Advances in Environmental Biology Neural Network

Advances in Environmental Biology, 8(22) November 2014, Pages: 783-790
AENSI Journals
Advances in Environmental Biology
ISSN-1995-0756
EISSN-1998-1066
Journal home page: http://www.aensiweb.com/AEB/
Water Level Elevation Variations Modeling Using Support Vector Machine and
Neural Network
1MojtabaNoury, 2Maryam
Khalilzadeh Poshtegal, 3Seyedahmad mirbagheri, 4Mansoor Pakmanesh,
5MahsaMemarianfard
1
Department of civil Engineering, College of Engineering, Islamic Azad University, Malard Branch, Malard, Iran.
Phdcandidate in Department of Civil Engineering, K.N.Toosi University of Technology, Tehran, Iran
Department of Civil Engineering, K.N.Toosi University of Technology, Tehran, IRAN
4
Phd student in Department of water Science and Engineering, College of Agriculture, Tehran Science and Research Branch, Islamic Azad
University, Tehran, Iran.
5
Environmental Faculty, Civil Engineering College, K.N.Toosi University of Technology, Tehran, Iran
2
3
ARTICLE INFO
Article history:
Received 25 September 2014
Received in revised form 26 October
2014
Accepted 25 November 2014
Available online 31 December 2014
Keywords:
Water level fluctuation, Urmia Lake,
Support Vector Machine (SVM),
Artificial Neural Network (ANN),
Neural Wavelet Network (NWN)
ABSTRACT
This study aimed at analyzing the hydrological changes in the Lake Urmiabasin with
focus on the response of the lake water level to meteorological factorsby means of two
models was applied. For this, Support Vector Machines (SVM) and MLP- Artificial
Neural Network (ANN) models developed for simulating the Urmia Lake water level
variations. The yearly historical data of rainfall, temperature and discharge of the Urmia
Lake basin and lake water level fluctuation were used. The outcome of the SVM based
models are compared with the ANN.The root mean squareerrors (RMSE), sum square
errors (SSE) and determination coefficient statistics (R2) are used as comparison
criteria. Analysis results showed that the (RMSEs) of 0.23and 0.5 m obtained by SVM
and ANN respectively and SSEs of 0.43 , 2.01 and R 2 of 0.97, 0.93 obtained by SVM
and ANN respectively. The results of SVM model show better accuracy in comparison
with the ANN models.
© 2014 AENSI Publisher All rights reserved.
To Cite This Article: MojtabaNoury, Maryam Khalilzadeh Poshtegal, Seyedahmad mirbagheri, Mansoor Pakmanesh, Mahsa
Memarianfard., Water Level Elevation Variations Modeling Using Support Vector Machine and Neural Network. Adv. Environ. Biol.,
8(22), 783-790, 2014
INTRODUCTION
An artificial neural network (ANN) has gained significant attention in past two decades and has been
widely used for hydrological forecasting. Dawson and Wilby give state-of-the-art reviews on ANN modeling in
hydrology [1]. Good state-of-the-art reviews on ANN modeling in hydrology. Wua, attempt to seek a relatively
optimal data-driven model for rainfall forecasting from three aspects: model inputs, modeling methods, and data
preprocessing techniques [2]. Chen et al proposes a two-step statistical downscaling method for projection of
daily precipitation [5]. The proposed statistical downscaling method is developed according support vector
machine (SVM) and support vector regression (SVR), and the other is multivariate analysis, including
discriminate analysis (for classification) and multiple regression. Results shown that projection of local daily
precipitation are performed, and future work to advance the downscaling method is proposed. Asefa et al,
present the SVMs have three advantages over back-propagation networks (BPNs), which are the most frequently
used convectional NNs. Firstly, SVMs have better generalization ability. Secondly, the architectures and the
weights of the SVMs are guaranteed to be unique and globally optimal. Finally, SVMs are trained much more
rapidly [4]. Wang et al. autoregressive moving-average (ARMA) models, artificial neural networks (ANNs)
approaches, adaptive neural-based fuzzy inference system (ANFIS) techniques, genetic programming (GP)
models and support vector machine (SVM) method are examined using the long-term observations of monthly
river flow discharges. Two case study river sites are also provided to illustrate their respective performances.
