# Prediction of Sediment Yields Using a Data-Driven Radial M5 Tree Model

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## Abstract

**:**

^{2}), the root-mean-square error (RMSE) and the mean absolute percentage error (MAPE). The prediction accuracy of the RM5Tree model during the testing period was superior to the ANN, MARS, SVR, M5Tree, RSM and SRC models with the R

^{2}, RMSE and MAPE being 0.72, 0.51 tons/day and 11.99%, respectively. The RM5Tree model predicted suspended sediment peaks better, with 84.10% relative accuracy, in comparison to the MARS, ANN, SVR, M5Tree, RSM and SRC models, with 80.62, 77.86, 81.90, 80.20, 74.58 and 62.49% relative accuracies, respectively.

## 1. Introduction

#### Literature Review

## 2. Materials and Methods

#### 2.1. Study Area

^{2}drainage area at the Gilgit gauging station. The river originates from the Shandoor Plains in the North of Gilgit Baltistan, Pakistan, with a right tributary of Baha Lake and small tributaries of Ghizar, Ishkoman, Yasin and Phandar.

^{3}/s, with a sediment load of 448 mg/L. The snow starts to accumulate at the end of October, whereas the ablation period starts after the snow-melting process in July. About 75% of basin rainfall is received during April–October. The recorded mean annual is 670 mm in the basin. Similarly, the monthly basin mean temperature varies from −19.8 to 7.20 °C. The geographical features and hydrological characteristics of the Gilgit River catchment are also shown in Figure 1 and Figure 2.

Variable | Data Source | Interval | Period | Source |
---|---|---|---|---|

Q * | Mean daily discharge (m^{3}/s) | Daily | 1981–2010 | Water and Power Development Authority (WAPDA), Pakistan |

SSC * | Suspended sediment concentration (mg/L) | Intermittent weekdays | 1981–2010 | Water and Power Development Authority (WAPDA), Pakistan |

SCF | Snow cover fractions calculated from MODIS satellite data ranging from 0 to 1 | Weekly | 2000–2010 | https://nsidc.org/data/MOD10A2 accessed on 24 April 2020 |

T | Daily maximum, minimum and mean basin air temperature for a grid of 5 × 5 km in size (°C) | Daily | 1981–2010 | [59,60] |

P | Daily mean rainfall (mm/day) on a grid of 5 × 5 km in size | Daily | 1981–2010 | [59,60] |

Evap | Daily mean evapotranspiration (mm/day) on a grid of 5 × 5 km in size | Daily | 1981–2010 | [59,60] |

Input Variable | Description (Basin Average) | Log Q (m ^{3}/Day) | log SSY (tons/Day) | SCA (Fractions) | T_{avg}(°C) | P (mm) | Evap (mm/Day) |
---|---|---|---|---|---|---|---|

log Q | Logarithm of discharge | 1.000 | |||||

log SSY | Logarithm of sediment yields | 0.870 | 1.000 | ||||

SCA | Snow cover area | −0.850 | −0.740 | 1.000 | |||

T_{avg.} | Temperature | 0.870 | 0.790 | −0.880 | 1.000 | ||

P | Effective rainfall | 0.160 | 0.150 | 0.090 | 0.100 | 1.000 | |

Evap. | Evapotranspiration | 0.860 | 0.810 | −0.820 | 0.930 | 0.060 | 1.000 |

#### 2.2. Snow cover Estimation Using the Temperature Index Snow Model

_{RS}) temperature data were used to separate the amount of snow and liquid rainfall using the following equations:

_{p}is the precipitation factor, which is proportionate to temperature difference and is calculated using the following system of equations:

_{RS}(°C) was used to group precipitation into the rain or snow categories, while T

_{SM}was used to calculate the snow-melting process. The snow-melting process depends on several environmental factors, such as the river basin boundary conditions of temperature and air relative humidity.

_{snow}(mm/day)) was estimated as follows:

_{snow}is the snow-melting day degree factor (mm/day °C), T

_{mean}is the daily mean/average air temperature (°C) and T

_{SM}is the threshold temperature (°C).

#### 2.3. Artificial Neural Networks

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

#### 2.5. Support Vector Regression

_{1}, x

_{2}, x

_{3}, …, x

_{n}) of the input layer, along with the kernel functions, i.e., $K\left(x,{x}_{i}\right)$ of the hidden layer.

