# Driving Factors and Trend Prediction for Annual Sediment Transport in the Upper and Middle Reaches of the Yellow River from 2001 to 2020

^{*}

## Abstract

**:**

## 1. Introduction

^{−1}during the next 10, 20, and 50 years, respectively. According to a large number of existing research results, it could be argued that the process of sediment transport in the YRB had highly nonlinear characteristics. However, commonly used methods only offer a qualitative understanding of the changes in sediment transport, and do not yet provide quantitative predictions [15]. Yu et al. [16] used the Soil and Water Assessment Tool (SWAT) and the Coupled Model Intercomparison Project Phase 5 (CMIP5) to predict the changes in the runoff and sediment transport at the Tangnaihai gauge station. In addition, Gao et al. [17] used gray system theory to predict the long-term trend in the runoff and sediment transport in the UMRYR. They discovered that the predicted values for the runoff and sediment transport were greater than the actual values, indicating that the long-term forecasting of runoff and sediment transport was still at the development and exploration stage. In these studies, the effect of changes in the climatic factors and human activities on the sediment transport in the Yellow River was confirmed, but the driving factors considered were relatively simple. At the same time, since the prediction models of the sediment transport in the UMRYR were too complex and their prediction results were not sufficiently accurate, it was not possible to apply these models widely.

## 2. Study Area

^{2}, originates in the Bayan Har Mountains, and eventually, flows into the Bohai Sea. The UMRYR account for 91% of the total area of the YRB. Our study area (94–114 E, 32–42 N) covers five main gauge stations along the Yellow River: Tangnahai, Lanzhou, Toudaoguai, Longmen, and Tongguan. The elevation is between 258 and 6254 m (Figure 1). The characteristics of the UMRYR include unconsolidated soil, broken terrain, a low vegetation coverage rate, and an uneven distribution of precipitation [15,18]. The upper reaches have an area of 386,000 km

^{2}, accounting for 51.3% of the YRB, located in arid and semiarid areas, with average temperatures ranging from 1 to 6 °C, and average annual precipitation of 105–756 mm. The middle reaches are located in semi-humid and semiarid monsoon climate regions, with average annual precipitation of 320–836 mm, and average temperatures between 7 and 11 °C. The area of the middle reaches accounts for 45.7% of the total area of the YRB, but the sediment transport in this area accounts for 92% of the YRB total. The area is characterized by large volumes of coarse sand, and it is one of the most frequent sites of rainstorms in China. In the UMRYR, the spatial distribution of precipitation is extremely uneven, decreasing from southeast to northwest.

## 3. Materials and Methods

#### 3.1. Data

#### 3.2. Research Methods

#### 3.2.1. Mann–Kendall Mutational Test

_{1}, x

_{2}, …, x

_{n}) existed. The specific method is as follows. S

_{k}is defined as Equation (1):

#### 3.2.2. Driving Force Analysis Method

- (1)
- Spearman correlation analysis

_{s}is computed as follows:

_{i}and y

_{i}are converted into ranks rgx

_{i}and rgy

_{i}, respectively, which are the ascending orders of x

_{i}and y

_{i}. The $cov({rgx}_{i},{rgy}_{i})$ is the covariance of the rank variables ${\sigma}_{{rgx}_{i}}$, and ${\sigma}_{{rgy}_{i}}$ are the standard deviations of the rank variables. However, a multiple regression model that involves more than one driving factor often contains the problem of multicollinearity. There are several ways to determine whether there is a multicollinearity:

- (a)
- The value of the correlation (the Spearman correlation between the driving factors). A high correlation value between the two driving factors shows that there is a linear relationship, and indicates that there may be a problem of collinearity [22].
- (b)
- The value of the variance inflation factor (VIF) is used as a criterion to detect the presence of multicollinearity in a multiple linear regression. When the value of the VIF is greater than 3, there may be a problem of multicollinearity [23].

- (2)
- Linear model

- (3)
- Nonlinear model

#### 3.2.3. Accuracy Validation and Prediction of Models

- (1)
- Model accuracy validation

- (2)
- Prediction of AST

## 4. Results

#### 4.1. Analysis of Variation Trend and Mutation of the AST

^{−1}(p > 0.05), 0.371 Mt yr

^{−1}(p < 0.05), and 3.423 Mt yr

^{−1}(p < 0.05) at the Tangnaihai, Lanzhou, and Toudaoguai gauge stations, respectively. However, the AST in the middle reaches of the Yellow River (MRYR), from the Toudaoguai to the Tongguan gauge station, showed a downward trend (Figure 3d,e). The annual change rates of the AST were 3.565 Mt yr

^{−1}(p > 0.05), and 12.771 Mt yr

^{−1}(p < 0.05) at the Longmen and Tongguan gauge stations, respectively.

