Abstract

In the present study, two non-linear mathematical modelling approaches, namely, extreme learning machine (ELM) and multilayer perceptron neural network (MLPNN) were developed to predict daily dissolved oxygen (DO) concentrations. Water quality data from four urban rivers in the backwater zone of the Three Gorges Reservoir, China were used. The water quality data selected consisted of daily observed water temperature, pH, permanganate index, ammonia nitrogen, electrical conductivity, chemical oxygen demand, total nitrogen, total phosphorus and DO. The accuracy of the ELM model was compared with the standard MLPNN using several error statistics such as root mean squared error, mean absolute error, the coefficient of correlation and the Willmott index of agreement. Results showed that the ELM and MLPNN models perform well for the Wubu River, acceptably for the Yipin River and moderately for the Huaxi River, while poor model performance was obtained at the Tributary of Huaxi River. Model performance is negatively correlated with pollution level in each river. The MLPNN model slightly outperforms the ELM model in DO prediction. Overall, it can be concluded that MLPNN and ELM models can be applied for DO prediction in low-impacted rivers, while they may not be appropriate for DO modelling for highly polluted rivers.

This article has been made Open Access thanks to the kind support of CAWQ/ACQE (https://www.cawq.ca).

INTRODUCTION

Dissolved oxygen (DO) is an essential resource of aquatic ecosystems. The DO concentration plays a critical role in regulating various biogeochemical processes and biological communities in rivers. DO concentrations can fluctuate over the day and night in response to climate changes and the respiratory requirements of aquatic plants (Heddam 2014a). Aquatic organisms are sensitive to fluctuations of DO levels in water bodies, especially for DO reductions. Severe oxygen depletion can lead to fish kills (Meding & Jackson 2003; Robarts et al. 2005), and changes in community composition and trophic state (Wetzel 2001; Ruuhijärvi et al. 2010; Branco et al. 2016). The overall DO concentrations in a river are balanced by re-aeration at the water surface, primary production by photosynthesis and consumptions by biochemical oxygen demands in the water column or sediment oxygen demand (Poulson & Sullivan 2010).

Due to the complexity of factors impacting DO levels, it is important to understand how these factors determine the level of oxygen available for living organisms, and prediction of DO concentrations is crucial for aquatic managers responsible for the maintenance of ecosystem health (Meding & Jackson 2003). Mathematical models provide useful tools to predict the spatio-temporal dynamics of DO in water bodies. Many sophisticated deterministic models have been developed in the past years to predict DO levels in rivers, such as QUAL2E, QUAL2 K and WASP (Cox 2003; Kannel et al. 2010). These mechanistic computer softwares can simulate processes which impact DO levels, such as hydrodynamics, dispersion and pollutant kinetics in the natural environment. These models have been widely used in different river systems, such as applications of the QUAL2E model in the Corumbataí River (Palmieri & Carvalho 2006) and Putzu River (Yang et al. 2011), and DO simulations with the QUAL2 K model (Du et al. 2008; Cho & Ha 2010). Generally, many input data are needed to run these models, such as topography, flow discharge and water level, water quality concentrations and meteorological data. The highly intensive data need sometimes limit the applications of these mechanistic models.

Except for the mechanistic models, there has been a widespread interest in the application of artificial intelligence techniques for DO modelling in water bodies, such as the artificial neural network (ANN)-based approach (Soyupak et al. 2003; Schmid & Koskiaho 2006; Diamantopoulou et al. 2007; Singh et al. 2009; Chen et al. 2010; Ay & Kisi 2012; Wen et al. 2013; Antanasijević et al. 2013; Heddam 2014a; Keshtegar & Heddam 2017; Csábrági et al. 2017), fuzzy logic models (Altunkaynak et al. 2005; Giusti & Marsili-Libelli 2009; Zounemat-Kermani & Scholz 2014), neurofuzzy models (Heddam 2014b; Najah et al. 2014; Ay & Kisi 2017), support vector machine models (Li et al. 2013; Liu et al. 2013; Ji et al. 2017; Heddam & Kisi 2018) and extreme learning machine (ELM) models (Heddam 2016; Heddam & Kisi 2017). These approaches use available water quality parameters, such as water temperature, pH, electrical conductivity (EC) as inputs. Various ANN models have been developed, and the most reported models are the multilayer perceptron neural networks (MLPNN) (Schmid & Koskiaho 2006; Ay & Kisi 2012; Wen et al. 2013; Keshtegar & Heddam 2017). Recently, Heddam (2016) and Heddam & Kisi (2017) proposed a new approach (ELM) to model DO concentrations in water bodies. The proposed ELM models were applied in eight rivers in the US for estimating DO using four water quality variables as inputs (water temperature, turbidity, pH and EC). In this study, the ELM model was applied in four urban rivers in the Three Gorges Reservoir (TGR) region, China, and model performance was compared with the MLPNN approach. The main objective of this study is to develop models which can be used to inform water quality management for one of the largest reservoirs in the world (TGR).

MATERIALS AND METHODS

Study area and data set

The Yangtze River is the largest river in China and the third largest in the world. The TGR is located at the end of the upper Yangtze River. It is one of the largest man-made reservoirs in the world with a surface area of 1,084 km2, a storage capacity of 39.3 billion m3 and a watershed area larger than 1 million km2 (Wang et al. 2005). Four urban tributaries in Chongqing City, located in the terminal of the backwater zone of the TGR, were studied in this paper. Observed data from ten monitoring stations in these four rivers were used in the water quality analysis (Table 1).

