Prediction of suspended sediment concentration in fluvial flows using

hybrid deep learning algorithms

Sadra Shadkani1, Yousef Hemmatzadeh1, Soroush Abolfathi2,*

1
Department of Water Engineering, Faculty of Agriculture, Tabriz University, Tabriz, Iran

2
School of Engineering, University of Warwick, CV4 7AL, Coventry, UK

Abstract

Accurate prediction of sediment concentration in fluvial systems is crucial for various

applications, including environmental practices, flood management, and engineering design in
rivers. The estimation of river sediment concentration is typically achieved through empirical
methods, involving the measurement of river discharge and suspended sediment concentration
(SSC) during a statistical period. This study develops a feed forward neural network (FFNN)
tool and a long short-term memory (LSTM) model, and propose a hybrid method for modeling
SSC. Daily time series of the antecedent discharge (Qt, Qt-3, Qt-2, Qt-1) and antecedent SSC
(SSCt-3, SSCt-2, SSCt-1) data from two stations of the Mississippi River including Chester and
Thebeswere used to develop the proposed deep learning SSC models. Six scenarios with the
combination of input paramters were considered. The performance of the proposed models was
evaluated using correlation coefficient (CC), Nash Sutcliffe efficiency (NSE), scatter index
(SI), and Willmott's index (WI). Sensitivity analysis revealed that SSCt-1 was the most
influential parameter for the developed models. Detailed model assessment showed the
superior performance of the selected FFNN-LSTM model with CC of 0.976 and 0.960, SI of
0.209 and 0.267, WI of 0.987 and 0.979, NSE of 0.950 and 0.919 and RAE of 0.196 and 0.238,
for Chester and Thebes stations, respectively. It was found that the developed FFNN-LSTM
predictive model can still provide robust predictions in the absence of data for current day
discharge, i.e. Qt. It was shown that the FFNN-LSTM hybrid method proposed in this study
can significantly improve SSC prediction.

Keywords: Suspended sediment, Hybrid model, Predictive model, Long Short-Term Memory,
Feed Forward Neural Network.
 1. Introduction

Suspended sediment concentration (SSC) is a crucial factor in determining river behavior and
controlling morphology in hydraulic and river engineering. Therefore, the accurate evaluation and
estimation of SSC have long been major issues in the fields of river engineering, water resources
management, and the environment. Determining the amount of SSC carried in rivers involves
various factors, including hydraulic, hydrological, and sedimentary parameters, which makes this
phenomenon complex. However, the scarcity of complete and precise information on the
parameters influencing the sedimentation process and the inability to examine temporal changes
in sediments carried by the stream make it impossible to introduce a comprehensive model to
estimate SSC. In natural conditions, sediment transport is not stable and undergoes temporal and
spatial changes (Batalla, 1997). One of the most significant reasons for the reduction in water
system quality is the entry of suspended sediments and nutrients through runoff into the outlet of
the watershed or the base levels. Estimating the amount of sediment load or its transfer rate is
crucial for various water resource applications and projects, including the catchment scale
management, design of hydraulic control structures, evaluation of sediment and pollution in
freshwater systems, and the design and maintenance of canals and waterways (Yang et al., 2009).
Robust information about SSC is necessary as a basis for various river projects, including the
removal of river arches, navigation, flood control, and water retreat. The significance of this issue
has led to extensive research in developing new empirical-based relationships of sediment
transport, primarily based on laboratory data. As a result, over 100 sediment transport relationships
have been derived and described by the literature (Yang et al., 2009). However, in many cases,
these relationships do not match the measured values due to the complexity and incomplete and
inaccurate understanding of sediment transfer mechanisms. A significant difference can be found
between the existing SSC prediction models.

The limitations of the available empirical-based formulae for evaluation of SSC, and the recent
advances in data-driven methodologies has led researchers to use intelligent methods such as
artificial neural networks, hybrid, and deep learning methods (e.g. Pham et al., 2017; Taşar et al.,
2017; Kargar et al., 2019; Horvat et al., 2020; Noori et al., 2022; Ghiasi et al., 2022;
Malekmohammadi et al., 2023; Sahoo et al., 2023; Baharvand et al., 2023). Haddadchi et al. (2011)
used six common bedload predictors, including the Meyer-Peter and Muller (MPM), Einstein,
Ackers and White, Parker, Engelund and Hansen, and Yang predictors to estimate the sediment
load in a river with coarse gravel bed. They found that the existing statistical formulae are not
capable of robust prediction of the sediment load, and amongst all the formulae, Van Rijn, Meier-
Peter, and Muller's formula provided the best SSC prediction results. Sasal et al. (2009) used a
feedforward backpropagation neural network (FFNN) to predict sediment bed load transfer; The
results show the optimal performance of this method compared to the existing empirical methods.
Yang et al. (2009) successfully extended an artificial neural network (ANN) model that uses four
key parameters affecting sediment transport, including mean flow velocity, water surface
inclination, mean flow depth and mean particle diameter. Their outcomes showed that the ANN
model contained four input nodes that can estimate the amount of sediment precisely; However,
the three-input ANN model showed similar accuracy to existing empirical formulas.

