pan evaporation based ET0 estimation methods
It has been emphasized in the above section that pan evaporation 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 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.
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 PE, 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 CS, mm/day
ETo
byPM,mm/day

188
The PE and CS methods selected for the present study were recalibrated with reference to PM
method. The recalibrated equations derived for the region of the study area are presented along with
original equation in Table 4. From this table it may be observed that there is a significant variation
on recalibration of coefficients compared to the original values. 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.
There was a marginal improvement in terms of R2
and EC of the recalibrated Christiansen equation.
However, the large deviation of regression coefficients of scatter plots (slope and intercept) from one
and zero indicates the significant amount of scatter around the regression line. This may be due to
inapplicability of the coefficients, even after recalibration, in the equation for the study area. Further,
the performance of the recalibrated PE method is better than the recalibrated CS method.
From the above discussion, it may be concluded that recalibrated PE method may be used for the
reasonable estimation of ET0 in the study area.
Table 4: Recalibrated pan evaporation based ET0 equations
Method Original Equation Recalibrated Equation
1.FAO-56
Pan
Evaporation
(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 = – 0.07 – 0.0082 u2 + 0.0422 ln(FET)
+ 0.2231 ln(RH)
– 0.000631[ln(FET)]2
ln(RH)
2.Christiansen
(CS)
where
CT = 0.393 + 0.02796 T + 0.0001189 (T)2
CW = 0.708 + 0.003393 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
where
CT = 1.069 – 0.07119 T + 0.0015029 (T)2
CW = 0.609 + 0.006977 W – 0.0000119
(W)2
CH = 1.01 – 0.00848 RH – 17.7x10-11
(RH)5
CS = 0.884 – 0.38 sp + 1.01 (sp)2
– 0.52 (sp)3
CE = 0.970 + 0.0000984 E
CM = ranges from 0.9 to 1.1depending on
the
latitude
Table 5: Performance indices of recalibrated pan evaporation 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
PE 0.9350 0.9047 0.3272 0.6076 0.9434 0.9171 0.32 0.38 94.34 91.71
CS 0.6106 0.5674 2.3143 2.3668 0.9439 0.9468 0.32 0.31 94.39 94.68

189
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 CS, mm/day
ETo
byPM,mm/day
Fig.3: Scatter plots of monthly average ET0 values estimated by recalibrated pan evaporation based
methods against PM ET0 values during testing period
Fig.4: Comparison of monthly average ET0 values estimated by recalibrated pan Evaporation based
methods with those estimated by PM method during testing period
5. CONCLUSION
The percentage deviations of ET0 values estimated by PE and CS methods with reference to
PM method are significant. Both the methods slightly improved their performance over inter-
relationships in terms of evaluation criteria in the region. There was a marginal improvement in
terms of R2
and EC of the recalibrated Christiansen equation. However, the large deviation of
regression coefficients of scatter plots (slope and intercept) from one and zero indicates the
significant amount of scatter around the regression line. The performance of recalibrated PE method
is better than that of the other method and it requires less climatic parameters as input. Hence,
recalibrated PE method may be used for 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 PE, mm/day
ETo
byPM,mm/day
Ideal line
Best fit line
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 PE CS

190
REFERENCES
[1] Allen, R. G., Pereira, L. S., Raes, D. and Smith, M. (1998), Crop evapotranspiration -
Guidelines for computing crop water requirements. FAO Irrigation and Drainage Paper 56,
FAO, Rome.
[2] Christiansen, J. E. (1968), Pan evaporation and evapotranspiration from climatic data. Journal
of Irrigation and Drainage, ASCE, Vol.94, No.2, pp.243-265.
[3] Frevert, D. K., Hill, R. W. and Braaten, B. C. (1983), Estimation of FAO evapotranspiration
coefficients. Journal of Irrigation and Drainage Engineering, ASCE, Vol.109, No.2, pp.265-
270.
[4] Grismer, M. E., Orang M., Snyder R. and Matyac R. (2002), Pan evaporation to reference
evapotranspiration conversion methods. Journal of Irrigation and Drainage Engineering,
ASCE, Vol.128, No.3, pp.180-184.
[5] Irmak, S., Haman, D. Z. and Jones, J. W. (2002), Evaluation of class A pan coefficients for
estimating reference evapotranspiration in humid location. Journal of Irrigation and Drainage
Engineering, ASCE, Vol.128, No.3, pp.153-159.
[6] Jensen, M.E., Burman, R.D. and Allen, R.G. (1990), Evapotranspiration and Irrigation water
requirements. ASCE Manuals and Reports on Engineering Practice, No 70, New York,
pp.332.
[7] Liang, G. C., O-Connor, K. M. and Kachroo, R. K. (1994), A multiple-input single-output
variable gain factor model. Journal of Hydrology, Vol.155, No.1-2, pp.185-198.
[8] Nash, J. E. and Sutcliffe, J. V. (1970), River flow forecasting through conceptual models part
I: A discussion of principles. Journal of Hydrology, Vol.10, No.3, pp.282-290.
[9] Snyder, R. L. (1992), Equation for evaporation pan to evapotranspiration conversions.
Journal of Irrigation and Drainage Engineering, ASCE, Vol.118, No.6. pp.977-980.
[10] Yu, P. S., Liu, C. L. and Lee, T. Y. (1994), Application of transfer function model to a
storage runoff process. In Hipel K. W., McLeod A.I. and Panu U.S. (Ed.), Stochastic and
Statistical Methods in Hydrology and Environmental Engineering, Vol.3, pp.87-97.
[11] K. Chandrasekhar Reddy, “Reference Evapotranspiration Estimation By Radiation Based
Methods” International Journal of Civil Engineering & Technology (IJCIET), Volume 5,
Issue 2, 2014, pp. 81 - 87, ISSN Print: 0976 – 6308, ISSN Online: 0976 – 6316.
[12] Sameer Ul Bashir, Younis Majid and Ubair Muzzaffer Rather, “Effect of Rapidite on
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Technology (IJCIET), Volume 4, Issue 6, 2013, pp. 126 - 133, ISSN Print: 0976 – 6308,
ISSN Online: 0976 – 6316.
[13] K. Chandrasekhar Reddy, “Evaluation And Calibration of Temperature Based Methods For
Reference Evapotranspiration Estimation In Tirupati Region” International Journal of
Advanced Research in Engineering & Technology (IJARET), Volume 5, Issue 2, 2014,
pp. 87 - 94, ISSN Print: 0976-6480, ISSN Online: 0976-6499.

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