Table 1

Characteristics of the studied rivers

RiverLength (km)Watershed area (km2)Annual flow rate (m3/s)Monitoring stations and data sets
Yipin 51.0 363.0 5.28 3 (CSZ, BJDK, YHQ from upstream to downstream), 108 data points 
Huaxi 63.62 268.46 3.6 3 (NHCK, JLY, SLQ from upstream to downstream), 108 data points 
Wubu 84.4 871.0 13.11 2 (JQ, ZC from upstream to downstream), 72 data points 
Tributary of Huaxi River 8.5 54.5 2 (CS1, CS2 from upstream to downstream), 72 data points 
RiverLength (km)Watershed area (km2)Annual flow rate (m3/s)Monitoring stations and data sets
Yipin 51.0 363.0 5.28 3 (CSZ, BJDK, YHQ from upstream to downstream), 108 data points 
Huaxi 63.62 268.46 3.6 3 (NHCK, JLY, SLQ from upstream to downstream), 108 data points 
Wubu 84.4 871.0 13.11 2 (JQ, ZC from upstream to downstream), 72 data points 
Tributary of Huaxi River 8.5 54.5 2 (CS1, CS2 from upstream to downstream), 72 data points 

The Wubu River is listed as a water source protection area for centralized drinking water supply, thus its water quality conditions are good generally (DO: 6.1–10.0). The Huaxi river basin is mainly an urban watershed where large and medium-sized enterprises and agricultural crop areas are densely distributed. In recent years, the population in the Huaxi basin has increased rapidly. Excessive household and municipal sewage, industrial wastewater and agricultural fertilizers contribute greatly to water pollution in the Huaxi River (DO: 2.9–10.0, COD: 10.0–39.0, TN: 0.69–8.17). The water quality conditions of the tributary of the Huaxi River are the poorest among all the rivers due to excessive household and municipal sewage (DO: 0.4–7.8, COD: 13.1–156.0, TN: 5.03–41.4). The Yipin River was also impacted by anthropogenic activities in recent years, and its water quality conditions are poor as well (DO: 5.2–10.5). Water quality assessment results indicated that Tributary of Huaxi River > Huaxi River > Yipin River > Wubu River for pollution level (Zhu et al. 2018). Water quality data sets used were in the period from 2013 to 2015, with one sampling per month. Water quality parameters include water temperature (TE), pH, DO, permanganate index (PI), NH3-N, EC, chemical oxygen demand (COD), total nitrogen (TN) and total phosphorus (TP). The statistical summary of the used data sets for all rivers are summarized in Table 2. According to the statistical indices reported in Table 2, the data are not homogenous and there is a large variability trend among the water quality variables. Except for water temperature and pH, for which the variability is not noticeable, it is clear from Table 2 that the Yangtze River and its tributaries result in a nonhomogeneous data set, especially for EC, TN, TP and PI. The biological variables (DO and COD) are the same, as shown by the mean, max and min values in Table 2. The high values of COD along the Tributary of Huaxi River indicate that the river receives highly non-biodegradable organic matter. The findings suggest the potential and substantial variability in water quality data across the four rivers, especially between the Tributary of Huaxi River and the other three rivers. The data set for the four rivers was divided into two sub-data sets: (i) training subset (70%) and (ii) validation subset (30%).