Kitsikodis et al. (2014) compared the efficiency of ANN, Adaptive Neuro-Fuzzy Inference System
(ANFIS), and Symbolic Regression (SR) based on Genetic Programming (GP) to predict bed load
transfer, using combinations of discharge, discharge per unit width, and shear stress as input. It
was shown that ANN and ANFIS models have more robust performance compared to SR model.
Mosfaei et al. (2017) examined ANN and sediment gauge curve methods to estimate the sediment
load based on data from 5 hydrometric stations. The outcomes demonstrated that across all the
stations, the ANN model better predicted the sediment load compared to the guage curve model.
Zaytar and Amrani (2016) utilized a deep neural network structure to perform time series
forecasting of meteorological data, utilizing long-short-term memory (LSTM) networks. Their
results showed appropriateness and robustness of LSTM as a predictive model for weather-based
environmental parameters. Baroni and Ziarati (2019) showed that LSTM neural network is capable
of well-approximiating the temperature variations. Kaveh et al. (2021) used LSTM, ANFIS, and
FFNN to predict the amount of daily suspended sediment in fluvial systems, and showed the
superior performance of LSTM in predicting the suspended load, with 62.8% better performance
compared to ANFIS and FFNn models in terms of the RMSE. Applications of Gaussian Process
(GP) and CNN models for fluvial processes have been investigated in recent years (Donnelly et
al., 2022; Khosravi et al., 2023). Al-Dahoul et al. (2021) examined the performance of Linear
Regression (LR), Multilayer Perceptron neural network (MLP), Extreme Gradient Boosting
algorithm (XGB), and LSTM for predicting suspended sediments, and concluded that LSTM is
the most accurate model in predicting the suspended sediment load. The review of recent studies
highlight the significance of establishing robust methodological approach for predicting SSC for
effective management of fluvial processes. It is clear that the complexities of the mechnisms that
are governing the sediment transport processes can heavily influence the accuracy of SSC
forecasting using both smart and classic regression-based methods. Developing robust
methodological approaches for forecasting SSC based on limited data obtained from
environmental sesing techniques to inform catchment scale environmental management schemes
remain a key challenge for engineers and scientists. To address these existing research gaps, this
study adopts the capabilities of advances machine learning techniques to develop and examine
SSC predictive models based on FFNN, LSTM, and the hybrid FFNN-LSTM techniques. The
appropriateness and robustness of the proposed predictive models are assessed for a case study of
Mississippi River, USA. The Mississippi River was chosen as the case study location given that
(a) the river carries a large amount of sediment, and this can lead to sediment deposition in the
navigation channels and ports along the river; (b) Mississippi River is prone to flooding, and
sediment transport plays a key role in flood control. Modeling sediment concentration can help
predict how sediment deposition will impact flood control structures such as levees and dams, and
can inform decisions about managing these structures to minimize the risk of flooding; and (c) The
sediment transport in Mississippi River also affect water quality, both by transporting pollutants
and by affecting the physical and chemical properties of the water. Two monitoring sites of Chester
(CH) and Thebes (TH) were selected for training and testing of the proposed models. LSTM type
deep learning neural network enable modeling temporal problems. This study, for the first time,
investigate the performance and efficiency of the proposed novel hybrid FFNN-LSTM model in
predicting SSC using daily discharge. Comparative study between the hybrid model and individual
FFNN and LSTM models are conducted to determine optimal predictive performance. This study
also investigates how to preserve memory during the training process and enhance the network
with reinforcement layers.

2. Materials and methods

2.1 Feed Forward Neural Network (FFNN)

Artificial neural networks (ANNs) have emerged as a prominent tool for data analysis in scientific
research and practical engineering problems. Comprised of interconnected neurons arranged in a
layered structure, ANNs offer a wide range of topologies and training models that can be
customized for diverse applications. Their adaptability has led to extensive usage in various
scientific fields, including finance, engineering, and environmental science. Researchers continue
to refine and improve ANNs through deep learning techniques and other methods, which hold
great promise for addressing the complex data analysis challenges of the modern era.

This perusal employed a feed-forward neural network (FFNN) to predict suspended sediment
concentration (SSC) in the research area. In this topology, neurons in each layer were linked via
weighted connections to all neurons in the next layer, and neural network training consisted of
repeated weight updates. Due to the lack of internal connections and return loops, the neurons in
this topology were incapable of retaining the current state and only permitted forward signal
propagation. The supervised test was used, with input SSC specification vectors generating actual
SSC values as the target output for the subsequent time. Levenberg-Marquardt Back Propagation
(LMBP), Bayesian Regularization, and Scaled Conjugate Gradient method are adopted as training
algorithms to construct the predictive models. In the training process, the input layer features were
transmitted to the subsequent layer through weighted connections. The data was processed through
the hidden layers and ultimately reached the output neuron. The difference between the network
result and actual goal was computed, and the error was propagated backward to update the weights
of the layers. The training process concluded when no further weight updates occurred.
Levenberg's algorithm was utilized to minimize errors in Levenberg's method. Additionally, the
behavior of the neural network was determined by the transfer function employed in each layer.
For the first and second hidden layers, the transfer functions used were sigmoid-tan and sigmoid-
log, as illustrated in Eq. (1) and (2), respectively. Furthermore, the sigmoid-log transfer function
was also implemented in the last layer.