^{2}= 73.84, p < 0.001). Multiple comparisons showed that there was a significant difference between the Tangnaihai and Toudaoguai gauge stations in the URYR (p = 0.002). Similarly, there was a significant difference between the Toudaoguai and Tongguan gauge stations in the MRYR (p = 0.001). However, after the first difference, there was no difference in the ΔAST at each gauge station (Figure 4b, χ

^{2}= 1.425, p < 0.840). The ΔAST data for the five gauge stations met the requirement of sample independence. The linear trend in the AST data was removed by the first-order difference.

#### 4.2. Driving Force Analysis

#### 4.2.1. Spearman Correlation Analysis

#### 4.2.2. Multicollinearity Test

#### 4.2.3. Stepwise Regression

^{2}= 0.445 (Table 3).

#### 4.2.4. RFM Regression

^{2}of 0.515, which was greater than that of the stepwise regression (R

^{2}= 0.445). Based on the driving force analysis of the ΔAST in the UMRYR, the following five variables were selected for further modeling and prediction: ΔNDVI, ΔOLS, ΔNPP, ΔSP, and ΔSM (100–289).

#### 4.3. Modeling and Prediction

#### 4.3.1. Cross–Validation and Selection of the Model

^{2}, the mean absolute error (MAE), and the root mean squared error (RMSE) were used. In Table 4, for the RFM prediction results, the evaluation metrics R

^{2}, RMSE, and MAE were 0.545, 0.485, and 0.322, respectively; for the MLR, the evaluation metrics R

^{2}, RMSE, and MAE, were 0.340, 1.128, and 0.875, respectively.

^{2}value indicates a better fit. Furthermore, lower values for the RMSE and MAE indicate a better fit and higher prediction accuracy. In this case, the RFM had the higher R

^{2}and the lower RMSE and MAE values, indicating that it had the better fit and higher prediction accuracy of the two models. Therefore, we used the RFM for the final modeling and prediction of the AST, while the simplest ARIMA model was used as a control model (CK) for the RFM model.

#### 4.3.2. Prediction of AST

^{2}results for the RFM were higher for the five gauge stations than the R

^{2}results for the CK model. Furthermore, the RFM’s average interpretation rate of 0.777 was higher than that for the CK model (0.318) (Figure 8f). This demonstrates that the prediction result for the RFM for the AST was better than that of the CK model. In addition, for the RFM, the goodness-of-fit order of the five gauge stations, from high to low, was: Lanzhou > Tangnaihai > Longmen > Toudaoguai > Tongguan. As a result, the nonlinear machine learning RFM was used to forecast the AST for the following 3 years. Table 6 uses the RFM to predict the specific values of the AST for the five gauge stations from 2021 to 2023. When the predictions were compared with the current measured AST for 2021, the predicted values at the Lanzhou, Longmen, and Tongguan gauge stations were close to the measured AST, and the prediction results were relatively accurate.

## 5. Discussion

#### 5.1. Changes in AST in the UMRYR

^{−1}, the average AST reduction in the terraces in the main sand-producing areas in the MRYR was 422 MT yr

^{−1}, and the average AST retention volume of the reservoirs in the MRYR was 98 MT yr

^{−1}[30]. This proves that the implementation of soil and water conservation projects can indeed effectively reduce AST in the YRB. Therefore, in this study, it was considered that the possible reason for the inconsistent variation in the AST in the UMRYR was that there were more soil and water conservation projects in the MRYR. In addition, more mutations occurred in the AST in the URYR than in the MRYR (Figure 5). This study considered that a possible reason for this was that the mountainous terrain in the URYR is relatively fragile and prone to flash flood disasters, resulting in the occurrence of more mutations in the AST [6]. In contrast, the MRYR area is relatively gentle, with stable riverbeds and relatively stable changes in the AST.

#### 5.2. Analysis of Driving Force of ΔAST and Modeling

^{2}(0.515) (Figure 7) was better than the R

^{2}(0.445) (Table 3) for the linear driving–force analysis. At the same time, after the 5–fold cross–validation of the RFM and MLR prediction models (Table 4), it was also found that the nonlinear driving-force analysis of the ΔAST data was a better method.