Table 2

Statistical summary of the used data sets for all rivers

VariablesUnitXmeanXmaxXminSxCvR
Yipin River 
TE °C 19.551 32.000 8.000 6.785 0.347 −0.703 
pH 7.688 8.090 7.200 0.196 0.026 −0.112 
EC μS/cm 398.299 734.800 207.800 123.246 0.309 0.166 
NH3-N mg/L 0.527 1.870 0.121 0.384 0.728 −0.020 
TN mg/L 2.344 4.030 0.930 0.777 0.332 −0.161 
TP mg/L 0.100 0.234 0.051 0.029 0.289 −0.241 
PI mg/L 3.727 6.100 2.400 0.623 0.167 −0.211 
COD mg/L 13.634 23.800 10.000 3.216 0.236 −0.017 
DO mg/L 7.637 10.500 5.200 1.101 0.144 1.000 
Huaxi River 
TE °C 19.050 33.000 7.000 7.011 0.368 −0.372 
pH 7.752 8.640 7.170 0.232 0.030 0.261 
EC μS/cm 508.050 962.700 144.300 208.893 0.411 −0.265 
NH3-N mg/L 1.315 2.290 0.172 0.725 0.551 −0.490 
TN mg/L 3.697 8.170 0.690 2.134 0.577 −0.500 
TP mg/L 0.182 0.415 0.016 0.130 0.715 −0.516 
PI mg/L 5.203 7.800 2.000 0.913 0.175 −0.352 
COD mg/L 18.787 39.000 10.000 6.246 0.332 −0.032 
DO mg/L 6.998 10.000 2.900 1.216 0.174 1.000 
Wubu River 
TE °C 19.482 34.000 8.000 7.083 0.364 −0.751 
pH 7.708 8.190 6.350 0.289 0.037 0.127 
EC μS/cm 434.368 938.000 202.000 142.466 0.328 0.452 
NH3-N mg/L 0.300 0.846 0.108 0.134 0.447 −0.248 
TN mg/L 1.378 3.220 0.810 0.598 0.434 −0.122 
TP mg/L 0.076 0.197 0.044 0.024 0.316 −0.420 
PI mg/L 3.089 4.700 1.100 0.676 0.219 −0.399 
COD mg/L 11.933 18.300 10.000 1.891 0.158 −0.132 
DO mg/L 7.938 10.000 6.100 1.008 0.127 1.000 
Tributary of Huaxi River 
TE °C 19.069 35.000 9.000 6.535 0.343 −0.358 
pH 7.710 8.090 7.420 0.150 0.020 0.004 
EC μS/cm 905.883 1,241.700 577.000 137.632 0.152 0.198 
NH3-N mg/L 7.297 25.400 1.100 5.488 0.752 −0.252 
TN mg/L 14.027 41.400 5.030 9.542 0.680 −0.305 
TP mg/L 0.783 2.740 0.153 0.457 0.583 0.070 
PI mg/L 9.044 32.300 4.100 5.194 0.574 −0.327 
COD mg/L 42.097 156.000 13.100 30.629 0.728 −0.212 
DO mg/L 4.002 7.800 0.400 1.765 0.441 1.000 
VariablesUnitXmeanXmaxXminSxCvR
Yipin River 
TE °C 19.551 32.000 8.000 6.785 0.347 −0.703 
pH 7.688 8.090 7.200 0.196 0.026 −0.112 
EC μS/cm 398.299 734.800 207.800 123.246 0.309 0.166 
NH3-N mg/L 0.527 1.870 0.121 0.384 0.728 −0.020 
TN mg/L 2.344 4.030 0.930 0.777 0.332 −0.161 
TP mg/L 0.100 0.234 0.051 0.029 0.289 −0.241 
PI mg/L 3.727 6.100 2.400 0.623 0.167 −0.211 
COD mg/L 13.634 23.800 10.000 3.216 0.236 −0.017 
DO mg/L 7.637 10.500 5.200 1.101 0.144 1.000 
Huaxi River 
TE °C 19.050 33.000 7.000 7.011 0.368 −0.372 
pH 7.752 8.640 7.170 0.232 0.030 0.261 
EC μS/cm 508.050 962.700 144.300 208.893 0.411 −0.265 
NH3-N mg/L 1.315 2.290 0.172 0.725 0.551 −0.490 
TN mg/L 3.697 8.170 0.690 2.134 0.577 −0.500 
TP mg/L 0.182 0.415 0.016 0.130 0.715 −0.516 
PI mg/L 5.203 7.800 2.000 0.913 0.175 −0.352 
COD mg/L 18.787 39.000 10.000 6.246 0.332 −0.032 
DO mg/L 6.998 10.000 2.900 1.216 0.174 1.000 
Wubu River 
TE °C 19.482 34.000 8.000 7.083 0.364 −0.751 
pH 7.708 8.190 6.350 0.289 0.037 0.127 
EC μS/cm 434.368 938.000 202.000 142.466 0.328 0.452 
NH3-N mg/L 0.300 0.846 0.108 0.134 0.447 −0.248 
TN mg/L 1.378 3.220 0.810 0.598 0.434 −0.122 
TP mg/L 0.076 0.197 0.044 0.024 0.316 −0.420 
PI mg/L 3.089 4.700 1.100 0.676 0.219 −0.399 
COD mg/L 11.933 18.300 10.000 1.891 0.158 −0.132 
DO mg/L 7.938 10.000 6.100 1.008 0.127 1.000 
Tributary of Huaxi River 
TE °C 19.069 35.000 9.000 6.535 0.343 −0.358 
pH 7.710 8.090 7.420 0.150 0.020 0.004 
EC μS/cm 905.883 1,241.700 577.000 137.632 0.152 0.198 
NH3-N mg/L 7.297 25.400 1.100 5.488 0.752 −0.252 
TN mg/L 14.027 41.400 5.030 9.542 0.680 −0.305 
TP mg/L 0.783 2.740 0.153 0.457 0.583 0.070 
PI mg/L 9.044 32.300 4.100 5.194 0.574 −0.327 
COD mg/L 42.097 156.000 13.100 30.629 0.728 −0.212 
DO mg/L 4.002 7.800 0.400 1.765 0.441 1.000 

Xmean, mean; Xmax, maximum; Xmin, minimum; Sx, standard deviation; Cv, coefficient of variation; R, coefficient of correlation with DO, TE, water temperature, EC, specific conductance, NH3-N, ammonia nitrogen, TN, total nitrogen, TP, total phosphorus, PI, permanganate index, COD, chemical oxygen demand, DO, dissolved oxygen; °C, Celsius; μS/cm, micro Siemens per centimetre; mg/L, milligram per litre.

Generally, DO in all rivers negatively correlated with TE, and with the increase of pollution level, the coefficient of correlation (R) decreased (Table 2). Additionally, DO presented poor correlations with other water quality parameters (Table 2). All the input water quality variables and DO were standardized using the Z-score method (Olden & Jackson 2002):
formula
(1)
where Zn is the normalized value of the observation n, xn is the measured value of the observation n, xm and σx are the mean value and standard deviation of the variable x. In the present study, we evaluated several combinations of the water quality variables based on the correlations between water quality variables and DO and, in total, nine scenarios were compared (Table 3).
Table 3

The input combinations of different models

Models
Inputs combinations
MLPNNELM
MLPNN1 ELM1 TE, pH, PI, EC, TP, NH3-N, TN, COD 
MLPNN2 ELM2 TE, EC, TP, NH3-N, TN 
MLPNN3 ELM3 pH, PI, EC, NH3-N, TN 
MLPNN4 ELM4 TE, pH, EC, NH3-N, TP 
MLPNN5 ELM5 EC, NH3-N, TP, TN 
MLPNN6 ELM6 TE, PI, EC, NH3-N 
MLPNN7 ELM7 TE, PI, EC, TP 
MLPNN8 ELM8 TE, EC, TP 
MLPNN9 ELM9 TE, PI, EC 
Models
Inputs combinations
MLPNNELM
MLPNN1 ELM1 TE, pH, PI, EC, TP, NH3-N, TN, COD 
MLPNN2 ELM2 TE, EC, TP, NH3-N, TN 
MLPNN3 ELM3 pH, PI, EC, NH3-N, TN 
MLPNN4 ELM4 TE, pH, EC, NH3-N, TP 
MLPNN5 ELM5 EC, NH3-N, TP, TN 
MLPNN6 ELM6 TE, PI, EC, NH3-N 
MLPNN7 ELM7 TE, PI, EC, TP 
MLPNN8 ELM8 TE, EC, TP 
MLPNN9 ELM9 TE, PI, EC 

ELM, extreme learning machines; MLPNN, multilayer perceptron neural network.

