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ISH Journal of Hydraulic Engineering
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Estimation of suspended sediment load using
regression trees and model trees approaches
(Case study: Hyderabad drainage basin in Iran)
Ali Talebi, Javad Mahjoobi, Mohammad Taghi Dastorani & Vahid Moosavi
To cite this article: Ali Talebi, Javad Mahjoobi, Mohammad Taghi Dastorani & Vahid Moosavi
(2016): Estimation of suspended sediment load using regression trees and model trees
approaches (Case study: Hyderabad drainage basin in Iran), ISH Journal of Hydraulic
Engineering, DOI: 10.1080/09715010.2016.1264894
To link to this article: http://dx.doi.org/10.1080/09715010.2016.1264894
Published online: 30 Dec 2016.
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ISH JOURNAL OF HYDRAULIC ENGINEERING, 2016
http://dx.doi.org/10.1080/09715010.2016.1264894
Estimation of suspended sediment load using regression trees and model trees
approaches (Case study: Hyderabad drainage basin in Iran)
Ali Talebi
a
, Javad Mahjoobi
b
, Mohammad Taghi Dastorani
c
and Vahid Moosavi
a
a
Faculty of Natural Resources, Yazd University, Yazd, Iran;
b
Ministry of Energy, Yazd Regional Water Authority, Yazd, Iran;
c
Faculty of Natural Resources
and Environment, Ferdowsi University of Mashhad, Mashhad, Iran
ABSTRACT
Estimation of suspended sediment load is one of the important topics in river engineering. Dierent
methods are used for estimating the sediment rate. In recent years, dierent articial intelligence (AI)
methods, such as articial neural network (ANN), have been used for the estimation of sediments in
rivers. In this research, the suspended sediment load has been studied by using regression trees (RTs)
and model trees (MTs). The study area has been located in Hyderabad watershed in west of Iran. The
input data included the ow discharge, sum of three days discharge, sum of ve days precipitation and
the suspended sediment discharge were considered as output in the models. The numbers of total
data of sediment discharge was 223 records. The obtained results were compared with ANN method
(feed forward back propagation algorithm) and sediment rating curve (SRC). Results showed that RT
and MT outperformed ANN method in the study area. The method of SRC had high accuracy for daily
sediment discharge less than 100 ton per day in comparison with AI models, while the AI models had
higher accuracy for high sediment discharge. Moreover, the combination of articial intelligent models
had high accuracy regarding to each model lonely.
1. Introduction
Estimation of sediment transport rate is one of the basic prob-
lems in river engineering. Several empirical methods have
been developed to solve this problem. As these methods have
been obtained based on climatic conditions of other parts of
the world, they have high level of errors when are used in
rivers of Iran. One of the common methods for estimating
the suspended load in rivers is the rating curve method in
which the relation between ow discharge and sediment dis-
charge is presented as a power equation. In recent years, the
methods based on articial intelligence (AI) and machine
learning have been used for the estimation and prediction
of dierent phenomena in river engineering. e articial
neural network (ANN) is one of these methods that were
used by many scientists for estimating the sediment rates
in rivers (Abrahart and White 2001; Jain 2001; Nagy et al.
2002; Tayfur 2002; Merritt et al. 2003; Yitian and Gu 2003;
Cigizoglu 2004; Kisi 2004; Agarwal et al. 2005; Cigizoglu and
Alp 2006; Cigizoglu and Kisi 2006; Cigizoglu and Alp 2007;
Dogan et al. 2007).
Decision trees (DT) are one of the other common and
strong tools for prediction and classication. In contrast to
ANN, DT produces the roles. is means that DT presents
its prediction based on the role set, while in the procedure in
ANN is not transparent and it is like a black box. Recently,
application of regression trees (RTs) and model trees (MTs)
have been presented in water resource engineering eld.
Mahjoobi and Etemad-Shahidi (2008) predicted the wave
height due to wind in Lake Michigan using RT and apply-
ing classication and regression trees (CART) algorithm.