eXn − e−Xn
T1 (n) = Tanh (Xn) = (1)
eXn + e−Xn

1
T2 (n) = (2)
1 + e−Xn

The common structure of the FFNN network outlined for this perusal is appeared in Figure 1.
 Figure 1: Structure of the FFNN model used in this study

2.2 Long Short-Term Memory (LSTM)

Deep learning is a widely employed technique in artificial neural network, and was initially
introduced by Eisenberg et al. (2000). A recurrent neural network (RNN) is a type of deep learning
neural network in which the output of the previous stage serves as input for the current stage.
Traditional neural networks lack the ability to retain past information since their inputs and outputs
are independent of one another. However, RNNs can overcome this limitation with the help of a
hidden layer. The most significant advantage of RNNs lies in their internal memory, which allows
them to store important information about the input received, thus enabling them to make accurate
predictions about future steps (Graves and Schmidhuber, 2005). RNNs suffer from the short-term
memory problem, including the gradient explosion and gradual vanishing over time. However,
Long Short-Term Memory (LSTM) networks have been introduced as an enhanced version of
RNNs, capable of learning long-term dependencies. The key component of LSTM is the state cell,
which can store or remove information, enabling the network to add new information to the cell
or remove it. To achieve the ability of adding or removing information from the state cell, the
LSTM network employs gates, which serve as the input pathway for information. The gates
include a sigmoid neural network layer, and a point-to-point multiplication operator. The sigmoid
layer outputs a value between zero and one, representing the proportion of input that should be
transmitted to the output. LSTM has three gates, namely the input gate, output gate, and forget
gate, which control the value of the state cell. The input gate specifies how much information
should be added to the state cell, while the forget gate defines how much information should be
removed from the state cell. . The output gate specifies how much of the state cell should be used
as output. The sigmoid function is responsible for determining the degree to which information is
passed through the gates. For each number in the cell of state Ct-1, the sigmoid function takes into
account the values of ht-1 and xt and outputs a value between zero and one. The LSTM network
can be represented using Figures 2 a and b, and is updated at each time step t using Eqs. (3) to (8).

Figure 2a. The LSTM structure used in this study with one hidden layer consisting of several LSTM blocks

Figure 2b. Schematic of LSTM network cell.

ft = σ(Wf xt + Uf ht−1 + bf ) (3)

it = σ(Wi xt + Ui ht−1 + bi ) (4)

Ot = σ(WO xt + UO ht−1 + bO ) (5)

C̃t = σh (Wz xt + Uz ht−1 + bz ) (6)

Ct = ft ⊙ Ct−1 + it ⊙ C̃t (7)

ht = Ot ⊙ σh (Ct ) (8)

where, 𝑥𝑡 is the input vector, ℎ𝑡−1 is the hidden state vector or the final output vector, 𝑓𝑡 is the
activator vector of the forgetting gate, 𝑖𝑡 is the activator vector of the input gate, 𝑂𝑡 denotes the
activator vector of the output gate, 𝐶̃𝑡 is the activator vector of the cell input, ht is the activator
vector of the cell output, Ct is the state vector cell, 𝑊 is the learnable weight matrix, U is the
learnable weight matrix with a time delay unit, b is the bias vector, σ and 𝜎ℎ are the sigmoid and
hyperbolic tangent activation function, and ⊙ represents the dot product of two vectors.

2.3 FFNN-LSTM model

The FFNN-LSTM method involves several steps (Figure 3). Firstly, the Differencing method is
applied to the SSC data to stabilize it (Eq. 9). Then, the stabilized SSC data and discharge are fed
into a multilayer feedforward neural network (FFNN). Additionally, the stabilized SSC outputs
are processed by an LSTM, which is specifically utilized for SSC due to the strong serial
correlation observed in daily SSC data but not in discharge data. The final step involves the use of
a shallow FFNN to combine the outputs of both the multilayer FFNN and LSTM sub-models,
resulting in the final SSC predictions. It is noteworthy that the sub-models in the training process
are interdependent. The parameters of all sub-models are updated simultaneously since each sub-
model influences the others.

XtDiff = Xt+1
O
− XtO (9)
 Figure 3. The frame of the suggested hybrid FFNN-LSTM model developed for this study

2.4 Study area and dataset

The Mississippi River is the second-longest river in North America, originating from Lake Itasca
and passing through the center of the American continent before flowing into the Gulf of Mexico.
Its total length from the source in Lake Itasca to the Gulf of Mexico is approximately 3781 km.
The Missouri River, which is about 160 kilometers longer, is a tributary of the Mississippi. When
compared to other rivers worldwide, the Mississippi River ranks fourth in terms of length. Figure
4 presents the geographical locations of the CH and TH stations.

