# Research and Application of the Calculation Method of River Roughness Coefficient with Vegetation

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{D}and vegetation Reynolds number and vegetation volume fraction. Yang and Choi [14] calculated the depth-averaged velocity based on solving the velocity distribution in the vegetation layer and the layer above the vegetation, and then obtained the Manning coefficient with vegetation according to the Manning formula. They proposed a coefficient C

_{u}in the velocity distribution of the layer above the vegetation, and C

_{u}= 1 for a ≤5.0 m

^{−1}, C

_{u}= 2 for a >5.0 m

^{−1}. C

_{u}was found to vary significantly among different vegetation, which caused a large deviation from the predicted Manning coefficient. Li S et al. [15] divided the vegetated flow into the suspension layer and basal layer, based on which the averaged velocity over the whole flow depth could be derived, and then the Manning coefficient was derived from the Manning formula. They introduced the representative length scale h* into the calculation, which was calculated with energy slope. However, the energy slope is very difficult to obtain in practice. Cheng [16] proposed a representative roughness height to quantify the effect of submerged vegetation on flow resistance in the surface layer, and then developed an approach to estimate the average flow velocity and resistance coefficients for both cases of rigid and flexible vegetation, which was also the calculation of the energy slope. Overall, the methods calculating the Manning coefficient proposed by previous researchers are relatively complicated and need many calculation parameters, especially the energy slope, which is difficult to obtain. Because the research object and derivation process of each method is different, the validation data used are also different, so the resistance coefficients predicted by each method also differ. Wang et al. [17] found that the resistance coefficients of the emerged vegetation calculated by different methods were basically the same, but the calculated resistance coefficients of inundated vegetation varied greatly, and the differences among the results of different methods could be up to 2~4 times.

## 2. Methods and Materials

#### 2.1. Calculation Method of Roughness Coefficient with Vegetation

_{D}can be described by using the drag coefficient C

_{D}.

_{D}is the vegetation resistance per unit mass of fluid; C

_{D}is the vegetation drag coefficient; a is the vegetation density defined by the projected area in the incoming flow plane per unit volume; a = N × d; N is the number of vegetation per unit area; d is the vegetation characteristic length, for cylindrical vegetation, the characteristic length can be used with diameter; U

_{1}is the mean velocity in the vegetated layer. According to previous research [6,7], the vegetation resistance coefficient varies with the vegetation Reynolds number, vegetation density, etc. For low vegetation density, the drag coefficient C

_{D}is generally taken as 1.0.

_{1}is the depth-averaged velocity within the vegetation layer. When vegetation is submerged, U

_{1}< U, when vegetation is emerged, U

_{1}= U; a is the vegetation density; h is the vegetation height below the water surface; H is the water depth when the vegetation is emerged, h = H; g is the acceleration of gravity; f is the Darcy–Weisbach coefficient; S

_{0}is the water surface slope; C

_{D}is the vegetation drag coefficient; Φ is the vegetation volume fraction; for cylindrical vegetation, Φ equals adπ/4 and d is the vegetation diameter.

_{0}and Darcy–Weisbach coefficient f can be calculated from the following equation,

_{0}is the roughness coefficient without vegetation.

_{1}= U, and the Manning coefficient, Equation (6), with vegetation can be simplified as

_{1}and U can be expressed as follows (see Chen et al. [18]).

#### 2.2. Materials

^{−1}to 29 m

^{−1}, and the vegetation volume fraction ranged from 0.14% to 11.9%. n

_{0}was determined by the corresponding test results, and where the model test was not given, it was generally taken as 0.011.

## 3. Results

#### 3.1. Model Validation

#### 3.2. Variation of Roughness Coefficient

- (1)
- Emerged vegetation flow

^{−1}. Based on the experience and the hydraulic calculation manual, the Manning coefficient n of the floodplain without vegetation was taken as 0.03. According to Equation (7), the variation of the Manning coefficient n with the vegetation density and floodplain water depth is shown in Figure 5. It can be seen that for emerged vegetation, the Manning coefficient tends to increase with the increase in the vegetation density and floodplain water depth. The Manning coefficient was about 0.032 for a floodplain water depth of 0.5 m and vegetation density of 0.01 m

^{−1}, 0.071 for a floodplain water depth of 0.5 m and vegetation density of 0.2 m

^{−1}, 0.056 for a floodplain water depth of 3 m and vegetation density of 0.01 m

^{−1}, and 0.214 for a floodplain water depth of 3 m and vegetation density of 0.2 m

^{−1}.