The results indicate that the best performance can be obtained by ANFIS, GP and SVM, in terms of different
evaluation criteria during the training and validation phases [5]. Lin et al. effective reservoir inflow forecasting
models based on the support vector machine (SVM), which is a novel kind of neural networks (NNs), are
Corresponding Author: MojtabaNoury, Department of civil Engineering, College of Engineering, Islamic Azad University,
Malard Branch, Malard Iran.
Tel: +989149382757; E-mail: [email protected].
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MojtabaNoury et al, 2014
Advances in Environmental Biology, 8(22) November 2014, Pages: 783-790
proposed. The results indicate that the proposed SVM-based models are more well-performed, robust and
efficient than the existing back propagation neural network (BPN-based) models. In addition to using SVMs
instead of BPNs, typhoon characteristics, which are seldom regarded as key input for inflow forecasting, are
added to the proposed models to further improve the long lead-time forecasting during typhoon-warning periods
[6]. A comparison between models with and without typhoon characteristics is also presented to confirm that the
addition of typhoon characteristics significantly improves the forecasting performance for long lead-time
forecasting. Finally, the proposed modeling technique is expected to be useful to improve the reservoir inflow
forecasting. Paulin investigates the potential of reservoir computing for long-term prediction of lake water levels
[7]. Great Lakes water levels from 1918 to 2005 are used to develop and evaluate the ESN models. Three datapreprocessing techniques, moving average (MA), singular spectrum analysis (SSA), and wavelet multiresolution analysis (WMRA), were coupled with artificial neural network (ANN) to improve the estimate of
daily flows [8]. Çimen and Kisi compares the potential of support vector machines (SVM) and artificial neural
network (ANN) in modeling lake level fluctuations. The SVM method is applied to the monthly level data of
Lake Van which is the biggest lake in Turkey and Lake Egirdir. The estimated lake levels are found to be in
good agreement with the corresponding observed values. The results of the SVM based models are compared
with those of the ANN. Based on the comparison, it is found that the SVM based model performs better than the
ANN [9]. Wu et al. a novel distributed support vector regression (SVR); (D-SVR) model is proposed [10]. It
implements a local approximation to training data because partitioned original training data are independently
fitted by each local SVR model. ANN-GA and LR models are also used to help determine input variables. A
two-step GA algorithm is employed to find the optimal triplets for D-SVR model. Results reveal that the
proposed D-SVR model can carry out the river flow prediction better in comparison with others, and
dramatically reduce the training time compared with the conventional SVR model.Yu and Lionga ridge linear
regression is applied in a feature space [11]. A support vector machine (SVM) approach is proposed for
statistical downscaling of precipitation at monthly time scale [12]. Wei used wavelet support vector machines
(wavelet SVMs), for forecasting the hourly channel downstream water levels at gauging stations. An ANN is a
massively parallel distributed information processing system with highly flexible configuration and so has an
excellent nonlinearity capturing ability. The feed-forward multilayer perceptron (MLP) among many ANNs is
by far the most popular, which usually uses the technique of error back propagation to train the network
configuration. The architecture of the ANN consists of the number of hidden layers and the number of neurons
in input layer, hidden layers and output layer. ANNs with on hidden layer are commonly used in Hydrologic
modeling [1, 13, 8] The combination of wavelets theory and neural networks has lead to the development of
neural wavelet networks [14, 15]. Moreover, there are other models regarding water level fluctuation modeling,
such as Hsu and Wei developed ANN model for simulation the water levels of gauging points that are affected
by tidal effects [16, 17,18] Pointed out that the neural networks are simpler and more reliable than the
conventional time-series methods such as the autoregressive model (AR). Chang and Chen employed radial
basis function (RBF) neural networks for estuary water-stage forecasting in order to solve the more complicated
problem of water level fluctuation simulation, Moreover, This study developed SVMs, MLP-ANN and Neural
wavelet Network (NWN) models that conjugated both the wavelet function and the ANN for simulating the
Urmia Lake water level fluctuation [19]. In this research, two intelligent models were applied; ANN and SVM
model for the simulation of the water level variations of Urmia Lake that is one of the important and strategic
lakes which is faces with the threat of drought were used and the results of models were compared with each
other.
MATERIALS AND METHODS
Case study, Urmia Lake:
Lake Urmia resembles the Great Salt Lake, U.S.A. in many respects of morphology, water chemistry, and
sediments. The present lake area is about 5000 km2, shallow (8–12 m), and a perennial sodium chloridesulfate
system (22% salts). Urmia Lake in the northwest of Iran is the second largest hyper-saline lake worldwide.