The daily datasets used in this study include discharge (Q) and SSC measurements at two stations
along the Mississippi River: Chester, IL (CH, Station ID: 07,020,500, Latitude: 37°40'02.6700 N,
Longitude: 89°48'48.7600 W) and Thebes, IL (TH, Station ID: 07022000, Latitude: 37°13'17.76"
N, Longitude: 89°27'46.71" W). These data were extracted from the U.S. Geological Survey
(USGS). Figures 5 and 6 show the results of descriptive and correlation analyses between the
discharge (Q) and suspended sediment concentration (SSC) datasets at different lags at two
monitoring stations (i.e. CH and TH) on the Mississipi River. A lag of up to 3 days was applied to
the data for comprehensive scenario planning. Table 1 displays the statistical measures of the
datasets, including mean, minimum, maximum, standard deviation, coefficient of variation, and
skewness, for both CH and TH stations. The scenarios used in this study were formed by
considering the autocorrelations between SSC and Q at different lags, as depicted in Figures 7 and
8 for CH and TH stations, respectively.
Figure 4. Case study location of Mississippi River, U.S., and the monitoring locations at CH and
TH stations
Figure 5. Descriptive analysis of SSC and discharge data for CH station

Figure 6. Descriptive analysis of SSC and discharge data for TH station

 Figure 7. Autocorrelation values between SSC and Q data set at CH station

Figure 8. Autocorrelation values between SSC and Q data set at TH station

Table 1. Statistical evaluation of the datasets measured at CH and TH stations

Standard Coefficient
Station Variable Mean Minimum Maximum Skewness
deviation of variation
SSC 275.037 25.000 1870.000 252.027 0.916 2.164
Chester
Q 269204.866 61100.000 940000.000 153287.011 0.569 0.897
 SSC 252.456 26.000 1850.000 233.866 0.926 2.150
Thebes
Q 281497.477 65000.000 1030000.000 160433.087 0.570 0.915

2.5 Performance parameters

To assess the execution of the models and ensure accurate predictions, several performance
indicators were used in this research, including the Correlation Coefficient (CC), Scatter Index
(SI), Nash Sutcliffe Efficiency (NSE), Willmott's Index (WI), and Relative Absolute Error (RAE).
The models' prediction accuracy is improved when CC, NSE, and WI are close to one, while SI
and RAE are close to zero. The equations for these parameters are as follows:
1
(∑n n n
i=1 Oi Pi − ∑i=1 Oi ∑i=1 Pi )
n
CC = 2 1 2
2 1 2 (10)
(∑n n n n
i=1 Oi −n(∑i=1 Oi ) )(∑i=1 Pi −n(∑i=1 Pi ) )

1
√ ∑n
i=1(Pi −Oi )
2
n
SI = (11)
O

∑n
i=1(Oi −Pi )
2
WI = 1 − [ __ __ 2 ] (12)
∑n
i=1(|Pi −Oi |+|Oi −Oi |)

∑n
i=1(Pi −Oi )
2
NSE = 1 − 2 (13)
∑n
i=1(Oi −O)

∑ni=1|Pi − Oi |
RAE = (14)
∑ni=1|O − Oi |

where 𝑃𝑖 and 𝑂𝑖 are predicted amounts and observed data for time the 𝑖, respectively, and 𝑂 is the
average observed data.

The Taylor diagram was utilized to facilitate a better understanding of the superior models. This
diagram serves to compare multiple model outputs in a single graph, displaying the level of error,
correlation, and standard deviation of the model outputs in relation to the actual values (Taylor,
2001). The azimuth angle of the diagram represents the CC value, while the radial distance from
the actual data point and the radial distance from the coordinate center (0,0) indicate the RMSE
and standard deviation values, respectively.
 3. Results and discussion

Based on the autocorrelations observed in Figures 8 and 9, six scenarios were selected for daily
SSC modeling using FFNN, LSTM, and hybrid FFNN-LSTM models at CH and TH stations
(Table 2). These scenarios included SSCt-1, SSCt-2, SSCt-3, Qt, Qt-1, Qt-2 and Qt-3. To train and test
the models, the 10-year data (2007-2017) of SSC and Q were divided into two parts, with 70% of
the data (2747 days) used for training and 30% (1178 days) for testing. The input parameters were
represented by a subscript t for the current day and t-n for the previous n days. The SSC and Q
data were measured in milligrams per liter (mg/L) and cubic meters per second (CMS),
respectively. In order to assess the efficacy of the models , different performance indexes,
consisting of Correlation Coefficient (CC), Scatter Index (SI), Nash Sutcliffe Efficiency (NSE),
Willmott's Index (WI), and Relative Absolute Error (RAE), were used.

