Reference Evapotranspiration Estimation Using ANN, LSSVM, and M5 Tree Models (Case Study: of Babolsar and Ramsar Regions, Iran)

Journal of Soft Computing in Civil Engineering 6-3 (2022) 101-118
How to cite this article: Dadrasajirlou Y, Ghazvinian H, Heddam S, Ganji M. Reference evapotranspiration estimation using ANN,
LSSVM, and M5 tree models (case study: of Babolsar and Ramsar regions, Iran). J Soft Comput Civ Eng 2022;6(3):101–118.
https://doi.org/10.22115/scce.2022.342290.1434
2588-2872/ © 2022 The Authors. Published by Pouyan Press.
This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
Contents lists available at SCCE
Journal of Soft Computing in Civil Engineering
Journal homepage: www.jsoftcivil.com
Reference Evapotranspiration Estimation Using ANN, LSSVM,
and M5 Tree Models (Case Study: of Babolsar and Ramsar
Regions, Iran)
Yashar Dadrasajirlou1*
, Hamidreza Ghazvinian1
, Salim Heddam2
, Mariam
Ganji3
1. Faculty of Civil Engineering, Semnan University, Semnan, Iran
2. Professor, Faculty of Science, Agronomy Department, Hydraulics Division, Laboratory of Research in
Biodiversity Interaction Ecosystem and Biotechnology, University 20 Août 1955, Skikda, Algeria
3. Faculty of Natural Resources and Environment, Islamic Azad University Science and Research Branch, Tehran,
Iran
Corresponding author: Dadras_yashar@semnan.ac.ir
https://doi.org/10.22115/SCCE.2022.342290.1434
ARTICLE INFO ABSTRACT
Article history:
Received: 14 May 2022
Revised: 02 October 2022
Accepted: 03 October 2022
Evapotranspiration is a non-linear and complex phenomenon
requiring different climatic variables for accurate estimation. In
this study, the performance of several artificial intelligence
models in estimating the amount of monthly reference
evapotranspiration was investigated. Babolsar and Ramsa
regions located in the north of Iran were selected as case study
models proposed in this study: artificial neural network (ANN),
least square support vector machines (LSSVM), and M5 tree
models. The data used in this study was gathered between 2009
till 2019 (11 consecutive years). In the present study, 70% of
the data were used for the training stage, and 30% of the data
were reserved for testing the proposed models. Models'
performances were evaluated using several evaluation criteria,
i.e., the coefficient of determination (R2), the root mean square
error (RMSE), and the mean absolute error (MAE). The results
for Babolsar and Ramsar stations showed that all three models
have a relatively good performance in estimating the rate of
reference evapotranspiration. However, the LSSVM model
performed better than the other models. The R2
, MAE, and
RMSE for the LSSVM model in the test stage were 0.982,
0.366 mm, 0.425 mm, 0.937, 0.018 mm, and 0.350 mm for
Babolsar and Ramsar stations, respectively.
Keywords:
Reference evapotranspiration;
LSSVM;
ANN;
M5 Tree;
Babolsar;
Ramsar.

102 Y. Dadrasajirlou et al./ Journal of Soft Computing in Civil Engineering 6-3 (2022) 101-118
1. Introduction
Reference evapotranspiration (ET0) is a variable that is used in irrigation planning, water
resources management and hydrological studies, and several other applications, especially for
estimating the water demand of crops in large irrigation areas [1]. ET0 is a non-linear and
complex phenomenon that requires different climatic variables [2]. Factors affecting ET0 include
relative humidity, solar radiation, wind speed, temperature, water solute concentration, and
atmospheric pressure. With decreasing relative humidity, the concentration of solutes in water,
atmospheric pressure, and increasing solar radiation, wind speed, and temperature, the rate of
ET0 increases. The ET0 rate is measured based on height, and its unit is millimeters, centimeters,
or inches [3–6]. The simplest way to measure evaporation is to use trays placed on the ground or
floating on water [7,8]. Calculating actual evapotranspiration is a difficult task and requires
extensive research. Therefore, evapotranspiration studies are raised in two methods: a) estimation
of actual evapotranspiration (the amount of water that evaporates under the current conditions)
and b) estimation of potential evapotranspiration (i.e., the amount of water that evaporates, if
resources are limited No water) [9]. Excessive estimation of plant water consumption leads to
wastage of irrigation water, wetting lands, and contamination of groundwater resources. Also, a
lower estimation of required water will cause drought stress on the plant and reduce yield
[10,11]. Researchers have conducted many studies to obtain evapotranspiration.
Many researchers worldwide have estimated reference evapotranspiration in different climates
under different conditions and scenarios. They have evaluated various experimental and
intelligent models and methods with minimum and maximum input data. This is due to the
importance of evapotranspiration in the water cycle and related issues.
SamadianFard and Panahi [12] estimated daily ET0 using support vector regression (SVR) and
M5Tree models and compared their results with Hargreaves and Torrent White experimental
models. Their study used meteorological variables from 1971 to 1994 in Tabriz synoptic station.
In addition, the Penman-Monteith-FAO method's output was considered the basis. Then 17
scenarios made of one to six meteorological data were examined. The results showed that
M5Tree and SVR models, considering all meteorological variables, showed better results in
estimating than Hargreaves and Torrent White model. Goodarzi et al. (2015) [13] calculate the
rate of evapotranspiration concerning climate change (B1, A2, A1B, and B2) in the watershed of
Lake Urmia using statistical microscale models LARS-WG and SDSM and model output
HadCM3 public circulation covered the next three time periods (2030-2011, 2065-2046 and
2099-2080). The rate of evapotranspiration was calculated at a monthly and seasonally time scale
using Priestley-Taylor and Hargreaves-Samani methods. The results showed that, on average, in
the long run at the basin level, the minimum temperature will increase between 0.2 to 3.4
degrees, and the maximum temperature varies between 0.9 to 2.9 degrees in future periods
compared to the base period (1990-1961). Also, under the influence of temperature, the estimated
evapotranspiration rate increases in all months and seasons in future periods.
Mohtarami et al. (2015) [14] improved the accuracy of the Hargreaves-Samani method in
estimating ET0 using the correction factor using the ANN model and the M5Tree between 2004