During the past two decades, a significant water level decline has occurred in the lake. The existing estimations
for the lake water balance are widely variable because the lake bathymetry is unknown. The Urmia Lake
surface water levels were 1275.67 meters and 1277.71 meters above open sea surface level on January 1966 and
December 2006, respectively.
Rainfall, temperature, river flow and fluctuation of water level data:
For simulation, at first all the historical data were evaluated and considering the common data, 41 years
were selected for investigation from 1996 to 2006. In this research the data of precipitation, temperature and
yearly discharge are considered as input of model which in the other hand the data of Lake water level are
considered as output of the model. The variation (fluctuation) of Urmia lake water level is shown as table 1 and
fig.1. It is clear that the minimum water level of the lake is 2.5m less than average that indicates the climate
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change and negative balance. According to the common statistic year, 18 rain gage station table 2, 24 rivers and
(table3 and fig. 3) 19 temperature survey station (table 4), were selected for simulation.
Fig. 1: map of study area.
Table 1: Related Information for Yearly Urmia Lake Water Level.
µx(m)
Sx(m)
TOTAL
1275.672
1.220
TR
1,275.942
0.857
CV
1276.562
0.927
TE
1274.363
1.315
TR: Training Data CV: Cross Validation Data TE: Testing Data
Xmax(m)
1277.951
1,277.951
1277.951
1276.967
Xmin(m)
1273.057
1,273.857
1275.337
1273.057
Fig. 2: Urmia lake Water Level fluctuation (1996-2006).
Table 2: Related Information for Yearly Rainfall.
µx(mm)
station
TR
CV
TE
SaeedAbad
428.88 438.52
314.01
Zinjenab
305.89 303.43
303.21
Tabriz
234.40 231.18
227.79
Maragheh
347.48 305.95
299.47
Gheblalo
391.32 436.38
493.14
Chobloche
338.94 328.79
269.91
Dashband
441.46 404.43
362.66
GizilGabir
341.72 348.33
328.82
P.Mahabad
379.93 392.63
344.16
G. Jacob
296.85 256.83
279.95
Pey Gala
532.43 496.25
474.55
Oshnaviye
484.52 508.32
440.97
Mirabad
659.88 649.32
526.15
M.Serow
379.75 413.96
373.82
Band
433.90 430.53
380.50
Mosh abad
278.91 254.33
226.63
Ghasemlo
333.15 387.58
342.45
Germzigol
320.91 310.04
278.50
TR: Training Data CV: Cross Validation Data
Sx(mm)
TR
CV
133.45
110.43
94.53
79.65
59.60
49.18
119.74
102.34
97.22
105.33
91.48
119.90
174.78
141.51
111.79
81.90
103.78
116.07
91.60
102.38
127.61
126.73
136.03
158.94
157.99
164.17
96.77
104.64
92.83
109.92
79.38
82.47
120.80
124.48
95.63
79.03
TE: Testing Data
TE
110.43
79.65
49.18
102.34
105.33
119.90
141.51
81.90
116.07
102.38
126.73
158.94
164.17
104.64
109.92
82.47
124.48
79.03
TR
813.7
549.5
345.0
774.5
602.5
544.0
920.4
742.5
622.5
485.0
778.0
810.6
941.8
564.0
624.0
510.0
581.0
593.0
Xmax(mm)
CV
TE
658.9
451.5
420.0
379.8
343.1
298.0
527.3
424.3
602.5
1049.0
544.0
441.0
675.7
657.8
476.5
696.0
598.4
747.8
455.0
630.0
765.0
834.0
746.2
776.0
926.1
1008.6
564.0
735.0
624.0
718.0
388.0
465.0
581.0
692.0
430.0
379.5
TR
247.0
151.0
49.4
180.5
209.0
172.5
197.8
200.5
232.9
21.5
317.0
257.0
325.0
179.0
288.5
151.0
110.5
159.0
Xmin(mm)
CV
250.9
151.0
151.0
180.5
315.0
163.0
197.8
230.0
232.9
21.5
335.0
257.0
436.8
249.0
291.8
154.5
223.0
159.0
TE
155.5
218.5
168.4
188.7
186.0
142.5
152.3
124.5
144.6
135.0
295.0
270.0
319.3
238.0
224.0
102.0
200.0
199.0
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Fig. 3: Urmia lake watershed rivers yearly discharges (1996-2006).
