Simultaneous modelling and forecasting of hourly dissolved ......Kisi et al. (2013) investigated the...
Transcript of Simultaneous modelling and forecasting of hourly dissolved ......Kisi et al. (2013) investigated the...
-
ORIGINAL ARTICLE
Simultaneous modelling and forecasting of hourly dissolvedoxygen concentration (DO) using radial basis function neuralnetwork (RBFNN) based approach: a case studyfrom the Klamath River, Oregon, USA
Salim Heddam1
Received: 11 July 2016 / Accepted: 12 July 2016 / Published online: 20 July 2016
� Springer International Publishing Switzerland 2016
Abstract In the present study, we developed and com-
pared two artificial intelligences technique (AI) for simul-
taneous modelling and forecasting hourly dissolved oxygen
(DO) in river ecosystem. The two techniques are: radial
basis function neural network (RBFNN) and multilayer
perceptron neural network (MLPNN). For the purpose of
the study, we choose two stations from the United States
Geological Survey: (USGS ID: 421015121471800) at Lost
River Diversion Channel nr Klamath River, Oregon, USA
(Latitude 42�1001500, Longitude 121�4701800 NAD83), witha total of 8703 data, and (USGS ID: 421401121480900) at
Upper Klamath Lake at Link River Dam, Oregon USA
(Latitude 42�1400100, Longitude 121�4800900 NAD83) witha total of 8552 data. The investigation is divided into two
distinguished phase. Firstly, using four water quality vari-
ables that are, water pH, temperature (TE), specific con-
ductance (SC), and sensor depth (SD); we compared five
models (M1 to M5) with different combination of input
variables. As a result of the first investigation we found that
generally RBFNN outperform MLPNN according to the
performances criteria calculated. In the second part of the
study, six Different models (FM1 to FM6) having the same
input data sets are developed for 1,12, 24,48,72 and 168 h
ahead (in advance) forecasting. The performance of the
RBFNN and MLPNN models in training, validation and
testing sets are compared with the observed data. Our
results reveal that the two models provided relatively
similar results and they successfully forecasting DO with a
high level of accuracy and the reliability of forecasting
decreases with increasing the step ahead.
Keywords Modelling � Forecasting � Dissolved oxygen �RBFNN � MLPNN � River
Introduction
One of the most important components of the aquatic life is
certainly Dissolved oxygen concentration (DO). The prin-
cipal sources of in-stream DO are: (1) diffusion from the
atmosphere at the stream surface exchange, (2) mixing of
the stream water at riffles, and (3) photosynthesis from in-
stream primary production (O’Driscoll et al. 2016). DO is
measured in milligrams per liter (mg/l). In the river
ecosystems, DO is produced and consumed continuously
and it is necessary to the fauna, flora and aquatic organ-
isms. A reduction of level of DO may cause long-term
adverse effects in the aquatic environment (Gonçalves and
Costa 2013), and a deficiency of DO is a sign of an
unhealthy river (Mondal et al. 2016). It is also reported that
DO is an important factor influencing the dynamics of
phytoplankton and zooplankton populations and a model
has been recently proposed and tested describing the role of
DO on the plankton dynamics (Dhar and Baghel 2016).
Misra and Chaturvedi (2016) reported that DO concentra-
tion is the most important factor affecting subsequent
survival of fish. Since then, some models using different
modelling approaches have been proposed for estimating
DO in rivers, streams and lakes ecosystems.
Abdul-Aziz et al. (2007a, b) developed an empirical
model to adjust discrete DO measurements to a common
time-reference value using an extended stochastic har-
monic analysis (ESHA) algorithm. The model was
& Salim [email protected]
1 Faculty of Science, Agronomy Department, Hydraulics
Division University, 20 Août 1955, Route EL Hadaik, BP 26,
Skikda, Algeria
123
Model. Earth Syst. Environ. (2016) 2:135
DOI 10.1007/s40808-016-0197-4
http://orcid.org/0000-0002-8055-8463http://crossmark.crossref.org/dialog/?doi=10.1007/s40808-016-0197-4&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1007/s40808-016-0197-4&domain=pdf
-
calibrated and validated for different stream sites across
Minnesota, USA, incorporating effects of different ecore-
gions and variable drainage areas. In order to validate the
model, the authors have used with independent data for
other sites in Minnesota. Considering DO as important
water quality indicator, Costa and Gonçalves (2011)
compared two approaches: the linear and the state-space
models, the two models have been associated to the clus-
tering technique. The authors have tried to identify and
classify homogeneous groups of water quality based on
similarities in the temporal dynamics of the DO concen-
tration. Subsequently, they have compared the two models
for predicting DO using data from River Ave basin, Por-
tugal. The authors have obtained root mean square errors
(RMSE) of 0.961 and 0.846 for the linear models and the
state space model, respectively. Prasad et al. (2011) used
MLR approach to develop a three dimensional model for
prediction of spatially explicit DO levels in Chesapeake
Bay, USA, by accounting for long-term variability of
nutrient concentrations: total dissolved nitrogen (TDN),
total dissolved phosphorus (TDP), water temperature (TE)
and salinity (SA) across the Bay. The model has been
applied at monthly time step and the step-wise regression
approach was used to select a starting point for the MLR
models relating DO concentrations to monthly water TE,
SA, TDN and TDP levels. Akkoyunlu et al. (2011)
examined the depth-dependent estimation of a lake’s DO
using two ANN methods: (1) the RBFNN and the MLPNN,
and (2) the multiple linear regression (MLR). The com-
parison results revealed that the ANN methods were
noticeably superior to those of MLR in modelling the DO.
Ay and Kisi (2012) developed and compared two dif-
ferent artificial neural network (ANN) techniques, the
multi-layer perceptron artificial neural network (MLPNN)
and the radial basis function neural network (RBFNN), for
modelling DO concentration. The ANN models were
developed using experimental data collected from the
upstream and downstream USGS stations on Foundation
Creek, Colorado, USA. Antanasijević et al. (2013) devel-
oped and compared three types of ANN namely, general-
ized regression neural network (GRNN), backpropagation
neural network (BPNN) and recurrent neural network
(RNN), for the prediction of DO concentration in the
Danube River, North Serbia. An innovative approach has
been proposed by Areerachakul et al. (2013) that combine
unsupervised and supervised artificial neural networks
(ANN) based approaches. Using thirteen (13) water quality
variables collected with a time step of 1 month, the authors
have applied in the first part, the standard multilayer per-
ceptron neural network (MLPNN). In the second part, they
have applied the MLPNN with a priori unsupervised
clustering methods: the K-mean and fuzzy c-mean algo-
rithms, the combined model is called k-MLPNN, and
applied to predict the DO in k clusters based on the 13
water quality. As a result of the investigation, the authors
have demonstrated that k-MLPNN had higher predictive
capability than a standard MLPNN model with coefficient
of correlation (CC) of 0.83 and 0.62 for the k-MLPNN and
MLPNN, respectively.
A model called real-value genetic algorithm support
vector regression (RGA-SVR) has been proposed by Liu
et al. (2013). The authors have applied the model for pre-
dicting water DO in in aquaculture river crab pond in
China, and demonstrated that RGA-SVR provided best
results in comparison to the standard support vector
regression (SVR) and MLPNN. The root mean square error
(RMSE) obtained in the testing phase was 0.0195, 0.051
and 0.283 for RGA-SVR, SVR and MLPNN, respectively.
Wavelet neural network (WNN), that uses morlet wavelet
as the wavelet transfer function in the hidden layer has
been proposed by Xu and Liu (2013). The authors have
applied the model for predicting DO in the Intensive
freshwater pearl breeding ponds in Duchang county,
Jiangxi province, China. Compared with prediction results
achieved by the MLPNN and the Elman neural network
(ELM), the low mean absolute percentage error (MAPE)
was obtained with WNN. Kisi et al. (2013) investigated the
accuracy of three artificial intelligence techniques, namely
MLPNN, ANFIS and gene expression programming (GEP)
in modelling daily DO in South Platte River at Englewood,
Colorado, USA. As a conclusion of the investigation, the
authors have demonstrated that GEP model performed
better than the MLPNN and ANFIS models in modelling
DO concentration. Liu et al. (2014) proposed at the first
time a particular model that combining both wavelet
analysis (WA) and least squares support vector regression
(LSSVR) with an optimal improved Cauchy particle swarm
optimization (CPSO) algorithm. The proposed hybrid
model called WA-CPSO-LSSVR has been applied to pre-
dict DO in river crab culture ponds, at the Yixing base of
intelligent aquaculture management systems in Jiangsu
pro-vince, China. For comparison, the authors have applied
for the same data set the standard LSSVR, and the flexible
structure radial basis function neural network (FS-
RBFNN). From the results obtained it can be concluded
that the estimation results were significantly different and
the WA-CPSO-LSSVR model provided good results in
comparison to the other two. The CC obtained in the
testing phase was 0.89, 0.92 and 0.96 for LSSVR, FS-
RBFNN and WA-CPSO-LSSVR, respectively.