Y. Dadrasajirlou et al / Journal of Soft Computing in Civil Engineering 6-3 (2022) 101-118 103
and 2013 at Farkushhar station and Shahrekord airport. The results of this study indicated that
the ANN and the M5Tree models have good performance in correction factor modeling. The
ANN model, on the other hand, performed more accurately. The accuracy of the Hargreaves-
Samani model before using the correction coefficient compared to the Penman-Monteith-FAO
method had an RMSE equal to 0.900; the value after applying the correction coefficient reached
RMSE of 0.69 and RMSE of 0.72 using ANN and M5Tree models respectively. The results show
that the performance of the Hargreaves-Samani method has improved after applying correction
coefficients. Zortipour et al. (2017) [15] simulated and compared potential evapotranspiration
daily using ANN, ANFIS (Adaptive Neuro Fuzzy Inference Systems), and M5 decision tree
methods at Shiraz synoptic station. ANFIS and ANN models had acceptable accuracy due to the
high correlation coefficient (R) and low error rate. Also, considering that the values of R, RMSE,
and MAE for the M5 model were estimated to be 0.7170, 0.1088 mm, and 0.0877 mm, the
results indicate good performance of the M5 Tree model in evaluating ET0.
The primary purpose of Ferreira et al. (2019) [1] study was to calculate daily ET0 with limited
data. They sought to investigate the performance of the MARS model when confronted with
limited data. After comparing the results of the Penman-Monteith equation and the MARS
model, he observed that the intelligent model performed better. Meanwhile, solar radiation
scenario, relative humidity, and wind speed were more effective in estimating ET0. Temperature-
based procedures had the highest performance. Using climatic data, Wu et al. (2019) [2]
evaluated the ET0. The results showed that the M5Tree model can successfully estimate ET0.
Babu and Thomas (2022) [16] modeled evaporation data from pans in South India from 2000 to
2019 with the help of three models: decision tree regression, random forest and regression and
Gradient Boosting Regression Trees. The input data in the models included dry bulb temperature,
wet bulb temperature, maximum and minimum air temperature, vapor pressure, relative
humidity, wind speed, wind direction, sunshine hours, and rainfall. The random forest model had
the best performance.
Batra and Gandhi (2022) [17] in a study on pan evaporation for Rajendranagar, Hyderabad, a
part of India with the help of maximum and minimum temperature data, wind speed, relative
humidity, precipitation and sunshine hours for the year 1993 Until 2008, different ANN models
were used, and the least error was reported for the MLP model.
Considering that relatively limited studies have been done in the field of evaporation and
transpiration with the ANN, LSSVM, M5 tree model, in the northern region of Iran, In the
present study, three data mining methods namely M5 tree, ANN and LSSVM in Babolsar and
Ramsarcites have been used to estimate the evapotranspiration of plants.
Studies related to the combination of artificial intelligence and evaporation studies in these areas
have not been combined with each other, and the innovation of this research is to combine these
studies. In this research, first, the meteorological data of the study stations were collected. After
checking the data, they were separated for the testing and training stages and then they were
simulated by intelligent algorithms considering different scenarios. In the following, using the
error criteria, a comparison was made between the performance of the algorithms to evaluate

their simulation capability in evaporation. Finally, the obtained results were expressed and
suggestions for future researches were mentioned.
2. Methods
2.1. Study area and available data
Mazandaran province is affected by latitude, Alborz Mountains, altitude, proximity to the sea,
local and regional winds, displacement of northern and western air masses, and even dense forest
cover. Mazandaran region has a unique climatic diversity. Figure 1 shows the geographical
location of Mazandaran province, and Table 1 shows the location of the studied stations.
Two major currents play an important role in the climate of Mazandaran province: one is the
north and northeast air current that travels from Siberia and the North Pole to the south and
southwest, causing cold weather, frost, and snow and rain [18]. This air mass has little effect on
the climate of Mazandaran. The other is the westerly winds that cross the Mediterranean Sea and
the Black Sea in winter, and after entering Iran, cause heavy and continuous rains [19]. In the
summer months, the rainmaking power of these winds decreases and only increases the humidity
and sultry weather, leading to unfavorable living conditions [7].
Fig. 1. Mazandaran Province [20].
Table 1
Synoptic stations of Mazandaran province.
Synoptic station Longitude
Degree Minute
Latitude
Degree Minute
Altitude
Babolsar 52 48 36 25 16
Ramsar 53 00 36 20 12