Multilayer perceptron neural network (MLPNN)

ANN and their several algorithms have played a critical role in modelling, forecasting and classifying water quality variables. The availability of large data sets and the increase of monitoring stations worldwide will continue to encourage the use of ANN models in several areas of environmental science. One of the principal advantages that have potentially increased the applications of ANN models is that they do not make any assumption about the structure of the data set, and the models are developed based on training algorithm. ANN is a special kind of non-linear model, proposed and inspired by the function of the human brain. The term network refers to a system of interconnected nodes or neurons, similar to biological neurons (Haykin 1999). Generally, the ANN models have three kinds of layers: (i) input layer that contains the water quality variables selected for developing the DO model (reported as xi), (ii) one or more hidden layers and (iii) the output layer, having only the dependent variable (the DO concentration reported as y). If the interconnection between the neurons is unidirectional, such an ANN model is called feed-forward neural network (FFNN).

The most widely used FFNN model is the multilayer perceptron neural network (Rumelhart et al. 1986), which generally is composed of only one hidden layer in addition to the input and output layers, and has been reported in the literature as universal approximators (Hornik et al. 1989; Hornik 1991). The neurons in the hidden layers are the most important component of the MLPNN model, and they play dual roles: (i) receiving signals from the input layers (the xi) and calculating a weighted sum by multiplying each input variable (xi) with a weight term (wi), adding a bias term (δi) and (ii) passing the sum via an activation function to the neuron in the next layer. The unique neuron in the output layer plays the same role as the neuron in the hidden layer, except that its activation function is generally the identity (linear). The number of neurons in the hidden layer are proceeded by trial and error. Determination of the optimal set of weights and biases of the MLPNN model is the most important task that must be achieved using the backpropagation (BP) algorithm. During this process, the weights and biases are updated to minimize a cost function, generally the mean square error (MSE) (Haykin 1999). MLPNN with one hidden layer contains n neurons and one output layer with only one neuron, expressed as follows (Figure 1):
formula
(2)
where xi is the input variable, wij is the weight between the input i and the hidden neuron j, δj is the bias of the hidden neuron j, f1 the activation sigmoid function, represented by Equation (3), wjk is the weight of connection of neuron j in the hidden layer to unique neuron k in the output layer; δ0 is the bias of the output neuron k, and finally f2 is a linear activation function for the neuron in the output layer:
formula
(3)
Figure 1

Multilayer perceptron neural network (MLPNN) architecture.

Figure 1

Multilayer perceptron neural network (MLPNN) architecture.

Extreme learning machines (ELM)

As stated earlier in the description of the MLPNN model, during the training process, the matrices of weights and biases must be updated, and consequently, the complexity of the model increases with the increase of the number of neurons in the hidden and input layers. One of the most important algorithms proposed during the last decade for training the MLPNN model is the ELM model introduced by Huang et al. (2006a, 2006b), for single layer feed-forward neural network (SLFN). Contrary to the SLFN in which the weights between the input and the hidden layer (Wij, Figure 1) are determined iteratively using the BP algorithm, they are randomly initialized and fixed using the ELM. Regarding the weights between the hidden and output layers (Wjk, Figure 1), they are optimized by solving the Moore–Penrose generalized inverse of matrix (Huang et al. 2006a, 2006b).

Let us consider two set of variables, dependent yi and independent xi which comprises a training data set {xi, yi}, i = 1, …, N, in which, xi ɛ Rd and yi ɛ Rc, the ELM with L hidden neuron can be expressed as:
formula
(4)
where βj is a weight vector connecting the jth hidden neuron and the output neurons, and h(x) = [h1(x), …, hL(x)] is the output vector of the hidden layer with respect to the input x, which maps the data from input space to the ELM feature space. Similar to the SLFN, several activations' functions can be used for the ELM, among them the sigmoidal, hardlim, triangular and radial basis. The N equations coming from Equation (4) can be written in a compact form and are represented by Hβ = Y, where H is the hidden layer output matrix. The weights connecting the hidden layer and the output layers, denoted by β, are achieved by minimal norm least square method (Wei et al. 2015; Yan et al. 2017; Zhang et al. 2018):
formula
(5)
where H+ is the Moore–Penrose generalized inverse of matrix H (Huang et al. 2006a, 2006b). For applying the ELM models, we used the Matlab codes available at http://www.ntu.edu.sg/ home/egbhuang/elm_codes.html.

Performance assessment of the models

In this study, model performance was evaluated using the following statistical indices metrics: the coefficient of correlation (R), the Willmott index of agreement (d), the root mean squared error (RMSE) and the mean absolute error (MAE):
formula
(6)
formula
(7)
formula
(8)
formula
(9)
where N is the number of data points, Oi is the measured and Pi is the corresponding model prediction of dissolved oxygen concentrations. Om and Pm are the average values of Oi and Pi.

RESULTS AND DISCUSSION

In the following, we assess the capability and usefulness of the MLPNN and ELM models for predicting DO concentrations at four rivers in China, using eight water quality variables as predictors (TE, pH, PI, EC, TP, NH3-N, TN and COD). To prevent overfitting, cross-validation is conducted for both models. The estimated values of the performance indices in the training and validation phases are shown in Tables 47, respectively. As a preliminary analysis, results obtained show that the ELM and MLPNN models perform well for the Wubu River, acceptably for the Yipin River, moderately for the Huaxi River, and poorly for the Tributary of Huaxi River in DO prediction. This can be explained by considering that: (i) model performance is negatively correlated with pollution level in each river, (ii) the MLPNN and ELM models can be applied for DO prediction in low-impacted rivers, while they may not be appropriate for DO modelling for highly polluted rivers. According to the obtained results, it is clearly shown that the MLPNN models performed best at two rivers (Wubu and Tributary of Huaxi River) and the ELM model performed best at the two other rivers (Huaxi and Yipin). Additionally, it was observed that the best accuracy obtained using MLPNN and ELM models differs widely from river to river, and it is sometimes difficult to select the best architecture among the nine input combinations. For example, at Wubu River the best accuracy using the MLPNN model was achieved using MLPNN4, while ELM1 performed better. At Yipin River, MLPNN6 performed better and ELM6 provided the best accuracy. Similarly, at the Huaxi River, the best accuracy was achieved using ELM2 and MLPNN2, respectively. Finally, at the tributary of the Huaxi River, MLPNN8 yielded higher accuracy, while the best accuracy was obtained using the ELM6 model. These statements reveal that, although the models used the same input variables at the four rivers, the effect of each independent water quality variable on DO concentrations differs from one river to another.