Heddam (2014a) applied generalized regression neural
network (GRNN) based model for modelling hourly DO, at
Klamath River, Oregon, USA. Evrendilek and Karakaya
(2014) investigated the effects of discrete wavelet transforms
(DWT)with the orthogonal Symmlet and the semi orthogonal
Chui-Wang B-spline on predictive power of multiple non-
135 Page 2 of 18 Model. Earth Syst. Environ. (2016) 2:135
123
-
linear regression models (MNLR) models for diel, daytime
(diurnal) and nighttime (nocturnal) DO dynamics. Using
three artificial intelligence-based models, Emamgholizadeh
et al. (2014) have conducted an investigation for modelling
DO in Karoon River, Iran. The authors have selected nine (9)
water quality variables with a time step of 1 month. The
investigated models were: radial basis function neural net-
work (RBFNN), multilayer perceptron neural network
(MLPNN) and adaptive neuro-fuzzy inference system
(ANFIS) models. From the results reported by the authors
MLPNN, outperforms ANFIS and RBFNN for DO predic-
tion, producing a CC of 0.86, while the other two models
(ANFIS and RBFNN) have provided a CC equal to 0.83 and
0.75, respectively. Abdul-Aziz and Ishtiaq (2014) conducted
an investigation for predicting hourly DO time-series from
different streams representing four distinctUSEnvironmental
Protection Agency (US EPA) Level III Ecoregions of Min-
nesota, USA. The authors have developed a scaling-based
robust, empirical model for simulating the diurnal cycle of
stream DO from a single reference observation, and have
obtained a high CC rather than 0.94. Antanasijević et al.
(2014) applied GRNN model with the Monte Carlo Simula-
tion (MCS) technique for modelling DO, across multiple
sites; located on the Danube River, North Serbia.
Heddam (2014b) developed and compared two adaptive
neuro-fuzzy inference systems (ANFIS) for modeling
hourly DO, at Klamath River, Oregon, USA. In another
study, Heddam (2014c) applied an artificial intelligence
(AI) technique model called dynamic evolving neural-fuzzy
inference system (DENFIS) based on an evolving clustering
method (ECM), for modelling hourly DO in Klamath River,
Oregon, USA. In another study, Evrendilek and Karakaya
(2015) used median and linear regression models of satu-
rated dissolved oxygen (DOsat) after denoising by using
discrete wavelet transform (DWT) with Chui-Wang
B-spline and Coiflet wavelets decomposition. Alizadeh and
Kavianpour (2015) compared two artificial neural networks
models: standard MLPNN and wavelet-neural network
(WNN) for predicting DO concentration, using a variety of
water quality variables as input. Using data collected from
Hilo Bay on the east side of the Big Island, the authors have
developed the models at daily and hourly time step. For the
model at hourly time step, they have reported a high CC
rather than 0.98 and 0.97 in the validation and testing phase,
respectively using the WNN model, while for the MLPNN
the CC were 0.89 and 0.94 in the validation and testing
phase, respectively. For the model at daily time step the CC
for the WNN model was slightly less than in hourly time
step but still well above the MLPNN model. In another
study, Nemati et al. (2015) have compared three artificial
intelligence modelling techniques namely, ANFIS,
MLPNN and MLR for predicting DO in Tai Po River, New
Territories, Hong Kong. In order to investigate the
capability of these techniques for predicting DO, they have
used data at time step of 1 month and eight (8) water quality
variables were selected as input variables according to their
correlations with DO. According to the results reported,
MLPNN model outperforms ANFIS and MLR. The CC was
0.798, 0.645 and 0.681, for MLPNN, ANFIS and MLR,
respectively. Recently, An et al. (2015) used the nonlinear
grey Bernoulli model (NGBM (1, 1)) to simulate and
forecasting DO in the Guanting reservoir (inlet and outlet),
located at the upper reaches of the Yongding River in the
northwest of Beijing, China. Bayram et al. (2015) investi-
gated the applicability of teaching–learning based opti-
mization (TLBO) algorithm in modeling stream DO in
turkey. The authors have used four stream water quality
indicators, namely, water temperature (TE), pH, electrical
conductivity (EC), and hardness (WH). The TLBO method
is compared with those of the artificial bee colony algorithm
(ABC) and conventional regression analysis methods
(CRA). These methods are applied to four different
regression forms: quadratic, exponential, linear, and power.
Heddam (2016a) applied optimally pruned extreme learning
machine (OP-ELM) in forecasting DO several hours in
advance, at Klamath River, Oregon, USA.
Artificial intelligence (AI) techniques have been fre-
quently applied in environmental modelling. Some of these
applications include, among others, the following: predic-
tion of reservoir permeability from porosity measurements
(Handhal 2016); predictive modeling of discharge in
compound open channel (Parsaie et al. 2015); automatic
inversion tool for geoelectrical resistivity (Raj et al. 2015);
forecasting monthly groundwater level (Kasiviswanathan
et al. 2016); predicting the dispersion coefficient (D) in a
river ecosystem (Antonopoulos et al. 2015); modelling the
permeability losses in permeable reactive barriers (San-
tisukkasaem et al. 2015); estimating the reference evapo-
transpiration (ET0) (Adamala et al. 2015); calculating the
dynamic coefficient in porous media (Das et al. 2015);
predicting Indian monsoon rainfall (Azad et al. 2015), and
modeling of arsenic (III) removal (Mandal et al. 2015).
Although RBFNN has been applied for modelling DO
concentration, to the best of our knowledge, there have
been no studies done on the application of RBFNN for
forecasting DO in rivers; hence the present study aims to
investigate the capabilities of the RBFNN in comparison to
the standard MLPNN for simultaneous modelling and
forecasting of hourly DO concentration.
Methodology
Two models of artificial neural networks (ANN) are
developed and compared in this study: the Multilayer
Perceptron Neural Network (MLPNN) and the Radial Basis
Model. Earth Syst. Environ. (2016) 2:135 Page 3 of 18 135
123
-
Function Neural Network (RBFNN). A brief description of
these models is set forth hereafter.
Multilayer perceptron neural network (MLPNN)
Multilayer perceptron neural network (MLPNN) (Rumel-
hart et al.1986) is the most important type of ANN and its
structure can be represented as in Fig. 1. The MLPNN is a
feedforward network and has three layers: the input layer,
the hidden layer and the output layer. Each layer contains a
number of neurons. The processing ability of the network is
stored in the inter unit connection strengths (or weights) that
are obtained through a process of adaptation to a set of
training pattern (Haykin 1999). The number of neurons in
the input layer corresponds to the number of input variables;
the input layer only collects information. The hidden layer
is the important layer in the MLPNN model and contains
several neurons, and each neuron in this layer is connected
to the every neuron in the next and previous layer. Each
neuron in the hidden layer calculates the sum of the
weighted input and adds a bias value. The sum value
obtained on this application is passed through a non-linear
function known as the transfer function, which is usually a
sigmoid function, to the output layer. The third layer is the
output layer. There is only one neuron in this layer: the
desired DO. The MLPNN are capable of approximating any
function with a finite number of discontinuities (Hornik
et al. 1989) and considered as a universal approximators
(Hornik et al. 1989; Hornik 1991).
Let us denote k as the number of input variables, m as
the number of neurons in the hidden layer, the mathemat-
ical structure of the MLPNN from the input to the output
can be formulated as follow:
Aj ¼ B1 þXk
i¼1wij � xi; ð1Þ
where Aj is the weighted sum of the j hidden neuron, k is
the total number of inputs, wij denotes the weight charac-
terising the connection between the nth input to the mthhidden neuron, and B1 is the bias term of each hidden
neuron. The output of the mth hidden neuron is given by
� j ¼ f Aj� �
: ð2Þ
The activation function f adopted for the present study
was the sigmoid, represented by Eq. (3).
f Að Þ ¼ 11þ e�A : ð3Þ
The neural network output is then given by
Ok ¼ B2 þXm
j¼1wjk �� j; ð4Þ
where wjk denotes the weight characterising the connection
between the mth hidden neuron to the pth output neuron,
m the total number of hidden neurons) and B2 is the bias
term. The linear activation function is most commonly
applied to the output layer.
MLPNN is the most widely used neural network model,
and has been applied to solve many difficult problems in
environmental sciences. Some different applications are as
follows. Prediction of uniaxial compressive strength of tra-
vertine rocks (Barzegar et al. 2016); temperature variations
and generate missing temperature data in Iran (Salami and
Ehteshami 2016); river flow forecasting (Kasiviswanathan
and Sudheer 2016); prediction of water quality index in
groundwater systems (Sakizadeh 2016); runoff simulation
x1
x2
x3
xn
.
Input Layer (n neurons)
Hidden Layer(m neurons)
Output Layer(k neurons)
wjk
wijB2 =biasB1 =bias
Fig. 1 Architecture ofmultilayer perceptron neural
network (MLPNN)
135 Page 4 of 18 Model. Earth Syst. Environ. (2016) 2:135
123
-
(Javan et al. 2015); runoff and sediment yield modeling
(Sharma et al. 2015); modeling Secchi disk depth (SD) in
river (Heddam 2016b); and predicting phycocyanin (PC)
pigment concentration in river (Heddam 2016c).
Radial basis function neural network (RBFNN)
Proposed by Broomhead and Lowe (1988), radial-basis
functions neural networks (RBFNN) is a feed-forward net-
work and have three layers: the input layer, the hidden layer
and output layer. The RBFNN uses a linear transfer function
for the output neurons and a nonlinear Gaussian function for
the hidden neurons (Moody and Darken 1989). The RBFNN
neural network model has been proven to be a universal
function approximator (Park and Sandberg 1991). To the
mathematical point of view, the RBFNN structure shown in
Fig. 2 can be presented as follow (Lin and Wu 2011):
ui xð Þ ¼ x� lik k i ¼ 1; 2; . . .;N; ð5Þ
u (x) is the output of the jth hidden neuron, �k kdenotes theEuclidean distance, x is the p-dimensional input vector, liis the center (vector) of the ith hidden neuron, and u is theactivation function (Lin and Wu 2011). The RBFNN
Gaussian function can be written as:
ui xð Þ ¼ exp �x� lik k2
2 r2i
!i ¼ 1; 2;N; ð6Þ
where ri is the widths (or spread) of the hidden neuron.The output of the RBFNN model can be calculated as
follow
� i ¼XN
j¼1wij uj xð Þ þ B2 ð7Þ
wij represents a weighted connections between the radial
basis function neuron and output neuron; and N = number
of hidden-layer neurons. The constant term B2 in Eq. (7)
represents a bias. The output of the network is a linear
combination of the basis functions computed by the hidden
layer nodes and the supervised gradient-descent-based
method is used for the network training (Poggio and Girosi,
1990a, b).