- (2)
- Submerged vegetation flow

^{−1}. When vegetation is in the submerged state, the height h of vegetation below the water surface is the effective height after bending under the action of water flow. According to Equation (9), the relationship of the Manning coefficient with vegetation density, floodplain water depth, and vegetation height is shown in Figure 6 and Figure 7. Under the same vegetation height condition, the greater the water depth, the smaller the Manning coefficient, and the greater the vegetation density, the larger the Manning coefficient; the Manning coefficient increases with the increase in the vegetation density and decreases with the increase in the floodplain water depth. Under the same condition of vegetation height h = 0.5 m, the Manning coefficient was 0.050 when the water depth was 1 m and the vegetation density was 0.2 m

^{−1}, 0.097 when the water depth was 1 m and the vegetation density was 5 m

^{−1}, 0.043 when the water depth was 3 m and the vegetation density was 0.2 m

^{−1}, and 0.063 when the water depth was 1 m and the vegetation density was 5 m

^{−1}.

^{−1}), the Manning coefficient increased from 0.03 to 0.257 during the increase in vegetation height from 0 to 1.0 m at a floodplain water depth of 1.0 m, and from 0.03 to 0.064 during the increase in vegetation height from 0 to 1.0 at a vegetation water depth of 3.0 m.

## 4. Practical Applications

#### 4.1. Emerged Vegetation Flow

^{−1}. The averaged elevation of the river floodplain is about 2.5 m, and the one hundred-year flood level is 5.73 m. During the one hundred-year flood, the averaged depth of floodplain is 3.23 m, and the trees are in an emerged state. The floodplain roughness coefficient without vegetation was taken as 0.025 (the parameters above can be found in Gao et al. [28]). According to Equation (7), the roughness coefficient of the river with trees is 0.057. This result is basically consistent with the roughness coefficient of 0.06 (see Gao et al. [28]) derived from the experiment.

#### 4.2. Submerged Vegetation Flow

^{2}, the height of vegetation is 50 cm, and the density of vegetation is 2 m

^{−1}. The averaged elevation of the floodplain is about 28 m, and the design flood level of this reach is 32.36 m. Under the design flood level, the average water depth of the floodplain is about 4.36 m. The height of vegetation after bending is 0.4 m under the design flood conditions. According to Equation (9), the Manning coefficient of the floodplain is 0.057. Due to the completion and operation of the Three Gorges Project, the chances of flooding in the river reach downstream of the Three Gorges have been significantly reduced. The vegetation coverage on the floodplain has increased compared with its status before the Three Gorges Project, in particular, the density of shrubs and other flexible vegetation has increased significantly. Assuming that the vegetation density before the completion of the Three Gorges was 1 m

^{−1}, other parameters of the vegetation remained unchanged. According to Equation (9), the Manning coefficient of the floodplain is 0.054. Therefore, when the vegetation density increases from 1 m

^{−1}to 2 m

^{−1}, the Manning coefficient of the floodplain increases from 0.054 to 0.057, which is an increase of about 5.5%.

_{i}, n

_{i}are the wetted perimeter and the Manning coefficient of the ith segmented section, respectively. The typical section of Figure 10 can be divided into two zones, namely, the main channel zone and the floodplain zone. The wetted perimeter of the floodplain and the main channel was 450 m and 2007 m, respectively. Combined with the results of the previous analysis, the Manning coefficients of the floodplain before and after the change in the vegetation density were 0.054 and 0.057, respectively; the Manning coefficient of the main channel remained unchanged at 0.025. The integrated roughness of the section before and after the change in vegetation density was 0.0303 and 0.0309, respectively. The integrated roughness of the section increased after an increase in the vegetation density by about 2.0%.