Table 4

Performances of different models in modelling DO at Wubu River

ModelsTraining
Validation
RdRMSEMAERdRMSEMAE
MLPNN1 0.998 0.999 0.061 0.044 0.885 0.937 0.554 0.477 
MLPNN2 0.994 0.997 0.105 0.079 0.917 0.943 0.560 0.422 
MLPNN3 0.930 0.960 0.391 0.281 0.845 0.897 0.783 0.605 
MLPNN4 0.984 0.991 0.178 0.134 0.937 0.968 0.365 0.262 
MLPNN5 0.897 0.940 0.439 0.354 0.542 0.729 1.137 0.942 
MLPNN6 0.992 0.996 0.121 0.090 0.878 0.932 0.586 0.387 
MLPNN7 0.974 0.986 0.227 0.161 0.880 0.928 0.577 0.485 
MLPNN8 0.962 0.980 0.266 0.206 0.929 0.961 0.431 0.341 
MLPNN9 0.954 0.976 0.294 0.226 0.723 0.860 0.793 0.513 
ELM1 0.826 0.898 0.553 0.446 0.918 0.953 0.418 0.322 
ELM2 0.854 0.916 0.511 0.420 0.832 0.890 0.586 0.421 
ELM3 0.609 0.733 0.778 0.592 0.647 0.766 0.793 0.675 
ELM4 0.791 0.874 0.600 0.508 0.870 0.923 0.518 0.359 
ELM5 0.620 0.742 0.769 0.631 0.698 0.828 0.753 0.653 
ELM6 0.821 0.894 0.559 0.453 0.916 0.944 0.439 0.326 
ELM7 0.761 0.852 0.636 0.535 0.862 0.925 0.526 0.391 
ELM8 0.856 0.918 0.507 0.430 0.893 0.945 0.472 0.357 
ELM9 0.859 0.920 0.503 0.384 0.824 0.905 0.632 0.473 
ModelsTraining
Validation
RdRMSEMAERdRMSEMAE
MLPNN1 0.998 0.999 0.061 0.044 0.885 0.937 0.554 0.477 
MLPNN2 0.994 0.997 0.105 0.079 0.917 0.943 0.560 0.422 
MLPNN3 0.930 0.960 0.391 0.281 0.845 0.897 0.783 0.605 
MLPNN4 0.984 0.991 0.178 0.134 0.937 0.968 0.365 0.262 
MLPNN5 0.897 0.940 0.439 0.354 0.542 0.729 1.137 0.942 
MLPNN6 0.992 0.996 0.121 0.090 0.878 0.932 0.586 0.387 
MLPNN7 0.974 0.986 0.227 0.161 0.880 0.928 0.577 0.485 
MLPNN8 0.962 0.980 0.266 0.206 0.929 0.961 0.431 0.341 
MLPNN9 0.954 0.976 0.294 0.226 0.723 0.860 0.793 0.513 
ELM1 0.826 0.898 0.553 0.446 0.918 0.953 0.418 0.322 
ELM2 0.854 0.916 0.511 0.420 0.832 0.890 0.586 0.421 
ELM3 0.609 0.733 0.778 0.592 0.647 0.766 0.793 0.675 
ELM4 0.791 0.874 0.600 0.508 0.870 0.923 0.518 0.359 
ELM5 0.620 0.742 0.769 0.631 0.698 0.828 0.753 0.653 
ELM6 0.821 0.894 0.559 0.453 0.916 0.944 0.439 0.326 
ELM7 0.761 0.852 0.636 0.535 0.862 0.925 0.526 0.391 
ELM8 0.856 0.918 0.507 0.430 0.893 0.945 0.472 0.357 
ELM9 0.859 0.920 0.503 0.384 0.824 0.905 0.632 0.473 
Table 5

