This document presents a study that uses Bayesian Regularized Neural Networks (BRNN) to model groundwater levels in the Mahabad aquifer in Iran. The study area and data collection process are described. Five factors - precipitation, evaporation, temperature, streamflow, and previous month's groundwater level - are used as inputs to the BRNN model to estimate current groundwater levels. The results show the BRNN model performs excellently with low errors and high accuracy and determination values. Previous month's groundwater level and streamflow are found to be the most important predictors of current groundwater levels.

1. Presented by Amir Mosavi
Application of Bayesian Regularized Neural
Networks for Groundwater Level Modeling

2. MATERIAL AND METHODS
Study area
The study area is the Mahabad plain which is located in the West Azarbaijan
Province, northwest of Iran. The plain is extended between longitudes of 45º 25ꞌ 19ꞌꞌ
and 45º 55ꞌ 30ꞌꞌ E and from latitudes of 36º 23ꞌ 20ꞌꞌ to 37º 1ꞌ 45ꞌꞌ N. Area of the plain is
about 1506.9 km2, which its aquifer has an area about
172.6 km2
Modeling process
In the current study, the Bayesian Regularized Neural Networks (BRNN) is used to
estimate the groundwater level

3. Results
Importance of the input variables
y = 0.9469x +0.1486
R² = 0.9494
1
2
3
4
5
1 2 3
GWL, BRNN
4 5
GWL,Observed
y = 0.8856x +0.2954
R² = 0.9098
1
2
3
4
5
1 2 3
GWL, BRNN
4 5
GWL,Observed
(b)Test
0 0.2 0.4 0.6 0.8 1
Importance
Groundwater level (t-1)
Outlet streamflow
Temperature
Evaporation
Precipitation
Scatter plot between observed and modeled
groundwater level (GWL): (a) train and (b) test