#### 2.6. Response Surface Method (RSM)

#### 2.7. M5Tree Model

_{i}is the samples subset with the ith potential test result; and sd is the standard deviation, which is given below as

_{i}is the numerical targeted value of the ith attribute sample.

#### 2.8. Radial M5Tree Model

_{min}X

_{max}], are randomly selected based on the domain of datasets.

- Creation of a randomly selected center point of RBF datasets.
- Transformation of input datasets of layer 1 into a radial space using Equation (21) on the basis of the RBF center point as follows:

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

^{3}/day), where both are log-transformed, and a and b are constants that depend on the river and catchment characteristics.

#### 2.10. Performance Metrics for Model Evaluation

^{2}):

_{io}is the actual sediment load, S

_{is}is the model-predicted sediment and $\overline{{S}_{is}}$ is the average estimated sediment load.

_{po}is the actual peak SSY value and S

_{ps}is the model-simulated peak SSY value.

#### 2.11. Application of the ANN, MARS, SVR, M5Tree, RM5Tree and RSM Models

^{2}and minimum RMSE and MAPE values as performance criteria. Out of various input combinations, the following best input scenarios (S

_{1}–S

_{8}) developed for predictions of sediment yields in this study are listed below:

- (a)
- Flows:

_{1}= SSC

_{t}= f (β

_{1}, β

_{2}, β

_{3}, β

_{4}, β

_{5}, Q

_{t}, Q

_{t−1}, Q

_{t−2}, Q

_{t−3}, Q

_{t−4},) + e

_{i}

- (b)
- Snow cover area and flows:

_{2}= SSC

_{t}= f (β

_{1}, β

_{6}, β

_{7}, β

_{8}, SCA

_{t}, SCA

_{t−1}, SCA

_{t−2}, Q

_{t},) + e

_{i}

- (c)
- Flow, snow cover area and effective rainfall:

_{3}= SSC

_{t}= f (β

_{1}, β

_{9}, β

_{6}, β

_{10}, R

_{t−1}, SCA

_{t}, SCA

_{t−4}, Q

_{t},) + e

_{i}

- (d)
- Flow, snow cover area, temperature and evapotranspiration:

_{4}= SSC

_{t}= f (β

_{1}, β

_{11}, β

_{12}, β

_{6}, β

_{10}, T

_{t−}

_{1}, Evap

_{t−}

_{1}, SCA

_{t}, SCA

_{t−}

_{4}, Q

_{t}) + e

_{i}

_{5}= SSC

_{t}= f (β

_{1}, β

_{2}, β

_{11}, β

_{12}, β

_{6}, T

_{t−}

_{1}, Evap

_{t−}

_{1}, SCA

_{t}, Q

_{t}, Q

_{t−1}) + e

_{i}

- (e)
- Mean basin air temperature:

_{6}= SSC

_{t}= f (β

_{13}, β

_{11}, β

_{14}, β

_{15}, β

_{16}, T

_{t}, T

_{t−1}, T

_{t−2}, T

_{t−3}, T

_{t−4}) + e

_{i}

- (f)
- Flow, snow cover area, temperature, rainfall and evapotranspiration:

_{7}= SSC

_{t}= f (β

_{1}, β

_{13}, β

_{12}, β

_{6}, β

_{9}, T

_{t}, Evap

_{t−1}, SCA

_{t}, R

_{t−1}, Q

_{t}) + e

_{i}

_{8}= SSC

_{t}= f (T

_{t−1}, Evap

_{t−1}, SCA

_{t}, R

_{t−1}, β

_{1}, β

_{11}, β

_{12}, β

_{6}, β

_{9}, Q

_{t},) + e

_{i}

## 3. Results and Discussions

#### 3.1. Simulation Results of Snow Melting and Snow Cover Area

_{snow}= 4.2 mm/day/°C [4] of the snowmelt model for the Gilgit Basin. The previous case studies in the regions of the Upper Indus Basin (UIB) [57,58,105,106,107,108] found that the value of K

_{snow}ranged from 3 to 7 mm/day/°C. Thus, the value of k

_{snow}= 4.2 mm/day/°C of the current study lay within the range of past studies carried out for the calibrations and validations of the snowmelt runoff model. The difference between the K

_{snow}values found during different case studies was due to the use of different periods and grid resolutions of input and output datasets, threshold temperatures for separation of rainfall and snowmelts, and Gilgit River basin characteristics.