In previous works, there have been reported some
important applications of RBFNN in different areas of
environmental science. Some of these applications are as
follows. Modelling coagulant dosage in water treatment
plant (Heddam et al. 2011); modelling daily ET0 (Ladlani
et al. 2012); sequestration of soil organic carbon (SOC) in
the agricultural surface soils and bottom sediments (Pal
et al. 2016); spatial variability of soil organic carbon
(Bhunia et al. 2016); predicting the side weir discharge
coefficient (Parsaie 2016); simulation of nitrate contami-
nation in groundwater (Ehteshami et al. 2016); ground-
water salinity prediction (Barzegar and Moghaddam 2016),
and predicting the longitudinal dispersion coefficient in
rivers (Parsaie and Haghiabi 2015).
Description of study area
The historical hourly dissolved oxygen concentration (DO)
and the four water quality variables data from (1 Jun 2014)
to (31 May 2015) were used in this study and are available
at the United States Geological Survey (USGS) website,
http://or.water.usgs.gov/cgi-bin/grapher/table_setup.pl?site_
id.Two stations are chosen: (USGS ID: 421015121471800)at
Lost River Diversion Channel nr Klamath River, Oregon
USA (Latitude 42�1001500, Longitude 121�4701800 NAD83),and (USGS ID: 421401121480900) at Upper Klamath Lake
at Link River Dam, Oregon USA (Latitude 42�1400100,Longitude 121�4800900 NAD83). Figure 3 shows the loca-tions of the stations in study area. For the two stations the
data set is divided into three sub-data sets: (i) a training set
(60 %), (ii) a validation set (20 %) and (iii) a test set
(20 %).
x1
x2
x3
xn
.
Input Layer (n neurons)
Hidden Layer(m neurons)
Output Layer(k neurons)
wij
wjk
B2 =bias
Fig. 2 Architecture of radialbasis function neural network
(RBFNN)
Model. Earth Syst. Environ. (2016) 2:135 Page 5 of 18 135
123
http://or.water.usgs.gov/cgi-bin/grapher/table_setup.pl%3fsite_id.Twohttp://or.water.usgs.gov/cgi-bin/grapher/table_setup.pl%3fsite_id.Two
-
Ranges of water quality data
The statistical parameters of the DO and water quality
variables data such as the mean, maximum, minimum,
standard deviation, and the coefficient of variation values
(i.e., Xmean, Xmax, Xmin, Sx, and Cv respectively) are given in
Table 2. Because the five variables described above had
different dimensions, and there was major difference
among values, it was considered to be necessary to stan-
dardize the primary data in order to enhance the training
speed and the precision of the models. Input data were
entered into the models after normalization. For this pur-
pose, Eq. (8) was utilized:
xni;k ¼xi;k �mkSdK
; ð8Þ
xni, k: is the normalized value of the variable k (input or
output) for each sample i,. xi,k the original value of the
variable k (input or output). mk and Sdk are the mean value
and standard deviation of the variable k (input or output).
Fig. 3 Map showing the study area [adopted from Sullivan et al. (2012, 2013a, b)]
135 Page 6 of 18 Model. Earth Syst. Environ. (2016) 2:135
123
-
All the input and output variables were normalized to have
zero mean and unit variance (Heddam et al. 2012, 2016;
Heddam 2014d, 2016b, c).
From the Table 1, it can be seen that pH and SC have a
direct relationship with the DO, with a CC equal to 0.16
and 0.49, respectively, while SD and TE water quality
variable have an inverse relationship with the DO with a
CC equal to -0.26 and -0.59, respectively, for the USGS
421015121471800 station. Always, in Table 1 for the
USGS 421401121480900 station, it can be seen that pH
and SD have a direct relationship with the DO, with a CC
equal to 0.09 and 0.25, respectively, while SC and TE
water quality variable have an inverse relationship with the
DO, with a CC equal to -0.25 and -0.63, respectively.
According to Table 2, for the USGS 421015121471800
station, DO concentrations ranged over three orders of
magnitude, with minimum and maximum values of 0.1 and
nearly 30 mg/L (30.50 mg/L). The mean of all observa-
tions was 8.20 mg/L. At the USGS 421401121480900, DO
concentrations ranged over three orders of magnitude, with
minimum and maximum values of 1.90 and nearly 16 mg/
L (15.80 mg/L). The mean of all observations was
9.58 mg/L. According to Table 2, temperature inversely
related to the concentration of DO in water; as temperature
increases, DO decrease. Conversely, a temperature decline
causes the oxygen concentration to increase.
Performance indices
Any developed models must be evaluated regarding their
performances. In the present study we computed three
performances indices in order to validate and compare the
models developed. The three indices are calculated
according to Legates and McCabe (1999) and Moriasi et al.
(2007): the coefficient of correlation (CC), the root mean
squared error (RMSE) and the mean absolute error (MAE).
CC ¼1N
POi �Omð Þ Pi � Pmð Þ
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1N
Pn
i¼1Oi �Omð Þ2
s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1N
Pn
i¼1Pi � Pmð Þ2
s ; ð9Þ
RMSE ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1
N
XN
i¼1Oi � Pið Þ2
vuut ; ð10Þ
MAE ¼ 1N
XN
i¼1Oi � Pij j; ð11Þ
where N is the number of data points, Oi is some measured
value and Pi is the corresponding model prediction. Om and
Pm are the average values of Oi and Pi.
Results and discussion
As stated above, the present study has two majors objec-
tives: one is modeling DO using water quality variables as
predictors and the second is the forecasting of DO at dif-
ferent hours in advance. In this section we present the
results obtained separately.
Modelling DO concentration
Modelling DO in the USGS 421015121471800 station
Five models were developed and compared. The five
models are the four-factor input vector model (TE, pH, SC
and SD), called M5; the three-factor input vector model
(TE, pH and SC), called M4; the three-factor input vector
model (TE, pH and SD), called M3; the two-factor input
vector model (TE and SC), called M2 and the two-factor
input vector model (TE and pH), called M1, respectively
(Table 3). A comparison of the performance of the RBFNN
model with that of the MLPNN model was carried out to
study their efficacy in modelling DO concentration. The
performances of the five (M1 to M5) developed models are
measured on the test set according to the three perfor-
mances indices and the results are reported in Table 4.
In all five RBFNN models developed, the key parameter
called spread (r) is the important parameter that must beoptimized during the training process. The spread param-
eter values providing the best testing performance of the
Table 1 Pearson correlation coefficients between and among physical water-quality parameters, and dissolved oxygen concentration
USGS421015121471800 USGS421401121480900
TE (�C) pH/ SC (lS/cm) SD (m) DO (mg/L) TE (�C) pH/ SC (lS/cm) SD (m) DO (mg/L)
TE (�C) 1.00 1.00pH 0.31 1.00 0.61 1.00
SC (lS/cm) -0.68 0.02 1.00 0.38 0.17 1.00
SD (m) 0.27 0.16 -0.07 1.00 -0.12 0.10 -0.66 1.00
DO (mg/L) -0.59 0.16 0.49 -0.26 1.00 -0.63 0.09 -0.25 0.25 1.00
�C degree Celsius, lS/cm microseimens per centimeter, m meter, mg/L milligrams per liter
Model. Earth Syst. Environ. (2016) 2:135 Page 7 of 18 135
123
-
RBNN were equal to 1. As is shown in Table 4, for the
RBFNN model, it is observed that the MAE, RMSE and
CC values vary in the range of 0.440–1.771 mg/L,
0.747–2.359 mg/L and 0.837–0.985, respectively, in the
training phase. In addition, in the validation phase, the
values of MAE, RMSE and CC, ranged from 0.521 to
1.759, 0.855 to 2.381 mg/L, and 0.838 to 0.981, respec-
tively. Finally, in the testing phase, the values of MAE,
RMSE and CC, ranged from 0.518 to 1.770, 0.884 to
2.388 mg/L, and 0.827 to 0.978, respectively. It may be
seen from Table 4, the CC values for all the six models are
reasonably good, being smallest (0.827) for M2 model and
greatest (0.985) for M5 model. The values of other model
performances such as RMSE, and MAE indicate that the
forecast performance of the RBFNN model is very good,
except the model M2 that is relatively acceptable, and the
RBFNN (M5) model performed better than the other
models in the training, validation, and testing phases. It is
important to state that the investigation showed that the
worst results were achieved using the model M2 that has
the TE and SC as inputs. The Scatterplots and comparison
of observed and calculated values of DO in the Training,
Validation and Testing phase, respectively, are shown in
Fig. 4 for the RBFNN M5 model, in the USGS
421015121471800 Station.
A multilayer perceptron neural network (MLPNN) as
shown in Fig. 2 has been developed for modelling DO using
the same input variables reported above. The proposed
MLPNN has three layers: an input layer with two to four
input variables under the (M1 to M5), a hidden layer with a
nonlinear sigmoid transfer function and a linear output layer
with only one neuron that correspond to the DO. The weights
and biases are the unique parameters that must be optimized
in the MLPNN model using a training algorithm. The opti-
mum number of neurons in the hidden layer is determined by
trial and error. We have varied the number of neurons from
one to twenty and we found that a model with thirteen
neurons at the hidden layer corresponds to the best model.