The ML model development was implemented in Python using the Keras deep learning library to
generate models with high accuracy. Apart from the number of neurons and epochs, the values and
learning rates associated with the batch size are also crucial for the precision of the LSTM
networks. These values need to be optimized through trial and error to achieve the best possible
results. The architecture of the network was optimized by evaluating the network's performance
with various layer combinations. The structure of the network was designed in a way that the input
data first entered the LSTM network with a dropout layer, followed by a middle layer with a
Rectified Linear Unit (ReLU) activation function, and finally connected to the output layer. The
dropout layer was used to prevent overfitting of the network. Additionally, the number of neurons
and epochs in the LSTM network, as well as the batch size and learning rates, were optimized
through trial and error to achieve higher accuracy. The dropout layer is a regularization technique
used to prevent overfitting in the neural network. During training, a random set of neurons is
ignored or "dropped out," so that the network learns from different architectures and sets of
neurons. In this study, a dropout rate of 5% was applied to the input layer. The middle (RELU
activation function. To update the weights, the ADAM optimizer function was employed, and the
number of epochs, batch size, and learning rate were set to 300, 32, and 0.005, respectively. These
values were determined through experimentation to optimize the precision of the network.

The proficiency of FFNN, LSTM, and FFNN-LSTM models for the considered scenarios at CH
and TH stations were investigated, and the test section outcomes were presented in Tables 3 and
4. Results showed that all three models demonstrated good performance for the selected
combinations. Among them, FFNN-LSTM-6 and FFNN-LSTM-5 hybrid models demonstrated
high accuracy at station CH with a CC of 0.976 and 0.972, SI of 0.209 and 0.226, WI of 0.987 and
0.985, NSE of 0.950 and 0.941, and RAE of 0.196 and 0.213, respectively. These results suggest
that having more input parameters has a positive effect on the modeling.

In addition, the third scenario of the hybrid model at station CH, which has a CC of 0.970, SI of
0.230, WI of 0.985, NSE of 0.939, and RAE of 0.202 in the deficiency of discharge data on the
current day, can be a good choice for SSC modeling. Similarly, at the TH station, the FFNN-
LSTM-6 model with CC of 0.960, SI of 0.267, WI of 0.979, NSE of 0.919, and RAE of 0.238 was
recognized as the best model and scenario. The FFNN-LSTM-3 model with CC of 0.958, SI of
0.269, WI of 0.978, NSE of 0.918, and RAE of 0.237 ranked second, with a slight difference
compared to the superior model. Finally, the FFNN-LSTM-5 model with CC of 0.957, SI of 0.274,
WI of 0.977, NSE of 0.915, and RAE of 0.241 was the third model in terms of SSC prediction
accuracy at the TH station, among the six used scenarios.

In the event of a lack of data for SSC simulation, scenarios 1, 2, and 4 may provide reliable results
due to reasonable errors and fewer input parameters. The use of the FFNN-LSTM hybrid model,
which combines FFNN and LSTM models, improves the performance of individual models in all
scenarios. For instance, the reduction of the SI error parameter by 14.34% at station CH and 5.32%
at station TH in the sixth scenario compared to FFNN models is an example that illustrates the
improved performance of the FFNN-LSTM hybrid model. To showcase the accuracy of the hybrid
model in predicting SSC with varying discharges, the total discharges were divided into three
𝑚3 𝑚3 𝑚3
categories: Low (65000 ⁓ 430000 ), Medium (430000 ⁓ 790000 ), and High (>790000 ).
𝑠 𝑠 𝑠

Based on Tables 5 and 6, the FFNN-LSTM-6 hybrid model performed well in all three discharge
subsets at both stations. However, the Medium subset, which ranges from 430000 to 790000 m3/s,
exhibited the lowest error compared to the other two subsets, with a CC of 0.960 and 0.953, SI of
0.158 and 0.178, WI of 0.976 and 0.975, NSE of 0.912 and 0.906, and RAE of 0.278 and 0.268 at
the CH and TH stations, respectively. Notably, the results obtained for the Medium and High
subsets were superior to those obtained using the full range of flowrates, indicating the
effectiveness of the hybrid model for forecasting SSC under varying flow conditions. . Therefore,
it can be concluded that the hybrid model is more effective for flow rates greater than 395,000
m3/s. Figures 9 and 10 display scatter plots of the best scenarios of each model, along with the
trendlines represented by dotted lines. Observing these results, it can be inferred that the proximity
of the blue trendline and the high dispersion of the hollow circular blue dots (representing FFNN-
LSTM-6) around the bisector line (y = x) are the factors contributing to the effectiveness of the
model at CH and TH stations. Additionally, Figures 11 and 12 display a comparison chart among
the best scenarios of each model, revealing that the chart of the FFNN-LSTM-6 method (solid blue
line) more closely aligns with the line of observational data (solid red line) than other models in
both CH and TH stations. Finally, Taylor diagrams (TDs) for both stations are presented in Figure
13, which illustrate the model's accuracy in estimating SSC amounts. The FFNN-LSTM-6 model
is shown to estimate SSC amounts with exceptional precision in both CH and TH stations.

Table 2. Input data combinations used for developing SSC predictive models.

