# Evolution Characteristics of Long Time Series of Secondary Perched River in Typical Reaches of the Lower Yellow River

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

^{3}/s before the flood in 2002 to 6650 m

^{3}/s after the flood in 2022. Floodwaters generally do not roam the beach, because the beach siltation is comparably small and the development of the secondary perched river has been curbed. However, with the continuous accumulation of the time of use of Xiaolangdi, the adequate reservoir capacity gradually declined, and the problem of insufficient follow-up power was highlighted [11]. The secondary perched river has been formed, and with the increased frequency of extreme weather around the globe, the existing secondary perched river is still a major threat to flood control.

## 2. Materials and Methods

#### 2.1. Study Area

^{2}, accounting for 84% of the river area, most of which is located in the river section above Taochengpu, with about 2770 km

^{2}accounting for 78% of the total area. In the case of flooding, the beach can be used as a channel for flooding and sediment transfer, but at the same time, it is the habitat of nearly 3 million residents, so the problem of human–water–land conflict is highlighted.

#### 2.2. Study Methods

#### 2.2.1. Data Sources

_{1}and H

_{2}are the elevation of the beach lip and the elevation of the beach near the levee, m; d

_{1}and d

_{2}are the distance from the start of the beach lip and the distance from the beginning of the beach near the levee, m, respectively; (H

_{1}− H

_{2}) is the difference in the elevation, m; and (d

_{1}− d

_{2}) is the width of the beach, m. Due to the change in the main channel position along the course, the width of the beach on the left and right banks varies greatly, resulting in a significant difference between the two banks of the same section of the transverse slope. In order to better represent the section of the beach’s transverse slope, take the average value of the left and right banks, and when there is no beach on one bank, the transverse slope of the other bank is the average transverse slope of the beach in the section.

#### 2.2.2. Data Processing Methods

- (1)
- Theil–Sen estimator

_{j}and x

_{i}are the sample data corresponding to time j and time i (j > i), respectively. k is the trend degree of the time series. When k > 0, the time series shows an upward trend, while k < 0 shows a downward trend.

- (2)
- Mann–Kendall test

_{k}of the normal distribution statistic can be calculated using the following equation:

_{k}is the cumulative total number when x

_{i}> x

_{j}.

_{i}is the variable of the i-th time series x. Under the assumption of random independence in the time series, the statistics are defined as the following:

_{1}= 0, Var (S

_{k}), and E (S

_{k}) are the variance and mean of the cumulative number S

_{k}, at x

_{1}, x

_{2}, ... x

_{n}are independent of each other and have the same continuous distribution; they can be calculated by the following equation:

_{k}is a sequential time series, while UB

_{k}is a reverse time series calculated using the same function, and their relationship is UF

_{k}= −UB

_{k}.

_{k}| ≤ (UF

_{k})

_{1−α/2}, then accept the null hypothesis at the significance level, which is (UF

_{k})

_{1−α/2.}The critical value of the standard normal distribution when the null hypothesis is rejected, expressed as probability α when any point in UF

_{k}exceeds the confidence interval of ±1.96, p = 0.05, a significant upward or downward trend is determined. UF

_{k}> 0 indicates a significant upward trend, while UF

_{k}< 0 indicates a significant downward trend.

- (3)
- The Pettitt test

_{i}of length n (i = 1,2,..., n), define the statistical variable as the following:

## 3. Evolution Characteristics of the Secondary Perched River from Dongbatou to Taochengpu

#### 3.1. Evolution Trend of Transverse Slope

^{2}= 0.71), and the correlation of the transverse slope and beach width is lower (R

^{2}= 0.02), which shows that the change in the elevation difference dominates the change in the transverse slope in the secondary perched river.

#### 3.2. Mutability of Transverse Slope

^{2}= 0.99). A series of mutation tests showed that the time points of the transverse slope mutations in the Dongbatou-Gaocun and Gaocun-Taochengpu reaches were 1990 and 1975, respectively.

