Simulation of Pan Evaporation Rate by ANN Artificial Intelligence Model in Damghan Region

Journal of Soft Computing in Civil Engineering 5-3 (2021) 75-87
How to cite this article: Shahi S, Mousavi SF, Hosseini Kh. Simulation of pan evaporation rate by ANN artificial intelligence
model in damghan region. J Soft Comput Civ Eng 2021;5(3):75–87. https://doi.org/10.22115/scce.2021.286933.1321.
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Simulation of Pan Evaporation Rate by ANN Artificial
Intelligence Model in Damghan Region
S. Shahi1*
, S.F. Mousavi1
, Kh. Hosseini1
1. Faculty of Civil Engineering, Semnan University, Semnan, Iran
Corresponding author: sinashahi@semnan.ac.ir
https://doi.org/10.22115/SCCE.2021.286933.1321
ARTICLE INFO ABSTRACT
Article history:
Received: 18 May 2021
Revised: 03 September 2021
Accepted: 14 September 2021
Regarding different aspects of management of drainage
basins and droughts, prediction of evaporation is very
important. Evaporation is an essential part of the water cycle
and plays an important role in the evaluation of climatic
characteristics of any region. The purpose of this research is
to predict daily pan evaporation rate of Damghan city using
an artificial neural network model. The data applied in this
research are daily minimum and maximum temperatures,
average relative humidity, wind speed, sunshine hours, and
evaporation during the statistical time period of 16 years
(2002-2018). Also, the artificial neural network was used as
a non-linear method to simulate evaporation. Since the units
of the inputs and outputs of the prediction model were
different, all the data were normalized. In the ANN model,
seven different scenarios were considered. About 70 and 30
percentage of the data were used for training and testing,
respectively. The model was analyzed by appropriate
statistics such as coefficient of determination (R2
), root mean
square error (RMSE), and mean absolute error (MAE).
Results showed that the seventh scenario including minimum
and maximum temperatures, average relative humidity, wind
speed, ‎
sunshine hours‎
, and pressure proved to be the superior
scenario among others. The values of R2
, RMSE, and MAE
for the superior scenario were 0.8030, 2.75 mm/day, and
1.88 mm/day, respectively.
Keywords:
Pan evaporation;
Evaporation prediction;
Artificial neural network;
Damghan.

76 S. Shahi et al./ Journal of Soft Computing in Civil Engineering 5-3 (2021) 75-87
1. Introduction
Management of water resources for supplying the water required for farming is a method to
handle the scarcity of the water required for agriculture that is caused by low water use
efficiency and overuse of the existing water resources [1]. Iran is an arid and semi-arid region
[2], and according to international definitions, it is in a critical circumstance and experiences
water scarcity [3]. Iran is faced with a severe water crisis [4]. In many places of Iran, water
consumption has become far greater than 43% of the renewable water resources, to the extent
that in most of the basins, the exploitation of water is practically more than their total annual
renewable water [3,5].
Evaporation is one of the main components of the water balance of a region, and it is an essential
item for an irrigation plan. In most hot and dry climates, a great volume of water held by dams,
agricultural irrigation pools, and water storages are wasted by evaporation [6]. Evaporation plays
an important role in a region’s water resources, climatic changes, and agriculture [7]. Regarding
the climate change issue, researchers have worked extensively on evaporation and its role in the
hydrologic cycle [8,9].
Evaporation could be predicted by soft computing technique [10–12]. The multilayer perceptron
(MLP) model of neural network is a model for estimation of evaporation pan with the input layer
of variables (such as temperature and sunshine hours) and the output layer of evaporation rate. In
what follows, the studies of the application of soft computing for the estimation of pan
evaporation will be outlined.
Eslamian et al. [13] compared artificial neural network (ANN) and support vector machine
(SVM) algorithms to estimate the greenhouse evaporation. The obtained correlation coefficients
of the ANN and SVM were 0.92 and 0.96, respectively. These values indicate the ability of SVM
and ANN models to estimate greenhouse evaporation.
Piri et al. (2009) [14] were among the first to use ANNs to model pan evaporation rates in arid
and semi-arid climates. They reported satisfactory performance for ANNs used in a research site
located in the southeast of Iran. Their study reported R2
= 0.93 for an ANN model with an
optimal combination of 4 meteorological inputs.
Kişi (2009) [10] compared the multi-layer perceptrons (MLP), radial basis neural networks
(RBNN), and generalized regression neural networks (GRNN) models for estimation of daily
pan evaporation. Meteorological data of air temperature, solar radiation, wind speed, pressure,
and humidity were considered as the factors affecting the evaporation. The results indicated the
superiority of the MLP and RBNN models.
Tezel and Buyukyildiz (2016) [15] used SVM and ANN models to analyze the monthly
evaporation in weather station of Beyşehir city. This research was conducted in the statistical
time period of 1972 to 2005. Temperature, relative humidity, wind speed, and precipitation were
the applied data. Results showed that the MLP functions properly.
Qasem et al. [16] used the three models of support vector regression (SVR), ANN, and their
combination with the wavelet transforms of wavelet support vector regression (WSVR) and

