# Prediction of Suspended Sediment Load Using Data-Driven Models

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Basin and Data

^{2}, the second largest tributary of the Yangtze River and one of the most important flood and sediment sources for the Three Gorges Reservoir, China was selected as a case study. The Qu River and Fu River are the two main tributaries of Jialing River basin from left and right banks, respectively. The upstream section of the basin rivers has very deep valleys with mountainous terrain, whereas the lower section has flat river beds. The Jialing River elevation varies from 126 m to 5024 m with mean annual rainfall of 935 mm and mean annual temperature of 16 °C.

^{3}, g/L; ${W}_{s}$ is the weight of dry sediment in a sample, g; V is the volume of the sample, mL.

^{3}; ${q}_{0},{q}_{1},\dots ,{q}_{n}$ are the partial discharges within various pairs of adjacent sampling verticals, m

^{3}/s.

#### 2.2. Used Methods

#### 2.2.1. Adaptive Neuro-Fuzzy Inference System with Fuzzy C-Means Clustering (ANFIS-FCM)

_{ij}represents the degree of membership of x

_{i}in the cluster j where x

_{i}denotes the ith measured data, ${c}_{j}$ is the centre of the jth cluster, and $\Vert \text{}\Vert $ is the norm distance between the ith measured data and the jth cluster centre.

_{ij}and cluster centres ${c}_{j}$. The iteration process continues as long as reaching to a predetermined threshold value:

#### 2.2.2. Multivariate Adaptive Regression Splines (MARS)

#### 2.2.3. The Evaluation Metrics Used for Model Comparison

## 3. Results and Discussion

^{2}value.

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 4.**Schematic structure of the modelling system for the DENFIS-based model for scenario 5 (S5).

**Figure 5.**Time variation graphs of the observed and estimated suspended sediment by DENFIS, ANFIS-FCM and MARS in the test period at Guangyuan Station.

**Figure 6.**Time scatterplots of the observed and estimated suspended sediment by DENFIS, ANFIS-FCM and MARS in the test period at Guangyuan Station.

**Figure 7.**Time variation graphs of the observed and estimated suspended sediment by DENFIS, ANFIS-FCM and MARS in the test period at Beibei Station.

**Figure 8.**Time scatterplots of the observed and estimated suspended sediment by DENFIS, ANFIS-FCM and MARS in the test period at Beibei Station.

Statistical Parameters | Guangyuan Station | Beibei Station | ||||
---|---|---|---|---|---|---|

Whole Data | Training Data | Testing Data | Whole Data | Training Data | Testing Data | |

Streamflow (m^{3}/s) | ||||||

x_{mean} | 175.1 | 198.3 | 93.9 | 2136 | 2231 | 1805 |

x_{min} | 4.5 | 4.5 | 10.8 | 105 | 105 | 281 |

x_{max} | 6290 | 6290 | 1890 | 34,700 | 34,700 | 20,800 |

C_{sx} | 6.84 | 6.26 | 7.06 | 4.32 | 4.15 | 4.77 |

S_{x} | 336 | 372 | 126 | 3230 | 3427 | 2388 |

$\frac{{x}_{max}}{{x}_{mean}}$ | 36 | 32 | 20 | 16 | 16 | 12 |

C_{v} (S_{x}/x_{mean}) | 1.92 | 1.88 | 1.34 | 1.51 | 1.54 | 1.32 |

Sediment (kg/s) | ||||||

x_{mean} | 431.9 | 541 | 49.9 | 971 | 1139 | 381 |

x_{min} | 0.349 | 0.91 | 0.349 | 0.105 | 0.105 | 1.69 |

x_{max} | 49,600 | 49,600 | 7660 | 113,000 | 113,000 | 36,600 |

C_{sx} | 12.1 | 10.7 | 19.2 | 10.5 | 9.73 | 9.96 |

S_{x} | 2673 | 3018 | 321 | 5681 | 6287 | 2533 |

$\frac{{x}_{max}}{{x}_{mean}}$ | 115 | 91.7 | 154 | 116 | 99 | 96 |

C_{v} (S_{x}/x_{mean}) | 6.19 | 5.58 | 6.44 | 5.85 | 5.52 | 6.65 |

**Table 2.**The training and test statistics of the DENFIS, ANFIS-FCM and MARS models using different combinations of sediment and streamflow for daily suspended sediment prediction, Guangyuan Station.

