# Improving Flow Discharge-Suspended Sediment Relations: Intelligent Algorithms versus Data Separation

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

_{2})) to optimize the coefficients of the SRC regression model. The second approach uses separation of data based on season and flow discharge (Q

_{w}) characteristics. A support vector regression (SVR) model using only Q

_{w}as an input was employed for SSC estimation and the results were compared with the SRC and its optimized versions. Metaheuristic algorithms improved the performance of the SRC model and the PSO model outperformed the other algorithms. These results also indicate that the model performance was directly related to the temporal separation of data. Based on these findings, if data are more homogenous and related to the limited climatic conditions used in the estimation of SSC, the estimations are improved. Moreover, it was observed that optimizing SRC through metaheuristic models was much more effective than separating data in the SCR model. The results also indicated that with the same input data, SVR was superior to the SRC model and its optimized version.

## 1. Introduction

_{w}) by power, linear, or polynomial functions [13,19,20,21,22,23].

_{2}) [24,31,32]. Despite their differences, the common aim of these models is to increase the accuracy of calculated values by SRC. Another way of tackling this problem is to prepare different SRC models based on time separation of data (e.g., seasons, months) and based on flow characteristics (e.g., high water and low water periods, similar hydrological periods, discharge classes). Various studies have confirmed that classification of data into hydrological groups and increasing time resolution can lead to better model performance [16,17,19,26,33,34,35,36,37,38,39,40]. In fact, the goal of data separation is to reduce data scatter around the regression line and increase the estimation power of the model.

_{2}); (2) improving the SRC-based on time separation of data (seasonal) and flow characteristics; and (3) developing a support vector regression (SVR) model using only Q

_{w}as an input to provide similar conditions to those in the SRC method. Besides, when developing intelligent models, the main emphasis is often on the optimum design of intelligent networks and determination of the type of input data, whereas the separation of input data has rarely been considered. Therefore, in our study, a comprehensive comparison of different SSC estimation models is conducted to accurately determine the most effective methods.

## 2. Study Area and Database

#### 2.1. Study Area

^{2}located between 37° 24′ 05″ and 37° 47′ 33″ North latitude and 54° 29′ 30″ and 56° 05′ 35″ East longitude is a sub-basin of GorganRoud basin. Golestan province, Iran (Figure 1). This watershed was selected as a case study due to the availability of data and the absence of major abstractions or dams in the upstream reaches. Boostan dam watershed has an elevation range from 108 to 2174 m a.s.l. (mean = 753 m) and an average slope gradient of 23%. According to the Amberje climate classification, the regional climate types include moderate semi-humid, cold humid, cold arid, and moderate semi-arid in different parts of the watershed. Average annual precipitation, average annual temperature, and relative humidity of the region are 483 mm, 17.8 °C, and 68.5%, respectively.

#### 2.2. Data and Data Preprocessing

_{w}and SSC data for a period of 44 years (from 1969 to 2013) from Tamar hydrometric station (located at the outlet) were collected and employed in modeling. The data were not completely continuous, containing numerous missing values; a total of only 687 records were used after deleting the outliers using box plots. In Iran, due to high costs and labor for conducting direct measurements, only one or two samples are collected each month. The statistical parameters of the field data used in this study are presented in Table 1. Figure 2 shows the time series graph for Q

_{w}and SSC during the statistical period. The dataset was classified in two groups at a 70:30 ratio for model building (as the training dataset) and model evaluation (as the testing dataset) in such a way that both datasets were relatively consistent in terms of statistical parameters. We tried to include the maximum and minimum data values in the training dataset. The statistical parameters for the training and testing phases are presented in Table 2 and Table 3, respectively. Because of very small and very large values and the high skewness, it can be inferred that the SSC modeling is a complex process.

## 3. Methodology

#### 3.1. Sediment Rating Curve (SRC)

_{w}is the flow discharge (m

^{3}/s), Q

_{s}is suspended sediment concentration (mg/L) or suspended sediment discharge (metric tons/day), and the regression coefficients (a and b) can be related to characteristics of soil erodibility and fluvial erosion, respectively [65].

#### 3.2. Optimization Tecnhiques

#### 3.2.1. Conventional Correction Factors

#### Food and Agriculture Organization (FAO)

_{s}, ${\overline{Q}}_{w}$ is the mean of Q

_{w}, and b is the coefficient used in Equation (2).