In this study, the statistical data of two synoptic stations of Mazandaran province namely
Babolsar and Ramsar have been collected in 11 consecutive years between 2009 and 2019 and
used for modelling the ET0. The meteorological data used are: air temperature, sunshine hours,
relative humidity, solar radiation and wind speed. Tables 2 and 3 show the monthly average of
some meteorological data of Babolsar and Ramsar stations To evaluate the simulated results, the
statistical indices of coefficient of determination (R2
)[21], root mean square error (RMSE) [21]
and mean absolute error (MAE)[8] were calculated [22–26]. The values of the mentioned
indicators are calculated from one to three relations.
In Equations (1) to (3), 𝑂𝑖 is the observed evaporation value in a month, 𝑃𝑖 is the predicted
evaporation value of the same month, 𝑂 is the average of the observed evaporation values, and 𝑃
is the similar average for the predicted values [27].
Table 2
Monthly average of Babolsar synoptic station.
Month
Average
maximum
temperature
(
°
C)
Average
minimum
temperature
(
°
C)
Average
temperature
(
°
C)
Monthly
rainfall
(mm)
Maximum
rainfall in a
day (mm)
Relative
humidity
(percentage)
Number
of hours
of
sunshine
Maximum
wind speed
(meters per
second)
April 18.2 11.1 14.2 91.4 28.2 73 134 15
May 24.1 14.1 21.1 34.1 13.2 71 165 19
June 29.1 20.5 22.1 60.3 21.2 72 247.4 5
July 31.2 33.5 25.8 38.3 23.2 80 233.2 7
August 33.0 21.9 28.1 30.3 10.3 71 248.3 7
September 32.4 20.1 23.3 61.2 51 72 222.7 34
October 26.4 17.1 22.2 123.1 35.6 70 172.1 13
November 10.1 11.1 13.2 61 22.4 81 91.7 16
December 12.2 3.9 8.3 57 25.5 83 134.2 17
Januray 12.1 1.9 7.4 3.8 3.1 75 129.1 10
Februrary 11.5 3.1 5.3 131.2 22.7 76 106.8 14
March 14.1 5.1 11.4 9 3.4 84 162.8 8
1
N
i i
i
P O
MAE
N




(1)
2
1
( )
N
i i
i
O P
RMSE
N




(2)
2
2 1
2 2
1 1
( )( )
( ) ( )
N
i i
i
N N
i i
i i
O O P P
R
O O P P

 
 
 
 
 

 
 
 
 
 

 
(3)

2.2. Network configuration
In this study, the ratio of data used in the testing phase to the training phase was 70%/30%.
Temperature, relative humidity, solar radiation, wind speed, and sunny hours were used as input
for the models, and the output of the Penman-Monteith-FAO model was used as the objective
function in the innovative models. In this study, intelligent models, namely ANN, M5Tree, and
LSSVM models, were used. The experimental method used is the Penman-Monteith-FAO
method (based on mass transfer). MATLAB software was used to calculate innovative models
[28,29].
2.3. Artificial neural network model (ANN)
Artificial neural networks (ANNs) are one of the methods of artificial intelligence techniques
that are inspired by the functional system of the human brain and cannot be compared with
natural systems [30]. Conquering strategic principles is the approach of the computational model
of ANNs, which is the basis of the brain process for answering questions and using them in
computer systems. ANN models must be able to store knowledge in similar ways and process it
accordingly [31]. The large number of simple computational units that can work together is
called a parallel structure [24]. One of the features of ANN is that it is three-layered. This three-
layer structure uses input, hidden, and output layers [7, 27]. The main application of this
structure is to establish communication between the mentioned layers to explain the relationships
between input and output data [28]. This structure is introduced by considering three components
(i, j, k), where i, j, and k represent the nodes of the input layer, the number of hidden layers, and
the number of output layers, respectively (figure 2) [32].
X1
X2
Xn
Input Neuron
Teach/Use
Teaching Input
Output
Fig. 2. Schematic structure of artificial neural network model.
2.4. M5 decision tree model
In 1992, Quinlan was the first researcher to propose the idea of the M5 tree. He based his method
presented in the middle based on three factors: binary decision making, linear regression
functions, and communication between input and output data [29]. Another reason why
researchers welcome the use of this intelligent method is its multidimensional space and sub-
layer [33]. The M5 can learn well and take on substantial tasks [34]. The M5 tree model is
created in two stages: the growth stage and tree pruning. In the tree growth stage, also known as
the division stage, the input space will be divided into several classes using linear regression

models that minimize errors between predicted and actual values. Finally, a decision tree is
constructed using the information obtained [29]. In the M5 tree model, the division of the idea
follows the decision tree, but with the difference that it can be used in quantitative data [33].
Standard deviation is used to select the best feature to divide the data set in each node [34]. The
M5 is obtained using a common deviation reduction calculated according to equation (4):
( ) ( )
Ei
SDR sd E sd Ei
i E
   (4)
In above equation, 𝐸 is a set of instances that reach the node, and 𝐸𝑖 is a subset of the input data
to the parent node. These steps are completed until a suitable tree structure is formed. The way to
deal with this problem is to prune the tree in the previous step.
2.5. Least square support vector machine (LSSVM)
SVM is an efficient learning system based on the theory of constrained optimization. This model
uses the inductive principle of structural error depreciation, leading to an optimal solution.
Unlike SVM, which uses quadratic programming to solve problems, LSSVM uses linear
equations to solve problems. For this reason, it has higher computational accuracy than the SVM
models [35]. The following regression equation is used in the LSSVM model to estimate various
problems (Equation 5) [35–37]:
  . ( )
T
i i
Y X W X b
   (5)
In this equation, Φ(𝑋𝑖)is called nonlinear drawing of inputs in the feature space with high
dimensions, and 𝑏 and 𝑊 are the deviation of the regression function and the values of the
weights, respectively, which are calculated using the minimization of the objective function
according to equation (6):
1 2
min ( , )
, , 1
2 2
N
T
j w e w w ei
w e b i