^{2}value of 0.90 between the MODIS-extracted snow cover fraction and simulated snow cover fraction during calibrations and testing. A greater than 70% goodness of fit for the snowmelt model was obtained using three performance criteria of R

^{2}, MAPE and RMSE for satisfactory estimations of the snow cover area and snowmelt. The time series plot between MODIS-observed snow cover and snow-model-simulated snow cover area during model calibration (2000–2007) and validation (2008–2010) period is shown in the Figure 9.

#### 3.2. Comparison of the ANN, MARS, SVR, M5Tree, RM5Tree, RSM and SRC Models

_{2}(SCA

_{t}− SCA

_{t−2}, Q

_{t}). The ANN model with input combination S

_{2}had the lowest RMSE value of 0.40 and the highest R

^{2}value of 0.67 during the testing period compared with the other input combinations for sediment load predictions. Similarly, Table 5 shows the results of different input scenarios when using the MARS algorithm for the Gilgit Basin during the training and testing phases. The MARS model performed the best using input scenario S

_{3}(SCA

_{t}, SCA

_{t−4}, Q

_{t}, R

_{t−1}). During the testing period, the best MARS model with scenario S

_{3}produced the lowest RMSE value of 0.53 and the highest R

^{2}value of 0.68.

_{4}(SCA

_{t}, SCA

_{t−4}, Q

_{t}, Evap

_{t−1}, T

_{t−1}). The best SVR algorithm with the S

_{4}scenario had the lowest value of RMSE (0.51) and the highest R

^{2}(0.70) during the testing period. As is apparent from Table 7, the input scenario of S

_{2}(SCA

_{t}, SCA

_{t−2}, Q

_{t}) gave the best performance of the M5Tree model for the prediction of sediment yields. The best M5Tree model provided the lowest RMSE value of 0.59 and the highest R

^{2}value of 0.63 during the testing period.

_{8}(SCA

_{t}, Q

_{t}, Evap

_{t−1}, R

_{t−1}, T

_{t−1}) performed the best compared with the other input scenarios during the testing period for the RM5Tree algorithm for predictions of suspended sediments for the Gilgit River basin. The RM5Tree model provided the lowest RMSE value of 0.44 and the highest R

^{2}value of 0.72.

_{8}(SCA

_{t}, Q

_{t}, Evap

_{t−1}, R

_{t−1}, T

_{t−1}) compared with the other input scenarios for the estimation of sediments. The best RSM model had the lowest RMSE value of 0.51 and the highest R

^{2}value of 0.68 during the testing phase.

^{2}= 0.72) after the introduction of snow cover and effective mean rainfall combination; additional input parameters included the flows, mean evapotranspiration and average air temperature of the Gilgit River basin.

^{2}value of 0.72 when testing the calibrated models.

^{2}value of 0.72 during testing, while M5Tree seemed to have the most scattered estimates.

#### 3.3. Discussions

^{2}ranged from 0.78 to 0.82 during the testing period. The accuracy of the ANN model was superior to the other models. Moreover, for the prediction of the peak sediment, the relative accuracy of models ranged from 66.33 to 81.31%.

^{2}ranges from 0.68 to 0.72 during the testing period using the ANN, MARS, SVR, M5 Tree, RM5 Tree, RSM and SRC models with a non-random sampling of the datasets. Moreover, during the prediction of the peak sediment, the relative accuracies also ranged from 62.49 to 84.10%. It was also found that the RM5Tree model performed superior compared with the M5Tree, ANN, MARS, SVR, RSM and SRC models for the prediction of sediment yields in the complex sediment generation processes in cold regions. Therefore, this suggests that soft computing models can be successfully used for the prediction of non-linear processes, such as sediment yields.

## 4. Conclusions

^{2}, RMSE and MAPE of 0.72, 0.51 tons/day and 11.99%, respectively. The limitation of the present research was the availability of scarce datasets, especially the lower frequency of sediment measurements. However, soft computing models can also help to bridge these data gaps with the selection of a suitable soft computing modeling approach. In future studies, predictions of flows should also be carried out using input parameters of the hydroclimate, snow cover and evapotranspiration to check the applicability of the RM5Tree model.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Map of the Gilgit River study area [4].