Models | Scenario | Model Inputs | Model Parameters | Training Period | Test Period | ||||
---|---|---|---|---|---|---|---|---|---|

RMSE | MAE | NSE | RMSE | MAE | NSE | ||||

S1 | Q_{t}, | 0.05 | 1968 | 356 | 0.575 | 217 | 37.9 | 0.541 | |

S2 | Q_{t}, Q_{t−1} | 0.14 | 1797 | 366 | 0.646 | 164 | 35.7 | 0.739 | |

S3 | Q_{t}, Q_{t−1}, Q_{t−2} | 0.11 | 2257 | 409 | 0.515 | 146 | 34.1 | 0.793 | |

DENFIS | S4 | Q_{t}, Q_{t−1}, Q_{t−2}, Q_{t−3} | 0.13 | 2167 | 418 | 0.832 | 134 | 32.2 | 0.861 |

S5 | Q_{t}, Q_{t−1}, Q_{t−2}, Q_{t−3}, S_{t−1} | 0.12 | 1986 | 353 | 0.567 | 168 | 22.4 | 0.726 | |

S6 | Q_{t}, Q_{t−1}, Q_{t−2}, Q_{t−3}, S_{t−1}, S_{t−2} | 0.11 | 2137 | 403 | 0.499 | 187 | 23.6 | 0.661 | |

S7 | Q_{t}, Q_{t−1}, Q_{t−2}, Q_{t−3}, S_{t−1}, S_{t−2}, S_{t−3} | 0.11 | 2340 | 435 | 0.399 | 228 | 29.4 | 0.495 | |

S1 | Q_{t}, | 5,100 | 1828 | 373 | 0.633 | 294 | 69.4 | 0.164 | |

S2 | Q_{t}, Q_{t−1} | 6,10 | 1787 | 367 | 0.650 | 270 | 55.9 | 0.293 | |

ANFIS-FCM | S3 | Q_{t}, Q_{t−1}, Q_{t−2} | 4,100 | 1803 | 372 | 0.643 | 295 | 59.9 | 0.157 |

S4 | Q_{t}, Q_{t−1}, S_{t−1} | 8,90 | 1322 | 243 | 0.808 | 318 | 46.5 | 0.020 | |

S5 | Q_{t}, Q_{t−1}, S_{t−1}, S_{t−2} | 8,70 | 1266 | 228 | 0.824 | 199 | 33.4 | 0.826 | |

S6 | Q_{t}, Q_{t−1}, S_{t−1}, S_{t−2}, S_{t−3} | 8,80 | 1807 | 363 | 0.642 | 258 | 52.1 | 0.353 | |

S1 | Q_{t}, | - | 1760 | 372 | 0.660 | 327 | 65.0 | −0.036 | |

S2 | Q_{t}, Q_{t−1} | - | 1758 | 376 | 0.661 | 368 | 80.3 | −0.316 | |

MARS | S3 | Q_{t}, S_{t−1} | - | 1578 | 337 | 0.727 | 239 | 64.5 | 0.446 |

S4 | Q_{t}, S_{t−1}, S_{t−2} | - | 1614 | 343 | 0.714 | 195 | 62.4 | 0.631 | |

S5 | Q_{t}, S_{t−1}, S_{t−2}, S_{t−3} | - | 1595 | 343 | 0.721 | 254 | 60.9 | 0.372 |

**Table 3.**The training and test statistics of the DENFIS, ANFIS-FCM and MARS models using different combinations of sediment and streamflow for daily suspended sediment prediction, Beibei Station.

Models | Scenario | Model Inputs | Model Parameters | Training Period | Test Period | ||||
---|---|---|---|---|---|---|---|---|---|

RMSE | MAE | NSE | RMSE | MAE | NSE | ||||

S1 | Q_{t}, | 0.01 | 4014 | 663 | 0.593 | 1546 | 229 | 0.628 | |

S2 | Q_{t}, Q_{t−1} | 0.17 | 3779 | 656 | 0.639 | 1417 | 233 | 0.687 | |

S3 | Q_{t}, Q_{t−1}, Q_{t−2} | 0.02 | 4158 | 711 | 0.563 | 1177 | 204 | 0.784 | |

DENFIS | S4 | Q_{t}, Q_{t−1}, Q_{t−2}, Q_{t−3} | 0.06 | 4302 | 732 | 0.532 | 1024 | 169 | 0.837 |

S5 | Q_{t}, Q_{t−1}, Q_{t−2}, Q_{t−3}, S_{t−1} | 0.15 | 4325 | 753 | 0.527 | 1153 | 184 | 0.793 | |

S6 | Q_{t}, Q_{t−1}, Q_{t−2}, Q_{t−3}, S_{t−1}, S_{t−2} | 0.05 | 3936 | 663 | 0.609 | 797 | 134 | 0.901 | |

S7 | Q_{t}, Q_{t−1}, Q_{t−2}, Q_{t−3}, S_{t−1}, S_{t−2}, S_{t−3} | 0.06 | 4237 | 752 | 0.547 | 884 | 149 | 0.878 | |

S1 | Q_{t}, | 8,20 | 3802 | 656 | 0.635 | 1214 | 228 | 0.770 | |

S2 | Q_{t}, Q_{t−1} | 8,10 | 3707 | 663 | 0.653 | 1235 | 224 | 0.762 | |

ANFIS-FCM | S3 | Q_{t}, Q_{t−1}, Q_{t−2} | 4,80 | 3742 | 657 | 0.646 | 1171 | 257 | 0.786 |