  

(6)
With considering the equation (7) as limits for above equation:
( ) i=1,2,3,...,N
T
i i i
y w x b e
    (7)
In the above relations, 𝑒𝑖 is the error of the training data and 𝑥 is the parameter regulating the
error section. Finally, the LSSVM model estimation function is defined as Equation (8):
( ) ( , )
1
N
y x a K x x b
i i j
i
 


(8)
In the above relation, x is a kernel function and is expressed as a function with internal
multiplication in the property space according to the equation (9):
( , ) ( ) ( ) i,j=1,2,3,...,N
i j i j
K x x x x
   (9)

Compared to conventional models such as neural networks (ANN) and partial least squares
regression, LSSVM is more preferred for signal processing, pattern recognition, and nonlinear
regression estimation because it takes less time to compute [38].
2.6. Penman-monteith-FAO model
The Penman-Monteith-FAO model is the reference model for calculating the evapotranspiration
rate of the reference plant, which was introduced by the FAO in 1998 in FAO Journal No. 24
Irrigation and Drainage, and is considered by many researchers around the world [39]. The
reference plant is grass with a height of 8 to 15 cm, radiation coefficient (albedo) of about 0.23,
shading resistance is 70 seconds per meter [39,40].
900
0.408 ( ) [ ] ( )
2
( 273
0 (1 0.34 )
2
R G U e e
n a d
T
ET
U


   


  
(10)
In the equation 10, ET0 is Evapotranspiration of reference plant (mm d-1), T is air temperature
(◦
c), U2 stands for wind speed at a height of 2 meters (ms-1), Rn refers to the net surface radiation
(MJ m-2 d-1), ea-ed is the lack of saturated vapor pressure (Kpa), ∆ stands for the Slope of
saturated steam pressure curve with temperature (KpaC-1), and 𝛾 is the Constant psychrometers
(KpaC-1).
3. Results
For Babolsar station, model M5 recorded an average R2
of 0.9069 and a coefficient of variation
of 0.0538. In addition, the average MAE and RMSE for the Babolsar station were 0.0411 mm
and 0.3133 mm, respectively, and the coefficient of variation was 0.9546 and 0.1548. The
LSSVM model recorded an average R2
of 0.9821 and a coefficient of variation of 0.0051. In
addition, the average MAE and RMSE for this station were 0.0425 mm and 0.3366 mm,
respectively, and the coefficients of variation were 0.0745 and 0.8121, respectively.
The ANN model recorded an average R2
of 0.9254 and a coefficient of variation of 0.0236. Also,
the average MAE and RMSE for this station were 0.0658 mm and 0.3432 mm, respectively, and
the coefficients of variation were 0.7232 and 0.0432, respectively. Among these, the M5 model
had the lowest average for R2
, and the LSSVM model had the highest standard for R2
.
Table 3 shows the modeling results for Babolsar station with the three mentioned models for the
test phase. Figures 3 to 5 compare experimental and simulation results of reference transpiration
evaporation for Babolsar station.
Table 3
Babolsar station modeling results.
Model R2
MAE (mm) RMSE (mm)
M5 0.9069 0.0411 0.3313
LSSVM 0.9821 0.0425 0.3366
ANN 0.9254 0.0658 0.3432

Fig. 3. R2
for M5 model for training and test data in Babolsar station.
Fig. 4. R2
for LSSVM model for training and test data in Babolsar station.
Fig. 5. R2
for ANN model for training and test data in Babolsar station.
For Ramsar station, M5 recorded an average R2
of 0.9023. In addition, the average MAE and
RMSE for Ramsar stations were recorded as 0.0321 mm and 0.4535 mm, respectively. The
LSSVM model recorded an average R2
of 0.9737. In addition, the average MAE and RMSE for
this station were recorded as 0.0318 mm and 0.3504 mm, respectively. The ANN model recorded
an average R2
of 0.9476. In addition, this station's average MAE and RMSE were recorded as
0.0672 mm and 0.4543 mm, respectively. Among these, the M5 model had the lowest average for
R2
, and the LSSVM model had the highest standard for R2
. Table 4 shows the modeling results
for the Ramsar station with the three models for the test phase. Figures 6 to 8 show a comparison
diagram of the experimental results and the simulation results of the reference transpiration
evaporation for the Ramsar station.
R² = 0.8883
0
2
4
6
8
10
0 2 4 6 8 10
ET
M5
-Test
(mm)
ETP.M.F -Test (mm)
Babolsar-M5 tree
R² = 0.8987
0
2
4
6
8
10
0 2 4 6 8 10
ET
M5
-Train
(mm)
ETP.M.F -Train (mm)
Babolsar-M5 tree
R² = 0.9734
0
2
4
6
8
0 2 4 6 8 10
ET
M5
-Test
(mm)
ETP.M.F -Test (mm)
Babolsar-LSSVM
R² = 0.9812
0
2
4
6
8
0 2 4 6 8 10
ET
M5
-Train
(mm)
ETP.M.F -Train (mm)
Babolsar-LSSVM
R² = 0.9088
0
2
4
6
8
10
0 2 4 6 8 10
ET
M5
-Test
(mm)
ETP.M.F -Test (mm)
Babolsar-ANN
R² = 0.9141
0
2
4
6
8
10
0 2 4 6 8 10
ET
M5
-Train
(mm)
ETP.M.F -Train (mm)
Babolsar-ANN