**Figure 2.**(

**a**) Mean temperature (T

_{mean}), discharge (Q) and SSC at the Gilgit gauge; (

**b**) snow-covered area (SCA), mean rainfall (R

_{mean}) and mean evapotranspiration (Evap

_{mean}) for the Gilgit Basin during 1981–2010.

**Figure 3.**MLPNN model structure with N input, M hidden and 1 output neurons [74].

**Figure 7.**Schematic diagram of a radial basis function transformation (

**K**) for $\mathit{C}$ = 0 and $\epsilon $ = 0.5.

**Figure 8.**Schematic diagram of a radial basis RM5 tree model [74].

**Figure 11.**Scatter plots of the observed and predicted SSYs that were found using the ANN, MARS, SVR, M5Tree, RM5Tree, RSM and SRC models.

**Figure 12.**Time series plots of the observed and predicted SSYs that were found using the ANN, MARS, SVR, M5Tree, RM5Tree, RSM and SRC models.

**Figure 13.**Time series plots of the best performance measures for the predictions of SSYs during high and low flow periods that were found using the ANN, MARS, SVR, M5Tree, RM5Tree, RSM and SRC models in predictions of sediment yields for the Gilgit Rive basin.

**Table 3.**Statistical measurements for the accuracy of the temperature index snow model’s results that predicted snowmelt and snow fractions during the calibration (2000–2007) and validation (2008) periods.

k_{snow} = 4.2 mm/Day/°C | ||
---|---|---|

Calibration Period (2000–2007) | Validation Period (2008–2010) | |

R^{2} | 0.90 | 0.90 |

MAPE | 0.12 | 0.10 |

RMSE | 0.15 | 0.15 |

**Table 4.**Training and testing statistics of the ANN algorithm using various input combinations for the Gilgit River basin.

Scenarios | Model Inputs | R^{2} | RMSE | MAPE (%) | |||
---|---|---|---|---|---|---|---|

Training | Testing | Training | Testing | Training | Testing | ||

S_{1} | Q_{t}, Q_{t−1} − Q_{t−4} | 0.86 | 0.62 | 0.40 | 0.61 | 9.89 | 12.90 |

S_{2} | SCA, _{t}SCA, _{t−2}Q_{t} | 0.86 | 0.67 | 0.40 | 0.54 | 9.94 | 12.45 |

S_{3} | SCA_{t}, SCA_{t−4}, Q_{t}, R_{t−1} | 0.86 | 0.64 | 0.40 | 0.58 | 9.83 | 12.74 |

S_{4} | SCA_{t}, SCA_{t−4}, Q_{t}, Evap_{t−1}, T_{t−1} | 0.85 | 0.64 | 0.40 | 0.57 | 9.93 | 13.17 |

S_{5} | SCA_{t}, Q_{t}, Q_{t−1}, T_{t−1}, Evap_{t−1} | 0.86 | 0.64 | 0.40 | 0.60 | 9.68 | 14.21 |

S_{6} | T_{t} − T_{t−4} | 0.81 | 0.60 | 0.46 | 0.61 | 11.49 | 14.14 |

S_{7} | SCA_{t}, Evap_{t−1}, Q_{t}, R_{t−1}, T_{t} | 0.86 | 0.64 | 0.40 | 0.60 | 13.17 | 9.83 |

S_{8} | SCA_{t}, Q_{t}, Evap_{t−1}, R_{t−1}, T_{t−1} | 0.86 | 0.65 | 0.40 | 0.57 | 9.80 | 12.71 |

**Table 5.**Training and testing statistics of the MARS algorithm using various input combinations for the Gilgit River basin.