Performances of different models in modelling DO at Yipin River

ModelsTraining
Validation
RdRMSEMAERdRMSEMAE
MLPNN1 0.999 0.999 0.050 0.036 0.677 0.843 0.929 0.711 
MLPNN2 0.947 0.975 0.352 0.270 0.768 0.887 0.752 0.583 
MLPNN3 0.861 0.897 0.564 0.426 0.274 0.587 1.216 1.045 
MLPNN4 0.976 0.988 0.237 0.176 0.693 0.850 0.861 0.670 
MLPNN5 0.845 0.861 0.588 0.421 0.355 0.688 1.136 0.866 
MLPNN6 0.958 0.977 0.315 0.239 0.824 0.906 0.656 0.536 
MLPNN7 0.963 0.976 0.298 0.238 0.719 0.863 0.829 0.654 
MLPNN8 0.938 0.960 0.379 0.288 0.789 0.896 0.746 0.584 
MLPNN9 0.916 0.958 0.441 0.348 0.717 0.865 0.821 0.606 
ELM1 0.831 0.926 0.609 0.488 0.654 0.823 0.893 0.722 
ELM2 0.858 0.923 0.562 0.433 0.701 0.851 0.840 0.627 
ELM3 0.431 0.419 0.989 0.813 0.409 0.567 0.966 0.709 
ELM4 0.855 0.916 0.568 0.451 0.686 0.850 0.796 0.584 
ELM5 0.505 0.443 0.946 0.752 0.270 0.579 1.061 0.810 
ELM6 0.856 0.934 0.567 0.437 0.828 0.913 0.600 0.481 
ELM7 0.873 0.920 0.535 0.420 0.714 0.860 0.784 0.624 
ELM8 0.864 0.921 0.551 0.434 0.781 0.884 0.660 0.510 
ELM9 0.837 0.922 0.600 0.492 0.731 0.865 0.727 0.576 
ModelsTraining
Validation
RdRMSEMAERdRMSEMAE
MLPNN1 0.999 0.999 0.050 0.036 0.677 0.843 0.929 0.711 
MLPNN2 0.947 0.975 0.352 0.270 0.768 0.887 0.752 0.583 
MLPNN3 0.861 0.897 0.564 0.426 0.274 0.587 1.216 1.045 
MLPNN4 0.976 0.988 0.237 0.176 0.693 0.850 0.861 0.670 
MLPNN5 0.845 0.861 0.588 0.421 0.355 0.688 1.136 0.866 
MLPNN6 0.958 0.977 0.315 0.239 0.824 0.906 0.656 0.536 
MLPNN7 0.963 0.976 0.298 0.238 0.719 0.863 0.829 0.654 
MLPNN8 0.938 0.960 0.379 0.288 0.789 0.896 0.746 0.584 
MLPNN9 0.916 0.958 0.441 0.348 0.717 0.865 0.821 0.606 
ELM1 0.831 0.926 0.609 0.488 0.654 0.823 0.893 0.722 
ELM2 0.858 0.923 0.562 0.433 0.701 0.851 0.840 0.627 
ELM3 0.431 0.419 0.989 0.813 0.409 0.567 0.966 0.709 
ELM4 0.855 0.916 0.568 0.451 0.686 0.850 0.796 0.584 
ELM5 0.505 0.443 0.946 0.752 0.270 0.579 1.061 0.810 
ELM6 0.856 0.934 0.567 0.437 0.828 0.913 0.600 0.481 
ELM7 0.873 0.920 0.535 0.420 0.714 0.860 0.784 0.624 
ELM8 0.864 0.921 0.551 0.434 0.781 0.884 0.660 0.510 
ELM9 0.837 0.922 0.600 0.492 0.731 0.865 0.727 0.576 
Table 6

Performances of different models in modelling DO at Huaxi River

ModelsTraining
Validation
RdRMSEMAERdRMSEMAE
MLPNN1 0.928 0.975 0.441 0.315 0.603 0.815 1.063 0.915 
MLPNN2 0.816 0.926 0.680 0.454 0.687 0.855 0.967 0.675 
MLPNN3 0.985 0.993 0.202 0.138 0.224 0.600 1.535 1.281 
MLPNN4 0.838 0.921 0.641 0.493 0.653 0.834 0.966 0.786 
MLPNN5 0.850 0.934 0.618 0.472 0.107 0.580 1.461 1.120 
MLPNN6 0.860 0.926 0.607 0.446 0.672 0.839 0.946 0.706 
MLPNN7 0.877 0.931 0.570 0.424 0.687 0.843 1.105 0.851 
MLPNN8 0.728 0.848 0.805 0.536 0.662 0.836 1.024 0.777 
MLPNN9 0.797 0.901 0.710 0.465 0.495 0.743 1.161 0.827 
ELM1 0.725 0.832 0.809 0.628 0.684 0.838 0.903 0.718 
ELM2 0.637 0.767 0.905 0.663 0.757 0.857 0.815 0.605 
ELM3 0.683 0.828 0.858 0.655 0.466 0.734 1.117 0.881 
ELM4 0.733 0.849 0.799 0.587 0.708 0.859 0.888 0.678 
ELM5 0.571 0.722 0.964 0.729 0.627 0.713 1.009 0.793 
ELM6 0.737 0.860 0.793 0.628 0.622 0.819 1.032 0.743 
ELM7 0.664 0.808 0.878 0.680 0.727 0.844 0.865 0.685 
ELM8 0.688 0.816 0.852 0.612 0.633 0.800 0.959 0.764 
ELM9 0.539 0.692 0.989 0.697 0.663 0.792 0.928 0.761 
ModelsTraining
Validation
RdRMSEMAERdRMSEMAE
MLPNN1 0.928 0.975 0.441 0.315 0.603 0.815 1.063 0.915 
MLPNN2 0.816 0.926 0.680 0.454 0.687 0.855 0.967 0.675 
MLPNN3 0.985 0.993 0.202 0.138 0.224 0.600 1.535 1.281 
MLPNN4 0.838 0.921 0.641 0.493 0.653 0.834 0.966 0.786 
MLPNN5 0.850 0.934 0.618 0.472 0.107 0.580 1.461 1.120 
MLPNN6 0.860 0.926 0.607 0.446 0.672 0.839 0.946 0.706 
MLPNN7 0.877 0.931 0.570 0.424 0.687 0.843 1.105 0.851 
MLPNN8 0.728 0.848 0.805 0.536 0.662 0.836 1.024 0.777 
MLPNN9 0.797 0.901 0.710 0.465 0.495 0.743 1.161 0.827 
ELM1 0.725 0.832 0.809 0.628 0.684 0.838 0.903 0.718 
ELM2 0.637 0.767 0.905 0.663 0.757 0.857 0.815 0.605 
ELM3 0.683 0.828 0.858 0.655 0.466 0.734 1.117 0.881 
ELM4 0.733 0.849 0.799 0.587 0.708 0.859 0.888 0.678 
ELM5 0.571 0.722 0.964 0.729 0.627 0.713 1.009 0.793 
ELM6 0.737 0.860 0.793 0.628 0.622 0.819 1.032 0.743 
ELM7 0.664 0.808 0.878 0.680 0.727 0.844 0.865 0.685 
ELM8 0.688 0.816 0.852 0.612 0.633 0.800 0.959 0.764 
ELM9 0.539 0.692 0.989 0.697 0.663 0.792 0.928 0.761 
Table 7