^{3}/s (Figure 8), and the medium-regular floods like those in 1992, 1994, and 1996 could occur. The elevation difference of the Dongbatou-Gaocun section has increased greatly, and the increase is more significant than that after 1975, so the transverse slope time series of the Dongbatou-Gaocun section had undergone a sudden change in 1990 instead of 1975.

## 4. Discussion

- (1)
- The different calculation methods used for the lateral gradient. When calculating the transverse slope, it is necessary to calculate the elevation near the embankment root and the main channel. The elevation at the embankment root is generally the average elevation of the 50–100 m beach or the average river bottom elevation of the embankment river; the elevation near the main channel is selected as the elevation of the high elevation beach lip or the average river bottom elevation of the main channel. Different calculation methods can lead to significant differences in the results and also reflect different information. When calculating the average river bottom elevation of the main channel, more consideration will be given to the changes in the elevation of the main channel. However, the focus of this study is on the actual changes in the beach, so selecting the beach lip elevation can better reflect the true transverse slope of the beach.
- (2)
- The hysteresis of riverbed evolution. The hysteresis response phenomenon is a typical feature of the non-equilibrium evolution process of rivers, which is commonly present in the riverbed evolution of impact rivers. The changes in the inflow and sediment conditions of natural rivers are relatively fast, while the corresponding riverbed erosion and sedimentation deformation are slower. When the construction or operation of a reservoir changes, the conditions for the incoming water and sediment change rapidly, while the changes in erosion and sedimentation in the lower reaches of the Yellow River are slower, and the evolution of the riverbed will lag behind the changes in incoming water and sediment to varying degrees.
- (3)
- Discontinuities in the beach erosion and sedimentation. The hysteresis of the riverbed evolution considers changes in water and sediment conditions. The original balance of sediment transport in the river channel is disrupted, and the river channel will slowly undergo erosion and sedimentation deformation until the equilibrium state. However, the floodplain only receives water during the flood season, and there is no continuous water flow erosion. The continuous effect of water and sediment changes cannot be fully exerted on the floodplain, and the erosion and sedimentation of the floodplain will not continue until the equilibrium stage of sediment transport, Therefore, the riverbed evolution of the tidal flat has the characteristic of discontinuity on the basis of hysteresis.
- (4)
- The changing characteristics of the different river types are different. The width of the wandering river reaches is large, and the main channel swings frequently, but the transverse slope is small. The width of the transitional river section is relatively small, and the main channel is stable. However, a stable main channel leads to a continuous cumulative elevation of the beach lip and a significant transverse slope.

## 5. Conclusions

- (1)
- After the 2022 flood season, the transverse slope fluctuation along the wandering section of the lower Yellow River is relatively small. The maximum difference in the transverse slope is 4.99‱ and the mean transverse slope is 5.81‱. In contrast, the transverse slope of the transitional section exhibits greater fluctuations along its course, with a maximum difference of 16.57‱ and a mean transverse slope of 8.89‱. The average transverse slope in the wandering section is 5.81‱, while in the transitional section it is 8.89‱, making the latter approximately 1.53 times steeper than the former.
- (2)
- During the period of 1960–1969, the transverse slope exhibited a small magnitude and a gradual trend of change. Subsequently, from 1969 until the Xiaolangdi reservoir run, the two river sections experienced a generally increasing transverse slope. Following the operation of the Xiaolangdi reservoir, the wandering section exhibited a decreasing trend in the transverse slope, while the transition section exhibited a gentle trend of change. The relationship between the change in the elevation difference and the change in the transverse slope demonstrated a stronger correlation (R
^{2}= 0.71), whereas the correlation with the change in the shoal width was weaker (R^{2}= 0.02). - (3)
- The time series data pertaining to the alterations in the transverse slope inside the transitional part and wandering section exhibited sudden shifts in 1975 and 1990, correspondingly. The sudden change can be attributed to several factors. Firstly, it has been observed that the frequency of floods in the beach area has increased significantly since 1975. This has led to a serious silting up of the beach lip, causing an increase in the transverse slope. Additionally, the transverse slope of the transitional section has experienced a sudden change during this period. Furthermore, after 1990, there has been a sharp decrease in the flow of the bank-full discharge. This has resulted in an increased likelihood of the downstream section of the Yellow River meandering across the beach. Consequently, the transverse slope of the wandering section has rapidly increased, leading to the occurrence of sudden changes.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Typical cross-section of a secondary perched river: ① main channel; ② beach area; ③ beach lip; ④ production levee; ⑤ levee root; ⑥ secondary perched river; ⑦ primary perched river; ⑧ levee; ⑨ ground behind levee.