Scenario Input Parameters

1 SSCt-1, Qt-1
2 SSCt-2, SSCt-1, Qt-2, Qt-1
3 SSCt-3, SSCt-2, SSCt-1, Qt-3, Qt-2, Qt-1
4 SSCt-1, Qt, Qt-1
5 SSCt-2, SSCt-1, Qt, Qt-2, Qt-1
6 SSCt-3, SSCt-2, SSCt-1, Qt, Qt-3, Qt-2, Qt-1

Table 3. Performance analysis of LSTM, FFNN, and FFNN-LSTM models for SSC prediction at CH station

Models Error parameters Scenario number

1 2 3 4 5 6
CC 0.942 0.960 0.967 0.960 0.970 0.969

SI 0.317 0.281 0.259 0.289 0.257 0.244

LSTM
WI 0.967 0.973 0.978 0.971 0.977 0.980

NSE 0.884 0.909 0.923 0.903 0.924 0.931

RAE 0.314 0.279 0.239 0.274 0.238 0.239

CC 0.943 0.965 0.969 0.961 0.971 0.970

SI 0.311 0.263 0.233 0.269 0.228 0.229

FFNN
 WI 0.970 0.977 0.983 0.976 0.983 0.983

NSE 0.888 0.920 0.937 0.916 0.940 0.939

RAE 0.269 0.267 0.208 0.243 0.224 0.212

CC 0.946 0.967 0.970 0.962 0.972 0.976

SI 0.303 0.239 0.230 0.264 0.226 0.209

FFNN-LSTM
WI 0.971 0.982 0.985 0.978 0.985 0.987

NSE 0.894 0.934 0.939 0.919 0.941 0.950

RAE 0.266 0.225 0.202 0.241 0.213 0.196

Table 4. Performance analysis of LSTM, FFNN, and FFNN-LSTM models for SSC prediction at TH
station

Models Error parameters Scenario number

1 2 3 4 5 6
CC 0.936 0.953 0.956 0.944 0.955 0.959

SI 0.400 0.305 0.306 0.340 0.322 0.282

LSTM
WI 0.937 0.968 0.967 0.958 0.962 0.974

NSE 0.818 0.894 0.893 0.869 0.883 0.910

RAE 0.576 0.320 0.371 0.349 0.376 0.263

CC 0.934 0.955 0.952 0.945 0.956 0.958

SI 0.345 0.281 0.298 0.329 0.292 0.279

FFNN
WI 0.959 0.975 0.971 0.963 0.972 0.975

NSE 0.865 0.910 0.899 0.877 0.903 0.912

RAE 0.328 0.254 0.274 0.305 0.272 0.270

CC 0.939 0.957 0.958 0.946 0.957 0.960

SI 0.323 0.271 0.269 0.304 0.274 0.267

FFNN-LSTM
WI 0.968 0.978 0.978 0.972 0.977 0.979

NSE 0.882 0.916 0.918 0.895 0.915 0.919

RAE 0.287 0.244 0.237 0.277 0.241 0.238

Table 5. Perforamcne analysis of the FFNN-LSTM-6 model for different discharge levels at the CH station

(FFNN-LSTM-6) 𝑚3 𝑚3 𝑚3
Low (61100 ⁓ 395000 ) Medium (395000 ⁓ 728000 ) High (>728000 )
𝑠 𝑠 𝑠

CC 0.970 0.960 0.880

SI 0.223 0.158 0.176
WI 0.984 0.976 0.926
NSE 0.939 0.912 0.682
RAE 0.233 0.278 0.387

Table 6. Perforamcne analysis of the FFNN-LSTM-6 model for different discharge levels at the TH station

(FFNN-LSTM-6) 𝑚3 𝑚3 𝑚3
Low (65000 ⁓ 430000 ) Medium (430000 ⁓ 790000 ) High (>790000 )
𝑠 𝑠 𝑠

CC 0.944 0.953 0.944

SI 0.302 0.178 0.205
WI 0.971 0.975 0.923
NSE 0.892 0.906 0.564
RAE 0.280 0.268 0.464

Figure 9. Comparison of the measured SSC with the predicted values at station CH.
Figure 10. Scatter plots of actual and estimated SSC amounts using the superior models at station TH.

Figure 11. Comparative charts of observed and predicted SSC using the superior models at station CH
 Figure 12. Comparative charts of observed and predicted SSC using the superior models at station TH

Figure 13. Taylor diagrams of estimated SSC values using the most accurate methods for stations CH and TH.

4. Sensitivity analysis
Sensitivity analysis is an effective method for simplifying numerical models. In models that
simulate sediment transport and the amount of sediment in rivers, numerous variables may not
have the same impact on the model output. Identifying less important variables and keeping them
constant at nominal values using sensitivity analysis methods can help in making predictions based
on more sensitive variables. In this study, sensitivity analysis was conducted on the parameters of
the sixth scenario of the FFNN-LSTM model, which included SSCt-3, SSCt-2, SSCt-1, Qt, Qt-1, Qt-2,
and Qt-3 and. The results in Table 7 indicate that removing the SSCt-1 parameter had the greatest
impact on the models in both studied stations, with an increase in error of 74.16% in CH and
61.79% in TH.