Table 3: Related Information for Yearly River Flow.
3
Station
Vanyar
Anakhaton
Pole sinikh
Zinjenab
Germizigul
Ajabshir
Khormazard
TazeKand
G. Amir
ShirinKand
QizKorpi
Chobloche
Dashband
Chalkhamaz
Kotar
Jan Agha
PoleBahramlo
Baba rud
Urban
Daryan
Tapik
Band
Bitas
Lighvan
TR: Training Data
3
µx( M / s )
Sx( M / s )
TR
CV
TE
TR
CV
TE
15.01
12.09
5.94
6.94
5.68
3.43
1.86
1.59
1.06
1.09
0.95
0.83
0.93
0.86
0.53
0.46
0.33
0.22
0.30
0.32
0.27
0.11
0.17
0.16
1.20
1.03
0.89
1.42
0.31
0.33
1.75
1.29
1.21
1.22
0.03
0.03
0.34
0.36
0.29
0.13
0.17
0.22
4.40
4.18
3.27
1.31
1.06
0.84
3.00
2.88
2.03
0.90
1.05
0.79
2.18
1.97
1.50
0.67
0.73
0.88
54.35
39.15
26.99
23.91
4.61
4.24
4.98
4.69
3.40
1.81
1.47
2.35
18.82
18.08
9.79
8.72
9.47
5.25
2.27
2.09
1.90
0.81
0.71
0.71
7.73
7.93
7.33
2.52
2.94
3.96
3.85
4.10
4.09
1.34
1.42
2.80
14.55
14.35
7.01
5.93
6.46
4.94
10.52
11.17
5.38
4.33
5.00
3.08
0.57
0.44
0.27
0.25
0.19
0.15
0.46
0.52
0.37
0.27
0.33
0.21
13.96
16.05
8.44
6.65
7.18
3.72
5.71
6.40
3.93
2.03
2.45
1.95
1.70
1.87
1.29
0.85
0.89
0.76
0.83
0.86
0.74
0.28
0.25
0.21
CV: Cross Validation Data TE: Testing Data
3
Xmax( M
TR
CV
42.84
5.68
5.52
0.95
2.33
0.33
0.53
0.17
8.65
0.31
7.83
0.03
0.71
0.17
8.50
1.06
5.10
1.05
3.42
0.73
157.86
4.61
10.04
1.47
39.43
9.47
4.42
0.71
14.50
2.94
7.05
1.42
31.28
6.46
19.27
5.00
1.21
0.19
1.13
0.33
28.70
7.18
10.81
2.45
3.98
0.89
1.52
0.25
/s)
TE
23.46
3.44
1.53
0.64
1.47
1.34
0.71
5.86
4.74
3.28
46.18
7.17
39.43
3.35
14.50
6.74
27.98
18.91
0.96
1.13
27.87
10.81
3.98
1.30
3
Xmin( M
TR
CV
11.28
6.08
2.45
0.32
0.88
0.30
0.64
0.10
1.47
0.54
1.25
0.96
0.88
0.12
4.06
2.47
3.24
1.37
3.49
1.08
33.39
24.50
8.33
2.73
18.46
7.73
3.39
1.17
16.30
3.84
10.64
1.99
15.87
6.86
9.69
4.98
0.60
0.30
0.89
0.04
13.27
3.56
6.55
3.03
2.34
0.81
1.01
0.32
/s)
TE
6.08
0.36
0.45
0.10
0.54
1.24
0.12
2.47
1.37
1.08
32.11
2.73
7.73
1.17
3.84
1.99
6.86
5.27
0.20
0.13
7.07
3.57
0.90
0.58
Table 4: Related Information for Yearly Temperature.