The parameters of MLPNN have been optimized using the
error back propagation algorithm which is an iterative
Learning algorithm. As seen from Table 4, the five MLPNN
models have shown significant variations based on the three
performance criteria. The lowest value of the RMSE in the
testing phase is 1.013 (inMLPNNM5) and the highest value
of the CC is 0.971 (in MLPNN M5). In addition, the lowest
value of MAE is 0.634 also (in MLPNN M5). From the
results of training, validation, and testing all the five models
developed in this study are evaluated all together, and the
M1, M3, M4, and M5 models are conspicuous. Among
these, the M4 and M5 models have quite low MAE and high
CC, and the M5 model is very successful on validation and
testing phase. All these five models were examined com-
paring their ability on modelling hourly DO concentration.
During training, the MLPNN (M5) performs slightly better
than the others. Also, in the validation and testing phases, the
MLPNN (M5) outperforms all other models in terms of
various performance criteria. The statistical indicators in the
Table 4 indicate that the calculated DO using RBFNN are
more accurate compared to MLPNN models (relatively low
values of MAE and RMSE, and high values of CC). In
conclusion, the M5 model is the best developed model for
modelling DO concentration, and RBFNN performs better
than MLPNN model. The Scatterplots and comparison of
observed and calculated values of DO in the Training,
Table 2 Hourly statisticalparameters of data set
Station Data Unit Xmean Xmax Xmin Sx Cv CC
USGS421015121471800 TE �C 12.73 26.90 0.70 6.84 0.54 -0.59pH / 8.18 10.20 7.10 0.70 0.09 0.16
SC lS/cm 233.54 518.00 116.00 136.53 0.58 0.49
SD m 1.03 1.16 0.77 0.06 0.06 -0.26
DO mg/l 8.20 30.50 0.10 4.31 0.53 1.00
USGS421401121480900 TE �C 12.39 26.20 0.20 7.06 0.57 -0.63pH / 8.23 10.30 7.10 0.74 0.09 0.09
SC lS/cm 120.08 146.00 107.00 8.06 0.07 -0.25
SD m 2.24 3.51 0.22 0.63 0.28 0.25
DO mg/l 9.58 15.80 1.90 2.11 0.22 1.00
Xmean mean, Xmax maximum, Xmin minimum, Sx standard deviation, Cv coefficient of variation, CC coef-
ficient de correlation with DO
Table 3 Combinations of input variables considered in developingmodels
Model Input structure Output
M1 TE and pH DO
M2 TE and SC DO
M3 TE, pH, and SD DO
M4 TE, pH, and SC DO
M5 TE, pH, SC and SD DO
135 Page 8 of 18 Model. Earth Syst. Environ. (2016) 2:135
123
-
Table 4 Performances of theRBFNN and MLPNN models in
different phases for USGS
421015121471800 station
Models Training Validation Testing
CC RMSE MAE CC RMSE MAE CC RMSE MAE
MLPNN
M1 0.951 1.334 0.851 0.954 1.321 0.848 0.956 1.255 0.827
M2 0.877 2.071 1.462 0.865 2.187 1.521 0.861 2.161 1.523
M3 0.960 1.205 0.772 0.963 1.186 0.764 0.966 1.109 0.723
M4 0.970 1.046 0.644 0.968 1.103 0.678 0.969 1.062 0.665
M5 0.970 1.042 0.647 0.972 1.021 0.657 0.971 1.013 0.634
RBFNN
M1 0.964 1.148 0.667 0.965 1.149 0.668 0.964 1.136 0.664
M2 0.837 2.359 1.771 0.838 2.381 1.759 0.827 2.388 1.770
M3 0.977 0.914 0.536 0.975 0.965 0.582 0.977 0.915 0.551
M4 0.977 0.915 0.524 0.972 1.038 0.616 0.973 0.996 0.588
M5 0.985 0.747 0.440 0.981 0.855 0.521 0.978 0.884 0.518
Fig. 4 Results with RBFNN model for USGS 421015121471800 station. Scatterplots and comparison of observed and calculated series of DO inthe: a training, b validation and c testing phase, respectively
Model. Earth Syst. Environ. (2016) 2:135 Page 9 of 18 135
123
-
Validation and Testing phases are shown in Fig. 5 for the
MLPNN M5 model, in the USGS 421015121471800
Station.
Modelling DO in the USGS 421401121480900 station
The accuracy and performance of RBFNN model for
modelling DO in the USGS 421401121480900 station are
evaluated and compared using RMSE, MAE, and CC sta-
tistical criterion. Table 5 shows all these criteria in the
training, validation and testing phases. The table shows
that, all models (M1 to M5) have a small RMSE value,
particularly M3, M4 and M5 models. According to Table 5
for all three RBFNN models (M3, M4 and M5), the per-
formance in the training phase was slightly better than the
performance for the validation and testing phases, with
only few improvements, with the exception of the model
M5 where the difference was statistically significant.
Nevertheless, the M5 model must be considered as the best
model developed. However, in accordance of the results
obtained in the previous station the M2 model that used SC
and TE as input, performed much poorer than that the
others in terms of RMSE, MAE, and CC. As seen from
Table 5, the five RBFNN models have shown significant
variations based on the three performance criteria. In the
training phase, the lowest value of the RMSE of the models
is 0.287 mg/L (in RBFNN M5) and the highest value of the
CC is 0.991 (in RBFNN M5). In addition, the lowest value
of MAE is 0.184 mg/L also (in RBFNN M5). Table 5
indicates that the RBFNN (M5) has the smallest MAE
(0.281 mg/L), RMSE (0.461 mg/L), and the highest CC
(0.978) in the validation phase; and in the testing phase the
RBFNN (M5) has the smallest MAE (0.312 mg/L), RMSE
(0.644 mg/L) and the highest CC (0.955). The Scatterplots
and comparison of observed and calculated values of DO in
the Training, Validation and Testing phase, respectively,
are shown in Fig. 6 for the RBFNN M5 model, in the
USGS 421401121480900 station.
Fig. 5 Results with MLPNN model for USGS 421015121471800 station. Scatterplots and comparison of observed and calculated series of DOin the: a training, b validation and c testing phase, respectively
135 Page 10 of 18 Model. Earth Syst. Environ. (2016) 2:135
123
-
Table 5 Performances of theRBFNN and MLPNN models in
different phases for USGS
421401121480900 station
Models Training Validation Testing
CC RMSE MAE CC RMSE MAE CC RMSE MAE
MLPNN
M1 0.941 0.706 0.474 0.946 0.693 0.473 0.934 0.761 0.509
M2 0.844 1.125 0.705 0.846 1.144 0.725 0.831 1.173 0.735
M3 0.964 0.559 0.367 0.965 0.562 0.383 0.954 0.641 0.409
M4 0.971 0.504 0.332 0.972 0.506 0.341 0.966 0.552 0.357
M5 0.976 0.453 0.300 0.976 0.469 0.320 0.972 0.497 0.324
RBFNN
M1 0.954 0.626 0.412 0.955 0.637 0.420 0.935 0.761 0.491
M2 0.825 1.184 0.748 0.828 1.201 0.785 0.810 1.236 0.774
M3 0.977 0.444 0.281 0.972 0.508 0.330 0.951 0.685 0.390
M4 0.977 0.444 0.267 0.975 0.481 0.303 0.951 0.670 0.370
M5 0.991 0.287 0.184 0.978 0.461 0.281 0.955 0.644 0.312
Fig. 6 Results with RBFNN model for USGS 421401121480900 station. Scatterplots and comparison of observed and calculated series of DO inthe: a training, b validation and c testing phase, respectively
Model. Earth Syst. Environ. (2016) 2:135 Page 11 of 18 135
123
-
As seen from Table 5, the five MLPNN models have
shown significant variations based on the three perfor-
mance criteria. The lowest value of the RMSE of fore-
casting models is 0.453 (mg/L) (in MLPNN M5) and the
highest value of the CC is 0.976 (in MLPNN M5). In
addition, the lowest value of MAE is 0.300 (mg/L) also (in
MLPNN M5). From the results of training, validation, and
testing all the five models developed in this study are
evaluated all together, and the M1, M3, M4, and M5
models are conspicuous. Among these, the M4 and M5
models have quite low MAE and high CC, and the M5
model is very successful on testing phase. All these models
were examined comparing their ability on modelling
hourly DO concentration. During training, the MLPNN
(M5) performs slightly better than the others. Also, in the
validation and testing phases, the MLPNN (M5) outper-
forms all other models in terms of various performance
criteria. In conclusion, the M5 model is the best developed
model for modelling DO concentration. The comparison
between the RBFNN and MLPNN clearly show the
differences between the two models which favour the
MLPNN in testing phase, while the RBFNN outperform
MLPNN in the training and validation phases, thereby
establishing the superiority of the RBFNN models. In the
training phase, the RBFNN M5 improved the MLPNN M5
of about 1.5 % regarding the CC value. In addition, in the
validation phase as seen in Tables 5, the RBFNN M5
improved the MLPNN M5 of about 0.2 % regarding the
CC value. In the testing phase, the MLPNN M5 improved
the RBFNN M5 of about 1.7 % regarding the CC value.
The Scatterplots and comparison of observed and calcu-
lated values of DO in the Training, Validation and Testing
phase, respectively, are shown in Fig. 7 for the MLPNN
M5 model, in the USGS 421401121480900 Station.
