# Influence of Vegetation Coverage on Hydraulic Characteristics of Overland Flow

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Experimental Design

^{®}(Figure 1). The dimensions of the flume were 4.5 m × 0.3 m × 0.25 m (length × width × height). A 40-grit water sandpaper was placed on the bottom of the flume to simulate slope surface roughness and to ensure stability of the underlying surface during the test. Starting from the flume entrance, the 1-m upstream section represents a bare slope, and the 3-m middle section represents a slope covered with vegetation. A total of seven observation sections (one in the upstream of the vegetation section, five in the vegetation section, and one in the downstream) were arranged. All the observation sections were equipped with two ultrasonic water level sensors (Sinomeasure SIN-DP, Hangzhou China).

^{2}/s to 0.00167 m

^{2}/s in this test.

#### 2.2. Simulation Accuracy Evaluation Method

#### 2.2.1. Nash–Sutcliffe Efficiency

#### 2.2.2. Regression Analysis

^{2}reflects the goodness-of-fit of the regression equation, which can be used to determine the fitting quality of the regression. If its value is close to one, the fitting effect is good; otherwise, the fitting effect is poor. The corresponding equation is as follows:

#### 2.2.3. Root Mean Square Error

_{i}is the predicted value of the sample, y

_{i}is its observed value, and n is the number of samples.

#### 2.2.4. Mean Absolute Error

## 3. Results

#### 3.1. Hydraulic Parameters under Various Degrees of Vegetation Coverage

^{2}/s to 0.00167 m

^{2}/s, overland flow water depth under vegetation cover can reach depths of up to 8.11 mm, and the depth values are all higher than those without vegetation cover. As the vegetation coverage increases, the average water flow velocity slows down. On the bare slope, the flow velocity is between 0.168 and 0.447 m/s; when the degree of coverage is 9.76%, the flow velocity decreases to 0.158–0.395 m/s; and when the degree of coverage increases to 95.01%, the flow velocity can drop to 0.105–0.206 m/s. In addition, the range of Reynolds number under vegetation cover is 243.38–1460.31. It is observed that the Froude number decreases with an increase in the degree of vegetation coverage, from 1.32–2.34 (without vegetation cover) to 0.65–0.73.

#### 3.2. Influence of Vegetation Coverage on Water Path and Flow Velocity

#### 3.3. Relationship between Darcy Resistance Coefficient and Vegetation Coverage

#### 3.4. Relationship between Manning Coefficient and Vegetation Coverage

#### 3.5. Analysis of Darcy Resistance Coefficient

#### 3.5.1. Relationship between Darcy Resistance Coefficient and Reynolds Number

#### 3.5.2. Relationship between Darcy Resistance Coefficient and Submergence Degree

#### 3.5.3. Influence of Flow Rate and Degree of Coverage on Ratio of Form Resistance

^{2}/s to 0.00083 m

^{2}/s, the ratio of form resistance increases from 0.176 to 0.521; however, as the flow rate continues to increase to 0.00167 m

^{2}/s, form resistance gradually drops to 0.309. When the degree of vegetation coverage is relatively high, the ratio of form resistance in the total water flow resistance increases with an increase in the flow rate, and the rate of increase gradually decreases with an increase in the density. For example, when the degree of vegetation coverage is 85.72%, as the unit discharge increases from 0.00028 to 0.00167 m

^{2}/s, the ratio of form resistance gradually increases from 0.663 to 0.874, which shows an increase of 0.211. However, when the degree of coverage is 95.01%, within the same range of flow rate, the ratio of form resistance increases from 0.758 to 0.903, which represents an increase of only 0.145.

#### 3.6. Empirical Formula for Resistance Coefficient

## 4. Discussion

#### 4.1. Experimental Phenomena during Vegetation Submergence

#### 4.2. Influence of Vegetation Coverage on Water Depth and Flow Velocity

#### 4.3. Flow Regime of Overland Flow under Vegetation Cover

#### 4.4. Resistance Generation Mechanism under Different Degrees of Vegetation Coverage

#### 4.5. Effects of Vegetation Coverage Change on Surface Runoff

#### 4.6. Evaluation and Analysis of Proposed Equation

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A

#### Calculation of Hydraulic Parameters

^{3}/s; B is the flume width (0.3 m in this test); and h is the average water depth of the sections, in m.

^{3}/s, which can be calculated using the Poiseuille formula as follows:

^{2}).

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**Figure 1.**Test device (the device was developed and setup by the authors in Key Laboratory of Agricultural Soil and Water Engineering of the Ministry of Education in Arid Areas).