Table 4
Ramsar station modeling results.
Model R2
MAE (mm) RMSE (mm)
M5 0.9023 0.0321 0.4535
LSSVM 0.9657 0.0318 0.3504
ANN 0.9476 0.0672 0.4543
Fig. 6. R2
for LSSVM model for training and test data in Ramsar station.
Fig. 7. R2
for ANN model for training and test data in Ramsar station.
Fig. 8. R2
for M5 model for training and test data in Ramsar station.
Also, Figures 9 and 10 give the scatter plot or scatter curve of the met values versus the Penman-
Monteith-FAO (observational) values for the test step. These figures show that all three models
perform relatively well in modeling, and the LSSVM model performs better than the other two
models.
R² = 0.981
0
2
4
6
8
0 2 4 6 8 10
ET
M5
-Test
(mm)
ETP.M.F -Test (mm)
Ramsar-LSSVM
R² = 0.9827
0
2
4
6
8
10
0 2 4 6 8 10
ET
M5
-Train
(mm)
ETP.M.F -Train (mm)
Ramsar-LSSVM
R² = 0.9178
0
2
4
6
8
10
0 2 4 6 8 10
ET
M5
-Test
(mm)
ETP.M.F -Test (mm)
Ramsar-ANN
R² = 0.9215
0
2
4
6
8
10
0 2 4 6 8 10
ET
M5
-Train
(mm)
ETP.M.F -Train (mm)
Ramsar-ANN
R² = 0.8956
0
2
4
6
8
10
0 2 4 6 8 10
ET
M5
-Test
(mm)
ETP.M.F -Test (mm)
Ramsar-M5 tree
R² = 0.9072
0
2
4
6
8
0 2 4 6 8 10
ET
M5
-Train
(mm)
ETP.M.F -Train (mm)
Ramsar-M5 tree

a b
c
Fig. 9. Scattering of estimated data with observational data in the test phase for Ramsar, a) M5 TREE, b)
LSSVM and c) ANN.
a b
c
Fig. 10. Scattering of estimated data with observational data in the test phase for Babolsar, a) M5 TREE,
b) LSSVM and c) ANN.
0
2
4
6
8
10
0 10 20 30 40
ET
(mm)
Months
ET-Model ET-Observation
0
2
4
6
8
0 10 20 30 40
ET
(mm)
Months
ET-Model ET-Observation
0
2
4
6
8
10
0 10 20 30 40
ET
(mm)
Months
ET-Model
ET-Observation
0
2
4
6
8
10
0 10 20 30 40 50 60
ET
(mm)
Months
ET-Model
ET-Observation
0
2
4
6
8
0 10 20 30 40 50 60
ET
(mm)
Months
ET-Model
ET-Observation
0
2
4
6
8
10
0 10 20 30 40 50 60
ET
(mm)
Months
ET-Model
ET-Observation

Figures 11 and 12 show a histogram of the difference between the Penman-Monteith-FAO
(observational) and metered data in the three models for Ramsar and Babolsar in the test phase.
The slightest difference in the LSSVM model is for both cities.
a b
c
Fig. 11. Histogram of the difference between the observed data and the estimated data for Babolsar: a)
ANN, b) LSSVM and c) M5 tree.
a b
c
Fig. 12. Histogram of the difference between the observed data and the estimated data for Ramsar: a)
ANN, b) LSSVM and c) M5 tree.
3.2
2.4
1.6
0.8
0.0
30
25
20
15
10
5
0
Error
Frequency
ET-ANN-Babolsar
0.6
0.4
0.2
0.0
-0.2
18
16
14
12
10
8
6
4
2
0
Error
Frequency
ET-LSSVM-Babolsar
3.75
3.00
2.25
1.50
0.75
0.00
-0.75
40
30
20
10
0
Error
Frequency
ET- M5 Tree -Babolsar
2.4
1.6
0.8
0.0
-0.8
20
15
10
5
0
Error
Frequency
ET- ANN- Ramsar
0.8
0.6
0.4
0.2
0.0
-0.2
14
12
10
8
6
4
2
0
Error
Frequency
ET- LSSVM- Ramsar
3.2
2.4
1.6
0.8
0.0
-0.8
30
25
20
15
10
5
0
Error
Frequency
ET- M5 Tree- Ramsar

The Taylor diagram [41] is a valuable tool for evaluating the outcomes of various methods and
has recently been used extensively in water engineering studies. This diagram is presented in two
forms, semicircle, and quadrilateral. In both cases, the correlation coefficient values are plotted
as the circle's radius on its arc, the standard deviation values are plotted as concentric circles
relative to the circle's center, and the RMSE values are plotted as concentric circles close to the
reference point.
The evaluation method in this diagram is that the estimated data based on three statistical criteria
(RMSE, correlation coefficient between observational data and calculated data, and standard
deviation) are plotted on the diagram. Based on Figure 13, the results show that the performance
of all three models for both cities is relatively high.
0.1 0.2
0.99
0.25 0.5 0.75 1 1.25 1.5 1.75 2
0.25
0.5
0.75
1
1.25
1.5
1.75
2
Standard Deviation
Standard
Deviation
ANN
LSSVM
M5 TREE
a
0.1 0.2
0.99
0.25 0.5 0.75 1 1.25 1.5 1.75 2
0.25
0.5
0.75
1
1.25
1.5
1.75
2
Standard Deviation
Standard
Deviation
ANN
LSSVM
M5 TREE
b
Fig. 13. Taylor diagram of the studied models, a: Ramsar and b: Babolsar.