Ayoubloo et al. (2010) investigated the regular wave scour
around a circular pile using regression tress (CART algo-
rithm). Moreover, Etemad-Shahidi and Mahjoobi (2009) pre-
dicted the signicant wave height in Lake Superior using MT
model and applying the M5′ algorithm. MTs have also been
applied in rainfall–runo modeling (Solomatine and Dulal
2003); ood forecasting (Solomatine and Yunpeng 2004);
modeling water-level discharge relationship (Bhattacharya
and Solomatine 2005), sediment transport (Bhattacharya
et al. 2007), derivation of wave spectrum (Sakhare and Deo
2009), estimation of wind speed from wave measurements
(Daga and Deo 2009) and prediction of suspended sediment
load in rivers. Reddy and Ghimire (2009) applied the M5
MT and Gene Expression Programming to predict suspended
sediment load. ey also compared the obtained results with
sediment rating curve (SRC) and multiple linear regressions
(MLRs) and concluded that MT gives good performance
as compared with other used models. Etemad-Shahidi and
Ghaemi (2011) used MT method to predict pile groups
scour due to waves. ey presented new equations using MT
method and demonstrated that the proposed equations were
as accurate as other so computing methods, such as ANN
and SVM. Bonakdar and Etemad-Shahidi (2011), predicted
wave run-up on rubble-mound structures using M5 MT. ey
stated that the main advantage of MTs, unlike the other so
computing tools, is their easier use and more importantly
their understandable mathematical rules. ey showed that
the predictive accuracy of the MT approach was superior to
that of Van der Meer and Stam’s empirical formula. Wolfs
and Willems (
2014) developed discharge-stage curves using
© 2016 Indian Society for Hydraulics
KEYWORDS
Suspended sediment;
CART; M5′ algorithm; ANN;
sediment rating curve
ARTICLE HISTORY
Received 28 May 2016
Accepted 22 November 2016
CONTACT Ali Talebi talebisf@yazd.ac.ir
2 A. TALEBI ET AL.
several various approaches, i.e., single rating curves, rating
curves with dynamic correction, ANNs and M5′ MTs. ey
showed that all abovementioned methods outperformed the
traditional rating curve. Abolfathi et al. (
2016), used M5′ DT
algorithm to predict the wave run-up using existing labora-
tory data. ey demonstrated that the M5′ MT algorithm
had high precision in predicting the wave run-up. ey also
showed that a good agreement existed between the proposed
run-up formulae and existing empirical relations. Zounemat-
Kermani et al. (2016) used 8-year data series from hydromet-
ric stations located in Arkansas, Delaware and Idaho (USA),
to assess the ability of ANN and support vector regression
(SVR) models to forecast/estimate daily suspended sediment
concentrations and to compare the results with traditional
MLR and SRC models. ey tested three dierent ANN model
algorithms, along with four dierent SVR model kernels. ey
showed that ANN and SVR outperformed traditional meth-
ods. Shamaei and Kaedi (2016) introduced stacking method
to predict the suspended sediment. ey used linear genetic
programming and neuro-fuzzy methods as two successful so
computing methods to predict the suspended sediment. en,
they increased the accuracy of prediction by combining their
results with the meta-model of neural network based on cross
validation. e obtained results demonstrated that the stack-
ing method greatly improved root mean square error (RMSE)
and R2 statistics compared to use of linear genetic program-
ming or neuro-fuzzy solitarily. Makarynskyy et al. (2015) used
two numerical current and wave models in addition to AI
technique of neural networks (ANNs) to reproduce values of
sediment concentrations observed at two sites. ey showed
that ANN method provides accurate results. Nourani et al.
(2016) used a two-stage modeling strategy in order to han-
dle spatio-temporal variation of SSL. At temporal stage, they
used support vector machine (SVM) to nd the nonlinear
relationship of SSL in time domain. In spatial modeling stage,
they used semivariogram of monthly SSL data and then they
tted theoretical semivariogram model to the empirical var-
iogram. e obtained results showed that the hybrid of SVM
and Spatial statistics methods could predict and simulate SSL
appropriately by enjoying unique features of both approaches.
Chen and Chau (2016) used a hybrid double feedforward
neural network (HDFNN) model for daily SSL estimation, by
combining fuzzy pattern-recognition and continuity equation
into a structure of double neural networks. ey showed that
HDFNN is appropriate for modeling the sediment transport
process with nonlinear, fuzzy and time-varying characteris-
tics. Shiau and Chen (2015) developed a probabilistic esti-
mation scheme for daily and annual suspended sediment
loads using quantile regression. ey used daily suspended
sediment load and discharge data to construct quantile-de-
pendent SRCs. eir proposed approach was applied to the
Laonung station located in southern Taiwan. e results indi-
cated that the proposed approach provided not only the prob-
abilistic description for daily and annual suspended sediment
loads, but also the single estimations including the mean,
median and mode of the derived probability distribution.
e main purpose of this research is to apply the RT model
(CART algorithm) and MTs (M5′ algorithm) for estimating
the suspended sediment load in Hyderabad watershed, west
Iran. In addition, the obtained results of these two methods
will be compared with the SRC method and ANN model (feed
forward back propagation algorithm).