#### 5.3. Limitations and Future Work

^{2}) for the ΔAST prediction model was relatively low, at 0.545 (Table 4). To address this limitation, future research should aim to incorporate these human-induced factors into the analysis in order to enhance the interpretability of the model.

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**Flowchart showing the analysis of the factors driving ΔAST in the UMRYR and the trend prediction of AST. The abbreviations, AST and ΔAST, denote the annual sediment transport and amount of the interannual variation in the annual sediment transport, respectively. Table 1 shows the short meanings of the variables. The abbreviations, MLR and RFM, denote the multiple linear regression and random forest model, respectively.

**Figure 3.**Variation trend in AST and ΔAST in the UMRYR, showing the gauge stations in the URYR (

**a**–

**c**) and the gauge stations in the MRYR (

**d**,

**e**), and the equation for the variation trend in the AST and ΔAST in the UMRYR (

**f**). The abbreviations, AST and ΔAST, denote the annual sediment transport and the amount of interannual variation in the annual sediment transport, respectively. The abbreviations, UMRYR and MRYR, denote the upper and the middle reaches of the Yellow River, respectively.

**Figure 4.**Friedman test of AST (

**a**) and ΔAST (

**b**) at the five gauge stations. The abbreviations, AST and ΔAST, denote the annual sediment transport and the amount of interannual variation in the annual sediment transport, respectively. The red line in (

**a**) is the trend line for the annual mean sediment transport (2001–2020) at each gauge station. The symbol ‘***’ indicates that there is a significant difference between the two gauge stations.

**Figure 5.**Mann–Kendall mutation test of the AST: URYR (

**a**–

**c**), MRYR (

**d**,

**e**), and a graph showing the cumulative amount of AST for the five gauge stations (

**f**). The abbreviation AST denotes the annual sediment transport. The abbreviations, URYR and MRYR, denote the upper and the middle reaches of the Yellow River, respectively.

**Figure 6.**Spearman correlation analysis of ΔAST in the UMRYR. The prefix ‘Δ’ indicates the amount of interannual variation in the data. In particular, the symbol ‘*’ indicates that there is a significant relationship between the two variables (p < 0.1). Refer to Table 1 for the abbreviated meanings of the variables.

**Figure 7.**Ranking of the driving factors by importance according to the RFM results. The definitions of the abbreviated variables can be found in Table 1. The symbols ‘**’ and ‘*’ indicate that the factors are very significant (p < 0.01) and significant (p < 0.05), respectively. The RFM is the random forest model.

**Figure 8.**(

**a**–

**e**) The prediction of AST at the five gauge stations in the UMRYR using the RFM and ARIMA models, and a comparison with the measured AST data. The left side of the black dotted line represents the forecast for the known years (2001 to 2020), while the right side represents the forecast for the unknown years (2021 to 2023). (

**f**) The prediction accuracy comparison for the five gauge stations using the RFM and ARIMA models.

**Figure 9.**Twenty-year comparison and trend analysis of the reservoirs in the UMRYR for 2000–2018. The URYR and MRYR indicate the upper reaches of the Yellow River and the middle reaches of the Yellow River, respectively.

Value (Abbreviation) | Unit | Data Source | |
---|---|---|---|

1 | Annual sediment transport (AST) | Mt yr^{−1} | The River Sediment Bulletin of China (2001–2020) |

2 | Normalized difference vegetation index (NDVI) | / | MOD13Q1 V6 |

3 | Enhanced vegetation index (EVI) | / | MOD13Q1 V6 |

4 | Normalized difference water index (NDWI) | / | Landsat 5 and 8 |

5 | Net primary production (NPP) | Kg C/m^{2} | Landsat Net Primary Production CONUS |

6 | Population (POP) | individuals | WorldPop Global Project Population Data |

7 | Soil moisture 0–7 cm (SM(0–7)) | m^{3}/m^{3} | ERA5-Land Monthly Averaged—ECMWF Climate Reanalysis |

8 | Soil moisture 7–28 cm (SM(7–28)) | m^{3}/m^{3} | ERA5-Land Monthly Averaged—ECMWF Climate Reanalysis |

