20320140503021

International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
ISSN 0976 – 6316(Online) Volume 5, Issue 3, March (2014), pp. 195-201 © IAEME
195
ARTIFICIAL NEURAL NETWORK MODELS FOR ESTIMATING
REFERENCE EVAPOTRANSPIRATION IN RAJENDRANAGAR REGION
K. CHANDRASEKHAR REDDY
Professor, Department of Civil Engineering & Principal,
Siddharth Institute of Engineering & Technology, Puttur, Andhra Pradesh, India
ABSTRACT
Artificial Neural Networks (ANNs) are effective tools to model non linear systems and
require fewer inputs. The goal of this study is to develop artificial neural network (ANN) models for
estimating daily, weekly and monthly reference evapotranspiration (ET0) in Rajendranagar region of
Andhra Pradesh. The climatic parameters influencing mostly the ET0 in the region of study area have
been identified through multiple and partial correlation analysis using observed climatic data and
ET0 estimated by FAO-56 Penman-Monteith (PM) method (PM ET0). The ANN models with these
input nodes (temperature, wind velocity, sunshine hours and relative humidity) varying the number
of nodes in the hidden layer have been tried to obtain optimal architectures. The performance of the
models was evaluated with respect to PM ET0 by the performance indicators such as regression
coefficients (slope and intercept of scatter plots), Root Mean Square Error (RMSE), Coefficient of
Determination (R2
) and Efficiency Coefficient (EC). The optimal ANN (4-3-1) model showed a
satisfactory performance in the daily, weekly and monthly ET0 estimation. These ANN models may
therefore be adopted for estimating ET0 in the study area with reasonable degree of accuracy.
Keywords: Artificial Neural Network, Reference Evapotranspiration, Multiple and Partial
Correlation Coefficients.
1. INTRODUCTION
Efficient use of water resources in agriculture is becoming an important issue in India
because of the depletion of freshwater resources due to the rapid increase of industries and
population. Reliable and consistent estimates of reference evapotranspiration (ET0) are a key element
of managing water resources efficiently. It is desirable to have a method that estimates reasonably
the reference Evapotranspiration (ET0). Most of the studies have shown that the FAO-56 Penman-
Monteith (PM) equation (Allen et al., 1998)[1]
is widely used in recent times for ET0 estimation and it
gives very accurate ET0 estimates in different environments. However, under limited climatic data,
INTERNATIONAL JOURNAL OF CIVIL ENGINEERING
AND TECHNOLOGY (IJCIET)
ISSN 0976 – 6308 (Print)
ISSN 0976 – 6316(Online)
Volume 5, Issue 3, March (2014), pp. 195-201
© IAEME: www.iaeme.com/ijciet.asp
Journal Impact Factor (2014): 7.9290 (Calculated by GISI)
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IJCIET
©IAEME

196
the simple empirical methods giving good results comparable with PM ET0 may be selected at
regional level for reasonable estimation of ET0.
Most of the ET0 estimation methods do not effectively represent the complete nonlinear
dynamics inherent in the ET0 process. Artificial Neural Networks (ANNs) are capable of
representing complex and nonlinear process effectively extracting the relation between the inputs and
outputs of a process without the physics being explicitly provided to them. ANNs also identify the
underlying rule even if the data is noisy and contaminated with errors (ASCE Task committee,
2000a[2]
and 2000b[3]
) and which may not be always possible with the application of traditional
statistical techniques. ANNs are therefore used in recent times as a successful soft computing tool in
ET0 modelling. Although ANNs belong to the class of data driven approaches, it is important to
determine the dominant network model inputs as this not only reduces the training time but also
increases the generalization ability of the network for a given data set. The present study examines
several aspects associated with the use of ANN structure including the type of input data, number of
hidden layers and nodes in each hidden layer to be included in the network in the ET0 estimation.
Khoob (2008)[4]
tested the ANNs, for converting pan evaporation data to estimate ET0 as a
function of the maximum and minimum air temperatures in semiarid climate. While comparing with
PM method, it was concluded that the ANN methods are better ET0 estimates than the conventional
methods. Landeras et al. (2008)[6]
evaluated the ANN models for daily ET0 estimation under the
situations of presence of only temperature and relative humidity data. ANNs showed better
performance over traditional ET0 equations. Kumar et al. (2009)[5]
developed generalized artificial
neural network (GANN) based reference crop evapotranspiration models corresponding to Turc,
FAO-56 Penman-Monteith, FAO-24 Radiation and FAO-24 Blaney-Criddle methods. It was
concluded that the GANN models can be used directly to predict ET0 under the arid conditions since
they performed better than the conventional ET0 estimation methods. The study reports the
identification of most influencing climatic parameters in ET0 estimation, development of ANN
models for estimation of daily, weekly and monthly ET0 for Rajendranagar region of Andhra
Pradesh.
2. MATERIALS AND METHODS
Rajendranagar region, located in Rangareddy district of Andhra Pradesh, India, has been
chosen as the study area. The meteorological data in the region for the period 1978-1993 were
collected from India Metrological Department, Pune. Data from 1978 to 1988 is used for the purpose
of training the model and that of 1989 to 1993 for testing the model. A brief description of region
selected for the present study is given in Table 1.
Table 1: Brief description of the Rajendranagar region
Longitude Latitude Altitude
Mean daily
relative
humidity
Mean
daily
temperature
Mean
daily
wind
velocity
Mean daily
sunshine
hours
Mean daily
vapour
pressure
Mean
annual
rainfall
(0
E) (0
N) (m) (%) (0
C) (kmph) (hr) (mm of Hg) (mm)
780
23′
170
19′
536.0 61.8 26.2 7.3 8.0 14.9 920
2.1 Artificial Neural Network (ANN) model development
A standard multilayer feed forward ANN with logistic sigmoid function was adopted for the
present study. A constant value of 0.1 for learning rate and a constant value of 0.9 for momentum
factor were considered. The input data were normalized in the range of (0.1, 0.9) to avoid any
saturation effect. Error back propagation which is an iterative nonlinear optimization approach based
on the gradient descent search method (Rumelhart, 1996)[9]
was used during calibration. The