#### Non-Parametric Smearing Estimator (CF_{2})

_{2}is a non-parametric correction factor used to improve estimated values in the SRC model by determining optimal coefficient values. CF

_{2}is calculated using Equations (4) and (5) as follows [32]:

_{i}is the error term or residual for each sample, ${Q}_{so}$ is observed suspended sediment concentration or discharge, and ${Q}_{se}$ is estimated suspended sediment concentration or discharge. CF

_{2}is used in SRC model as follows:

#### 3.2.2. Metaheuristic Algorithms

#### Genetic Algorithm (GA)

- Developing a set of initial random answers; these answers, which are the primary solutions to the problem, are called chromosomes and each one is made up of sets of genes. In the present study, the coefficients a and b in the SRC model are considered as genes and form a chromosome.
- Comparing, ranking, and selecting the best chromosomes; after developing the initial population of chromosomes, to determine its suitability, the efficiency of each chromosome in estimating the suspended sediment must be determined. At this point, using Equation (2) and the values of genes in each chromosome (a and b coefficients), the amount of suspended sediment for the training data is estimated. Then, the suitability of that chromosome using the objective function (root mean squared error (RMSE)) is determined as [57]:$$\mathrm{RMSE}=\sqrt{\frac{1}{n}{\displaystyle \sum}_{i=1}^{n}{\left({O}_{i}-{S}_{i}\right)}^{2}}$$
_{i}and S_{i}are the ith observed and estimated SSC in mg/L, respectively. After determining the suitability of the initial population of chromosomes in the natural selection stage, 50% of the most inefficient chromosomes are removed from the initial population. - Selecting pairs (parents) for reproduction; at this stage, using selection operators, a pair of chromosomes from the set of primary chromosomes in the previous stage are determined as the parents of the next generation. To accomplish this, the widely used roulette wheel selection method was applied [61]. In fact, in this method, chromosomes with more favorable answers are more likely to be selected.
- Crossover; the production of new and better chromosomes is accomplished to further investigate the solution space (space containing possible coefficients for the SRC model). In this study, the blending method was employed to combine genes in the parent chromosomes and perform the reproduction. In each generation, the number of reproductions was determined by a parameter called the crossover rate.
- Mutation; mutation is a mechanism that leads to a completely random change in the genes of chromosomes (answers to the problem). This prevents the early convergence and getting stuck in local minima, enabling a better search within the answers space.
- Convergence; convergence implies that the GA, by repeating successive generations, is no longer able to find better answers to the problem. There are various ways to stop the genetic algorithm, e.g., the number of repetitions of generations reaching a certain level of error and lack of significant progress in error reduction.

#### Particle Swarm Optimization (PSO)

- Generation of the initial random population with random positions and velocities, each called a particle (a and b coefficients in the SRC model are assumed to be equivalent to one particle).
- Evaluation of the cost or fitness of each particle; at this stage, the amount of suspended sediment for the training dataset is estimated using Equation (2) and the values for each particle (a and b coefficients). Then, their suitability is evaluated using the objective function (Equation (7)).
- Recording the best position for each particle (pbest) and the best position among all particles (gbest); at this step, each particle moves at a speed that can be adjusted to the search space and retains the best previous position in its memory. In addition, in the total search space, the best gained position by the group is shared with all particles. Each particle in an assumed space is shown as a position and velocity vector. The position of each particle is obtained by comparison between the current position and the best value it has achieved (pbest). Moreover, the best response that each particle has attained so far from the pbest is identified as gbest;
- Updating the position and velocity vector of all particles; in this step, the transition of the particles to new positions is evaluated. In addition, the velocity and position of each particle are corrected by Equations (8) and (9), respectively.$${V}_{i}\left(t+1\right)=\omega {V}_{i}\left(t\right)+{R}_{1}\left(pbes{t}_{i}\left(t\right)-{x}_{i}\left(t\right)\right)+{R}_{2}\left(gbes{t}_{i}\left(t\right)-{x}_{i}\left(t\right)\right)$$$${x}_{i}\left(t+1\right)={x}_{i}\left(t\right)+{V}_{i}\left(t+1\right)$$
_{1}and R_{2}are learning parameters which determine the movement slope of the local search, and ω is the inertia coefficient. - Convergence test; this algorithm is repeated for a predetermined number of generations or it is executed until the problem converges to an optimal solution.