Abed et al. (2021) [42] used minimum temperature, maximum temperature, average temperature,
wind speed, relative humidity, and solar radiation data as input to estimate the evaporation rate
using Extreme Gradient Boosting (EGB), ElasticNet Linear Regression, and LSTM models.
Also, Majhi et al. (2019) [43] have used minimum and maximum temperature, morning and
afternoon relative humidity, wind speed, and solar radiation data as input for LSTM and
Multilayer Perceptron(MLP) models. The best results for the above pieces of research are
obtained when all the input data are considered in the estimation process. Adding to that, the
results of Qasem et al. (2019) [44] also showed that the higher the number and types of inputs,
the higher the accuracy of the results by ANN, Wavelet-Artificial Neural Network (WANN),
SVR, and Wavelet-Support Vector Regression (WSVR) models. The above-cited articles' results
support scenario No. 4, where all data were considered input.
Alsumaiei (2020) [45] used the ANN for the dry area of Kuwait International Airport (KIA) to
model the evaporation rate, the results of which are consistent with the obtained results in the
current study. It was stated that the MLP model could have a relatively good performance in
predicting evaporation in arid and very arid regions, which is confirmed by the results obtained
in the present study.
Arid and semi-arid climates have unique climate regimes characterized by "scarce water
resources", "bare vegetation" and "high evaporation rates." According to the report of the Food
and Agriculture Organization of the United Nations, extremely dry climates are defined as areas
where annual precipitation does not exceed 3% of annual evaporation. It is necessary to compare
the performance of smart models with other experimental and practical models, by addressing
the issue of the contribution of the pan body in heat exchange. In the future research, we can
mention this issue, considering that the temporal behavior of daily evaporation is unstable, it is
better to investigate and compare other intelligent methods for modeling.
4. Conclusions
Evapotranspiration of reference plant (ET0) is a variable used in irrigation planning, water
resources management, and hydrological studies. Its other application is to estimate the water
requirement of crops in large irrigation areas. Evapotranspiration is a nonlinear and complex
phenomenon that requires different climatic parameters. Calculation of evapotranspiration helps
to save water and agricultural issues. This study used three intelligent models: the M5 decision
tree model, least square support vector machine (LSSVM), and artificial neural network (ANN).
This study used two synoptic stations of Mazandaran province with humid climates named
Ramsar station and Babolsar station, located in the north of Iran. At Babolsar station, the
LSSVM model had the best coefficient of determination and the lowest error rate, and the ANN
model was in the next rank. In Ramsar station, the highest coefficient of perseverance and the
lowest error rate belongs to the LSSVM model. The necessary suggestions for continuing this
research are presented as follows:
1) Investigation of intelligent and experimental models in the desired stations in limited data
conditions under different scenarios

2) Investigation of climate change in the studied stations
3) Using TOPSIS and AHP methods to weight the criteria as well as ranking the models
Funding
This research received no external funding.
Conflicts of interest
The authors declare no conflict of interest.
Authors contribution statement
YD, HG: Conceptualization; SA, HG: Data curation; SH, HG: Formal analysis; YA, HG, SH:
Investigation; YD, SH: Methodology; HG, YD: Project administration; HG, YD, SH: Resources;
YD, HG: Software; SH: Supervision; HG, YD: Validation; HG, YD: Visualization; HG, YD, SH:
Roles/Writing – original draft; HG, YD, SH: Writing – review & editing.
References
[1] Ferreira LB, França F, Oliveira RA De, Inácio E, Filho F. Estimation of reference
evapotranspiration in Brazil with limited meteorological data using ANN and SVM ; a new
approach. J Hydrol 2019. https://doi.org/10.1016/j.jhydrol.2019.03.028.
[2] Wu L, Zhou H, Ma X, Fan J, Zhang F. Daily reference evapotranspiration prediction based on
hybridized extreme learning machine model with bio-inspired optimization algorithms: Application
in contrasting climates of China. J Hydrol 2019;577:123960.
https://doi.org/10.1016/j.jhydrol.2019.123960.
[3] Ghazvinian H, Karami H, Farzin S, Mousavi SF. Effect of MDF-Cover for Water Reservoir
Evaporation Reduction, Experimental, and Soft Computing Approaches. J Soft Comput Civ Eng
2020;4:98–110. https://doi.org/10.22115/scce.2020.213617.1156.
[4] Karami H, Ghazvinian H, Dehghanipour M, Ferdosian M. Investigating the Performance of Neural
Network Based Group Method of Data Handling to Pan’s Daily Evaporation Estimation (Case
Study: Garmsar City). J Soft Comput Civ Eng 2021;5:1–18.
https://doi.org/10.22115/scce.2021.274484.1282.
[5] Ghazvinian H, Karami H, Farzin S, Mousavi SF. Experimental Study of Evaporation Reduction
Using Polystyrene Coating, Wood and Wax and its Estimation by Intelligent Algorithms. Irrig
Water Eng 2020;11:147–65. https://doi.org/10.22125/iwe.2020.120727.
[6] Ghazvinian H, Farzin S, Karami H, Mousavi SF. Investigating the Effect of using Polystyrene
sheets on Evaporation Reduction from Water-storage Reservoirs in Arid and Semiarid Regions
(Case study: Semnan city). J Water Sustain Dev 2020;7:45–52.
https://doi.org/10.22067/jwsd.v7i2.81748.