o
µx( c )
TR
CV
TE
Maragheh
11.30
11.96
11.83
Gheblalo
12.05
11.61
12.63
Dashband
11.79
10.99
11.46
P. Mahabad
13.03
13.12
13.39
Pey Gala
12.30
12.38
11.87
Oshnaviye
12.79
12.98
13.27
Ghasemlo
10.75
10.70
11.64
Mirabad
9.83
9.63
10.57
M.Serow
8.15
8.33
9.51
TR: Training Data CV: Cross Validation Data
station
o
Sx( c )
TR
CV
1.09
0.67
0.60
0.44
0.86
0.36
0.81
0.98
1.45
1.83
0.77
0.71
0.89
0.74
1.11
0.82
1.69
1.18
TE: Testing Data
o
TE
0.59
0.51
0.78
0.72
0.58
0.57
0.59
0.52
1.41
TR
7.20
11.16
9.80
10.90
9.40
11.00
8.40
7.20
4.50
Xmax( c )
CV
10.94
11.16
10.43
11.50
9.40
11.10
9.30
7.80
5.60
o
TE
10.80
11.80
10.33
12.50
11.10
12.80
10.70
9.89
6.70
TR
12.92
13.50
13.80
15.30
14.64
14.90
12.60
12.70
10.80
Xmin( c )
CV
12.92
12.63
11.54
15.30
14.64
14.20
12.00
10.40
9.80
TE
12.90
13.50
12.40
15.00
13.10
14.60
12.60
11.30
11.00
Implementation of models:
This study investigate two different data-driven models, support vector machines (SVM) and artificial
neural network (ANN) in order to modeling lake level variations. SVM method which are a new procedure in
water resources are applied to the yearly level data of Urmia Lake that is the biggest and the hyper saline lake in
Iran.
Support vector machine (SVM):
In 1995, Cortes and Vapnik suggested a modified maximum margin idea that allows for mislabeled
examples If there exists no hyper plane that can split the "yes" and "no" examples, the Soft Margin method will
choose a hyper plane that splits the examples as cleanly as possible, while still maximizing the distance to the
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nearest cleanly split examples[20]. The method introduces slack variables, ξi, which measure the degree of
misclassification of the datum xi. The objective function is then increased by a function which penalizes nonzero ξi, and the optimization becomes a tradeoff between a large margin, and a small error penalty. If the
penalty function is linear, the optimization problem becomes: subject to (for any).This constraint along with the
objective of minimizing can be solved using Lagrange multipliers as done above. One has then to solve the
following problem with [20]. Support vector machine (SVM), which is analytically solved to reach its optimal
structural formula, can be represented as a network architecture resembling artificial neural networks (multilayer
perceptrons) that have been pruned to obtain model parsimony or improve generalization. New examples are
then mapped into that same space and predicted to belong to a category based on which side of the gap they fall
on. More formally, a support vector machine constructs a hyper plane or set of hyper planes in a high or infinite
dimensional space, which can be used for classification, regression or other tasks. Intuitively, a good separation
is achieved by the hyper plane that has the largest distance to the nearest training data points of any class (socalled functional margin), since in general the larger the margin the lower the generalization error of the
classifier.
Artificial neural networks (ANN):
Artificial neural networks (ANN) can be an efficient way of modeling the water level fluctuations process
in situations where explicit knowledge of the internal hydrologic processes is not available. An ANN is a
flexible mathematical structure that is capable of identifying complex nonlinear relationships between input and
output data sets[21]. The structure of neural network is shown in the fig5.
Fig. 4: The structure of ANN.
RESULTS AND DISCUSSION
The mean square errors (RMSE), sum square errors (SSE) and determination coefficient statistics are used
as comparison criteria.
N
RMSE  (
N
2
1
 Ym  Yo  ) 2
N i 1
R2  1
 (Y
i 1
N
m
 (Y
i 1
m
 Yo )
N
 Y ) SSE   (Ym  Yo ) 2
In which N is the number of data set,
i 1
Yo
is the yearly observed values lake level,
Ym
is the measured values
lake level and Y is the average observed Urmia lake water level.