Forecasting DO concentration
Notwithstanding, the importance of the developed models
for estimating DO, it should be noted that they are linked to
the water quality variables, and the models cannot be done
Fig. 7 Results with MLPNN model for USGS 421401121480900 station. Scatterplots and comparison of observed and calculated series of DOin the: a training, b validation and c testing phase, respectively
135 Page 12 of 18 Model. Earth Syst. Environ. (2016) 2:135
123
-
and if they are done they can only be done with available,
timely and reliable water quality data (Heddam 2016a). It
would be interesting to investigate the capabilities of the
proposed models (RBFNN and MLPNN) for forecasting
DO at different level in advance using only the time series
of DO and without the need for water quality variables as
input to the models. Attempts to do this have not been
entirely investigated in the past, and the present study is
one of the first studies presented in the literature for fore-
casting DO time series. The statistics of the hourly DO
Time series used for developing the forecasting models are
shown in Table 6. We have developed six forecasting
models called FM1 to FM6 using the same input data and
have different output, the structure are shown in Table 7
below. It can be seen from Table 7; the six forecasting
models have the same input structure: the input variables
present the previously measured DO (t - 3, t - 2, t - 1
and t) and the output variable corresponds to the DO at
time t ? 1, t ? 12, t ? 24, t ? 48, t ? 72 and t ? 168,
where DO (t) corresponds to the DO at time t. Figure 8
shows how the input and output data sets are created.
According to Table 7, all the six developed models are
basically approximators of the general equation, where n is
the next time step:
DOðtþnÞ¼ f DOðtÞþDOðt�1ÞþDOðt�2ÞþDOðt�3Þ½ �:ð12Þ
Table 8 represents the MLPNN and RBFNN results of
DO forecasting in different phases, several hours in
advance, for USGS421401121480900 station. On
analyzing Table 8, it is apparent that the performance of
the RBFNN and MLPNN are good until 72 h in advance,
since the CC are rather than 0.92 in the validation phase. In
the testing phase the two models have a CC equals to 0.74.
From the Table 8 it can be observed that the model FM1
whose output is the DO at (t ? 1) performed better than the
others models in the training, validation, and testing pha-
ses. For the RBFNN model and according to Table 8, in the
training phase, the values of CC, RMSE and MAE, ranged
from 0.796 to 0.989, 0.322 to 1.356, and 0.220 to 0.948,
respectively. In addition, in the validation phase, the values
of CC, RMSE, and MAE ranged from 0.753 to 0.997, 0.089
to 0.807, and 0.065 to 0.649, respectively. Finally, in the
testing phase, the values of CC, RMSE, and MAE ranged
from 0.533 to 0.997, 0.071 to 0.704, and 0.054 to 0.606,
respectively. It may be seen from Table 8, the results
obtained using the MLPNN models are generally similar to
those obtained by the RBFNN models, and there were
some noticeable differences. In the training phase, MLPNN
models FM1, FM3, FM4 and FM5 are superior to the same
RBFNN models and the difference was more marked
amongst the CC coefficients. From the Table 8 it can be
revealed that RBFNN and MLPNN FM1 models with 1 h
ahead obtained the best statistics of CC (0.997 and 0.997),
RMSE (0.067 mg/L and 0.071 mg/L), and MAE
(0.052 mg/L and 0.054 mg/L) respectively, in the testing
phase. An important conclusion from the results obtained is
that that increasing the forecasting horizon from (1) to
(168) h ahead decreases the model accuracy. The CC
decreases from 0.99 to 0.53 in testing phase and the RMSE
Table 6 Hourly statisticalparameters of data set for
forecasting models
Station Period Unit Xmean Xmax Xmin Sx Cv
USGS421015121471800 Training mg/l 6.347 14.400 0.100 3.500 0.551
Validation mg/l 12.120 30.500 7.000 5.257 0.434
Testing mg/l 9.653 15.300 6.000 1.218 0.126
Whole period mg/l 8.163 30.500 0.100 4.328 0.530
USGS421401121480900 Training mg/l 8.883 15.800 1.900 2.205 0.248
Validation mg/l 11.709 14.600 10.100 1.170 0.100
Testing mg/l 11.709 14.600 10.100 1.170 0.100
Whole period mg/l 9.606 15.800 1.900 2.128 0.222
Xmean mean, Xmax maximum, Xmin minimum, Sx standard deviation, Cv coefficient of variation
Table 7 Combinations of inputvariables considered in
developing forecasting models
Model Input structure Output
FM1 DO (t - 3), DO (t - 2), DO (t - 1), DO (t) DO (t ? 1): ?1 h ahead
FM2 DO (t - 3), DO (t - 2), DO (t - 1), DO (t) DO (t ? 12): ?12 h ahead
FM3 DO (t - 3), DO (t - 2), DO (t - 1), DO (t) DO (t ? 24): ?24 h ahead
FM4 DO (t - 3), DO (t - 2), DO (t - 1), DO (t) DO (t ? 48): ?48 h ahead
FM5 DO (t - 3), DO (t - 2), DO (t - 1), DO (t) DO (t ? 72): ?72 h ahead
FM6 DO (t - 3), DO (t - 2), DO (t - 1), DO (t) DO (t ? 168): ?168 h ahead
Model. Earth Syst. Environ. (2016) 2:135 Page 13 of 18 135
123
-
and MAE increases from (0.067 and 0.052) to (0.704 and
0.606) always in the testing phase.
Table 9 represents the MLPNN and RBFNN results of
DO forecasting in different phases, for USGS
421015121471800 station. In general, CC were high (0.79
to 0.99), RMSE and MAE are low (0.450 mg/L to
2.143 mg/L, 0.253 mg/L to 1.581 mg/L) in the training
phase. From the Table 9 it can be observed that the model
FM1 either for the MLPNN or RBFNN, performed better
than the others models in the training, validation, or testing
phases. Overall, in the testing phase, RBFNN have higher
CC value and lower RMSE and MAE values than those of
the MLPNN. According to Table 9, the FM6 model is good
in the training phase, but very poor with very low CC and
very high RMSE and MAE in the validation and testing
phases. The CC ranged from (0.111 to 0.224), RMSE from
(1.210 to 1.171 mg/L), and MAE from (0.934 to 0.895 mg/
L). An important conclusion from the results obtained is
that that increasing the forecasting horizon from (1) to
(168) hours ahead decreases the model accuracy. The CC
decreases from 0.97 to 0.111 in testing phase and the
RMSE and MAE increases from (0.287 and 0.192) to
(1.210 and 0.934) always in the testing phase. Finally, two
points have to be highlighted: first, we think it is very
important that we should investigate the capabilities of the
proposed models using a long-term data set rather than
1 year. The second and final point to be stated is that the
proposed models are a powerful tool for forecasting DO up
to 72 h (3 days) ahead with good accuracy.
Conclusion
In this study, two well know artificial intelligences tech-
niques namely, RBFNN and MLPNN were developed for
modeling and forecasting DO using water quality
x1 x2 x3 x4 x5 x16 x28 x52 x76 x172 xn
Model1 : DO (t+1)
Model 2 : DO (t+12)
Model 3 : DO (t+24)
Model 4 : DO (t+48)
Model 5 : DO (t+72)
Model1 : DO (t+168)
The hourly time step (t): the value of x correspond to the DO (mg/L) at one hour interval Fig. 8 Illustration of data inputand output format for the
MLPNN and RBFNN
forecasting models and the
multi hours in advances
forecasting scheme
Table 8 Performances of theMLPNN and RBFNN
forecasting models in different
phases several hours in advance
for USGS 421401121480900
station
Forecasting interval Training Validation Testing
CC RMSE MAE CC RMSE MAE CC RMSE MAE
MLPNN model
?1 h 0.997 0.159 0.107 0.997 0.097 0.073 0.997 0.067 0.052
?12 h 0.831 1.232 0.847 0.942 0.454 0.350 0.896 0.390 0.307
?24 h 0.960 0.621 0.415 0.980 0.238 0.182 0.939 0.286 0.223
?48 h 0.927 0.833 0.562 0.954 0.363 0.287 0.845 0.444 0.353
?72 h 0.900 0.974 0.674 0.920 0.472 0.375 0.741 0.562 0.463
?168 h 0.791 1.377 0.964 0.753 0.806 0.648 0.542 0.687 0.584
RBFNN model
?1 h 0.989 0.322 0.220 0.997 0.089 0.065 0.997 0.071 0.054
?12 h 0.838 1.207 0.828 0.926 0.453 0.339 0.901 0.370 0.293
?24 h 0.949 0.700 0.468 0.980 0.236 0.181 0.935 0.296 0.231
?48 h 0.913 0.907 0.610 0.952 0.368 0.297 0.841 0.449 0.355
?72 h 0.886 1.031 0.714 0.917 0.481 0.388 0.743 0.555 0.450
?168 h 0.796 1.356 0.948 0.753 0.807 0.649 0.533 0.704 0.606
?1 h 1 h in advance, ?12 h 12 h in advance, ?24 h 24 h in advance (1 day ahead), ?48 h 48 h in advance
(2 day ahead), ?72 h 72 h in advance (3 day ahead), ?168 h 168 h in advance (1 week ahead)
135 Page 14 of 18 Model. Earth Syst. Environ. (2016) 2:135
123
-
variables and antecedent values of DO, respectively.