**Figure 5.**Evolution of Secondary Perched Rivers from 1960 to 2022: (

**a**) transverse slope, (

**b**) beach width, (

**c**) elevation difference.

**Figure 6.**Linear relationship between transverse slope variation and changes in elevation difference and beach width.

**Figure 7.**Mutation test for transverse slope time series: (

**a**,

**b**) M−K test, (

**c**) Pettitt test, (

**d**) double cumulative curve method.

Dongbatou-Gaocun | Gaocun-Taochengpu | ||
---|---|---|---|

Time Period | k | Time Period | k |

1960–1969 | −0.015 | 1960–1969 | −0.001 |

1969–1982 | 0.350 | 1969–1982 | 0.067 |

1982–1987 | 0.056 | 1982–1990 | −0.030 |

1987–1999 | −0.134 | 1990–1999 | 0.205 |

1999–2004 | 0.272 | -- | -- |

2004–2022 | 0.005 | 1999–2022 | −0.031 |

Time | Peak Discharge (m^{3}/s) | Bank-Full Discharge (m^{3}/s) | Water Amount (10^{8} m^{3}) | Sediment Amount (10^{8} t) | Average Sediment Concentration (kg/m^{3}) | Incoming Sediment Coefficient (kg·s/m^{6}) | Floodplain Coefficient | Change in Elevation Difference(m) | |
---|---|---|---|---|---|---|---|---|---|

DBT–GC | GC–TCP | ||||||||

8 July/30 November 1975 | 7580 | 4500 | 37.65 | 1.48 | 39.35 | 0.0063 | 1.68 | 0.02 | 0.44 |

8 July/30 November 1976 | 9210 | 5510 | 80.82 | 2.86 | 35.44 | 0.0049 | 1.67 | 0.11 | 0.23 |

24 September/12 October 1981 | 8060 | 5320 | 94.63 | 2.20 | 23.30 | 0.0040 | 1.52 | 0.24 | 0.33 |

30 July/28 August 1982 | 15,300 | 6000 | 61.09 | 1.99 | 32.64 | 0.0051 | 2.55 | 0.34 | 0.13 |

27 July/24 October 1992 | 6430 | 4300 | 24.87 | 4.54 | 182.63 | 0.0634 | 1.50 | 0.20 | 0.04 |

6 August/19 August 1994 | 6300 | 3700 | 30.47 | 4.64 | 152.37 | 0.0605 | 1.70 | 0.11 | 0.05 |

17 July/26 August 1996 | 7860 | 3420 | 58.92 | 5.29 | 89.82 | 0.0277 | 2.30 | 0.41 | 0.08 |

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**MDPI and ACS Style**

Yan, J.; Xu, H.; Xu, L.; Gurkalo, F.; Gao, X.
Evolution Characteristics of Long Time Series of Secondary Perched River in Typical Reaches of the Lower Yellow River. *Water* **2023**, *15*, 3674.
https://doi.org/10.3390/w15203674

**AMA Style**

Yan J, Xu H, Xu L, Gurkalo F, Gao X.
Evolution Characteristics of Long Time Series of Secondary Perched River in Typical Reaches of the Lower Yellow River. *Water*. 2023; 15(20):3674.
https://doi.org/10.3390/w15203674

**Chicago/Turabian Style**

Yan, Jun, Haifan Xu, Linjuan Xu, Filip Gurkalo, and Xiangyu Gao.
2023. "Evolution Characteristics of Long Time Series of Secondary Perched River in Typical Reaches of the Lower Yellow River" *Water* 15, no. 20: 3674.
https://doi.org/10.3390/w15203674