4. Application of Bayesian Regularized Neural
Networks for Groundwater Level Modeling
Bahram Choubin *
Soil Conservation and Watershed
Management Research Department
West Azarbaijan Agricultural and
Natural Resources Research and
Education Center, AREEO
Urmia, Iran
Farzaneh Sajedi Hosseini
Reclamation of Arid and Mountainous
Regions Department
Faculty of Natural Resources,
University of Tehran
Karaj, Iran
Amir Mosavi 1,2*
1Kando Kalman Faculty of Electrical
Engineering, Óbuda University
Budapest, Hungary
2 School of Economics and Business
Norwegian University of Life Sciences
1430 Ås, Norway
amir.mosavi@kvk.uni-obuda.hu
ZoltanFried
John von Neumann Faculty of
Informatics
Obuda University
Budapest, Hungary
Abstract— Current research uses a novel machine learning
method (i.e., Bayesian Regularized Neural Networks; BRNN) to
model the groundwater level (GWL) in the Mahabad Aquifer in
West Azarbaijan, Iran. Five exploratory factors including the
precipitation, evaporation, temperature, outlet streamflow, and
GWL (t-1) are considered as inputs to estimate the GWL (t) as
a response variable. The mean monthly of datasets for the
aquifer from April 2001 to March 2013 (i.e., 12 years) was
calculated using the Voronoi map in the ArcGIS based on the
data monitoring locations. A ratio of 70/30 was used for model
calibration and validation. Evaluation of the results indicated
that the model has an excellent performance in the GWL
modeling (RMSE = 0. 219; NSE= 0. 908; R-Squared = 0. 910).
Importance analysis of the variables indicated that the variables
of GWL (t-1), outlet streamflow, temperature, evaporation, and
precipitation respectively were the important variables and
have a higher contribution in groundwater level prediction.
Keywords—Bayesian regularized neural networks; machine
learning; groundwater; hydroinformatics; artificial intelligence;
earth system modeling
I. INTRODUCTION
The global groundwater resources hold approximately
one-fifth of the world’s freshwater supply [11, 12, 14, 22, 24].
Its total amount of freshwater makes up about the entire
planet’s frozen freshwater resources including ice sheets, ice
caps, glaciers, snow resources, ice packs, and icebergs [11, 15,
16, 17, 18, 26, 33]. Groundwater is extracted from the aquifers
under the land-surface where rocks, unconsolidated materials,
and soil are saturated with water. It is a cheaper, safer, and
more convenient reservoir of the natural water cycle [5, 34].
With less vulnerability to the surface pollutions and surface
droughts it had remained a reliable and important resource for
drinking and irrigation since the ancient era, and the early
explorations may date back to the first millennium BC [9, 10,
13, 19, 21, 27, 28, 29, 31, 32].
Population growth, increasing demand, and limited
surface water resources increase the need for groundwater
resources. Monitoring and accurate estimation of the
groundwater level are utmost of importance for managing the
water resources. Recently, the development of technology and
the emergence of artificial intelligence models have greatly
contributed to the study and prediction in the groundwater and
other related environmental fields. Previous studies have
applied artificial neural networks (ANN) [6], adaptive neuro-
fuzzy inference system (ANFIS) [3], support vector machine
(SVM) [25], extreme learning machines (ELM) [30], etc. for
groundwater level (GWL) prediction. However, advances in
the emergence of more powerful models can be a further aid
to the modeling process of these phenomena. The main
objective of this study was to estimate the GWL in the
Mahabad plain by application of a novel machine learning
model namely Bayesian Regularized Neural Networks
(BRNN) in this field.
II. MATERIAL AND METHODS
Study area
The study area is the Mahabad plain which is located in
the West Azarbaijan Province, northwest of Iran. The plain is
extended between longitudes of 45º 25ꞌ 19ꞌꞌ and 45º 55ꞌ 30ꞌꞌ E
and from latitudes of 36º 23ꞌ 20ꞌꞌ to 37º 1ꞌ 45ꞌꞌ N. Area of the
plain is about 1506.9 km2, which its aquifer has an area about
172.6 km2 (Fig. 1). The main structure of the plain is alluvial
deposits and fine-grained terraces. The thickness of the
groundwater aquifer is between 30 to 90 m [2]. Mahabad city
with 170,000 population is in this city. The main source of
agriculture and drinking water in this plain is groundwater.
The location of groundwater monitoring wells in this plain is
presented in Fig. 2.
Modeling process
In the current study, the Bayesian Regularized Neural
Networks (BRNN) is used to estimate the groundwater level