Table 7. Impact of eliminating input parameters on the FFNN-LSTM-6 model efficiency for SSC prediction in CH
and TH stations
 (FFNN-LSTM-6) Statistical Parameter

Model Input Parameters SI (CH station) SI (TH station)

1 All 0.209 0.267

2 Delete Qt 0.238 (+13.88%ꜛ) 0.275 (+3%ꜛ)
3 Delete Qt-1 0.238 (+13.88%ꜛ) 0.270 (+1.12%ꜛ)
4 Delete Qt-2 0.238 (+13.88%ꜛ) 0.272 (+1.87%ꜛ)
5 Delete Qt-3 0.240 (+14.83%ꜛ) 0.278 (+4.11%ꜛ)
6 Delete SSCt-1 0.364 (+74.16%ꜛ) 0.432 (+61.79%ꜛ)
7 Delete SSCt-2 0.235 (+12.45%ꜛ) 0.288 (+7.86%ꜛ)
8 Delete SSCt-3 0.236 (+12.92%ꜛ) 0.277 (+3.74%ꜛ)

5. Conclusions

Robust prediction of suspended sediments is vital for understanding erosion, sediment transport,
and deposition issues in fluvial systems, facilitating the development of effective interventions for
sustainable watershed management. This study adopted advanced deep learning approach to
develop novel hybrid FFNN-LSTM model for the prediction of SSC. The performance of the
proposed model is tested for case study location of Mississippi River. Ten years of environmental
sensing data including Q and SSC, measured at two locations (i.e. CH and TH) were used to
examine the performance of the proposed predictive models. Six combinations of input parameters
were considered. The data obtained from the two monitoring stations were divided into training
(70%) and testing (30%) sets, and the performance of the mL-based models was analysed using
CC, SI, NSE, WI, and RAE statistical error indices. Comparison of the models performance
metrics show that the FFNN-LSTM-6 model with the input parameters of SSCt-3, SSCt-2, SSCt-1,
Qt, Qt-3, Qt-2, and Qt-1, provided the best predictive performance for both CH and TH stations, with
statistical measures of CC of 0.976 and 0.960, SI of 0.209 and 0.267, WI of 0.987 and 0.979, NSE
of 0.950 and 0.919 and RAE of 0.196 and 0.238, respectively. The results showed that SSCt-1 is
the most influential factor in prediction of the SSC at both stations. The data stabilization and
integration capability of the FFNN and LSTM models played a significant role in minimizing the
prediction errors. The FFNN-LSTM model is proposed for robust prediction of SSC due to its
superior predictive proficiency. Future research can explore the effectiveness of the FFNN-LSTM
model for predicting SSC in rivers and climates other than those examined in this study.
Additionally, stabilizing input data and incorporating other hybrid techniques based on deep
learning could enhance the accuracy of SSC estimation at the TH and CH stations.

References

Aizenberg I., Naum N., Aizenberg, Joos P.L., Vandewalle. 2000. MultiValued and Universal Binary
Neurons: Theory, Learning and Applications. Springer Science and Business Media, New York, 276.

AlDahoul, N., Essam, Y., Kumar, P., Ahmed, A.N., Sherif, M., Sefelnasr, A., and Elshafie, A. 2021.
Suspended sediment load prediction using long short-term memory neural network. Scientific Reports. 11:
7826.

Baharvand, S., Ahmari, H., and Taghvaei, P. 2023. Developing a Lagrangian sediment transport model for
open channel flows. International Journal of Sediment Research. 38:2. 153-165.

Baroni, A., and Ziarati, K. 2019. Modeling of minimum temperature in Fars province using LSTM recurrent
neural network model. 4th International Congress of Developing Agriculture, Natural Resources,
Environment and Tourism of Iran, Tehran, Iran.

Batalla, R.J. 1997. Evaluating bed material transport equations from field measurements in a sandy gravel-
bed river. Earth Surface Process and Landforms. 21: 121-130.

Bengio, Y., Simard, P., and Frasconi, P. 1994. Learning long-term dependencies with gradient descent is
difficult. IEEE Transactions on Neural Networks. 5: 2. 157-166.

Borzooei, S., Teegavarapu, R., Abolfathi, S., Amerlinck, Y., Nopens, I. and Zanetti, M. C. 2018. Impact
evaluation of wet-weather events on influent flow and loadings of a water resource recovery facility.
Published in: New Trends in Urban Drainage Modelling. UDM 2018. Green Energy and Technology pp.
706-711. ISBN 9783319998664. ISSN 1865-3529. DOI: 10.1007/978-3-319-99867-1_122

Donnelly, J., Abolfathi, S., Pearson, J. M., Chatrabgoun, O., Daneshkhah, A. 2022. Gaussian Process
emulation of spatiotemporal outputs of a 2D inland flood model. Water Research.
doi:10.1016/j.watres.2022.119100

Ghiasi, B., Noori, R., Sheikhian, H., Zeynolabedin, A., Sun, Y., Jun., C., Hamouda, M., Bateni, S., and
Abolfathi, S. 2022. Uncertainty quantification of granular computing‑neural network model for prediction
of pollutant longitudinal dispersion coefficient in aquatic streams. Scientific Reports, 12. 4610.
doi:10.1038/s41598-022-08417-4

Graves, A., and Schmidhuber, J. 2005. Framewise phoneme classification with bidirectional LSTM and
other neural network architectures. Neural Networks. 12: 5-6.