2. Materials and methods
2.1. Study area and data
is research has been done on Hyderabad watershed in
Kermanshah province in western part of Iran (Figure 1). e
total area of watershed is 1719km
2
, mean height is 1871m,
maximum height 3300m and minimum height is 1325m. is
watershed has been located in 47° 04′–47° 52′ longitudes and
34° 25′–34° 52′ latitude. e main river of the watershed is the
Jamishan permanent river. e meteorological station of the
watershed is Hyderabad station with 47° 27′ longitude and 34°
42′ latitude (Figure 2). e precipitation regime of the study
area is rainy-snowy and mean annual precipitation is 420mm
which is mostly occurred in winter and spring. e used data
in this research involve precipitation, ow discharge and sed-
iment discharge. e length of data period is 21years (from
Figure 1.The position of the study area in Iran. Source: The authors.
ISH JOURNAL OF HYDRAULIC ENGINEERING 3
1985 to 2006) with the total number of 223 samples. Eighty
percent of these data have been used for training and 20% for
testing and evaluating the models. One of the problems that
occur during training process is called overtting. e error on
the training set is driven to a very small value, but when new
data is presented to the network the error is large. e network
has memorized the training examples, but it has not learned
to generalize to new situations. One of the main ways to avoid
overtting (or recognize if occurs) is to separate data to training
and test data sets. e training subset is composed of 60–80%
of all the records. e remaining records are usually used as
test data set. Gharagheizi (2007) showed that the percent of test
set allocated from the main data set should be between 5% and
35%. If this percent is lower than 5%, the accuracy of the model
over the training set is much greater than the test set. Also, if
the percent is greater than 40%, the obtained model cannot pre-
dict the test set as well as the training set. Each record should
be randomly chosen from the data set and placed in one of the
two subsets. erefore, the data were separated to training and
test data sets using a common random method. e ranges and
average values of water and sediment discharge for training and
testing have been shown in Table 1.
2.2. RTs (CART algorithm)
e CART method developed by Breiman et al. (1984) gen-
erates binary DTs. CART is a nonparametric statistical meth-
odology developed for analyzing classication issues either
from categorical or continuous dependent variables. If the
dependent variable is categorical, CART produces a clas-
sication tree. When the dependent variable is continuous,
it produces a RT. e CART tree is constructed by splitting
subsets of the data set using all predictor variables to create
two child nodes repeatedly, beginning with the entire data
set. e best predictor is chosen using a variety of impurity
or diversity measures. e goal is to produce subsets of the
data which are as homogeneous as possible with respect to
the target variable. In CART algorithm for each split, each
predictor is evaluated to nd the best cut point (continuous
predictors) or groupings of categories (nominal and ordinal
predictors) based on improvement score or reduction in impu-
rity (Breiman et al. 1984). en, the predictors are compared
and the predictor with the best improvement is selected for the
split. e process repeats recursively until one of the stopping
rules is triggered. RT building centers on three major com-
ponents: (1) a set of questions of the form: is
X ≤ d?
where X
is a variable and d is a constant. (2) Goodness of split criteria
for choosing the best split on a variable and (3) the generation
of summary statistics for terminal nodes. e least-squared
deviation (LSD) impurity measure is used for splitting rules
and goodness of t criteria. e LSD measure R(t) is simply
the weighted within node variance for node t, and it is equal
to the resubstitution estimate of risk for the node (Breiman
et al. 1984). It is dened as:
where N
W
(t) is the weighted number of records in node t, ω
i
is the value of the weighting eld for record i (if any), f
i
is the
value of the frequency eld (if any), y
i
is the value of the target
eld, and
y(t)
is the mean of the dependent variable (target
eld) at node t. e LSD criterion function for split s at node
t is dened as follows:
(1)
R
(t)=
1
N
W
(t)
∑
i∈t
𝜔
i
f
i
(
y
i
− y(t)
)
2
(2)
y(t)=
1
N
W
(t)
∑
i∈t
𝜔
i
f
i
y
i
(3)
N
W
(t)=
∑
i∈t
𝜔
i
f
i
Figure 2.Drainage network and hydrometry station in Hydrabad watershed. Source: The authors.
Table 1.Ranges and average values of different parameters in training and test data sets.