Scenarios | Model Inputs | R^{2} | RMSE | MAPE (%) | |||
---|---|---|---|---|---|---|---|

Training | Testing | Training | Testing | Training | Testing | ||

S_{1} | Q_{t}, Q_{t−1} − Q_{t−4} | 0.84 | 0.64 | 0.42 | 0.58 | 10.69 | 12.97 |

S_{2} | SCA_{t}, SCA_{t−2}, Q_{t} | 0.82 | 0.67 | 0.44 | 0.54 | 10.65 | 12.03 |

S_{3} | SCA, _{t}SCA, _{t−4}Q, _{t}R_{t−1} | 0.83 | 0.68 | 0.44 | 0.53 | 10.79 | 11.71 |

S_{4} | SCA_{t}, SCA_{t−4}, Q_{t}, Evap_{t−1}, T_{t−1} | 0.85 | 0.64 | 0.40 | 0.55 | 10.03 | 12.21 |

S_{5} | SCA_{t}, Q_{t}, Q_{t−1}, T_{t−1}, Evap_{t−1} | 0.84 | 0.66 | 0.42 | 0.55 | 10.38 | 12.24 |

S_{6} | T_{t} − T_{t−4} | 0.77 | 0.56 | 0.51 | 0.60 | 12.64 | 13.74 |

S_{7} | SCA_{t}, Evap_{t−1}, Q_{t}, R_{t−1}, T_{t} | 0.86 | 0.64 | 0.40 | 0.57 | 9.91 | 12.49 |

S_{8} | SCA_{t}, Q_{t}, Evap_{t−1}, R_{t−1}, T_{t−1} | 0.84 | 0.65 | 0.42 | 0.54 | 10.33 | 12.04 |

**Table 6.**Training and testing statistics of the SVR algorithm using various input combinations for the Gilgit River basin.

Scenarios | Model Inputs | R^{2} | RMSE | MAPE (%) | |||
---|---|---|---|---|---|---|---|

Training | Testing | Training | Testing | Training | Testing | ||

S_{1} | Q_{t}, Q_{t−1} − Q_{t−4} | 0.82 | 0.69 | 0.45 | 0.53 | 10.79 | 11.94 |

S_{2} | SCA_{t}, SCA_{t−2}, Q_{t} | 0.86 | 0.69 | 0.40 | 0.57 | 9.37 | 11.80 |

S_{3} | SCA_{t}, SCA_{t−4}, Q_{t}, R_{t−1} | 0.83 | 0.69 | 0.43 | 0.51 | 10.35 | 11.30 |

S_{4} | SCA, _{t}SCA, _{t−4}Q, _{t}Evap, _{t−1}T_{t−1} | 0.84 | 0.70 | 0.42 | 0.51 | 9.81 | 10.92 |

S_{5} | SCA_{t}, Q_{t}, Q_{t−1}, T_{t−1}, Evap_{t−1} | 0.85 | 0.62 | 0.41 | 0.60 | 9.76 | 12.38 |

S_{6} | T_{t} − T_{t-4} | 0.84 | 0.53 | 0.42 | 0.67 | 8.93 | 13.54 |

S_{7} | SCA_{t}, Evap_{t−1}, Q_{t}, R_{t−1}, T_{t} | 0.85 | 0.69 | 0.41 | 0.55 | 9.81 | 11.93 |

S_{8} | SCA_{t}, Q_{t}, Evap_{t−1}, R_{t−1}, T_{t−1} | 0.85 | 0.68 | 0.41 | 0.53 | 9.72 | 11.16 |

**Table 7.**Training and testing statistics of the M5Tree algorithm using various input combinations for the Gilgit River basin.

Scenarios | Model Inputs | R^{2} | RMSE | MAPE (%) | |||
---|---|---|---|---|---|---|---|

Training | Testing | Training | Testing | Training | Testing | ||

S_{1} | Q_{t}, Q_{t−1} − Q_{t−4} | 0.94 | 0.62 | 0.25 | 0.64 | 5.02 | 15.13 |

S_{2} | SCA, _{t}SCA, _{t−2}Q_{t} | 0.95 | 0.63 | 0.24 | 0.59 | 4.71 | 14.07 |

S_{3} | SCA_{t}, SCA_{t−4}, Q_{t}, R_{t−1} | 0.95 | 0.52 | 0.24 | 0.72 | 5.08 | 16.06 |

S_{4} | SCA_{t}, SCA_{t−4}, Q_{t}, Evap_{t−1}, T_{t−1} | 0.95 | 0.56 | 0.23 | 0.65 | 5.11 | 15.64 |