9 | Soil moisture 28–100 cm (SM(28–100)) | m^{3}/m^{3} | ERA5-Land Monthly Averaged—ECMWF Climate Reanalysis |

10 | Soil moisture 100–289 cm (SM(100–289)) | m^{3}/m^{3} | ERA5-Land Monthly Averaged—ECMWF Climate Reanalysis |

11 | Water body (WB) | % | MCD12Q1.006 |

12 | Forest (FO) | % | MCD12Q1.006 |

13 | Summer precipitation (SP) | mm | CHIRPS Daily |

14 | Night light (OLS) | nanoWatts/cm^{2}/sr | DMSP OLS |

15 | Shrubland (SL) | % | MCD12Q1.006 |

16 | Farmland (FL) | % | MCD12Q1.006 |

**Table 2.**Multicollinearity diagnosis of the driving factors. Dependent variable: ΔAST. The definitions of the abbreviated variables can be found in Table 1.

Model | Unstandardized Coefficients | Standardized Coefficients | t | p | Collinearity Statistics | ||
---|---|---|---|---|---|---|---|

B | SE | Beta | Tolerance | VIF | |||

(Intercept) | −0.058 | 0.107 | −0.538 | 0.592 | |||

ΔNDVI | 7.426 | 13.316 | 0.220 | 0.558 | 0.579 | 0.044 | 22.857 |

ΔEVI | 5.246 | 13.101 | 0.151 | 0.400 | 0.690 | 0.048 | 20.733 |

ΔNDWI | 0.533 | 1.137 | 0.043 | 0.469 | 0.641 | 0.827 | 1.210 |

ΔNPP | −2.367 | 6.609 | −0.054 | −0.358 | 0.721 | 0.299 | 3.350 |

ΔPOP | 0.000 | 0.000 | −0.158 | −1.359 | 0.178 | 0.503 | 1.987 |

ΔSM (0–7) | 4.199 | 26.598 | 0.046 | 0.158 | 0.875 | 0.080 | 12.430 |

ΔSM (7–28) | 9.073 | 31.783 | 0.080 | 0.285 | 0.776 | 0.086 | 11.564 |

ΔSM (28–100) | 1.466 | 3.648 | 0.035 | 0.402 | 0.689 | 0.876 | 1.142 |

ΔSM (100–289) | −55.202 | 16.815 | −0.324 | −3.283 | 0.002 | 0.700 | 1.429 |

ΔWB | −96.096 | 128.584 | −0.167 | −0.747 | 0.457 | 0.137 | 7.281 |

ΔFO | 70.096 | 192.925 | 0.059 | 0.363 | 0.717 | 0.262 | 3.814 |

ΔFL | 50.005 | 150.836 | 0.080 | 0.332 | 0.741 | 0.118 | 8.475 |

ΔSP | 0.004 | 0.003 | 0.214 | 1.578 | 0.119 | 0.370 | 2.703 |

ΔOLS | 0.528 | 0.168 | 0.304 | 3.141 | 0.002 | 0.727 | 1.375 |

ΔSL | −16.074 | 232.564 | −0.008 | −0.069 | 0.945 | 0.553 | 1.810 |

**Table 3.**Stepwise regression analysis. Dependent variable: ΔAST. The definitions of the abbreviated variables can be found in Table 1.

Unstandardized Coefficients | Standardized Coefficients | t | p | Collinearity Statistics | |||
---|---|---|---|---|---|---|---|

B | SE | Beta | Tolerance | VIF | |||

(Intercept) | −0.161 | 0.076 | −2.127 | 0.036 | |||

ΔNDVI | 12.388 | 3.000 | 0.368 | 4.129 | 0.000 | 0.812 | 1.232 |

ΔOLS | 0.481 | 0.144 | 0.277 | 3.332 | 0.001 | 0.929 | 1.076 |

ΔSP | 0.005 | 0.002 | 0.247 | 2.854 | 0.005 | 0.858 | 1.166 |

ΔSM(100–289 cm) | −44.362 | 14.160 | −0.261 | −3.133 | 0.002 | 0.930 | 1.076 |

ΔWB | −100.358 | 47.795 | −0.174 | −2.100 | 0.039 | 0.936 | 1.068 |

Multiple R-squared: 0.445 | Adjusted R-squared: 0.407 | ||||||

F-statistic: 11.75 | p-value: 1.236 × 10^{−9} |

**Table 4.**Comparison of the model prediction accuracies. The RMSE and MAE indicate the root mean squared error and mean absolute error. The RFM and MLR indicate the random forest model and multiple linear regression model, respectively.