Given a set of training data, the two models provide a
good and powerful tool for estimating DO. To demon-
strate the usefulness of the models, we used data obtained
from two particular stations operate by the USGS data
survey. In the modeling phase, we developed five models
with different combinations of input variables and we
select the model that has the best performance according
to three performances criteria: RMSE, MAE and CC. As a
result we have obtained a CC ranged from 0.82 to 0.99,
0.82 to 0.98 and 0.81 to 0.97, in the training, validation
and testing phase respectively and the best results are
obtained with the model that contains all candidate input
variables:water pH, TE, SC, and SD. Also, it is important
to note that using only two variables as inputs, which are
TE and pH, we have obtained a high CC approximately
0.96 in the testing phase that is very promising and
encouraging. In the forecasting phase, we compared six
models using the same input structure and we have
attempted, however, to forecast, as much as possible the
DO at different hours in advance, from 1 h in advance up
to 168 h (7 days) in advance. The results obtained are
very promising, and we demonstrated that until 72 h in
advance we have a high CC approximately 0.92 in the
validation phase and 0.74 in the testing phase. At 168 h
(7 days) in advance we obtained a low result with a CC
close to 0.54. The reasons for this low level of results can
be explained in a number of ways. Firstly, the length of
the data set is probably insufficient and a data base that
covers more than 1 year is necessary, this is in order to
include in the validation and testing phases the all four
seasons. Furthermore, it may also help if we applied data-
preprocessing techniques like wavelet multi-resolution
analysis, coupled with artificial intelligences techniques,
especially for forecasting longer hours in advance. In the
future, further research is necessary to improve the pre-
diction accuracy of the proposed models and it would be
interesting to evaluate the applied models for a long
period rather than 1 year.
Acknowledgments The author thanks the staffs of USGS web serverfor providing the data that makes this research possible.
References
Abdul-Aziz OI, Ishtiaq KS (2014) Robust empirical modelling of
dissolved oxygen in small rivers and streams: scaling by a single
reference observation. J Hydrol 511:648–657. doi:10.1016/j.
jhydrol.2014.02.022
Abdul-Aziz OI, Wilson BN, Gulliver JS (2007a) An extended
stochastic harmonic analysis algorithm: application for dissolved
oxygen. Water Resour Res 43:W08417. doi:10.1029/
2006WR005530
Abdul-Aziz OI, Wilson BN, Gulliver JS (2007b) Calibration and
validation of an empirical dissolved oxygen model. J Environ
Eng 133(7):698–710. doi:10.1061/(ASCE)0733-9372(2007)133:
7(698)
Adamala S, Raghuwanshi NS, Mishra A (2015) Generalized quadratic
synaptic neural networks for ET0 modeling. Environ Process
2:309–329. doi:10.1007/s40710-015-0066-6
Akkoyunlu A, Altun H, Cigizoglu H (2011) Depth-integrated
estimation of dissolved oxygen in a lake. ASCE J Environ
Eng. 137(10):961–967. doi:10.1061/(ASCE)EE.1943-7870.
0000376
Alizadeh MJ, Kavianpour MR (2015) Development of wavelet-ANN
models to predict water quality parameters in Hilo Bay, Pacific
Ocean. Mar Pollut Bull 98:171–178. doi:10.1016/j.marpolbul.
2015.06.052
Table 9 Performances of theMLPNN and RBFNN
forecasting models in different
phases several hours in advance
for USGS 421015121471800
station
Forecasting interval Training Validation Testing
CC RMSE MAE CC RMSE MAE CC RMSE MAE
MLPNN model
?1 h 0.992 0.450 0.253 0.996 0.478 0.248 0.943 0.446 0.208
?12 h 0.925 1.332 0.945 0.963 1.647 1.137 0.685 0.880 0.640
?24 h 0.957 1.045 0.728 0.970 1.360 0.869 0.835 0.615 0.447
?48 h 0.930 1.292 0.909 0.924 2.175 1.435 0.700 0.791 0.617
?72 h 0.913 1.434 1.007 0.850 2.889 2.002 0.576 0.940 0.733
?168 h 0.832 1.957 1.448 0.630 4.211 3.238 0.111 1.210 0.934
RBFNN model
?1 h 0.987 0.563 0.330 0.997 0.458 0.254 0.970 0.287 0.192
?12 h 0.905 1.491 1.061 0.974 1.319 0.840 0.712 0.837 0.638
?24 h 0.955 1.042 0.710 0.968 1.404 0.897 0.833 0.620 0.444
?48 h 0.924 1.344 0.922 0.917 2.203 1.429 0.683 0.826 0.647
?72 h 0.904 1.505 1.061 0.856 2.828 1.944 0.586 0.936 0.739
?168 h 0.794 2.143 1.581 0.594 4.334 3.309 0.224 1.171 0.895
?1 h 1 h in advance, ?12 h 12 h in advance, ?24 h 24 h in advance (1 day ahead), ?48 h 48 h in advance
(2 day ahead), ?72 h 72 h in advance (3 day ahead), ?168 h 168 h in advance (1 week ahead)
Model. Earth Syst. Environ. (2016) 2:135 Page 15 of 18 135
123
http://dx.doi.org/10.1016/j.jhydrol.2014.02.022http://dx.doi.org/10.1016/j.jhydrol.2014.02.022http://dx.doi.org/10.1029/2006WR005530http://dx.doi.org/10.1029/2006WR005530http://dx.doi.org/10.1061/(ASCE)0733-9372(2007)133:7(698)http://dx.doi.org/10.1061/(ASCE)0733-9372(2007)133:7(698)http://dx.doi.org/10.1007/s40710-015-0066-6http://dx.doi.org/10.1061/(ASCE)EE.1943-7870.0000376http://dx.doi.org/10.1061/(ASCE)EE.1943-7870.0000376http://dx.doi.org/10.1016/j.marpolbul.2015.06.052http://dx.doi.org/10.1016/j.marpolbul.2015.06.052
-
An Y, Zou Z, Zhao Y (2015) Forecasting of dissolved oxygen in the
Guanting reservoir using an optimized NGBM (1, 1) model.
J Environ Sci. 29:158–164. doi:10.1016/j.jes.2014.10.005
Antanasijević D, Pocajt V, Povrenović D, Perić-Grujić A, Ristić M
(2013) Modelling of dissolved oxygen content using artificial
neural networks: Danube River, North Serbia, case study.
Environ Sci Pollut Res 20:9006–9013. doi:10.1007/s11356-
013-1876-6
Antanasijević D, Pocajt V, Povrenović D, Perić-Grujić A, Ristić M
(2014) Modelling of dissolved oxygen in the Danube River using
artificial neural networks and Monte Carlo Simulation uncer-
tainty analysis. J Hydrol 519:1895–1907. doi:10.1016/j.jhydrol.
2014.10.009
Antonopoulos VZ, Georgiou PE, Antonopoulos ZV (2015) Dispersion
coefficient prediction using empirical models and ANNs.
Environ Process 2:379–394. doi:10.1007/s40710-015-0074-6
Areerachakul S, Sophatsathit P, Lursinsap C (2013) Integration of
unsupervised and supervised neural networks to predict dis-
solved oxygen concentration in canals. Ecol Model
261–262:1–7. doi:10.1016/j.ecolmodel.2013.04.002
Ay M, Kisi O (2012) Modeling of dissolved oxygen concentration
using different neural network techniques in Foundation Creek,
El Paso County, Colorado. ASCE J Environ Eng
138(6):654–662. doi:10.1061/(ASCE)EE.1943-7870.0000511
Azad S, Debnath S, Rajeevan M (2015) Analysing predictability in
indian monsoon rainfall: a data analytic approach. Environ
Process 2(1):717–727. doi:10.1007/s40710-015-0108-0
Barzegar R, Moghaddam AA (2016) Combining the advantages of
neural networks using the concept of committee machine in the
groundwater salinity prediction. Model Earth Syst Environ 2:26.
doi:10.1007/s40808-015-0072-8
Barzegar R, Sattarpour M, Nikudel MR, Moghaddam AA (2016)
Comparative evaluation of artificial intelligence models for
prediction of uniaxial compressive strength of travertine rocks,
case study: Azarshahr area, NW Iran. Model Earth Syst Environ
2:76. doi:10.1007/s40808-016-0132-8
Bayram A, Uzlu E, Kankal M et al (2015) Modeling stream dissolved
oxygen concentration using teaching-learning based optimiza-
tion algorithm. Environ Earth Sci 73:6565–6576. doi:10.1007/
s12665-014-3876-3
Bhunia GS, Shit PK, Maiti R (2016) Spatial variability of soil organic
carbon under different land use using radial basis function
(RBF). Model Earth Syst Environ. 2:17. doi:10.1007/s40808-
015-0070-x
Broomhead DS, Lowe D (1988) Multivariable functional interpola-
tion and adaptive networks. Complex Syst. 2:321–355
Costa M, Gonçalves AM (2011) Clustering and forecasting of
dissolved oxygen concentration on a river basin. Stoch Environ
Res Risk Assess 25:151–163. doi:10.1007/s00477-010-0429-5
Das DB, Thirakulchaya T, Deka L, Hanspal NS (2015) Artificial
neural network to determine dynamic effect in capillary pressure
relationship for two-phase flow in porous media with micro-
heterogeneities. Environ Process 2:1–18. doi:10.1007/s40710-
014-0045-3
Dhar J, Baghel RS (2016) Role of dissolved oxygen on the plankton
dynamics in spatiotemporal domain. Model Earth Syst Environ
2:6. doi:10.1007/s40808-015-0061-y
Ehteshami M, Farahani ND, Tavassoli S (2016) Simulation of nitrate
contamination in groundwater using artificial neural networks.