S_{5} | SCA_{t}, Q_{t}, Q_{t−1}, T_{t−1}, Evap_{t−1} | 0.96 | 0.59 | 0.21 | 0.63 | 4.66 | 15.14 |

S_{6} | T_{t} − T_{t−4} | 0.96 | 0.50 | 0.21 | 0.72 | 4.73 | 17.16 |

S_{7} | SCA_{t}, Evap_{t−1}, Q_{t}, R_{t−1}, T_{t} | 0.95 | 0.57 | 0.23 | 0.67 | 4.90 | 16.36 |

S_{8} | SCA_{t}, Q_{t}, Evap_{t−1}, R_{t−1}, T_{t−1} | 0.95 | 0.59 | 0.22 | 0.65 | 4.81 | 15.08 |

**Table 8.**Training and testing statistics of the RM5Tree algorithm using various input combinations for the Gilgit River basin.

Scenarios | Model Inputs | R^{2} | RMSE | MAPE (%) | |||
---|---|---|---|---|---|---|---|

Training | Testing | Training | Testing | Training | Testing | ||

S_{1} | Q_{t}, Q_{t−1} − Q_{t−4} | 0.81 | 0.71 | 0.46 | 0.53 | 11.08 | 11.85 |

S_{2} | SCA_{t}, SCA_{t−2}, Q_{t} | 0.83 | 0.70 | 0.44 | 0.52 | 10.73 | 11.70 |

S_{3} | SCA_{t}, SCA_{t−4}, Q_{t}, R_{t−1} | 0.81 | 0.70 | 0.47 | 0.52 | 11.47 | 12.00 |

S_{4} | SCA_{t}, SCA_{t−4}, Q_{t}, Evap_{t−1}, T_{t−1} | 0.83 | 0.71 | 0.44 | 0.51 | 10.75 | 11.76 |

S_{5} | SCA_{t}, Q_{t}, Q_{t−1}, T_{t−1}, Evap_{t−1} | 0.82 | 0.72 | 0.44 | 0.52 | 10.69 | 12.03 |

S_{6} | T_{t} − T_{t−4} | 0.76 | 0.60 | 0.51 | 0.58 | 12.92 | 13.67 |

S_{7} | SCA_{t}, Evap_{t−1}, Q_{t}, R_{t−1}, T_{t} | 0.83 | 0.71 | 0.44 | 0.54 | 10.66 | 12.36 |

S_{8} | SCA, _{t}Q, _{t}Evap, _{t−1}R, _{t−1}T_{t−1} | 0.83 | 0.72 | 0.44 | 0.51 | 10.76 | 11.99 |

**Table 9.**Training and testing statistics of the RSM algorithm using various input combinations for the Gilgit River basin.

Scenarios | Model Inputs | R^{2} | RMSE | MAPE (%) | |||
---|---|---|---|---|---|---|---|

Training | Testing | Training | Testing | Training | Testing | ||

S_{1} | Q_{t}, Q_{t−1} − Q_{t−4} | 0.82 | 0.66 | 0.45 | 0.59 | 10.90 | 13.07 |

S_{2} | SCA_{t}, SCA_{t−2}, Q_{t} | 0.83 | 0.66 | 0.43 | 0.55 | 10.56 | 12.36 |

S_{3} | SCA_{t}, SCA_{t−4}, Q_{t}, R_{t−1}, | 0.83 | 0.65 | 0.44 | 0.55 | 10.68 | 12.10 |

S_{4} | SCA_{t}, SCA_{t−4}, Q_{t}, Evap_{t−1}, T_{t−1} | 0.83 | 0.66 | 0.43 | 0.54 | 10.46 | 12.22 |

S_{5} | SCA_{t}, Q_{t}, Q_{t−1}, T_{t−1}, Evap_{t−1} | 0.84 | 0.67 | 0.42 | 0.53 | 10.46 | 11.75 |

S_{6} | T_{t} − T_{t−4} | 0.77 | 0.58 | 0.50 | 0.60 | 12.54 | 14.08 |

S_{7} | SCA_{t}, Evap_{t−1}, Q_{t}, R_{t−1}, T_{t} | 0.84 | 0.68 | 0.42 | 0.53 | 10.38 | 12.00 |

S_{8} | SCA, _{t}Q, _{t}Evap, _{t−1}R, _{t−1}T_{t−1} | 0.84 | 0.68 | 0.42 | 0.51 | 10.42 | 11.72 |

**Table 10.**Performance accuracy comparison between the SRC, ANN, MARS, SVR, M5Tree, RM5Tree, RSM and SVR model results in the predictions of sediment yields in the Gilgit River basin.