#### Imperialist Competitive Algorithm (ICA)

- Generating the random initial countries (a and b coefficients in the SRC model are assumed equivalent to one country).
- Dividing the countries into two categories based on the objective function of the problem (Equation (7)). Countries with the lowest amounts of objective function are assumed as imperialist and the rest are colonies.
- Determining the number of colonies of each imperialist; to this aim, the power of each imperialist must be evaluated. It is obvious that the stronger the imperialist, the greater the number of its colonies.
- Applying the assimilation policy after the formation of the initial empires; in this algorithm, the assimilation policy is modeled as the movement of colonies towards imperialists.
- Revolution in countries can be considered as a sudden and accidental change in the situation of the colonized countries.
- Comparing the colonies and imperialists (intra-group competition); sometimes a colony, by moving towards an imperialist, reaches a new situation in which it has a lower cost function than the imperialist. In this case, the colony and the imperialist change positions.
- Evaluation of empires (intergroup competition); at this stage, a colony is removed from a weaker empire and transferred to another empire. If the empire has no colony, its imperialist is transferred as a colony to another empire. As a result, during colonial competition, the power of larger empires gradually increases, and weaker empires will be eliminated.
- Finally, continuing the algorithm until the termination condition is observed. The end limit of colonial competition is when we have a single empire in the world with colonies that are very close to the imperialist country in terms of situation.

_{1}and R

_{2}) = 2, the inertia coefficient (ω) = 0.7, and maximum number of iterations = 500. For ICA: the number of initial countries = 100, the number of initial imperialist countries = 20, colony assimilation coefficient = 2, revolution probability = 0.1, and the maximum number of iterations = 500.

#### 3.3. Data Separation Techniques

- Seasonal: The measured data for SSC were classified into spring, summer, autumn, and winter [71];
- Discharge classes: Data were divided based on annual average discharge such that in the first category discharge was less than average discharge; in the second category, discharge was ≥the average, but less than twice the average; in the third category, discharge was ≥twice the average [72];
- High water and low water periods: Mean monthly discharge was compared to the mean annual discharge. The months in which mean discharge was ≥ mean annual discharge were considered as the high water period and the months in which the mean discharge was less than the mean annual were considered as the low water period [73];
- Hydrograph state: The daily hydrograph of each water year was plotted and data were classified into three series based on rising and falling limbs or base flow of the hydrograph [23]. Moreover, to assess the effect of these groups on the efficiency of models in estimating suspended sediment, results were compared with a group without data separation (group 5).

#### 3.4. Machine Learning (ML) Model

_{i}) is the kernel function. In our study, the SVR model was tested using the radial basis function (RBF) kernel, which has proven better in performance than other kernel functions and is currently the most widely used function [44,76], as follows [77]:

#### 3.5. Model Evaluation and Comparison

^{2}) were calculated as follows [57]:

^{2}values represent more and less correlation between estimated and observed values. The RMSE ranges from 0 to +∞, with 0 indicating a perfect match of estimated and observed values. The range of NS values is from −∞ to 1 with $\mathrm{NS}\text{}\text{}0.6$ being considered as acceptable model performance [45].

## 4. Results and Discussion

#### 4.1. Results of the SRC Model Based on Data Separation and Non-Separation

_{w}and SSC were log-transformed prior to the analysis. Then, a regression relationship for each of the groups in Section 3.3 between log Q

_{w}and log SSC was established based on the training dataset. Finally, the anti-log was calculated and the ‘’a’’ and ‘’b’’ coefficients in the SRC model (i.e., Equation (2)) were determined (Table 4).

_{w}was lower than the mean Q

_{w}(NS = 0.29) and in low water period (NS = 0.33). Overall, estimated values were in closer agreement with observed values for lower flow discharge than for higher discharge.

_{w}, SSC varies between rising and falling limbs, lower in the falling limb, which complicates the SSC process, hence weakening the modeling performance.