If too many neurons are used, the network has too many parameters and may over fit the data. In constant,
if too few neurons are included in the network, it might not be possible to fully detect the signal and variance of
a complex data set[9]. In this paper the number of hidden neuron and delay and translation factor determined
using the trial and error method. The optimum hidden neuron numbers of NWN models and are found to vary
between 1 and 20 and delay and translation factor are found 1-10.A difficult task with SVM involves choosing
the
capacity (Cc), epsilon (  ) and gamma (  ) parameters values. For the Urmia lake, the capacity (Cc),
epsilon (  ) and gamma (  ) parameters of optimum SVM model for each input combination are given in table
6. In this research the value of the capacity (Cc), epsilon (  ) and gamma (  ) parameters determined using the
trial and error method. The optimum capacity (Cc), epsilon (  ) and gamma (  ) parameters SVM models are
found to vary between 1-50, (0.01-0.9) and (0.0001-0.9) respectively. Here the SVM (25, 0.002, and 0.078)
denotes a SVM model having the capacity, epsilon and gamma parameter value as 25, 0.002 and 0.078
respectively. Table 6 indicates that the SVM (25, 0.002, and 0.078) model whose inputs are the lake level of one
previous year and rainfall, temperature and runoff of each year has the lowest RMSE and SSE and best R 2.
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Table 5 indicates that the ANN(18,24,1) model whose inputs are the lake level of one previous year and
rainfall, temperature and runoff of each year has the lowest RMSE and SSE and best R 2 .
Table 5: The SSE, RMSE and R2 statistics of ANN in test period.
Model inputs
Ann structures
SSE
RMSE
R2
ANN(18,28,1)
10.25
4.83
0.43
ANN(24,29,1)
8.68
4.15
0.61
ANN(42,32,1)
4.16
3.84
0.74
L  F [( P1 ,..., P18 ), (Q1 ,..., Q24 ), (T1 ,..., T9 )]
ANN(51,33,1)
4.12
3.56
0.76
L  F [( P1 ,..., P18 ), (Q1 ,..., Q24 ), (T1 ,..., T9 )], Lt 1
ANN(52,44,1)
2.01
0.50
0.93
L  F ( P1 ,..., P18 )
L  F (Q1 ,..., Q24 )
L  F [( P1 ,..., P18 ), (Q1 ,..., Q24 )]
Table 6: The SSE, RMSE and R2 statistics of SVM in test period.
Model inputs
L  F ( P1 ,..., P18 )
L  F (Q1 ,..., Q24 )
L  F [( P1 ,..., P18 ), (Q1 ,..., Q24 )]
L  F [( P1 ,..., P18 ), (Q1 ,..., Q24 ), (T1 ,..., T9 )]
L  F [( P1 ,..., P18 ), (Q1 ,..., Q24 ), (T1 ,..., T9 )], Lt 1
1277.500
1277.000
1276.500
SSE
5.58
RMSE
4.27
R2
0.54
SVM(10,0.61,0.25)
5.07
4.16
0.68
SVM(20,0.52,0.81)
4.34
3.26
0.73
SVM(15,0.5,0.61)
1.92
1.32
0.81
SVM(25,0.002,0.078)
0.43
0.23
0.97
SVM
Predict SVM
1278.000
SVM structures
SVM(20,0.02,0.63)
Linear (SVM)
y = 0.8766x + 157.27
R2 = 0.9786
1276.000
1275.500
1275.000
1274.500
1274.000
Observed
1273.500
1273.000
1273.000
1274.000
1275.000
1276.000
1277.000
1278.000
1279
1278
predict ANN
Fig. 5: Comparison of SVM lake level estimates with the observation for the test period.
ANN
Linear (ANN)
y = 1.0721x - 92.051
R2 = 0.9371
1277
1276
1275
1274
1273
Observed
1272
1273.000
1274.000
1275.000
1276.000
1277.000
1278.000
Fig. 6: Comparison of ANN lake level estimates with the observation for the test period.
Conclusion:
In this research two models were applied for simulation of the water level variations of Urmia Lake. This
study investigates the potential of SVM model to simulation the yearly Urmia lake water level variations. The
lake level variations estimates of SVM and ANN are compared and the results shown that the SVM results are
better than ANN model. Finally it is recommended that the SVM model is suitable alternative for the which can
be applied in different fields of hydrology and water resource modeling.
789
MojtabaNoury et al, 2014
Water Level
Advances in Environmental Biology, 8(22) November 2014, Pages: 783-790
1279.000
1278.000
Observed
SVM
1277.000
1276.000
1275.000
1274.000
1273.000
1272.000
Year
1271.000
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
1279.000
1278.000
Water Level
Fig. 7: Yearly lake level estimates of SVM model in test period.
Observed
ANN
1277.000
1276.000
1275.000
1274.000
1273.000
1272.000
1271.000
Year
1270.000
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
Fig. 8: Yearly lake level estimates of ANN model in test period.
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