Model Earth Syst Environ 2:28. doi:10.1007/s40808-016-0080-3
Emamgholizadeh S, Kashi H, Marofpoor I, Zalaghi E (2014)
Prediction of water quality parameters of Karoon River (Iran)
by artificial intelligence-based models. Int J Environ Sci Technol
11:645–656. doi:10.1007/s13762-013-0378-x
Evrendilek F, Karakaya N (2014) Regression model-based predictions
of diel, diurnal and nocturnal dissolved oxygen dynamics after
wavelet denoising of noisy time series. Phys A 404:8–15. doi:10.
1016/j.physa.2014.02.062
Evrendilek F, Karakaya N (2015) Spatiotemporal modeling of
saturated dissolved oxygen through regressions after wavelet
denoising of remotely and proximally sensed data. Earth Sci Inf
8:247–254. doi:10.1007/s12145-014-0148-4
Gonçalves AM, Costa M (2013) Predicting seasonal and hydro-
meteorological impact in environmental variables modelling via
Kalman filtering. Stoch Environ Res Risk Assess 27:1021–1038.
doi:10.1007/s00477-012-0640-7
Handhal AM (2016) Prediction of reservoir permeability from
porosity measurements for the upper sandstone member of
Zubair Formation in Super-Giant South Rumila oil field,
southern Iraq, using M5P decision tress and adaptive neuro-
fuzzy inference system (ANFIS): a comparative study. Model
Earth Syst Environ 2:111. doi:10.1007/s40808-016-0179-6
Haykin S (1999) Neural networks a comprehensive foundation.
Prentice Hall, Upper Saddle River
Heddam S (2014a) Generalized regression neural network (GRNN)
based approach for modelling hourly dissolved oxygen concen-
tration in the Upper Klamath River, Oregon, USA. Environ
Technol 35(13):1650–1657. doi:10.1080/09593330.2013.878396
Heddam S (2014b) Modelling hourly dissolved oxygen concentration
(DO) using two different adaptive neuro-fuzzy inference systems
(ANFIS): a comparative study. Environ Monit Assess
186:597–619. doi:10.1007/s10661-013-3402-1
Heddam S (2014c) Modelling hourly dissolved oxygen concentration
(DO) using dynamic evolving neural-fuzzy inference system
(DENFIS) based approach: case study of Klamath River at miller
island boat ramp, Oregon, USA. Environ Sci Pollut Res
21:9212–9227. doi:10.1007/s11356-014-2842-7
Heddam S (2014d) Generalized regression neural network (GRNN)-
based approach for colored dissolved organic matter (CDOM)
retrieval: case study of Connecticut River at Middle Haddam
Station, USA. Environ Monit Assess 186:7837–7848. doi:10.
1007/s10661-014-3971-7
Heddam S (2016a) Use of optimally pruned extreme learning
machine (OP-ELM) in forecasting dissolved oxygen concentra-
tion (DO) several hours in advance: a case study from the
Klamath River. Environ Process, Oregon, USA. doi:10.1007/
s40710-016-0172-0
Heddam S (2016b) Secchi disk depth estimation from water quality
parameters: artificial neural network versus multiple linear
regression models? Environ Process. doi:10.1007/s40710-016-
0144-4
Heddam S (2016c) Multilayer perceptron neural network based
approach for modelling Phycocyanin pigment concentrations:
case study from lower Charles River buoy. Environ Sci Pollut
Res, USA. doi:10.1007/s11356-016-6905-9
Heddam S, Bermad A, Dechemi N (2011) Applications of radial basis
function and generalized regression neural networks for mod-
elling of coagulant dosage in a drinking water treatment: a
comparative study. ASCE J Environ Eng 137(12):1209–1214.
doi:10.1061/(ASCE)EE.1943-7870.0000435
Heddam S, Bermad A, Dechemi N (2012) ANFIS-based modelling
for coagulant dosage in drinking water treatment plant: a case
study. Environ Monit Assess 184:1953–1971. doi:10.1007/
s10661-011-2091-x
Heddam S, Lamda H, Filali S (2016) Predicting effluent biochemical
oxygen demand in a wastewater treatment plant using general-
ized regression neural network based approach: a comparative
study. Environ Process 3(1):153–165. doi:10.1007/s40710-016-
0129-3
Hornik K (1991) Approximation capabilities of multilayer feed
forward networks. Neural Netw 4(2):251–257. doi:10.1016/
0893-6080(91)90009-T
135 Page 16 of 18 Model. Earth Syst. Environ. (2016) 2:135
123
http://dx.doi.org/10.1016/j.jes.2014.10.005http://dx.doi.org/10.1007/s11356-013-1876-6http://dx.doi.org/10.1007/s11356-013-1876-6http://dx.doi.org/10.1016/j.jhydrol.2014.10.009http://dx.doi.org/10.1016/j.jhydrol.2014.10.009http://dx.doi.org/10.1007/s40710-015-0074-6http://dx.doi.org/10.1016/j.ecolmodel.2013.04.002http://dx.doi.org/10.1061/(ASCE)EE.1943-7870.0000511http://dx.doi.org/10.1007/s40710-015-0108-0http://dx.doi.org/10.1007/s40808-015-0072-8http://dx.doi.org/10.1007/s40808-016-0132-8http://dx.doi.org/10.1007/s12665-014-3876-3http://dx.doi.org/10.1007/s12665-014-3876-3http://dx.doi.org/10.1007/s40808-015-0070-xhttp://dx.doi.org/10.1007/s40808-015-0070-xhttp://dx.doi.org/10.1007/s00477-010-0429-5http://dx.doi.org/10.1007/s40710-014-0045-3http://dx.doi.org/10.1007/s40710-014-0045-3http://dx.doi.org/10.1007/s40808-015-0061-yhttp://dx.doi.org/10.1007/s40808-016-0080-3http://dx.doi.org/10.1007/s13762-013-0378-xhttp://dx.doi.org/10.1016/j.physa.2014.02.062http://dx.doi.org/10.1016/j.physa.2014.02.062http://dx.doi.org/10.1007/s12145-014-0148-4http://dx.doi.org/10.1007/s00477-012-0640-7http://dx.doi.org/10.1007/s40808-016-0179-6http://dx.doi.org/10.1080/09593330.2013.878396http://dx.doi.org/10.1007/s10661-013-3402-1http://dx.doi.org/10.1007/s11356-014-2842-7http://dx.doi.org/10.1007/s10661-014-3971-7http://dx.doi.org/10.1007/s10661-014-3971-7http://dx.doi.org/10.1007/s40710-016-0172-0http://dx.doi.org/10.1007/s40710-016-0172-0http://dx.doi.org/10.1007/s40710-016-0144-4http://dx.doi.org/10.1007/s40710-016-0144-4http://dx.doi.org/10.1007/s11356-016-6905-9http://dx.doi.org/10.1061/(ASCE)EE.1943-7870.0000435http://dx.doi.org/10.1007/s10661-011-2091-xhttp://dx.doi.org/10.1007/s10661-011-2091-xhttp://dx.doi.org/10.1007/s40710-016-0129-3http://dx.doi.org/10.1007/s40710-016-0129-3http://dx.doi.org/10.1016/0893-6080(91)90009-Thttp://dx.doi.org/10.1016/0893-6080(91)90009-T
-
Hornik K, Stinchcombe M, White H (1989) Multilayer feedforward
networks are universal approximators. Neural Netw 2:359–366.
doi:10.1016/0893-6080(89)90020-8
Javan K, Lialestani MR, Nejadhossein M (2015) A comparison of
ANN and HSPF models for runoff simulation in Gharehsoo
River watershed, Iran. Modell Earth Syst Environ. 1:41. doi:10.
1007/s40808-015-0042-1
Kasiviswanathan KS, Sudheer KP (2016) Comparison of methods
used for quantifying prediction interval in artificial neural
network hydrologic models. Model Earth Syst Environ 2:22.
doi:10.1007/s40808-016-0079-9
Kasiviswanathan KS, Saravanan S, Balamurugan M, Saravanan K
(2016) Genetic programming based monthly groundwater level
forecast models with uncertainty quantification. Model Earth
Syst Environ 2:27. doi:10.1007/s40808-016-0083-0
Kisi O, Akbari N, Sanatipour M, Hashemi A, Teimourzadeh K, Shiri J
(2013) Modeling of dissolved oxygen in river water using
artificial intelligence techniques. J Environ Inform JEI
22(2):92–101. doi:10.3808/jei.201300248
Ladlani I, Houichi L, Djemili L, Heddam S, Belouz K (2012)
Modeling daily reference evapotranspiration (ET0) in the north
of Algeria using generalized regression neural networks (GRNN)
and radial basis function neural networks (RBFNN): a compar-
ative study. Meteorol Atmos Phys 118:163–178. doi:10.1007/
s00703-012-0205-9
Legates DR, McCabe GJ (1999) Evaluating the use of ‘‘goodness of
fit’’ measures in hydrologic and hydroclimatic model validation.
Water Resour Res 35:233–241. doi:10.1029/1998WR900018
Lin GF, Wu MC (2011) An RBF network with a two-step learning
algorithm for developing a reservoir inflow forecasting model.
J Hydrol 405:439–450. doi:10.1016/j.jhydrol.2011.05.042
Liu S, Tai H, Ding Q, Li D, Xu L, Wei Y (2013) A hybrid approach of
support vector regression with genetic algorithm optimization for
aquaculture water quality prediction. Math Comput Model
58:458–465. doi:10.1016/j.mcm.2011.11.021
Liu S, Xu L, Jiang Y, Li D, Chen Y, Li Z (2014) A hybrid WA-
CPSO-LSSVR model for dissolved oxygen content prediction in
crab culture. Eng Appl Artif Intell 29:114–124. doi:10.1016/j.
engappai.2013.09.019
Mandal S, Mahapatra SS, Adhikari S, Patel RK (2015) Modeling of
arsenic (III) removal by evolutionary genetic programming and
least square support vector machine models. Environ Process
2:145–172. doi:10.1007/s40710-014-0050-6
Misra OP, Chaturvedi D (2016) Fate of dissolved oxygen and survival
of fish population in aquatic ecosystem with nutrient loading: a
model. Model Earth Systems Environ 2:112. doi:10.1007/
s40808-016-0168-9
Mondal I, Bandyopadhyay J, Paul AK (2016) Water quality modeling
for seasonal fluctuation of Ichamati River, West Bengal, India.