197
calibration set was used to minimize the error and validation set was used to ensure proper training
of the neural network employed such that it does not get over-trained. The performance of the model
was checked for its improvement on each iteration to avoid over-learning. The optimal network
corresponding to minimum mean squared error was obtained through trial and error process. Care
was taken to avoid too few and too many neurons which can respectively cause difficulties in
mapping each input and output in the training set and increases the training time, in the process of
determination of optimal number of hidden layers and nodes in each hidden layer to arrive at the
optimal neural network. The entire process was carried out using MATLAB routines.
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) and the Efficiency Coefficient (EC).
3.1 Coefficient of Determination (R2
)
It is defined as 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. This parameter 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)[10]
n
op
RMSE
ii
n
i
2
1
)( −
=
∑=
3.3 Efficiency Coefficient (EC)
It is used to assess the performance of different models (Nash and Sutcliffe, 1970)[8]
. 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 is expressed as
( )
( )∑
∑
=
=
−
−
−= n
i
i
n
i
ii
oo
po
EC
1
2
1
2
1
2/1
1
2
1
2
1
)()(
))((




∑ −∑ −
−−∑
=
==
=
n
i
i
n
i
i
ii
n
i
ppoo
ppoo
R

198
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 analysis of multiple linear correlation between FAO-56 Penman-Monteith reference
evapotranspiration (PM ET0) and the climatic parameters was carried out by omitting one of the
climatic factors each time. While carrying out the analysis, the data period was divided into training
and testing periods. The training period data set was used to identify the parameters influencing the
region and to develop linear ET0 models in terms of these parameters. The verification of
applicability of the models developed was checked using the testing period data set. The multiple
linear correlation coefficients and partial correlation coefficients between PM ET0 and climatic
parameters for the regions selected for the present study were computed for both training and testing
periods are presented in Table 2 and 3.
Table 2: Multiple correlation co-efficients
Time step
Multiple correlation co-efficient
Independent variable omitted
---- T S W RH VP R
Training
period
Testing
period
Training
period
Testing
period
Training
period
Testing
period
Training
period
Testing
period
Training
period
Testing
period
Training
period
Testing
period
Training
period
Testing
period
Daily
0.9643 0.9689 0.8684 0.8533 0.9099 0.9134 0.8865 0.8487 0.9531 0.9657 0.9642 0.9687 0.9643 0.9687
Weekly 0.9755 0.9804 0.8816 0.8584 0.9521 0.9544 0.9161 0.8967 0.9697 0.9783 0.9753 0.9804 0.9754 0.9803
Monthly 0.9900 0.9886 0.9209 0.8884 0.9805 0.9775 0.9509 0.9387 0.9872 0.9869 0.9899 0.9884 0.9900 0.9884
Table 3: Partial correlation co-efficients
Time
step
Partial correlation co-efficient
T S W RH VP R
Training
period
Testing
period
Training
period
Testing
period
Training
period
Testing
period
Training
period
Testing
period
Training
period
Testing
period
Training
period
Testing
period
Daily 0.8455 0.8802 0.7697 0.7940 0.8201 0.8838 0.4842 0.3030 0.0524 0.0793 0.0000 0.0793
Weekly 0.8847 0.9233 0.6945 0.7513 0.8360 0.8955 0.4348 0.3095 0.0894 0.0000 0.0634 0.0709
Monthly 0.9322 0.9447 0.6962 0.7003 0.8901 0.8996 0.4665 0.3592 0.0993 0.1309 0.0000 0.1309