#### 4.2. Results of Optimization of the SRC Using Classical Methods and Metaheuristic Algorithms

_{2}) and three metaheuristic algorithms (namely, GA, PSO, and ICA) without data separation with the aim of only modifying the SRC coefficient to improve its efficiency. To this goal, after establishing a regression relationship between log Q

_{w}and log SSC during the training phase and determining ‘’a’’ and ‘’b’’ coefficients; these coefficients were modified using the previously discussed classical techniques. Optimization of the coefficients using algorithms of GA, PSO, and ICA was conducted without log-transforming data using RMSE as the objective function in the Matlab environment. After modifying the SRC equations at this stage, the efficiency and accuracy of each equation was evaluated based on the test data (Table 6). SRC-PSO had the highest estimation capability (NS = 0.44), followed by SRC-GA (NS = 0.41), SRC-ICA (NS = 0.40), SRC-CF2 (NS = 0.29), SRC-FAO (NS = 0.25), and the original SRC (NS = 0.19). Overall, the modified SRC models using the metaheuristic algorithms achieved better results than the modified SRC models using FAO and CF2 correction factors. However, although NS was low for both methods, they improved the estimation power of the original SRC. The low NS values could be due to high sensitivity to peak values of the hydrologic models, as it used squared errors [78]. The same condition was observed with RMSE, which minimized the square of residuals, while MAE was less sensitive to large values [79]. Moreover, low NS values could originate from sparse data at high discharge as well as the large amount of missing SSC-Q

_{w}data. As previously noted, field data are available only once or twice monthly in Iran; hence, finding a robust and reliable model to estimate SSC accurately is a challenging task.

#### 4.3. Results of SVR Models with Data Separation and Non-Separation

_{w}was considered as an input and SSC as an output. The proper architectural structure of the SVR model, like other ML models, improves the suspended sediment estimate [63]. Therefore, we used trial and error to achieve the optimal network design and improve model performance. Considering the lowest RMSE values, the optimal values for model parameters (namely,$\sigma $, C and ε) were assessed for all groups (Table 7).

^{2}= 0.52). However, in most cases, the SVR model with separated data had better performance; additionally, it had the best performance in winter (RMSE = 796.17 mg/L, MAE = 167.85 mg/L, NS = 0.68 and R

^{2}= 0.71) and the weakest performance (lower than the entire period) during the falling limbs of hydrographs (RMSE = 1119.2 mg/L, MAE = 237.3 mg/L, NS = 0.38 and R

^{2}= 0.43).

#### 4.4. Determination of the Best Method of Data Separation

#### 4.5. The Most Effective Model for Estimating SSC

^{2}= 0.59) followed in order by high water/low water period SVR (NS = 0.52), discharge classes SVR (NS = 0.51), hydrograph state SVR (NS = 0.50), SVR (NS = 0.50), SRC-PSO (NS = 0.44), SRC-GA (NS = 0.41), SRC-ICA (NS = 0.40), seasonal SRC (NS = 0.32), high water/low water period SCR (NS = 0.30), SRC-CF2 (NS = 0.29), discharge classes SRC (NS = 0.26), SRC-FAO (NS = 0.25), hydrograph state SCR (NS = 0.23) and SRC (NS = 0.19).

^{2}than the SRC, including its optimized versions. In general, according to our results, the SVR model can be used to estimate SSC in similar seasons instead of applying a model for the entire dataset. Moreover, findings show that optimizing SRC through metaheuristic algorithms leads to higher performance than data separation for SRC.

_{w}[82,83].

_{w}are necessary for building an effective input scenario. Several studies have shown that the utilization of antecedent values of Q

_{w}and Qs [63], meteorological parameters such as rainfall, temperature, and potential evapotranspiration [84,85], hydro-geomorphic variables such as the index of sediment connectivity [48], and biophysical data such as the normalized difference vegetation index (NDVI) [84,86], along with the hydrological parameters utilized in this study, can most likely improve estimates of suspended sediment production.

_{w}as an input and without data separation) indicates that ML models can better capture nonlinear relationships between system inputs and outputs due to their: (1) non-linear structure of the ML models, (2) robustness to missing data and (3) high flexibility [87]. Previous studies by Chiang et al. [43], Zounemat-Kermani et al. [45], Rajaee et al. [88], Muhammadi et al. [89], Kisi et al. [90], Alp and Cigizoglu [91], and Cobaner et al. [92] have also noted the superiority of ML models over traditional regression models (e.g., SRC model) for estimating suspended sediment.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 4.**Comparison of the average performance indices (RMSE, MAE, NS, and R

^{2}) for the SRC model with different methods of data separation.