Performances of different models in modelling DO at Tributary of Huaxi River

ModelsTraining
Validation
RdRMSEMAERdRMSEMAE
MLPNN1 0.823 0.902 1.058 0.717 0.447 0.692 1.494 1.122 
MLPNN2 0.979 0.988 0.377 0.293 0.387 0.663 1.855 1.360 
MLPNN3 0.990 0.995 0.262 0.190 0.196 0.460 2.808 2.351 
MLPNN4 0.916 0.946 0.747 0.572 0.566 0.756 1.365 1.019 
MLPNN5 0.987 0.993 0.294 0.210 0.571 0.718 2.054 1.506 
MLPNN6 0.878 0.930 0.867 0.630 0.549 0.766 1.525 1.161 
MLPNN7 0.895 0.937 0.815 0.622 0.347 0.544 2.008 1.450 
MLPNN8 0.964 0.981 0.480 0.343 0.649 0.765 1.984 1.535 
MLPNN9 0.951 0.973 0.564 0.423 0.564 0.471 4.494 3.542 
ELM1 0.649 0.761 1.374 1.136 0.351 0.629 1.532 1.292 
ELM2 0.636 0.752 1.393 1.142 0.235 0.545 1.643 1.286 
ELM3 0.563 0.665 1.492 1.167 0.139 0.456 1.752 1.483 
ELM4 0.607 0.722 1.436 1.176 0.212 0.561 1.692 1.327 
ELM5 0.651 0.764 1.371 1.061 0.359 0.647 1.563 1.197 
ELM6 0.719 0.820 1.256 0.971 0.400 0.631 1.481 1.197 
ELM7 0.613 0.734 1.426 1.157 0.146 0.454 1.643 1.398 
ELM8 0.609 0.731 1.432 1.119 0.238 0.509 1.576 1.276 
ELM9 0.608 0.725 1.434 1.194 0.313 0.493 1.529 1.304 
ModelsTraining
Validation
RdRMSEMAERdRMSEMAE
MLPNN1 0.823 0.902 1.058 0.717 0.447 0.692 1.494 1.122 
MLPNN2 0.979 0.988 0.377 0.293 0.387 0.663 1.855 1.360 
MLPNN3 0.990 0.995 0.262 0.190 0.196 0.460 2.808 2.351 
MLPNN4 0.916 0.946 0.747 0.572 0.566 0.756 1.365 1.019 
MLPNN5 0.987 0.993 0.294 0.210 0.571 0.718 2.054 1.506 
MLPNN6 0.878 0.930 0.867 0.630 0.549 0.766 1.525 1.161 
MLPNN7 0.895 0.937 0.815 0.622 0.347 0.544 2.008 1.450 
MLPNN8 0.964 0.981 0.480 0.343 0.649 0.765 1.984 1.535 
MLPNN9 0.951 0.973 0.564 0.423 0.564 0.471 4.494 3.542 
ELM1 0.649 0.761 1.374 1.136 0.351 0.629 1.532 1.292 
ELM2 0.636 0.752 1.393 1.142 0.235 0.545 1.643 1.286 
ELM3 0.563 0.665 1.492 1.167 0.139 0.456 1.752 1.483 
ELM4 0.607 0.722 1.436 1.176 0.212 0.561 1.692 1.327 
ELM5 0.651 0.764 1.371 1.061 0.359 0.647 1.563 1.197 
ELM6 0.719 0.820 1.256 0.971 0.400 0.631 1.481 1.197 
ELM7 0.613 0.734 1.426 1.157 0.146 0.454 1.643 1.398 
ELM8 0.609 0.731 1.432 1.119 0.238 0.509 1.576 1.276 
ELM9 0.608 0.725 1.434 1.194 0.313 0.493 1.529 1.304 

Estimated DO concentrations at the Wubu River using the ELM and MLPNN models are shown in Table 4. In the following, a more detailed evaluation for each of the different models is provided and several main points are highlighted. First, in the training phase, the MLPNN models worked very well and provided high accuracy for all input combinations compared to the ELM models. DO concentrations were better fitted to the measured values using MLPNN with R and d ranging from 0.897 to 0.998 and 0.940 to 0.999, respectively, compared to the ELM models which supplied values of R and d ranging from 0.609 to 0.859 and 0.733 to 0.920, respectively. Second, the best accuracy in the training phase was obtained using MLPNN1, while the best accuracy for ELM models was obtained using the ELM9 model. This statement leads to the conclusion that the influence of the different water quality variables on the estimation of DO in rivers during model calibration is not as similar, and the MLPNN models that benefit from training times higher than the ELM models are capable of capturing the non-linear relationships between water quality variables and DO concentrations. By comparing the performances of the MLPNN and ELM models during the validation phase, it is clear that for the MLPNN models, the best results were achieved using the MLPNN4 model (R= 0.937, d= 0.968) with five water quality variables, TE, pH, EC, NH3-N and TP, as inputs. Significant variability was observed between the nine developed models. R and d ranged from 0.542 to 0.937 and 0.860 to 0.968, with an average of 0.837 and 0.906, respectively. Although MLPNN4 is the best model, MLPNN2, MLPNN4 and MLPNN8 showed relatively similar results and MLPNN4 is slightly better than MLPNN2 and MLPNN8 when focusing only on the R and d values. However, when comparing the three models based on the error indices (RMSE and MAE), MLPNN4 performed much better than the other two models. Regarding the remaining set of models, it is clear from Table 4 that MLPNN1, MLPNN3, MLPNN6 and MLPNN7 showed relatively similar results, with average R values of 0.872 and average d values of 0.923, respectively, and performed better when compared to the MLPNN5 and MLPNN9 models. Finally, the MLPNN5 model performs worst compared to all the other developed models (RMSE= 1.137 mg/L, MAE= 0.942 mg/L, R= 0.542, d= 0.729). However, the MLPNN5 model would have the worst performance for DO estimation because the TE variable is removed from the input variables. MLPNN9 that uses fewer input variables (three inputs), may have the same problem, but suffers less than MLPNN5, because TE is included accompanied by the PI and EC variables.