Model Earth Syst Environ 2:113. doi:10.1007/s40808-016-0153-3
Moody J, Darken C (1989) Fast learning in networks of locally tuned
processing units. Neural Comput 1(2):281–294. doi:10.1162/
neco.1989.1.2.281
Moriasi DN, Arnold JG, Van Liew MW, Bingner RL, Harmel RD,
Veith TL (2007) Model evaluation guidelines for systematic
quantification of accuracy in watershed simulations. Trans
ASABE 50(3):885–900. doi:10.13031/2013.23153
Nemati S, Fazelifard MH, Terzi O, Ghorbani MA (2015) Estimation
of dissolved oxygen using data-driven techniques in the Tai Po
River, Hong Kong. Environ Earth Sci 74:4065–4073. doi:10.
1007/s12665-015-4450-3
O’Driscoll C, O’Connor M, Asam Z, Eyto E, Brown LE, Xiao L
(2016) Forest clear felling effects on dissolved oxygen and
metabolism in peatland streams. J Environ Manag 166:250–259.
doi:10.1016/j.jenvman.2015.10.031
Pal S, Manna S, Chattopadhyay B, Mukhopadhyay SK (2016) Carbon
sequestration and its relation with some soil properties of East
Kolkata Wetlands (a Ramsar Site): a spatio-temporal study using
radial basis functions. Model Earth Syst Environ 2:80. doi:10.
1007/s40808-016-0136-4
Park J, Sandberg IW (1991) Universal approximation using radial
basis function networks. Neural Comput 3(2):246–257. doi:10.
1162/neco.1991.3.2.246
Parsaie A (2016) Predictive modeling the side weir discharge
coefficient using neural network. Model Earth Syst Environ
2:63. doi:10.1007/s40808-016-0123-9
Parsaie A, Haghiabi AH (2015) Predicting the longitudinal dispersion
coefficient by radial basis function neural network. Model Earth
Syst Environ 1:34. doi:10.1007/s40808-015-0037-y
Parsaie A, Yonesi HA, Najafian S (2015) Predictive modeling of
discharge in compound open channel by support vector machine
technique. Model Earth Syst Environ 1:1. doi:10.1007/s40808-
015-0002-9
Poggio T, Girosi F (1990a) Regularization algorithms for learning
that are equivalent to multilayer networks. Sci New Ser
247(4945):978–982. doi:10.1126/science.247.4945.978
Poggio T, Girosi F (1990b) Networks for approximation and learning.
Proc IEEE 78:1481. doi:10.1109/5.58326
Prasad MB, Long W, Zhang X, Wood RJ, Murtugudde R (2011)
Predicting dissolved oxygen in the Chesapeake Bay: applicationsand implications. Aquat Sci 73:437–451. doi:10.1007/s00027-
011-0191-x
Raj AS, Oliver DH, Srinivas Y (2015) An automatic inversion tool for
geoelectrical resistivity data using supervised learning algorithm
of adaptive neuro fuzzy inference system (ANFIS). Model Earth
Syst Environ 1:6. doi:10.1007/s40808-015-0006-5
Rumelhart DE, Hinton GE, Williams RJ (1986) Learning internal
representations by error propagation. In: Rumelhart DE,
McClelland PDP, Research Group (eds) Parallel distributed
processing: explorations in the microstructure of cognition.
Foundations, vol I. MIT Press, Cambridge, pp 318–362
Sakizadeh M (2016) Artificial intelligence for the prediction of water
quality index in groundwater systems. Model Earth Syst Environ
2:8. doi:10.1007/s40808-015-0063-9
Salami ES, Ehteshami M (2016) Application of neural networks
modeling to environmentally global climate change at San
Joaquin Old River Station. Model Earth Syst Environ 2:38.
doi:10.1007/s40808-016-0094-x
Santisukkasaem U, Olawuyi F, Oye P, Das DB (2015) Artificial
neural network (ANN) For evaluating permeability decline in
permeable reactive barrier (PRB). Environ Process 2:291–307.
doi:10.1007/s40710-015-0076-4
Sharma N, Zakaullah Md, Tiwari H, Kumar D (2015) Runoff and
sediment yield modeling using ANN and support vector
machines: a case study from Nepal watershed. Model Earth
Syst Environ 1:23. doi:10.1007/s40808-015-0027-0
Sullivan AB, Rounds SA, Deas ML, Sogutlugil IE (2012) Dissolved
oxygen analysis, TMDL model comparison, and particulate
matter shunting-preliminary results from three model scenarios
for the Klamath River upstream of Keno Dam, Oregon: US
Geological Survey Open-File Report 2012-1101, 30 p. http://
pubs.usgs.gov/of/2012/1101/. Accessed 13 June 2016
Sullivan AB, Rounds SA, Asbill-Case JR, Deas ML (2013a)
Macrophyte and pH buffering updates to the Klamath River
water-quality model upstream of Keno Dam, Oregon: US
Geological Survey Scientific Investigations Report 2013-5016,
Model. Earth Syst. Environ. (2016) 2:135 Page 17 of 18 135
123
http://dx.doi.org/10.1016/0893-6080(89)90020-8http://dx.doi.org/10.1007/s40808-015-0042-1http://dx.doi.org/10.1007/s40808-015-0042-1http://dx.doi.org/10.1007/s40808-016-0079-9http://dx.doi.org/10.1007/s40808-016-0083-0http://dx.doi.org/10.3808/jei.201300248http://dx.doi.org/10.1007/s00703-012-0205-9http://dx.doi.org/10.1007/s00703-012-0205-9http://dx.doi.org/10.1029/1998WR900018http://dx.doi.org/10.1016/j.jhydrol.2011.05.042http://dx.doi.org/10.1016/j.mcm.2011.11.021http://dx.doi.org/10.1016/j.engappai.2013.09.019http://dx.doi.org/10.1016/j.engappai.2013.09.019http://dx.doi.org/10.1007/s40710-014-0050-6http://dx.doi.org/10.1007/s40808-016-0168-9http://dx.doi.org/10.1007/s40808-016-0168-9http://dx.doi.org/10.1007/s40808-016-0153-3http://dx.doi.org/10.1162/neco.1989.1.2.281http://dx.doi.org/10.1162/neco.1989.1.2.281http://dx.doi.org/10.13031/2013.23153http://dx.doi.org/10.1007/s12665-015-4450-3http://dx.doi.org/10.1007/s12665-015-4450-3http://dx.doi.org/10.1016/j.jenvman.2015.10.031http://dx.doi.org/10.1007/s40808-016-0136-4http://dx.doi.org/10.1007/s40808-016-0136-4http://dx.doi.org/10.1162/neco.1991.3.2.246http://dx.doi.org/10.1162/neco.1991.3.2.246http://dx.doi.org/10.1007/s40808-016-0123-9http://dx.doi.org/10.1007/s40808-015-0037-yhttp://dx.doi.org/10.1007/s40808-015-0002-9http://dx.doi.org/10.1007/s40808-015-0002-9http://dx.doi.org/10.1126/science.247.4945.978http://dx.doi.org/10.1109/5.58326http://dx.doi.org/10.1007/s00027-011-0191-xhttp://dx.doi.org/10.1007/s00027-011-0191-xhttp://dx.doi.org/10.1007/s40808-015-0006-5http://dx.doi.org/10.1007/s40808-015-0063-9http://dx.doi.org/10.1007/s40808-016-0094-xhttp://dx.doi.org/10.1007/s40710-015-0076-4http://dx.doi.org/10.1007/s40808-015-0027-0http://pubs.usgs.gov/of/2012/1101/http://pubs.usgs.gov/of/2012/1101/
-
52 p. http://pubs.usgs.gov/sir/2013/5016/. Accessed 13 June
2016
Sullivan AB, Sogutlugil IE, Rounds SA, Deas ML (2013b) Modeling
the water-quality effects of changes to the Klamath River
upstream of Keno Dam, Oregon: US Geological Survey
Scientific Investigations Report 2013-5135, 60 p. http://pubs.
usgs.gov/sir/2013/5135. Accessed 13 June 2016
Xu L, Liu S (2013) Study of short-term water quality prediction
model based on wavelet neural network. Math Comput Model
58:807–813. doi:10.1016/j.mcm.201
135 Page 18 of 18 Model. Earth Syst. Environ. (2016) 2:135
123
http://pubs.usgs.gov/sir/2013/5016/http://pubs.usgs.gov/sir/2013/5135http://pubs.usgs.gov/sir/2013/5135http://dx.doi.org/10.1016/j.mcm.201
Simultaneous modelling and forecasting of hourly dissolved oxygen concentration (DO) using radial basis function neural network (RBFNN) based approach: a case study from the Klamath River, Oregon, USAAbstractIntroductionMethodologyMultilayer perceptron neural network (MLPNN)Radial basis function neural network (RBFNN)Description of study areaRanges of water quality dataPerformance indices
Results and discussionModelling DO concentrationModelling DO in the USGS 421015121471800 stationModelling DO in the USGS 421401121480900 station
Forecasting DO concentration
ConclusionAcknowledgmentsReferences