S4 | Q_{t}, Q_{t−1}, Q_{t−2}, Q_{t−3} | 5,30 | 4084 | 801 | 0.579 | 1864 | 328 | 0.459 | |

S5 | Q_{t}, S_{t−1} | 8,20 | 3685 | 620 | 0.657 | 1312 | 215 | 0.732 | |

S6 | Q_{t}, S_{t−1}, S_{t−2} | 6,60 | 3332 | 606 | 0.720 | 1616 | 229 | 0.784 | |

S7 | Q_{t}, S_{t−1}, S_{t−2}, S_{t−3} | 5,50 | 4410 | 871 | 0.509 | 2772 | 407 | −0.197 | |

S1 | Q_{t}, | - | 3646 | 631 | 0.664 | 1423 | 284 | 0.685 | |

S2 | Q_{t}, Q_{t−1} | - | 3596 | 629 | 0.673 | 1509 | 271 | 0.645 | |

MARS | S3 | Q_{t}, S_{t−1} | - | 3089 | 518 | 0.759 | 1252 | 213 | 0.756 |

S4 | Q_{t}, S_{t−1}, S_{t−2} | - | 2945 | 523 | 0.781 | 1362 | 229 | 0.711 | |

S5 | Q_{t}, S_{t−1}, S_{t−2}, S_{t−3} | - | 2905 | 520 | 0.787 | 1397 | 234 | 0.696 |

**Table 4.**The comparison of DENFIS, ANFIS-FCM and MARS peak-estimates for the test period, Guangyuan Station.

Date | Peaks > 900 kg/s | Relative Error | |||||
---|---|---|---|---|---|---|---|

DENFIS kg/s | ANFIS-FCM kg/s | MARS kg/s | DENFIS % | ANFIS-FCM % | MARS % | ||

7 July 2014 | 1690 | 733.37 | 1191.2 | 946.26 | −56.6 | −29.5 | −44.0 |

21 July 2014 | 1850 | 1376.5 | 2970.8 | 3977.1 | −25.6 | 60.6 | 115.0 |

11 September 2014 | 1120 | 590.73 | 1764.6 | 1600.9 | −47.3 | 57.6 | 42.9 |

12 September 2014 | 917 | 511.98 | 1573.3 | 1839.7 | −44.2 | 71.6 | 100.6 |

28 June 2015 | 7660 | 10,309 | 8704.3 | 8585.3 | 34.6 | 13.6 | 12.1 |

29 June 2015 | 1920 | 2302.3 | 3756.8 | 4758.9 | 19.9 | 95.7 | 147.9 |

Total (Absolute) = | 228 | 329 | 462 |

**Table 5.**The comparison of DENFIS, ANFIS-FCM and MARS peak-estimates for the test period, Beibei Station.

Date | Peaks > 11,000 kg/s | Relative Error | |||||
---|---|---|---|---|---|---|---|

DENFIS kg/s | ANFIS-FCM kg/s | MARS kg/s | DENFIS % | ANFIS-FCM % | MARS % | ||

12 September 2014 | 21,900 | 13,021 | 19,377 | 10,258 | −40.5 | −11.5 | −53.2 |

13 September 2014 | 21,300 | 18,516 | 21,817 | 14,659 | −13.1 | 2.4 | −31.2 |

14 September 2014 | 36,600 | 26,760 | 25,166 | 31,414 | −26.9 | −31.2 | −14.2 |

15 September 2014 | 26,300 | 33,871 | 29,084 | 31,615 | 28.8 | 10.6 | 20.2 |

16 September 2014 | 11,100 | 11,219 | 20,040 | 18,622 | 1.1 | 80.5 | 67.8 |

26 June 2015 | 16,800 | 11,704 | 18,896 | 9720.9 | −30.3 | 12.5 | −42.1 |

30 June 2015 | 29,600 | 32,742 | 28,895 | 28,031 | 10.6 | −2.4 | −5.3 |

1 July 2015 | 11,400 | 19,727 | 23,768 | 20,847 | 73.1 | 108.5 | 82.9 |

Total (Absolute) = | 224 | 260 | 317 |

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**MDPI and ACS Style**

Adnan, R.M.; Liang, Z.; El-Shafie, A.; Zounemat-Kermani, M.; Kisi, O. Prediction of Suspended Sediment Load Using Data-Driven Models. *Water* **2019**, *11*, 2060.
https://doi.org/10.3390/w11102060

**AMA Style**

Adnan RM, Liang Z, El-Shafie A, Zounemat-Kermani M, Kisi O. Prediction of Suspended Sediment Load Using Data-Driven Models. *Water*. 2019; 11(10):2060.
https://doi.org/10.3390/w11102060

**Chicago/Turabian Style**

Adnan, Rana Muhammad, Zhongmin Liang, Ahmed El-Shafie, Mohammad Zounemat-Kermani, and Ozgur Kisi. 2019. "Prediction of Suspended Sediment Load Using Data-Driven Models" *Water* 11, no. 10: 2060.
https://doi.org/10.3390/w11102060