# Estimating Sediment Discharge Using Sediment Rating Curves and Artificial Neural Networks in the Shiwen River, Taiwan

^{*}

^{†}

## Abstract

**:**

^{2}of 0.903) compared to CANFISM, TLRN, FRNN and RBF. SRC had the lowest R

^{2}(0.765), and resulted in underestimations of peak sediment discharge (−47%).

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

^{2}. The average slope is about 0.03 with a design flood at 1300 m

^{3}/s (50-year return period). The watershed is dominated by forests and agricultural activities as shown in Figure 2. Forests occupy about 88% of the watershed, and agriculture about 7%. Built up land within the watershed comprises about 0.1%. The poor geologic characteristics of Taiwanese watersheds [4] combined with the location of agricultural activities in this watershed (Shiwen) have resulted in increased rates of sediment discharge as demonstrated by [2]. Figure 2 shows the location of agricultural fields in close proximity to the main river channel, which could be another source of the accelerated sediment volumes in this river.

#### 2.2. Sediment Rating Curve

#### 2.3. Artificial Neural Networks

#### 2.3.1. Fully Recurrent Neural Networks (FRNNs)

Training Variables | Assigned Value |
---|---|

Step size | 1 |

Momentum | 0.7 |

Iterations | 1000 |

Training threshold | 0.001 |

#### 2.3.2. Multilayer Perceptron (MLP)

Training Variables | Assigned Value |
---|---|

Step size | 1 |

Momentum | 0.7 |

Iterations | 5000 |

Training threshold | 0.001 |

#### 2.3.3. Time Lagged Recurrent Networks (TLRNs)

^{−1}denotes the delay operator and i is 1, 2, 3…).

Training Variables | Assigned Value |
---|---|

Depth in samples | 10 |

Trajectory length | 50 |

Momentum | 0.7 |

Iterations | 1000 |

Training threshold | 0.001 |

#### 2.3.4. Radial Basis Function (RBF)

_{i}and the connection weight, w

_{j}, can be computed by Equation (2) [25].

_{j}, for the jth hidden unit, the Gaussian basis function smoothing parameter for the j neuron is denoted by σ

_{j}. Finally, a linear output will yield RBF as:

_{k}is a linearly weighted sum of the outputs of the hidden units, ${W}_{k}^{T}$ is the weight vector for the output neuron k and φ is the vector of outputs from the hidden layer; T indicates the transpose operation. Conditions of the training performance variables of the RBF were similar to those of MLP above (Table 2).

#### 2.3.5. Coactive Neurofuzzy Inference System Model (CANFISM)

Training Variables | Assigned Value |
---|---|

Membership function | Gaussian |

MFs per input | 2 |

Fuzzy model | TSK |

Step size | 1 |

Momentum | 0.7 |

Iterations | 1000 |

Training threshold | 0.001 |

#### 2.4. Data Normalization

#### 2.5. Models Evaluation

## 3. Results and Discussion

#### 3.1. Sediment Discharge—Based on Rating Curve

^{2}of 0.621 as shown in Figure 7a. The best fit power function in Figure 7a shows more variation between the observed and estimated discharge. After using the allocated data set (34) for testing, the observed and estimated R

^{2}is 0.765 as seen in Figure 7b.

**Figure 7.**Scatter plot of (

**a**) relationship between water and sediment discharge, (

**b**) observed and estimated sediment discharge.

#### 3.2. Sediment Discharge—Based on ANNs

^{2}as shown by Figure 8. A summary of the model’s statistical performance is shown in Table 5. The RMSE values of MLP for training, cross validation and testing stage were 1431.536, 1091.186 and 721.175 kg/s, respectively. The R

^{2}values in the training, cross validation and testing stages were 0.709, 0.823 and 0.912, respectively.