[7] Dehghanipour MH, Karami H, Ghazvinian H, Kalantari Z, Dehghanipour AH. Two Comprehensive
and Practical Methods for Simulating Pan Evaporation under Different Climatic Conditions in Iran.
Water 2021;13:2814. https://doi.org/10.3390/w13202814.
[8] Ghazvinian H, Karami H, Farzin S, Mousavi S-F. Introducing affordable and accessible physical
covers to reduce evaporation from agricultural water reservoirs and pools (field study, statistics,
and intelligent methods). Arab J Geosci 2021;14:2543. https://doi.org/10.1007/s12517-021-08735-
3.
[9] Karamouz M, Nazif S, Falahi M. Hydrology and hydroclimatology: principles and applications.
6000 Broken Sound Parkway NW, Suite 300: CRC Press; 2012.
[10] Dehghanipour MH, Ghazvinian H, Dehghanipour A. Evaluation of the efficiency of artificial
intelligence models for simulating evaporation in arid, semi-arid, and very-wet climates of Iran.
Iran-Water Resour Res 2021.
[11] Babamiri O, Dinpazhoh Y. Comparison and Evaluation of Twenty Methods for Estimating
Reference Evapotranspiration Based on Three General Categories: Air Temperature, Solar
Radiation and Mass Transfer in the Basin of Lake Urmia. JSTNAR 2016;20:145–61.
https://doi.org/10.18869/acadpub.jstnar.20.77.145.
[12] Samadianfard S, Panahi S. Estimating Daily Reference Evapotranspiration using Data Mining
Methods of Support Vector Regression and M5 Model Tree. Jwmr 2019;9:157–67.
https://doi.org/10.29252/jwmr.9.18.157.
[13] Goudarzi M, Salahi B, Hosseini SA. Estimation of Evapotranspiration Rate Due to Climate Change
in the Urmia Lake Basin. Ijwmse 2018;12:1–12.
[14] Mohtarami O, Hosseini MR, Fattahi R. Hargreaves Method Improves Accuracy in Estimating
Reference Evapotranspiration Adjustment Weight With the Help of Artificial Neural Network and
Decision Tree. Water Eng 2018;6:112–23.
[15] Zorati pur E, Neisi L, Golabi M, Bazaz A, Zoratipur A. Simulation and Comparison of Potential
Evapotranspiration by Artificial Neural Networks, ANFIS (Fuzzy Neural Network) and Decision
Making M5 (Case Study; Synaptic Station of Shiraz). Iran-Water Resour Res 2019;15:365–71.
[16] Babu S, Thomas B. Modeling Daily Pan Evaporation Using Tree-Based Regression Methods,
2022, p. 605–14. https://doi.org/10.1007/978-981-19-0475-2_53.
[17] Batra K, Gandhi P. Artificial Neural Network-Based Model for the Prediction of Evaporation in
Agriculture, 2022, p. 561–9. https://doi.org/10.1007/978-981-16-8542-2_46.
[18] Solaimani K. Seasonal relationship between climatic variables and evaporation based on Bayesian
quantile regression method in southern Caspian region. Arab J Geosci 2022;15:1000.
https://doi.org/10.1007/s12517-022-10263-7.
[19] Jannar Fereidouni F, Nahavandian Esfahani S, Mahmoudi N. Seasonal variations of the water
column structure and estimation of the mixed layer depth based on the temperature using threshold
method in Babolsar and Ramsar regions. J Earth Sp Phys 2020;46:159–74.
https://doi.org/10.22059/jesphys.2020.286089.1007154.
[20] Moghaddam AS, Massoud J, Mahmoodi M, Mahvi AH, Periago MV, Artigas P, et al. Human and
animal fascioliasis in Mazandaran province, northern Iran. Parasitol Res 2004;94.
https://doi.org/10.1007/s00436-004-1169-6.

[21] Karami H, DadrasAjirlou Y, Jun C, Bateni SM, Band SS, Mosavi A, et al. A Novel Approach for
Estimation of Sediment Load in Dam Reservoir With Hybrid Intelligent Algorithms. Front Environ
Sci 2022;10. https://doi.org/10.3389/fenvs.2022.821079.
[22] Ghazvinian H, Mousavi S-F, Karami H, Farzin S, Ehteram M, Hossain MS, et al. Integrated
support vector regression and an improved particle swarm optimization-based model for solar
radiation prediction. PLoS One 2019;14:e0217634. https://doi.org/10.1371/journal.pone.0217634.
[23] Ghazvinian H, Bahrami H, Ghazvinian H, Heddam S. Simulation of Monthly Precipitation in
Semnan City Using ANN Artificial Intelligence Model. J Soft Comput Civ Eng 2020;4:36–46.
https://doi.org/10.22115/scce.2020.242813.1251.
[24] Naderpour H, Rafiean AH, Fakharian P. Compressive strength prediction of environmentally
friendly concrete using artificial neural networks. J Build Eng 2018;16:213–9.
[25] Naderpour H, Rezazadeh Eidgahee D, Fakharian P, Rafiean AH, Kalantari SM. A new proposed
approach for moment capacity estimation of ferrocement members using Group Method of Data
Handling. Eng Sci Technol an Int J 2020;23:382–91. https://doi.org/10.1016/j.jestch.2019.05.013.
[26] Naderpour H, Nagai K, Fakharian P, Haji M. Innovative models for prediction of compressive
strength of FRP-confined circular reinforced concrete columns using soft computing methods.
Compos Struct 2019;215:69–84. https://doi.org/10.1016/j.compstruct.2019.02.048.
[27] Dadrasajirlou Y. Quantitative flood mitigation in urban basins with optimal low-impact
development and best management practices designs under climate change conditions. Semnan
Universtiy, 2021.
[28] Eftekhari M, Eslaminezhad SA, Akbari M, DadrasAjirlou Y, Haji Elyasi A. Assessment of the
Potential of Groundwater Quality Indicators by Geostatistical Methods in Semi-arid Regions. J
Chinese Soil Water Conserv 2021;52:158–67.
https://doi.org/10.29417/JCSWC.202109_52(3).0004.
[29] Javadi S, Maghami A, Hosseini SM. A deep learning approach based on a data-driven tool for
classification and prediction of thermoelastic wave’s band structures for phononic crystals. Mech
Adv Mater Struct 2021:1–14. https://doi.org/10.1080/15376494.2021.1983088.
[30] Heddam S, Kisi O. Modelling daily dissolved oxygen concentration using least square support
vector machine, multivariate adaptive regression splines and M5 model tree. J Hydrol
2018;559:499–509. https://doi.org/10.1016/j.jhydrol.2018.02.061.
[31] Rezazadeh Eidgahee D, Jahangir H, Solatifar N, Fakharian P, Rezaeemanesh M. Data-driven
estimation models of asphalt mixtures dynamic modulus using ANN, GP and combinatorial
GMDH approaches. Neural Comput Appl 2022;34:17289–314. https://doi.org/10.1007/s00521-
022-07382-3.
[32] Naderpour H, Parsa P, Mirrashid M. Innovative Approach for Moment Capacity Estimation of
Spirally Reinforced Concrete Columns Using Swarm Intelligence–Based Algorithms and Neural
Network. Pract Period Struct Des Constr 2021;26. https://doi.org/10.1061/(ASCE)SC.1943-
5576.0000612.
[33] Wang L, Niu Z, Kisi O, Li C, Yu D. Pan evaporation modeling using four different heuristic
approaches. Comput Electron Agric 2017;140:203–13.
https://doi.org/10.1016/j.compag.2017.05.036.