199
From Tables 2 and 3, it may be observed that the influence of Temperature (T), Sunshine
hours (S), Wind velocity (W) and Relative humidity (RH) is relatively more on ET0 in the region of
the study area irrespective of the time step. Further, no significant effect of Vapour Pressure (VP)
and Rainfall (R) on ET0 is found in the region. This may be due to the fact that the region lies in the
semi-arid zone, mostly experienced by high temperature and radiation.
The ANN models with these input nodes (T, S, W and RH) varying the number of nodes in
the hidden layer have been tried to obtain optimal architectures. The performance indicators of these
ANN models are presented in Table 4. The high values of EC represent the satisfactory performance
of ANN (4-4-1) models for Rajendranagar region. The low RMSE values also indicate that the
models proposed estimate ET0 satisfactorily. The scatter plots as shown in Fig.1 also depict similar
results. The nearly unit slope and zero intercept of scatter plots indicate that ANN models predict
ET0 comparable with that of FAO-56 Penman-Monteith method. The models proposed may therefore
be adopted for ET0 estimation in the selected regions of the study area with reasonable degree of
accuracy.
Table 4: Performance indices of Artificial Neural Network (ANN) models
Time
step
ANN
Architecture
Slope of the
scatter plot
Intercept of the
scatter plot
R2
RMSE
(mm)
EC
(%)
Training
period
Testing
period
Training
period
Testing
period
Training
period
Testing
period
Training
period
Testing
period
Training
period
Testing
period
Daily
4-3-1 1.0014 0.9132 -0.0059 0.2641 0.9822 0.9739 0.23 0.24 98.22 97.39
3-4-1 1.0003 0.9495 -0.0015 0.2042 0.9240 0.9000 0.47 0.47 92.40 90.00
2-5-1 0.9998 1.1050 0.0006 -0.1308 0.7887 0.6988 0.78 0.82 78.87 69.88
1-5-1 1.0000 0.6923 -0.0004 1.3734 0.4119 0.1752 1.30 1.36 41.19 17.52
Weekly
4-3-1 1.0007 1.0016 -0.0009 -0.0052 0.9876 0.9888 0.17 0.14 98.76 98.88
3-4-1 1.0016 0.9209 -0.0074 0.8793 0.9655 0.8290 0.28 0.55 96.55 82.90
2-5-1 1.0004 0.9516 -0.0018 0.7923 0.8726 0.7469 0.53 0.67 87.26 74.69
1-5-1 1.0001 0.6675 -0.0004 1.8909 0.4848 0.2130 1.07 1.19 48.48 21.30
Monthly
4-3-1 1.0007 1.0017 -0.0034 -0.0075 0.9956 0.9953 0.09 0.09 99.56 99.53
3-4-1 1.0001 0.9933 -0.0009 0.2268 0.9884 0.8995 0.15 0.41 98.84 89.95
2-5-1 1.0021 0.7954 -0.0094 1.0130 0.9455 0.8062 0.32 0.57 94.55 80.62
1-5-1 1.0022 0.5864 -0.0108 2.0349 0.5220 0.1727 0.95 1.18 52.20 17.27

200
Training period Testing period
Fig.1: Scatter plots of ET0 values estimated using Artificial Neural Network (ANN) models with
those estimated by Penman-Monteith (PM) method

201
5. CONCLUSION
The effect of climatic parameters on ET0 at Rajendranagar region is brought out through
multiple and partial correlation analysis. The sunshine hours, wind velocity, temperature and relative
humidity mostly influenced ET0 in the study area. The ANN ET0 models comparable with FAO-56
Penman-Monteith method for the region have been developed in terms of the influencing climatic
parameters. The performance ANN models developed was verified based on the evaluation criteria.
The slope and intercept of scatter plots nearly equal to one and zero respectively, high values of R2
and EC and low values of RMSE indicate satisfactory performance of the models. The ANN(4-4-1)
model showed better performance for all time steps in ET0 estimation. This ANN(4-4-1) model may
therefore be adopted for estimating ET0 in the study area and also the other regions of similar
climatic conditions with reasonable degree of accuracy.
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] ASCE Task Committee on Application of Artificial Neural Networks in Hydrology. (2000a).
Artificial neural networks in hydrology. I: Preliminary concepts. Journal of Hydrologic
Engineering, ASCE, Vol.5, No.2, pp.115-123.
[3] ASCE Task Committee on Application of Artificial Neural Networks in Hydrology. (2000b).
Artificial neural networks in hydrology. II: Hydrologic applications.Journal of Hydrologic
Engineering, ASCE, Vol.5, No.2, pp.124-137.
[4] Khoob, A.R. (2008). Artificial neural network estimation of reference evapotranspiration from
pan evaporation in a semi-arid environment. J. Irrig. Sci., 27(1), 35-39.
[5] Kumar, M., Raghuwanshi, N. S., & Singh, R. (2009). Development and validation of GANN
model for evapotranspiration estimation. J. Hydrol. Eng., ASCE, 14(2). 131-233.
[6] Landeras, G., Barredo, A. O., & Lopez, J. J. (2008). Comparison of artificial neural network
models and empirical and semi-empirical equations for daily reference evapotranspiration
estimation in the Basque Country (Northern Spain). Agricultural Water Management, 95(5),
553-565.
[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
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[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 Strength of
Concrete in Warm Climates”, International Journal of Civil Engineering & 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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