Parameters
Training data set Test data set
Minimum Maximum Average Minimum Maximum Average
Water discharge (m
3
/s) 0.04 285.41 17.95 0.25 188.67 23.35
Suspended sediment discharge (ton/day) 0.0001 215.897 2027.66 0.397 68,107.35 2696.08
4 A. TALEBI ET AL.
calculated by averaging the absolute dierence between the
predicted value and the actual value for each of the training
examples that reach that node. is results in underestima-
tion of the expected error outside the calibrating data. e
expected error is multiplied by (n+v)/(n−v), where n is the
number of training instances that reach the node and the v
is the number of parameters in the model that represent the
value at that node (Wang and Witten 1997). Aer pruning,
the adjacent linear models will be sharply discontinuous at
the leaves of the pruned tree. M5 applies smoothing process
combining the model at a leaf with the models on the path to
the root to form the nal model that is placed at the leaf. In
the smoothing process, the estimated value of the leaf model
is ltered along the path back to the root. At each node, that
value is combined with the value predicted by the linear model
for that node as follows:
where P′ is the prediction passed up to the next higher node,
p is the prediction passed to this node from the below, q is the
value predicted by the model at this node, n is the number of
training instances that reach the node below, and k is a constant
(Wang and Witten 1997). Experiments of Wang and Witten,
(1997) have showed that smoothing substantially increases the
accuracy of predictions.
2.4. ANNs and SRC
ANNs are powerful nonlinear modeling approaches based
on the function of human brain. ey can identify and learn
correlated patterns between input data sets and target values.
Neural networks can be described as a network of simple pro-
cessing nodes or neurons, interconnected to each other in a
specic order, performing simple numerical manipulations
(See and Openshaw 1999). A three-layered neural network
is consists of several elements namely nodes. ese networks
are made up of an input layer consisting of nodes representing
(6)
P
�
=
np + kq
n + k
where R(t
R
) is the sum of squares of the right child node and
R(t
L
) is the sum of squares of the le child node. e split s is
chosen to maximize the value of Q(s, t). Stopping rules con-
trol how the algorithm decides when to stop splitting nodes
in the tree. Tree growth proceeds until every leaf node in the
tree triggers at least one stopping rule. Any of the following
conditions will prevent a node from being split:
(1) All records in the node have the same value for all
predictor elds used by the model.
(2) e number of records in the node is less than the
minimum parent node size (user dened).
(3) If the number of records in any of the child nodes
resulting from the node’s best split is less than the
minimum child node size (user dened).
(4) e best split for the node yields a decrease in
impurity that is less than the minimum change in
impurity (user dened).
In RTs, each terminal node’s predicted category is the
weighted mean of the target values for records in the node
(
y(t)
).
2.3. MTs (M5′ algorithm)
MTs (Quinlan 1992) are an extension of RTs in the sense that
they associate leaves with multivariate linear models. MTs
are a technique for dealing with continuous class problems
that provide a structural representation of the data and a
piecewise linear t of the class. ey have a conventional
DT structure but use linear function at the leaves instead of
discrete class labels (Figure 3). M5 MTs were rst introduced
by Quinlan (1992), and then, the idea was reconstructed and
improved in a system called M5′ by Wang and Witten, (1997).
An M5′ MT is an eective learning method for predicting real
values. M5′ MT algorithm rst constructs a RT by recursively
splitting the instance space. e splitting criterion is used
to minimize the intrasubset variability in the values down
from the root through the branch to the node. e variabil-
ity is measured by the standard deviation of the values that
reach that node from the root through the branch with cal-
culating the expected reduction in error as a result of testing
each attribute at that node. e attribute that maximizes the
expected error reduction is chosen. e splitting stops if the
values of all instances that reach a node vary slightly or only
a few instances remain. e standard deviation reduction
(SDR) is calculated by:
where T is the set of examples that reach the node, T
i
is the
sets that are resulted from splitting the node according to the
chosen attribute and SD is the standard deviation (Wang and
Witten 1997). Aer the tree has been grown, M5′ computes
a linear multiple regression model for every interior node.
e data associated with that node and only the attributes
tested in the subtree rooted at that node are used in the regres-
sion. e attributes will be dropped one by one if they lower
the estimated error. en the tree is pruned from the leaves
if that results in a lower expected estimated error. In Wang
and Witten, (1997)’s implementation, the expected error is
(4)
Q
(
s, t
)=
R
(
t
)−
R
(
t
L
)−
R
(
t
R
)
(5)
SDR
= sd(T)−
i
T
i
T
× sd(T
i
)
X1
<= a > a
Training
data set
X2
X3
LM5
LM6
LM4
X1
LM1
LM2
LM3
X2
<= b
<= d
> e
> b
> c
<= c
>d
<= e
Figure 3.MT used to split input space (X
i
: inputs, LM
i
: linear model).