Models | R^{2} | RMSE | MAE |
---|---|---|---|

RFM Prediction Model | 0.545 | 0.485 | 0.332 |

MLR Prediction Model | 0.340 | 1.128 | 0.875 |

**Table 5.**Predicted values for the five driving factors (2021–2023). The definitions of the abbreviated variables can be found in Table 1. The prefix ‘Δ’ indicates the amount of interannual variation in the data.

Gauge Stations | Year | ΔNDVI | ΔOLS | ΔNPP | ΔSP | ΔSM (100–289) |
---|---|---|---|---|---|---|

Tangnaihai | 2021 | −0.008469776 | 0.047935561 | 0.00049489 | −28.92988857 | −0.003606281 |

2022 | 0.003678309 | 0.036382925 | 0.00022413 | −7.465995264 | 0.000653275 | |

2023 | 0.003789897 | 0.03863334 | −0.00004662 | −8.100876928 | 0.000702471 | |

Lanzhou | 2021 | −0.013486897 | 0.065244886 | −0.0012948 | −34.85416005 | −0.004571964 |

2022 | 0.004905457 | 0.006091741 | −0.0016423 | −9.49682083 | −0.000427942 | |

2023 | 0.004750819 | 0.005208895 | −0.0019899 | −36.16739651 | −0.000340503 | |

Toudaoguai | 2021 | −0.02532223 | 0.079224243 | −0.0022115 | −49.84926486 | −0.002503088 |

2022 | −0.0021852 | −0.107179825 | −0.0027162 | −14.74115543 | −0.001866121 | |

2023 | −0.00266316 | −0.114141706 | −0.0032208 | −15.27368132 | −0.001730933 | |

Longmen | 2021 | −0.03150929 | 0.074433277 | −0.0026485 | −57.20250634 | −0.002363319 |

2022 | 0.024095419 | −0.149968857 | −0.0033447 | −18.36618505 | 0.00259626 | |

2023 | −0.02737186 | −0.159664341 | −0.0040409 | −18.97639053 | 0.004800315 | |

Tongguan | 2021 | −0.027818798 | 0.091943714 | −0.0030094 | −33.88406194 | 0.003120987 |

2022 | −0.003459783 | −0.161176695 | −0.003814 | −9.50323058 | 0.000239401 | |

2023 | −0.00427008 | −0.175411692 | −0.0046185 | −9.723017661 | 0.000325405 |

**Table 6.**AST data for the five gauge stations for the next 3 years, predicted by the RFM. The abbreviation AST denotes the annual sediment transport and RFM denotes the random forest model.

Year | Tangnaihai (Mt yr^{−1}) | Lanzhou (Mt yr^{−1}) | Toudaoguai (Mt yr^{−1}) | Longmen (Mt yr^{−1}) | Tongguan (Mt yr^{−1}) |
---|---|---|---|---|---|

2021 | 23.249 | 3.358 | 162.733 | 52.650 | 165.658 |

2022 | 23.912 | 1.409 | 167.035 | 21.293 | 224.810 |

2023 | 24.575 | 16.460 | 170.318 | 156.870 | 220.370 |

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**MDPI and ACS Style**

Wu, J.; Tian, J.; Liu, J.; Feng, X.; Wang, Y.; Ya, Q.; Li, Z.
Driving Factors and Trend Prediction for Annual Sediment Transport in the Upper and Middle Reaches of the Yellow River from 2001 to 2020. *Water* **2023**, *15*, 1107.
https://doi.org/10.3390/w15061107

**AMA Style**

Wu J, Tian J, Liu J, Feng X, Wang Y, Ya Q, Li Z.
Driving Factors and Trend Prediction for Annual Sediment Transport in the Upper and Middle Reaches of the Yellow River from 2001 to 2020. *Water*. 2023; 15(6):1107.
https://doi.org/10.3390/w15061107

**Chicago/Turabian Style**

Wu, Jingjing, Jia Tian, Jie Liu, Xuejuan Feng, Yingxuan Wang, Qian Ya, and Zishuo Li.
2023. "Driving Factors and Trend Prediction for Annual Sediment Transport in the Upper and Middle Reaches of the Yellow River from 2001 to 2020" *Water* 15, no. 6: 1107.
https://doi.org/10.3390/w15061107