S. Shahi et al./ Journal of Soft Computing in Civil Engineering 5-3 (2021) 75-87 77
Wavelet artificial neural networks (WANN) to predict the evaporation rate in Tabriz, Iran, and
the Turkish city of Antalya. In both stations, the ANN model showed better results than other
models.
Patle et al. [17] compared MLR and ANN models to estimate monthly pan evaporation in two
regions in northern India. Results of this research indicated that ANN model works better than
the MLR model.
Alsumaiei [18] used ANN to model daily evaporation rate in Kuwait. The studied station was the
Kuwait international airport (KIA). The meteorological input data of the network included mean
temperature, wind speed, and relative humidity that were presented in four scenarios. Results of
this research indicated that the combined scenario of average temperature and wind speed as
inputs for the estimation of daily evaporation showed a better function than other scenarios.
Neural network-based group method of data handling was used by Karami et al. [19] to estimate
and simulate pan evaporation rate in the synoptic station of Garmsar city, located in Semnan
province, Iran. For this purpose, daily meteorological data of evaporation, minimum and
maximum temperatures, wind speed, relative humidity, air pressure, and sunshine hours during
the nine years of 2009-2018 were used. This study showed that R2
, RMSE, and MAE values in
the test stage were 0.84, 2.65, and 1.91, respectively, in the most optimal state. From the third
layer onwards, the amount of RMSE of the validation data have converged to 0.062, and it is not
affordable to use more layers for modeling of the evaporation pan in this station. Table 1 shows
some recent studies of evaporation using the ANN model. Based on this table and the results of the
present study, the ANN model can have good performance in estimating evaporation.
Table 1
Literature review on estimating pan evaporation using MLP neural network.
Summary of results
Meteorological parameters
Methods
Case study
Research
Results presented here
collectively suggest that
MLP-KH is a good choice to
be used as an estimation
model in the study area.
rainfall; air temperature
(maximum, minimum and
mean); relative humidity
(maximum, minimum and
mean); actual sunshine hours;
and wind speed
MLP,
krill herd
optimization
– the MLP-
KH model
Anzali and
Astara, Iran
Ashrafzadeh
et al.
(2019)
[20]
The ANN model had better
results than the other
presented models.
Air temperatures, Solar
radiation, relative humidity,
wind speed, evaporation
SVR
ANN
WSVR
WANN
Tabriz, Iran
Qasem et al.
(2019)
[16]
The proposed ANN was
satisfactorily efficient in
modeling pan evaporation in
these hyper-arid climatic
conditions.
mean temperature, wind
speed and mean relative
humidity
ANN
Kuwait
International
Airport
Alsumaiei
(2020)
[18]
The ANN model performs
better than MLR model.
Minimum and maximum air
temperatures, maximum and
minimum relative humidity,
wind speed, sunshine hours
MLR
ANN
Gangtok and
Imphal,
India
Patle et al.
2020
[17]