[34] Rezaie-Balf M, Kim S, Fallah H, Alaghmand S. Daily river flow forecasting using ensemble
empirical mode decomposition based heuristic regression models: Application on the perennial
rivers in Iran and South Korea. J Hydrol 2019;572:470–85.
https://doi.org/10.1016/j.jhydrol.2019.03.046.
[35] Nikpour MR, Sani Khani H, Mahmodi Babelan S, Mohammadi A. Application of LS-SVM, ANN,
WNN and GEP in rainfall- runoff modeling of Kiyav-Chay River. Iran J Ecohydrol 2017;4:627–39.
https://doi.org/10.22059/ije.2017.61501.
[36] Hu Z, Karami H, Rezaei A, DadrasAjirlou Y, Piran MJ, Band SS, et al. Using soft computing and
machine learning algorithms to predict the discharge coefficient of curved labyrinth overflows. Eng
Appl Comput Fluid Mech 2021;15:1002–15. https://doi.org/10.1080/19942060.2021.1934546.
[37] Naderpour H, Mirrashid M, Parsa P. Failure mode prediction of reinforced concrete columns using
machine learning methods. Eng Struct 2021;248:113263.
https://doi.org/10.1016/j.engstruct.2021.113263.
[38] Barzegar R, Ghasri M, Qi Z, Quilty J, Adamowski J. Using bootstrap ELM and LSSVM models to
estimate river ice thickness in the Mackenzie River Basin in the Northwest Territories, Canada. J
Hydrol 2019;577:123903.
[39] Cunha AC, Gabriel Filho LRA, Tanaka AA, Goes BC, Putti FF. Influence Of The Estimated
Global Solar Radiation On The Reference Evapotranspiration Obtained Through The Penman-
Monteith Fao 56 Method. Agric Water Manag 2021;243:106491.
[40] Córdova M, Carrillo-Rojas G, Crespo P, Wilcox B, Célleri R. Evaluation of the Penman-Monteith
(FAO 56 PM) method for calculating reference evapotranspiration using limited data. Mt Res Dev
2015;35:230–9.
[41] Taylor KE. Summarizing multiple aspects of model performance in a single diagram. J Geophys
Res Atmos 2001;106:7183–92. https://doi.org/10.1029/2000JD900719.
[42] Abed M, Imteaz MA, Ahmed AN, Huang YF. Application of long short-term memory neural
network technique for predicting monthly pan evaporation. Sci Rep 2021;11:1–19.
[43] Majhi B, Naidu D, Mishra AP, Satapathy SC. Improved prediction of daily pan evaporation using
Deep-LSTM model. Neural Comput Appl 2020;32:7823–38. https://doi.org/10.1007/s00521-019-
04127-7.
[44] Qasem SN, Samadianfard S, Kheshtgar S, Jarhan S, Kisi O, Shamshirband S, et al. Modeling
monthly pan evaporation using wavelet support vector regression and wavelet artificial neural
networks in arid and humid climates. Eng Appl Comput Fluid Mech 2019;13:177–87.
https://doi.org/10.1080/19942060.2018.1564702.
[45] Alsumaiei AA. Utility of Artificial Neural Networks in Modeling Pan Evaporation in Hyper-Arid
Climates. Water 2020;12:1508. https://doi.org/10.3390/w12051508.

Reference Evapotranspiration Estimation Using ANN, LSSVM, and M5 Tree Models (Case Study: of Babolsar and Ramsar Regions, Iran)

More Related Content

Similar to Reference Evapotranspiration Estimation Using ANN, LSSVM, and M5 Tree Models (Case Study: of Babolsar and Ramsar Regions, Iran) (20)

More from Journal of Soft Computing in Civil Engineering (20)

Recently uploaded (20)

Reference Evapotranspiration Estimation Using ANN, LSSVM, and M5 Tree Models (Case Study: of Babolsar and Ramsar Regions, Iran)