**Figure 5.**Comparison of the average performance indices (RMSE, MAE, NS, and R

^{2}) for the SVR model with different methods of data separation.

**Figure 6.**Observed SSC versus estimated SSC using the best models (i.e., SVR) for the testing dataset.

Variable | ${\mathit{x}}_{\mathit{m}\mathit{i}\mathit{n}}$ | ${\mathit{x}}_{\mathit{m}\mathit{a}\mathit{x}}$ | $\overline{\mathit{x}}$ | ${\mathit{\sigma}}_{\mathit{x}}$ | ${\mathit{G}}_{1}$ | $\mathit{C}\mathit{v}$ |
---|---|---|---|---|---|---|

${Q}_{w}$ (m^{3}/s) | 0.00 | 25.71 | 1.92 | 2.04 | 4.62 | 1.06 |

SSC (mg/L) | 0.01 | 15,152.21 | 454.41 | 1556.05 | 6.41 | 3.42 |

^{1}Note: ${x}_{min}$ is the minimum value of the data, ${x}_{max}$ is the maximum value, $\overline{x}$ is the mean, ${\sigma}_{x}$ is the standard deviation, ${G}_{1}$ is the skewness, $Cv$ is the coefficient of variation, Q

_{w}is flow discharge, and SSC is suspended sediment concentration.

Study Period | Statistical Parameter | ||||||
---|---|---|---|---|---|---|---|

Dataset | ${\mathit{x}}_{\mathit{m}\mathit{i}\mathit{n}}$ | ${\mathit{x}}_{\mathit{m}\mathit{a}\mathit{x}}$ | $\overline{\mathit{x}}$ | ${\mathit{\sigma}}_{\mathit{x}}$ | ${\mathit{G}}_{1}$ | $\mathit{n}$ | |

Entire period | Training | 0 | 25.71 | 2.18 | 1.79 | 1.67 | 480 |

Testing | 0.02 | 20.13 | 1.17 | 1.06 | 2.22 | 207 | |

Spring | Training | 0.13 | 25.71 | 2.55 | 1.92 | 1.09 | 177 |

Testing | 0.32 | 20.13 | 1.09 | 1.08 | 78.2 | 76 | |

Summer | Training | 0 | 2.98 | 0.46 | 0.56 | 2.39 | 70 |

Testing | 0.02 | 0.96 | 0.39 | 0.26 | 0.45 | 31 | |

Autumn | Training | 0.19 | 3.18 | 0.87 | 0.42 | 2.24 | 84 |

Testing | 0.45 | 2.36 | 1.06 | 0.42 | 0.87 | 36 | |

Winter | Training | 0.42 | 16.6 | 1.67 | 0.9 | 2.42 | 149 |

Testing | 0.68 | 10.48 | 2.07 | 1.43 | 2.2 | 64 | |

${Q}_{w}<{\overline{Q}}_{w}$ | Training | 0 | 2.42 | 0.63 | 0.47 | 1.15 | 236 |

Testing | 0.02 | 2.3 | 0.96 | 0.44 | 0.31 | 102 | |

${\overline{Q}}_{w}\le {Q}_{w}<2{\overline{Q}}_{w}$ | Training | 0.62 | 5.95 | 2.13 | 0.87 | 1.59 | 126 |

Testing | 0.84 | 4.44 | 2.04 | 0.93 | 0.83 | 55 | |

${Q}_{w}\ge 2{\overline{Q}}_{w}$ | Training | 1.84 | 25.71 | 4.56 | 1.42 | 2 | 117 |