Models | Results for Training Period | Results for Testing Period | ||||
---|---|---|---|---|---|---|

R^{2} | RMSE | MAPE (%) | R^{2} | RMSE | MAPE (%) | |

SRC | 0.80 | 0.49 | 13.29 | 0.71 | 0.60 | 13.82 |

ANN | 0.86 | 0.40 | 9.94 | 0.67 | 0.54 | 12.45 |

MARS | 0.83 | 0.44 | 10.79 | 0.68 | 0.53 | 11.71 |

SVR | 0.84 | 0.42 | 9.81 | 0.70 | 0.51 | 10.92 |

M5Tree | 0.95 | 0.24 | 4.71 | 0.63 | 0.59 | 14.07 |

RM5Tree | 0.83 | 0.44 | 10.76 | 0.72 | 0.51 | 11.99 |

RSM | 0.84 | 0.42 | 10.42 | 0.68 | 0.51 | 11.72 |

**Table 11.**Comparison of the ANN, MARS, SVR, M5Tree, RM5Tree, RSM and SRC models’ absolute sediment fluxes and relative accuracies (%) for the peak estimations of the SSY for the Gilgit gauging station.

Year | Peaks > 3200 [tons/Day] | ANN [tons/Day] | MARS [tons/Day] | SVR [tons/Day] | M5Tree [tons/Day] | RM5Tree [tons/Day] | RSM [tons/Day] | SRC [tons/Day] |
---|---|---|---|---|---|---|---|---|

1983 | 3901 | 4092 (95.09) | 3603 (89.81) | 4376 (93.07) | 3432 (87.99) | 3861 (98.99) | 4163 (93.28) | 5008 (71.62) |

1984 | 4955 | 3945 (79.61) | 3960 (79.93) | 2937 (74.46) | 4410 (89.01) | 3135 (63.28) | 3428 (69.19) | 4704 (94.93) |

1991 | 3256 | 3013 (92.52) | 2917 (89.57) | 2916 (96.80) | 3140 (96.43) | 3024 (92.87) | 3022 (92.80) | 4806 (52.40) |

2003 | 4057 | 3085 (76.03) | 2741 (67.57) | 2516 (81.56) | 3332 (82.12) | 2904 (71.57) | 2568 (63.29) | 4732 (83.38) |

2005 | 16,898 | 10,113 (59.85) | 10,585 (62.4) | 13,794 (63.60) | 7678 (45.44) | 17,961 (93.71) | 9184 (54.35) | 35,507 (10.12) |

Mean(Relative Accuracy %) | 6613 | 4849(80.62) | 4741(77.86) | 5308(81.90) | 4398(80.20) | 6177(84.10) | 4473(74.58) | 10,951(62.49) |

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Keshtegar, B.; Piri, J.; Hussan, W.U.; Ikram, K.; Yaseen, M.; Kisi, O.; Adnan, R.M.; Adnan, M.; Waseem, M.
Prediction of Sediment Yields Using a Data-Driven Radial M5 Tree Model. *Water* **2023**, *15*, 1437.
https://doi.org/10.3390/w15071437

**AMA Style**

Keshtegar B, Piri J, Hussan WU, Ikram K, Yaseen M, Kisi O, Adnan RM, Adnan M, Waseem M.
Prediction of Sediment Yields Using a Data-Driven Radial M5 Tree Model. *Water*. 2023; 15(7):1437.
https://doi.org/10.3390/w15071437

**Chicago/Turabian Style**

Keshtegar, Behrooz, Jamshid Piri, Waqas Ul Hussan, Kamran Ikram, Muhammad Yaseen, Ozgur Kisi, Rana Muhammad Adnan, Muhammad Adnan, and Muhammad Waseem.
2023. "Prediction of Sediment Yields Using a Data-Driven Radial M5 Tree Model" *Water* 15, no. 7: 1437.
https://doi.org/10.3390/w15071437