The purpose of this study is to use ANN (MLP) to model pan evaporation rate at Damghan
weather station, Semnan province, Iran. In the process of modelling for calculation of daily
evaporation, different scenarios are presented. The scenarios are composed of effective
meteorological parameters of minimum and maximum temperatures, relative humidity, wind
speed, sunshine hours, and pressure. The best scenario is the one that comes up with the more
precise prediction of pan evaporation rate. Figure. 1 shows the flowchart of the steps in this
study.
Fig. 1. Flowchart of the proposed methodology.
2. Materials and methods
2.1. Study region
The studied region is city of Damghan, located in the Semnan province, at geographical
coordinates of 54° 32' longitude and 36° 14'‫‏‬ latitude, and elevation of 1155 m above mean sea
level. Record length of the data used in this research is 16 years (2002-2018). These data
included minimum and maximum temperature, air pressure, relative humidity, sunshine hours,
wind speed, and daily pan evaporation rates.
Meteorological Data:
Minimum temperature
Maximum temperature
Relative humidity
Wind speed
Sunshine hours
Air pressure
Evaporation
Soft computing analysis:
ANN (MLP)
Results:
Results of the Scenarios
Results of the Best Scenario
Taylor diagram

2.2 Parameters and statistical properties of data
In this research, efficiency of the ANN model for prediction of pan evaporation rate was
evaluated by using daily parameters of minimum and maximum temperature, relative humidity,
wind speed, sunshine hours, and air pressure. Table 2 shows the studied parameters, symbols,
and statistical properties. Figure 2 shows the histogram of the input and frequency data. The
input data are normalized by Eq.1 and Table 3 to function better. Therefore, all the data are set
between 0.1 and 0.9, and then are used to extend the equation. This is based on the method used
by Naderpour and Mirrashid [21] and Ghazvinian et al. [22].
min
max min
(0.8) 0.1
Scaled
Parameter Parameter
Parameter
Parameter Parameter
 
 

 
 
 

 
 
(1)
Table 2
Statistical properties of data.
Parameter Unit Symbol Mean
Standard
deviation
Minimum Maximum
Minimum temperature c
̊ Tmin 11.05 9.17 -12 30
Maximum temperature c
̊ Tmax 23.39 10.94 -4.4 42.6
Relative humidity % RHmean 40.39 14.41 10.2 96.00
Wind speed m/s WS 8.84 6 0 36.0
Sunshine hours hr N 8.6 3.22 0 13.4
Air pressure hPa PA 814.18 3.68 0 899.83
Evaporation rate mm E 7.42 6.15 0 30
2.3. Artificial neural network
Artificial neural network (ANN) is composed of an arbitrary number of cells, nodes, units, or
neurons which connect the set of inputs to outputs. It is used for predicting and solving
complicated processes in various fields such as civil and hydraulic engineering [23]. The ANN is
a mathematical structure that is formed based on the biological model of the human brain. A
neuron is a small set of data processing components in each neural network. Neurons are related
to each other by their specific weights. The weights show the information required for the
network to find the solution to a problem. A biological neuron consists of three main parts of
axon, soma, and dendrite. The signals received from other neurons are corrected by a huge
number of dendrites. Soma, namely the body of processing unit, collects the input signals. If the
sum of inputs exceeds a certain limit, the processor is activated and some signals will be
transmitted through the axon to the next cell. Neural cells work in series and parallel. After
processing, the set of parallel neural cells produce a set of outputs. The resulted outputs can be
used as the inputs to other sets of neural cells which are connected in series to the primary cells.
Consequently, the output of each neuron is multiplied by the weighting coefficients and is given
to the non-linear activation function as inputs. The set of parallel neural cells are composed of
one layer. Each neural network can have one or a few layers so that it can produce its own
output. Usually, these layers are called hidden layers. The last layer produces the output of the
network [24,25]. Figure 3 demonstrates the flowchart of the structure of an artificial neuron and
the structure of artificial networks.