Testing | 1.36 | 20.13 | 4.43 | 2.34 | 0.93 | 51 | |

High water period | Training | 0.07 | 25.71 | 3.1 | 1.95 | 1.3 | 215 |

Testing | 0.06 | 20.13 | 2.06 | 1.55 | 1.9 | 93 | |

Low water period | Training | 0 | 5.41 | 1.31 | 1 | 2.01 | 265 |

Testing | 0.02 | 4.31 | 0.68 | 0.58 | 2.59 | 114 | |

Rising limb | Training | 0.65 | 25.71 | 2.85 | 1.58 | 1.46 | 142 |

Testing | 0.72 | 16.6 | 3.26 | 2.28 | 1.43 | 62 | |

Falling limb | Training | 0.13 | 9.6 | 2.32 | 1.86 | 1.22 | 118 |

Testing | 0.24 | 7.41 | 1.85 | 1.49 | 1.42 | 51 | |

Base flow | Training | 0 | 7.65 | 1.17 | 0.88 | 3.75 | 220 |

Testing | 0.02 | 4.31 | 0.63 | 0.57 | 3.06 | 94 |

^{2}Note: ${x}_{min}$ is the minimum value of the data, ${x}_{max}$ is the maximum value of the data, $\overline{x}$ is the mean of the data, ${\sigma}_{x}$ is the standard deviation, ${G}_{1}$ is the skewness, $n$ is the amount of data.

Study Period | Statistical Parameter | ||||||
---|---|---|---|---|---|---|---|

Dataset | ${\mathit{x}}_{\mathit{m}\mathit{i}\mathit{n}}$ | ${\mathit{x}}_{\mathit{m}\mathit{a}\mathit{x}}$ | $\overline{\mathit{x}}$ | ${\mathit{\sigma}}_{\mathit{x}}$ | ${\mathit{G}}_{1}$ | $\mathit{n}$ | |

Entire period | Training | 0.13 | 15,152.21 | 497.17 | 1602.92 | 6.84 | 480 |

Testing | 0.01 | 13,152.13 | 354.83 | 1439.82 | 6.16 | 207 | |

Spring | Training | 0.39 | 15,152.21 | 944.54 | 2342.31 | 5.02 | 191 |

Testing | 4.22 | 7585.72 | 278.85 | 1080.45 | 6.17 | 82 | |

Summer | Training | 0.01 | 6583.52 | 162.99 | 1080.19 | 5.43 | 56 |

Testing | 0.17 | 444.88 | 69.09 | 111.95 | 1.45 | 25 | |

Autumn | Training | 0.14 | 5894.95 | 273.23 | 1096.45 | 4.61 | 84 |

Testing | 0.92 | 2140.45 | 103.51 | 326.98 | 4.90 | 36 | |

Winter | Training | 1.93 | 12,256.62 | 293.73 | 1334.35 | 7.51 | 149 |

Testing | 5.52 | 6065.7 | 597.12 | 1286.53 | 2.80 | 64 | |

${Q}_{w}<{\overline{Q}}_{w}$ | Training | 0.01 | 7585.72 | 92.2 | 709.85 | 10.59 | 264 |

Testing | 0.13 | 2140.45 | 67.24 | 167.42 | 8.38 | 114 | |

${\overline{Q}}_{w}\le {Q}_{w}<2{\overline{Q}}_{w}$ | Training | 0.14 | 13,152.13 | 1257.3 | 3357.62 | 3.51 | 126 |

Testing | 4.22 | 12,583.52 | 379.23 | 1257.41 | 8.00 | 55 | |

${Q}_{w}\ge 2{\overline{Q}}_{w}$ | Training | 34.77 | 15,152.21 | 1159.2 | 2140.72 | 4.92 | 90 |

Testing | 59.82 | 11,964.84 | 1697.5 | 2797.51 | 2.54 | 38 | |

High water period | Training | 0.14 | 15,152.21 | 611.06 | 2028.42 | 6.35 | 215 |

Testing | 0.39 | 13,152.13 | 884.83 | 2270.51 | 4.57 | 93 | |

Low water period | Training | 0.01 | 8231.67 | 264.22 | 1257.81 | 5.91 | 265 |

Testing | 0.13 | 3996.55 | 147.39 | 413.62 | 6.40 | 114 | |

Rising limb | Training | 5.5 | 14,426.4 | 1387.2 | 2910.18 | 3.07 | 142 |

Testing | 6.73 | 4673.56 | 462.44 | 733.04 | 3.4 | 62 | |

Falling limb | Training | 0.39 | 15,152.21 | 646.2 | 2566.84 | 5.73 | 118 |

Testing | 0.79 | 13,152.13 | 473.59 | 1537.42 | 8.02 | 51 | |

Base flow | Training | 0.01 | 12,583.52 | 288.15 | 1386.16 | 7.2 | 220 |

Testing | 0.13 | 8231.67 | 135.81 | 955.45 | 9.47 | 94 |

^{3}Note: ${x}_{min}$ is the minimum value of the data, ${x}_{max}$ is the maximum value, $\overline{x}$ is the mean, ${\sigma}_{x}$ is the standard deviation, ${G}_{1}$ is the skewness, $n$ is the amount of data.