Estimated DO at Yipin River using the ELM and MLPNN models is shown in Table 5. At first glance, the two models MLPNN and ELM provided low accuracy compared to the performances obtained at the Wubu River. For the MLPNN models, R values range from 0.274 to 0.824 and d values range from 0.587 to 0.906. Similarly, for the ELM models, R values range from 0.270 to 0.828 and d values range from 0.579 to 0.913. In the validation phase, the average R and d values using the MLPNN models were 0.646 and 0.821, respectively, while the average values of the same indices for the ELM models were 0.642 and 0.799, respectively. MLPNN3 gives the worst performances with the highest RMSE and MAE, and lowest R and d, among the nine models. Regarding the ELM models, ELM5 gives the worst performances among the nine ELM models. For overall comparison, ELM6 was the most predictive model and performed slightly better than the MLPNN6 model. For numerical comparison between the best two models, ELM6 yielded a high and best improvement of the MLPNN6, improving its accuracy by increasing the values of the R and d by 0.4% and 0.7%, respectively, and decreasing the values of the RMSE and MAE by 8.53%, and 10.26%, respectively.

The summary of statistical indices of the training and validation data in prediction of DO using ELM and MLPNN models at the Huaxi River are presented in Table 6. According to the obtained results, it is clear that the two models performed less well than for the two previous rivers (Wubu and Yipin), and this leads to an informed judgement: increases in pollution level associated with low level of DO concentrations in the river results in the models being unable to correctly capture the relationship between DO and water quality variables. The R and d values of MLPNN models ranged between 0.107 and 0.687 and 0.580 and 0.855, with average values of 0.532 and 0.771, respectively. Similarly, the R and d values of ELM models ranged between 0.466 and 0.757 and 0.713 and 0.857, with average values of 0.654 and 0.806, respectively. Overall, the ELM models performed better compared to the MLPNN models. At Huaxi River, the ELM2 model provides better DO estimates than the MLPNN2, and the results indicate that DO can be predicted with R and d values equal to 0.757 and 0.857 (RMSE= 0.815 mg/L, MAE= 0.605 mg/L), respectively, which are higher than the values obtained using the MLPNN2 model. According to Legates & McCabe (1999) and Moriasi et al. (2007), values of R greater than 0.70 are considered acceptable; consequently, none of the nine MLPNN models' results are acceptable.

Training and validation results of the ELM and MLPNN models at the tributary of Huaxi River are presented in Table 7. Models' performances were generally unsatisfactory for all nine input combinations according to the guidelines from Legates & McCabe (1999) and Moriasi et al. (2007). Although the performances of the MLPNN models in the training phase were very satisfactory, the models performed poorly during the validation phase. As is shown in Table 7, the average values of R and d for the MLPNN models during the validation phase were 0.475 and 0.648, respectively, while for the ELM models the values of the two indices dropped to 0.266 and 0.547, with 20% and 10% reduction, respectively. There are several potential factors that could impact the accuracy of the models at this specific site. First, the low correlation coefficient between DO and TE certainly has a great influence. Second, the accuracy of the models decreased dramatically with the increase of the pollution level in the studied rivers, and it is difficult for the models to consider the impact of anthropogenic influences in highly polluted rivers. Measured and predicted DO concentrations with MLPNN and ELM models in the four rivers in the validation phase are presented in Figures 2 and 3.

Figure 2

Scatterplots of predicted versus measured values of dissolved oxygen (DO) concentration using the best MLPNN models in the validation phase for: (a) Wubu River, (b) Yipin River, (c) Huaxi River and (d) Tributary of Huaxi River.

Figure 2

Scatterplots of predicted versus measured values of dissolved oxygen (DO) concentration using the best MLPNN models in the validation phase for: (a) Wubu River, (b) Yipin River, (c) Huaxi River and (d) Tributary of Huaxi River.

Figure 3

Scatterplots of predicted versus measured values of dissolved oxygen (DO) concentration using the best ELM models in the validation phase for: (a) Wubu River, (b) Yipin River, (c) Huaxi River and (d) Tributary of Huaxi River.

Figure 3

Scatterplots of predicted versus measured values of dissolved oxygen (DO) concentration using the best ELM models in the validation phase for: (a) Wubu River, (b) Yipin River, (c) Huaxi River and (d) Tributary of Huaxi River.

CONCLUSIONS

In this study, ELM and MLPNN models were implemented to predict the DO concentrations using the daily observed river temperature, pH, PI, NH3-N, EC, COD, TN and TP for four urban rivers in the backwater zone of the TGR. Model results showed that the ELM and MLPNN models perform well for the Wubu River, acceptably for the Yipin River, moderately for the Huaxi River, and poorly for the Tributary of Huaxi River in DO prediction, and model performance is negatively correlated with pollution level in each river. It can be concluded that MLPNN and ELM models can be applied for DO prediction in low-impacted rivers, while they may not be appropriate for DO modelling for highly polluted rivers since it is difficult for these models to consider the impact of anthropogenic influences.

ACKNOWLEDGEMENTS

This work was jointly funded by the National Key R&D Program of China (2018YFC0407200), China Postdoctoral Science Foundation (2018M640499), and the research project from Nanjing Hydraulic Research Institute (Y118009). The authors acknowledge Chongqing Environment Protection Bureau for providing the water quality data used in this manuscript.

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