Fig. 2. Histograms of the input data.
49
42
35
28
21
14
7
0
250
200
150
100
50
0
Tmax
Frequency
30
24
18
12
6
0
-6
-12
250
200
150
100
50
0
Tmin
Frequency
15.75
13.50
11.25
9.00
6.75
4.50
2.25
0.00
250
200
150
100
50
0
n
Frequency
36
30
24
18
12
6
0
700
600
500
400
300
200
100
0
WS
Frequency
1260
1080
900
720
540
360
180
0
4000
3000
2000
1000
0
PA
Frequency
96
84
72
60
48
36
24
12
300
250
200
150
100
50
0
RHmean
Frequency
30
25
20
15
10
5
0
-5
1400
1200
1000
800
600
400
200
0
evt
Frequency

Table 3
Normalization of the input data.
Symbol Parameter Normalized value
Tmin Minimum temperature
min
min
( 12)
0.8 0.1
30 ( 12)
normal
T
T
 
 
 
Tmax Maximum temperature
max
max
4.4
0.8 0.1
42.6 ( 4.4)
normal
T
T

 
 
RHmean Relative humidity
10.2
0.8 0.1
96 10.2
normal
mean
mean
RH
RH

 

WS Wind speed
0
0.8 0.1
36
normal
WS
WS

 
n Sunshine hours 0.8 0.1
899.82
normal
PA
PA  
PA Air pressure
3.73
0.8 0.1
8.81
normal
n
n

 
E Evaporation rate 0.8 0.1
30
normal
E
E  
Fig. 3. The structure of artificial neural networks.
In order to predict daily evaporation rate by ANN (MLP) model, 70% of the total series of daily
data (years 2002 to 2018) were chosen for training and the remaining 30% of data (years 2002 to
2018) was devoted to testing. Eight and one neurons were used in the input and output layers,
respectively. Also, in the hidden layer, different number of layers were used and their optimum
number was determined by trial and error in order to minimize the error. In the hidden layer, the
hyperbolic tangent transfer function and in the output layer, the nonlinear transfer function was
used. For training, the Levenberg-Marquardt algorithm was used with 2000 constant iterations.
In order to find out the possibility of using different combinations of meteorological data for a
more precise simulation of daily evaporation, seven different scenarios including various
meteorological data were defined (Table 4). Then, these scenarios were applied for simulation of
evaporation rates.

Table 4
The input scenarios used in ANN.
Scenario No. Input parameters
1 Tmin - Tmax
2 RHmean - WS
3 Tmin - Tmax - RHmean
4 Tmin - Tmax - WS
5 Tmin - Tmax - RHmean - WS
6 Tmin - Tmax - RHmean – WS - PA
7 Tmin - Tmax - RHmean – WS – PA - n
2.4. Evaluation criteria
In order to evaluate and analyze the proposed models, the error indexes must be calculated with
several functions [26]. In this research, the preciseness and ability of the models are evaluated by
correlation coefficient (R2
), root mean square error (RMSE), mean square error (MSE) and mean
absolute error (MAE) based on Eqs. (2)-(5). The best values for these three criteria are 1, 0, 0,
and 0, respectively.
2
2 1
2 2
1 1
( )( )
( ) ( )
n
i i
i
n n
i i
i i
x x y y
R
x x y y

 
 
 
 

 
 
 
 

 
(2)
(3)
(4)
2
1
1
( )
n
i i
i
MSE y x
N 
 
 (5)
here, N is number of data, is daily measured evaporation, is predicted daily evaporation,
is average value of measured evaporation, and is average value of predicted evaporation.
3. Results
3.1. Results of the scenarios
In this research, daily evaporation rate was prediced by ANN for Damghan region by using
different inputs in 7 scenarios. Different scenarios were analyzed to choose the optimum
structure of each model. Table 5 presents the values of R2
, RMSE, and MAE of the ANN model
in training and testing stages. According to the results, the seventh scenario of the ANN model
with R2
= 0.803, RMSE = 2.75 mm/day, and MAE = 1.88 mm/day was chosen as the best
pattern. The third scenario ranked second. In this scenario, daily evaporation rate could be
2
1
( )
n
i i
i
y x
RMSE
N
=
-
=
å
1
1
( )
n
i i
i
MAE y x
N =
= -
å
i
x i
y x
y