Model | Stage | RMSE (m^{3}/s) | MAE (m^{3}/s) | R^{2} |
---|---|---|---|---|

MLP | Training | 1431.536 | 893.700 | 0.709 |

Cross validation | 1091.186 | 706.003 | 0.823 | |

Testing | 721.175 | 509.584 | 0.912 | |

CANFISM | Training | 1380.483 | 890.829 | 0.721 |

Cross validation | 1122.562 | 758.043 | 0.826 | |

Testing | 775.401 | 591.837 | 0.906 | |

TLRN | Training | 1329.052 | 900.685 | 0.743 |

Cross validation | 1187.290 | 786.072 | 0.801 | |

Testing | 860.803 | 649.805 | 0.878 | |

FRNN | Training | 1400.275 | 931.110 | 0.716 |

Cross validation | 1142.759 | 775.643 | 0.823 | |

Testing | 782.847 | 588.648 | 0.906 | |

RBF | Training | 1359.194 | 844.964 | 0.729 |

Cross validation | 1124.365 | 730.110 | 0.828 | |

Testing | 859.805 | 615.986 | 0.876 |

#### 3.3. Comparison of Models

^{2}of 0.621 (Figure 7); however, during testing, the R

^{2}shoots up to 0.765 to an almost similar R

^{2}for the ANN models as seen in Figure 12. Moreover, Figure 13 shows that the high SRC R

^{2}obtained during the testing stage may be misleading as it underestimated sediment discharge especially at the peaks and overestimated low sediment discharge values when compared with observed Qs. The observed and estimated peak Qs are shown in Table 6. The ANNs (MLP and FRNN = 1%), model peak Qs values are almost similar to the observed values compared to the developed sediment rating curve (−47%). Lin [28] observed that SRC can underestimate sediment load by as much as −73% and can overestimate by as high as 224%. These findings demonstrate the inappropriateness of employing linear models in solving non-linear and complex hydrological systems like that of Taiwan. Leahy et al. [14] concluded that river studies are necessary but are a challenging mission because their hydrologic systems are very complex. Boukhrissa et al. [29] compared a feed forward back propagation (FFBP) neural network with sediment rating curves, and the FFBP model results showed high efficiencies in reproducing daily sediment loads and global annual sediment yields.

Observed | MLP | CANFISM | FRNN | TLRN | RBF | SRC | Relative Error (%) | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

(Kg/s) | MLP | CANFISM | FRNN | TLRN | RBF | SRC | ||||||

6402 | 5341 | 4954 | 5104 | 4689 | 4625 | 3414 | −17 | −23 | −20 | −27 | −28 | −47 |

6339 | 7312 | 7046 | 6701 | 7002 | 7062 | 4392 | 15 | 11 | 6 | 10 | 11 | −31 |

7520 | 7822 | 7760 | 7202 | 7095 | 7749 | 4775 | 4 | 3 | −4 | −6 | 3 | −37 |

3418 | 4768 | 4461 | 4218 | 4641 | 4087 | 3186 | 39 | 31 | 23 | 36 | 20 | −7 |

2160 | 2901 | 2977 | 2932 | 2872 | 2923 | 2437 | 34 | 38 | 36 | 33 | 35 | 13 |

5904 | 6671 | 6271 | 5936 | 5815 | 6197 | 4017 | 13 | 6 | 1 | -2 | 5 | −32 |

6904 | 6969 | 6616 | 6243 | 5927 | 6595 | 4180 | 1 | −4 | −10 | −14 | −4 | −39 |

6065 | 4915 | 4584 | 4280 | 4123 | 4216 | 3244 | −19 | −24 | −29 | −32 | −30 | −47 |

## 4. Conclusions

^{2}of 0.903 obtained during application. Finally, the inaccuracies associated with using SRC in estimating sediment loads and discharge can be overcome by employing articial neural networks. Different catchments are likely to have different outcomes from our findings; however, extensive data collection during storm events before applying the outlined methodologies is recommended for better results.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**MDPI and ACS Style**

Tfwala, S.S.; Wang, Y.-M.
Estimating Sediment Discharge Using Sediment Rating Curves and Artificial Neural Networks in the Shiwen River, Taiwan. *Water* **2016**, *8*, 53.
https://doi.org/10.3390/w8020053

**AMA Style**

Tfwala SS, Wang Y-M.
Estimating Sediment Discharge Using Sediment Rating Curves and Artificial Neural Networks in the Shiwen River, Taiwan. *Water*. 2016; 8(2):53.
https://doi.org/10.3390/w8020053

**Chicago/Turabian Style**

Tfwala, Samkele S., and Yu-Min Wang.
2016. "Estimating Sediment Discharge Using Sediment Rating Curves and Artificial Neural Networks in the Shiwen River, Taiwan" *Water* 8, no. 2: 53.
https://doi.org/10.3390/w8020053