5. (GWL). The BRNN refers to a forward neural network based
on Bayesian regularization training. Regularization refers to
limiting the scale of thresholds and weights to improve the
generalization ability of the neural network [8]. The model has
good potential to handle and avoid overfitting problems [1].
Five exploratory factors including the precipitation,
evaporation, temperature, outlet streamflow, and GWL (t-1)
are considered as inputs to estimate the GWL (t) as a response
variable. Datasets were received from the Regional Water
Authority of the West Azarbaijan Province. At first, using the
Voronoi map in the ArcGIS the mean monthly GWL (t) for
the aquifer was calculated. Voronoi map is a partition of a
plane into regions close to points or sites, which is used to
calculate the weighted mean of a variable in an area [4, 7]. Fig.
2 shows the Voronoi map created based on 24 groundwater
monitoring wells.
Fig. 1. Studyarea
Also, the Voronoi map based on the weather stations (Fig.
1) was used for calculating the mean monthly values of
climate factors (i.e., precipitation, evaporation, and
temperature). Also, the streamflow in the outlet of the plain
was considered as input. It is noted that there is not a
hydrologic station for considering the streamflow in the inlet
of the plain. Moreover, the GLW from the previous month (t-
1) was considered to improve the modeling.
According to the data availability, datasets were from
April 2001 to March 2013 (i.e., 12 years) which as monthly
was used for the modeling process. From this period, 70 % of
data were randomly used for training the model and the rest
(30%) was applied for the validation. A k-fold cross-
validation methodology by the BRNN R package [23] was
conducted for running the BRNN model and estimating the
GWL. Three metrics of root mean square error (RMSE),
Nash–Sutcliffe efficiency (NSE) coefficient, and coefficient
of determination (R2) was used for evaluating the model
performance.
III. RESULTS AND DISCUSSION
In this study, after calculating the mean values of the
dataset for the aquifer, the modeling was conducted using the
BRNN model. The parameter of the model (i.e., number of
neurons) was optimized using the BRNN R package [23]. Fig.
2 shows the number of 2 neurons (with an RMSE equal to
0.177) was identified as the optimum number of neurons
among 1 to 10 based on the trial and error procedure. After
optimizing the model parameters, the GWL was estimated and
modeling results were evaluated. Results indicated that the
model have an excellent performance during the training
(RMSE = 0.165; NSE= 0.949; R2 = 0.949) and testing (RMSE
= 0. 219; NSE= 0. 908; R2 = 0. 910) phases (Table 1).
Fig. 3. Optimum number of neurons
The importance analysis of the variables indicated that the
variables of groundwater level (t-1), outlet streamflow,
temperature, evaporation, and precipitation respectively were
the important variables and have a higher contribution for
0.177
Fig. 2. Voronoi map to calculate the mean groundwater level for the aquifer
Fig. 4 shows the distribution of the observed values versus
the estimated values by the BRNN model. As can be seen, the
points are distributed around the 1:1 line which means a good
relationship between the observations and estimations.
0.20
0.19
0.18
0.16
0.17
1 2 3 4 5 6 7 8 9 10
Number of neurons
RMSE(m)

6. groundwater level prediction. In this regard, Choubin and
Malekian (2017) [6] indicated that the use of previous
groundwater level (t-1) improves the GWL modeling.
TABLE I. PERFORMANCE OF THE BRNN MODEL
Metric Train Test
RMSE 0.165 0.219
NSE 0.949 0.908
R2 0.949 0.910
Note: RMSE: Root Mean Square Error; NSE: Nash–
Sutcliffe efficiency; R2: Coefficient of Determination
(a) Train
Fig. 4. Scatter plot between observed and modeled groundwater level
(GWL): (a) train and (b) test
IV. CONCLUSION
Current research applied a novel machine learning model
namely the BRNN model for groundwater level modeling.
Modeling results indicated that the model have an excellent
performance in the GWL modeling (RMSE = 0. 219; NSE= 0.
908; R-Squared = 0. 910). Importance analysis of the input
factors showed that the variables of GWL (t-1), outlet
streamflow, temperature, evaporation, and precipitation
respectively were the important variables and have a higher
contribution in groundwater level prediction. Therefore, our
results highlighted that the BRNN model can successfully
predict the GWL and it can be valuable for water resource
managers within the data-scarce areas with low budgets for
monitoring objectives.
Fig. 5. Importance of the input variables
ACKNOWLEDGMENT
We acknowledge the financial support of this work by the
Hungarian-Mexican bilateral Scientific and Technological
(2019-2.1.11-TÉT-2019-00007) project. The support of the
Alexander von Humboldt Foundation is acknowledged. We
acknowledge the financial support of this work by the
Hungarian State and the European Union under the EFOP-
3.6.1-16-2016-00010 project and the 2017-1.3.1-VKE-2017-
00025 project. The research presented in this paper was
carried out as part of the EFOP-3.6.2-16-2017-00016 project
in the framework of the New Szechenyi Plan. The completion
of this project is funded by the European Union and co-
financed by the European Social Fund. We acknowledge the
financial support of this work by the Hungarian State and the
European Union under the EFOP-3.6.1-16-2016-00010
project. The support of the Alexander von Humboldt
Foundation is acknowledged.
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GWL, BRNN
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