**Figure 3.**Flow velocity measurement using potassium permanganate (

**a**) at the start of the experiment and (

**b**) after 0.79 s.

**Figure 8.**Relationship between resistance coefficient (f) and Reynolds number (Re): (

**a**) without vegetation cover; (

**b**) with vegetation cover.

**Figure 9.**Relationship between resistance coefficient (f) and submergence degree ($\Lambda $): (

**a**) without vegetation cover; (

**b**) with vegetation cover.

**Figure 11.**The process of vegetation being submerged for (

**a**) 9.76%, (

**b**) 19.97%, (

**c**) 47.66%, and (

**d**) 66.42% vegetation coverage.

Coverage Treatment (%) | Unit Discharge (m^{2}/s) | Water Depth (mm) | Flow Velocity (m/s) | Reynolds Number | Froude Number | Resistance Coefficient |
---|---|---|---|---|---|---|

0 | 0.000278–0.00167 | 1.65–3.73 | 0.168–0.447 | 243.38–1460.31 | 1.32–2.34 | 0.30–0.95 |

9.76 | 0.000278–0.00167 | 1.76–4.22 | 0.158–0.395 | 243.38–1460.31 | 1.20–1.94 | 0.44–1.15 |

19.97 | 0.000278–0.00167 | 1.80–4.41 | 0.154–0.378 | 243.38–1460.31 | 1.16–1.80 | 0.50–1.23 |

38.78 | 0.000278–0.00167 | 1.83–4.70 | 0.152–0.355 | 243.38–1460.31 | 1.13–1.65 | 0.61–1.30 |

47.66 | 0.000278–0.00167 | 1.94–4.71 | 0.143–0.354 | 243.38–1460.31 | 1.03–1.64 | 0.61–1.54 |

66.42 | 0.000278–0.00167 | 1.97–6.01 | 0.141–0.277 | 243.38–1460.31 | 1.01–1.14 | 1.23–1.62 |

76.73 | 0.000278–0.00167 | 2.22–6.79 | 0.125–0.245 | 243.38–1460.31 | 0.84–0.95 | 1.84–2.31 |

85.72 | 0.000278–0.00167 | 2.37–7.44 | 0.117–0.224 | 243.38–1460.31 | 0.77–0.83 | 2.42–2.82 |

95.01 | 0.000278–0.00167 | 2.65–8.11 | 0.105–0.206 | 243.38–1460.31 | 0.65–0.73 | 3.13–3.94 |

Study | Characteristic Lengths | Reynolds Number |
---|---|---|

Wu et al. 1999 | Normalized flow depth (D/T) a) Unsubmerged vegetation D/T = 0.6–1.0; b) submerged vegetation D/T = 1.0–7.4 | 20–3000 |

Ishikawa et al. 2000 | Solid volume fraction ($\mathsf{\Phi}$) Laboratory measurements are presented for $\mathsf{\Phi}$= 0.091 (Square);$\mathsf{\Phi}$= 0.15 (Left triangle); $\mathsf{\Phi}$ = 0.20 (Cross);$\mathsf{\Phi}$= 0.27 (Hexagram);$\mathsf{\Phi}$= 0.35 (Circle) | 25–685 |

Tanino and Nepf 2008 | Diameter of model tree (d) Model trees with different diameters (0.40 and 0.64) were used to set two different spacing (6.32 and 3.16) for comparison | <5000 |

Coverage Degree (%) | Q/(L/min) | ||||||
---|---|---|---|---|---|---|---|

5 | 6.4 | 10 | 12.5 | 15 | 20 | 30 | |

0 | 29.65 | 25.28 | 17.33 | 15.23 | 13.88 | 12.27 | 10.07 |

9.76 | 31.39 | 26.98 | 20.25 | 20.54 | 22.09 | 17.50 | 12.69 |

19.97 | 29.16 | 25.92 | 18.52 | 19.83 | 20.68 | 16.44 | 11.39 |

38.78 | 26.73 | 25.09 | 18.63 | 19.38 | 19.87 | 15.59 | 11.91 |

47.66 | 28.51 | 27.28 | 20.53 | 18.85 | 17.73 | 14.38 | 12.72 |

66.42 | 31.91 | 30.24 | 22.92 | 20.87 | 19.49 | 17.78 | 16.23 |

76.73 | 35.96 | 33.92 | 24.71 | 23.52 | 22.73 | 20.53 | 18.33 |

85.72 | 38.39 | 34.88 | 25.27 | 25.11 | 25.00 | 24.87 | 20.09 |

95.01 | 42.93 | 37.42 | 26.24 | 27.56 | 28.43 | 29.52 | 21.90 |

Statistical Indicators | NSE | ${\mathit{R}}^{2}$ | RMSE | MAE |
---|---|---|---|---|

Calculation results | 0.734 | 0.731 | 0.344 | 0.290 |

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**MDPI and ACS Style**

Cai, Z.; Wang, J.; Yang, Y.; Zhang, R. Influence of Vegetation Coverage on Hydraulic Characteristics of Overland Flow. *Water* **2021**, *13*, 1055.
https://doi.org/10.3390/w13081055

**AMA Style**

Cai Z, Wang J, Yang Y, Zhang R. Influence of Vegetation Coverage on Hydraulic Characteristics of Overland Flow. *Water*. 2021; 13(8):1055.
https://doi.org/10.3390/w13081055

**Chicago/Turabian Style**

Cai, Zekang, Jian Wang, Yushuo Yang, and Ran Zhang. 2021. "Influence of Vegetation Coverage on Hydraulic Characteristics of Overland Flow" *Water* 13, no. 8: 1055.
https://doi.org/10.3390/w13081055