Haddadchi, A., Omid, M.H., and Dehghani, A.A. 2011. Assessment of bedload predictors based on
bampling in a gravel bed river. Journal of Hydrodynamic. 24: 1. 145-151.

Horvat, M., & Horvat, Z. 2020. Long term sediment transport simulation of the Danube, Sava, and
Tisa rivers. International Journal of Sediment Research, 35:5. 550-561.

Kargar, K., Safari, M.J.S., Mohammadi, M.A., & Samadianfard, S. 2019. Sediment transport
modeling in open channels using neuro-fuzzy and gene expression programming techniques.
Water Science Technology, 79:12. 2318–2327.

Kaveh, K., Kaveh, H., Duc Bui, M., and Rutschmann, P. 2021. Long short-term memory for predicting
daily suspended sediment Concentration. Engineering with Computers. 37: 1. 2013-2027.

Kitsikoudis, V., Sidiropoulos, E., and Hrissanthou, V. 2014. Machine learning utilization for bed load
transport in gravel-bed rivers. Water Resources Management. 28: 11. 3727-3743.

Khosravi, K., Rezaie, F., Cooper, J., Kalantari, Z., Abolfathi, S., Hatamiafkoueieh, J. 2023. Soil water
erosion susceptibility assessment using deep learning algorithms. Journal of Hydrology. 129229.
doi:10.1016/j.jhydrol.2023.129229 ISSN 0022-1694.

Malekmohammadi, B., Uvo, C. B., Moghadam, N., Noori, R., and Abolfathi, S. 2023. Environmental risk
assessment of wetland ecosystems using Bayesian belief networks. Hydrology, 10 (1). 16.
doi:10.3390/hydrology10010016

Mosfaei, J., Salehpour Jam, A., and Tabatabai, M.R. 2017. Comparison of the efficiency of sediment rating
curves model and artificial neural network in the study of river bed load. Geography and environmental
sustainability. 24: 7. 33-44.

Noori, R., Ghiasi, B., Salehi, S., Esmaeili Bidhendi, M., Raeisi, A., Partani, S., Meysami, R., Mahdian, M.,
Hosseinzadeh, M., and Abolfathi, S. 2022. An efficient data driven-based model for prediction of the total
sediment load in rivers. Hydrology, 9 (2). 36. doi:10.3390/hydrology9020036

Pham, B.T., Shirzadi, A., Bui, D.T., Prakash, I., & Dholakia, M.B. 2017. A hybrid machine
learning ensemble approach based on a Radial Basis Function neural network and Rotation Forest
for landslide susceptibility modeling: A case study in the Himalayan area, India. International
Journal of Sediment Research, 33:2. 157-170.

Sahoo, G.K., Sahoo, A., Samantara, S., Satapathy, D.P., Satapathy, S.C. 2023. Application of Adaptive
Neuro-Fuzzy Inference System and Salp Swarm Algorithm for Suspended Sediment Load Prediction. In:
Bhateja, V., Sunitha, K.V.N., Chen, YW., Zhang, YD. (eds) Intelligent System Design. Lecture Notes in
Networks and Systems, 494. Springer.

Sasal, M., Kashyap, S., Rennie, C.D., and Nistor, I. 2009. Artificial neural network for bedload estimation
in alluvial rivers. Journal of Hydraulic Research. 47: 2. 223-232.

Tasar, B., Kaya, Y.Z., Varcin, H., Unes, F., & Demirci, M. 2017. Forecasting of suspended
sediment in rivers using artificial neural networks approach. International Journal of Advanced
Engineering Research and science, 4. 79–84.

Taylor, K. E. 2001. Summarizing multiple aspects of model performance in a single diagram. Journal of
Geophysical Research Atmospheres, 106, 7183-7192.

Yang, C.T. 1996. Sediment Transport Theory and Practice. McGraw-Hill Companies, Inc. 396p.

Yang, C.T., Marsooli, R., and Aalami, M.T. 2009. Evaluation of total load sediment transport formulas
using ANN. International Journal of Sediment Research. 24: 3. 274-286.

Yeganeh-Bakhtiary, A., Eyvaz'Oghli, H., Shabakhty, N., Kamranzad, B., and Abolfathi, S. 2022. Machine
learning as a downscaling approach for prediction of wind characteristics under future climate change
scenarios. Complexity, 2022. 8451812. doi:10.1155/2022/8451812

Zaytar, M.A., and El Amrani, C. 2016. Sequence to sequence weather forecasting with long short-term
memory recurrent neural networks. International Journal of Computer Applications. 143: 11. 7-11.