**Table 4.**Coefficients of the SRC equations in each of the data separation methods for the training dataset.

Group | Study Period | Equation | a | b |
---|---|---|---|---|

Without any separation (a) | Entire period | $\mathrm{SSC}=35.04{Q}_{w}^{1.86}$ | 35.04 | 1.86 |

Spring | $\mathrm{SSC}=34.43{Q}_{w}^{1.97}$ | 34.43 | 1.97 | |

Seasonal (b) | Summer | $\mathrm{SSC}=32.88{Q}_{w}^{1.36}$ | 32.88 | 1.36 |

Autumn | $\mathrm{SSC}=29.51{Q}_{w}^{1.81}$ | 29.51 | 1.81 | |

Winter | $\mathrm{SSC}=17.45{Q}_{w}^{2.66}$ | 17.45 | 2.66 | |

${Q}_{w}<{\overline{Q}}_{w}$ | $\mathrm{SSC}=31.69{Q}_{w}^{1.48}$ | 31.69 | 1.48 | |

Discharge Classes (c) | ${\overline{Q}}_{w}\le {Q}_{w}<2{\overline{Q}}_{w}$ | $\mathrm{SSC}=15.92{Q}_{w}^{2.8}$ | 15.92 | 2.8 |

${Q}_{w}\ge 2{\overline{Q}}_{w}$ | $\mathrm{SSC}=11.29{Q}_{w}^{2.69}$ | 11.29 | 2.69 | |

High water-low water periods (d) | High water period | $\mathrm{SSC}=25.46{Q}_{w}^{2.18}$ | 25.46 | 2.18 |

Low water period | $\mathrm{SSC}=35.21{Q}_{w}^{1.69}$ | 35.21 | 1.69 | |

Rising limb | $\mathrm{SSC}=22.64{Q}_{w}^{2.31}$ | 22.64 | 2.31 | |

Hydrograph State (e) | Falling limb | $\mathrm{SSC}=60.58{Q}_{w}^{1.54}$ | 60.58 | 1.54 |

Base flow | $\mathrm{SSC}=27.94{Q}_{w}^{1.69}$ | 27.94 | 1.69 |

Model | Study Period | RMSE (mg/L) | NS | MAE (mg/L) | R^{2} |
---|---|---|---|---|---|

without any separation | Entire period | 1366.96 | 0.19 | 292.23 | 0.35 |

Spring | 1093.17 | 0.31 | 279.18 | 0.36 | |

Seasonal | Summer | 683.8 | 0.20 | 201.08 | 0.31 |

Autumn | 1083.25 | 0.34 | 219.17 | 0.41 | |

Winter | 950.22 | 0.44 | 258.69 | 0.59 | |

${Q}_{w}<{\overline{Q}}_{w}$ | 1118.38 | 0.29 | 267.99 | 0.40 | |

Discharge Classes | ${\overline{Q}}_{w}\le {Q}_{w}<2{\overline{Q}}_{w}$ | 1148.47 | 0.26 | 275.73 | 0.36 |

${Q}_{w}\ge 2{\overline{Q}}_{w}$ | 1255.92 | 0.24 | 330.71 | 0.32 | |

High water/low water periods | High water period | 1189.56 | 0.27 | 287.07 | 0.36 |

Low water period | 1151.44 | 0.33 | 265.54 | 0.41 | |

Rising limb | 926.33 | 0.30 | 232.77 | 0.45 | |

Hydrograph State | Falling limb | 1310.15 | 0.13 | 399.12 | 0.24 |

Base flow | 1109.78 | 0.25 | 244.75 | 0.38 |

Model Name | Equation | RMSE (mg/L) | NS | MAE (mg/L) | R^{2} |
---|---|---|---|---|---|