simulated with allowable error only by using minimum and maximum temperature and daily
relative humidity inputs.
3.2. Results of the best scenario
Figure 4 shows time series of the measured evaporation values and simulated by ANN in the best
scenario (namely the seventh scenario). The more the simulated values correspond to the
measured values, the more accurate the model is.
Figure 5 shows the evaporation rates predicted by the ANN based on the seventh scenario at two
stages of training and testing. As it is evident, there is an almost strong correlation between the
measured and simulated evaporation data at two stages of training and testing with R2
values of
0.8096 and 0.803, respectively. Moghaddamnia et al. (2009) [27] used the ANFIS method on a
research site located in the Southeast. The R2
value was reported 0.91 for the best performance of
the ANFIS model during the validation period. However, a similar prediction orientation was
observed for the ANFIS model.
Table 5
Results of error criteria for different scenarios.
Scenario No. Stage R2
RMSE MAE MSE
1
Training 0.592 9.991 6.421 99.820
Testing 0.612 8.312 6.012 69.089
2
Training 0.574 10.012 7.733 100.240
Testing 0.593 9.732 7.105 94.692
3
Training 0.770 4.442 3.323 19.731
Testing 0.780 4.321 2.991 18.671
4
Training 0.704 5.768 4.887 33.269
Testing 0.710 5.021 3.993 25.210
5
Training 0.719 5.070 4.904 25.704
Testing 0.728 4.786 4.020 22.906
6
Training 0.750 4.819 3.981 23.223
Testing 0.766 3.025 3.652 9.151
7
Training 0.809 2.679 1.909 7.177
Testing 0.803 2.750 1.881 7.562
Fig. 4. Time series of the observed values and the values predicted by ANN model at training and testing
stages.
0
5
10
15
20
25
30
35
0 1000 2000 3000 4000 5000 6000
Evaporation
(mm)
Days
Observation
Scenario 7
line
Training Testing

Visual display and comparison of the experimental and model results can be illustrated using the
Taylor diagram for providing an easy and comprehensive evaluation [28]. Taylor diagrams can
reflect the quality of different approaches in comparison with the experimental samples in a
diagonal display (Fig. 6). In these diagrams, the Azimuth angle addresses the correlation
coefficient between the modeled and the experimentally measured data, while the radial distance
from the origin indicates the standard deviation (SD) for the outcomes of each approach. In
addition, the concentric circles indicate centered RMSE values, which can be evaluated using the
following equation.
(a)
(b)
Fig. 5. Simulated vs. observed daily evaporation rates at different stages: (a) training and (b) testing.
0
5
10
15
20
25
30
0 5 10 15 20 25 30
Simulation
Evaporation
Observation Evaporation
0
5
10
15
20
25
30
0 5 10 15 20 25 30
Simulation
Evaporation
Observation Evaporation

Fig. 6. The Taylor diagram for the estimated evaporation.
4. Conclusions
Evaporation is one of the most important input data of hydrologic systems. Due to the
importance of evaporation for arid regions in Iran, this research has been conducted to predict
evaporation rates in Damghan region. The process of evaporation is nonlinear, and if the linear
regression model is used as a semi-linear method for these kinds of processes. In recent years,
various methods have been developed for prediction of climatic variables. Each of these
prediction methods has specific weaknesses and strengths. In this research, the ANN model was
used for prediction of daily evaporation rates by using 16 years of daily evaporation data of
Damghan synoptic station. Seven scenarios presenting different inputs of the model were used to
predict evaporation rate. The R2
coefficient for the seven scenarios in the test phase is 0.61, 0.59,
0.78, 0.71, 0.72, 0.76 and 0.80, respectively. Comparison of different scenarios showed that by
increasing the number of inputs, the model’s function will be improved.
Conflicts of Interest
The authors declare no conflict of interest.

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