SRC | $\mathrm{SSC}=35.04{Q}_{w}^{1.86}$ | 1366.96 | 0.19 | 292.23 | 0.34 |

SRC-FAO | $\mathrm{SSC}=43.21{Q}_{w}^{1.86}$ | 1345.72 | 0.25 | 289.1 | 0.35 |

SRC-CF2 | $\mathrm{SSC}=46.93{Q}_{w}^{1.86}$ | 1335.75 | 0.29 | 288.2 | 0.36 |

SRC-PSO | $\mathrm{SSC}=17.50{Q}_{w}^{2.81}$ | 1099.91 | 0.44 | 236.95 | 0.45 |

SRC-GA | $\mathrm{SSC}=17.45{Q}_{w}^{2.71}$ | 1113.31 | 0.41 | 245.84 | 0.43 |

SRC-ICA | $\mathrm{SSC}=17.49{Q}_{w}^{2.68}$ | 1127.92 | 0.40 | 250.07 | 0.42 |

Model | Study Period | SVR | ||
---|---|---|---|---|

$\mathit{\sigma}$ | C | ε | ||

without any separation | Entire period | 2.5 | 1 | 0.1 |

Spring | 0.3 | 5 | 0.001 | |

Seasonal | Summer | 2 | 2.5 | 0.0001 |

Autumn | 0.4 | 5 | 0.001 | |

Winter | 0.1 | 1 | 0.01 | |

${Q}_{w}<{\overline{Q}}_{w}$ | 0.15 | 1 | 0.1 | |

Discharge Classes | ${\overline{Q}}_{w}\le {Q}_{w}<2{\overline{Q}}_{w}$ | 0.1 | 3.5 | 0.001 |

${Q}_{w}\ge 2{\overline{Q}}_{w}$ | 0.17 | 5 | 0.01 | |

High water-low water periods | High water period | 2 | 2.5 | 0.1 |

Low water period | 0.1 | 1 | 0.01 | |

Rising limb | 0.21 | 1 | 0.01 | |

Hydrograph State | Falling limb | 0.1 | 1.5 | 0.1 |

Base flow | 0.1 | 5 | 0.0001 |

^{4}Note: C is cost of constraint violation, ε is error insensitive zone, and $\sigma $ is width of the Gaussian kernel function.

Model | Study Period | RMSE (mg/L) | NS | MAE (mg/L) | R^{2} |
---|---|---|---|---|---|

without any separation | Entire period | 1069.89 | 0.50 | 201.09 | 0.52 |

Spring | 1063.77 | 0.52 | 199.19 | 0.55 | |

Seasonal | Summer | 461.86 | 0.41 | 101.77 | 0.45 |

Autumn | 957.84 | 0.56 | 185.5 | 0.63 | |

Winter | 796.17 | 0.68 | 167.85 | 0.71 | |

${Q}_{w}<{\overline{Q}}_{w}$ | 970.86 | 0.55 | 182.83 | 0.56 | |

Discharge Classes | ${\overline{Q}}_{w}\le {Q}_{w}<2{\overline{Q}}_{w}$ | 1023.99 | 0.52 | 200.08 | 0.54 |

${Q}_{w}\ge 2{\overline{Q}}_{w}$ | 1088.75 | 0.46 | 217.38 | 0.48 | |

High water—low water periods | High water period | 1106.5 | 0.51 | 201.63 | 0.53 |

Low water period | 929.72 | 0.53 | 189.78 | 0.55 | |

Rising limb | 911.29 | 0.57 | 171.63 | 0.59 | |

Hydrograph State | Falling limb | 1119.2 | 0.38 | 237.3 | 0.43 |

Base flow | 1059.23 | 0.56 | 193.46 | 0.58 |

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Asadi, H.; Dastorani, M.T.; Sidle, R.C.; Shahedi, K.
Improving Flow Discharge-Suspended Sediment Relations: Intelligent Algorithms versus Data Separation. *Water* **2021**, *13*, 3650.
https://doi.org/10.3390/w13243650

**AMA Style**

Asadi H, Dastorani MT, Sidle RC, Shahedi K.
Improving Flow Discharge-Suspended Sediment Relations: Intelligent Algorithms versus Data Separation. *Water*. 2021; 13(24):3650.
https://doi.org/10.3390/w13243650

**Chicago/Turabian Style**

Asadi, Haniyeh, Mohammad T. Dastorani, Roy C. Sidle, and Kaka Shahedi.
2021. "Improving Flow Discharge-Suspended Sediment Relations: Intelligent Algorithms versus Data Separation" *Water* 13, no. 24: 3650.
https://doi.org/10.3390/w13243650