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Costanza, R.; d’Arge, R.; de Groot, R.; Farber, S.; Grasso, M.; Hannon, B.; Limburg, K.; Naeem, S.; O’Neill, R.V.; Paruelo, J.; et al. The value of the world’s ecosystem services and natural capital. Nature
**1997**, 387, 253–260. [Google Scholar] [CrossRef] - Nepf Heidi, M. Flow and Transport in Regions with Aquatic Vegetation. Annu. Rev. Fluid Mech.
**2012**, 44, 123–142. [Google Scholar] [CrossRef] [Green Version] - Liu, C.; Shan, Y. Impact of an emergent model vegetation patch on flow adjustment and velocity. Proc. Inst. Civ. Eng.-Water Manag.
**2022**, 175, 55–66. [Google Scholar] [CrossRef] - Liu, C.; Yan, C.; Sun, S.; Lei, J.; Nepf, H.; Shan, Y. Velocity, turbulence, and sediment deposition in a channel partially filled with a Phragmites australis canopy. Water Resour. Res.
**2022**, 58, e2022WR032381. [Google Scholar] [CrossRef] - Nicosia, A.; Ferro, V. Flow resistance due to shrubs and woody vegetation. Flow Meas. Instrum.
**2023**, 89, 102308. [Google Scholar] [CrossRef] - Lauria, A. Flow Resistance in Open Channel due to Vegetation at Reach Scale: A Review. Water
**2021**, 13, 116. [Google Scholar] - Ikhsan, C.; Permana, A.S.; Negara, A.S. Armor layer uniformity and thickness in stationary conditions with steady uniform flow. Civ. Eng. J.
**2022**, 8, 1086–1099. [Google Scholar] [CrossRef] - Ree, W. Hydraulic characteristics of vegetation for vegetated waterways. Agric. Eng.
**1949**, 30, 184–189. [Google Scholar] - Kouwen, N.; Unny, T.; Hill, H.M. Flow retardance in vegetated channels. J. Hydraul. Div. ASCE
**1969**, 95, 329–342. [Google Scholar] [CrossRef] - Kouwen, N.; Unny, T.E. Flexible roughness in open channels. J. Hydraul. Div. ASCE
**1973**, 99, 713–728. [Google Scholar] [CrossRef] - Järvelä, J. Flow resistance of flexible and stiff vegetation: A flume study with natural plants. J. Hydrol.
**2002**, 269, 44–54. [Google Scholar] [CrossRef] - Stone, B.M.; Shen, H.T. Hydraulic resistance of flow in channels with cylindrical roughness. J. Hydraul. Eng.
**2002**, 128, 500–506. [Google Scholar] [CrossRef] - Tanino, Y.; Nepf, H.M. Laboratory investigation of mean drag in a random array of rigid, emergent cylinders. J. Hydraul. Eng.
**2008**, 134, 34–41. [Google Scholar] [CrossRef] - Yang, W.; Choi, S. A two-layer approach for depth-limited open-channel flows with submerged vegetation. J. Hydraul. Res.
**2010**, 48, 466–475. [Google Scholar] [CrossRef] - Li, S.; Shi, H.; Xiong, Z.; Huai, W.; Cheng, N. New formulation for the effective relative roughness height of open channel flows with submerged vegetation. Adv. Water Resour.
**2015**, 86, 46–57. [Google Scholar] [CrossRef] - Cheng, N.S. Representative roughness height of submerged vegetation. Water Resour. Res.
**2011**, 47, 427–438. [Google Scholar] [CrossRef] - Wang, J.; Zhang, Z. Evaluating riparian vegetation roughness computation methods integrated within HEC-RAS. J. Hydraul. Eng.
**2019**, 145, 04019020. [Google Scholar] [CrossRef] - Chen, Z.; Jiang, C.; Nepf, H. Flow adjustment at the leading edge of a submerged aquatic canopy. Water Resour. Res.
**2013**, 49, 5537–5551. [Google Scholar] [CrossRef] - Shimizu, Y.; Tsujimoto, T.; Nakagawa, H.; Kitamura, T. Experimental study on flow over rigid vegetation simulated by cylinders with equi-spacing. Proc. Jpn. Soc. Civ. Eng.
**1991**, 438, 31–40. (In Japanese) [Google Scholar] [CrossRef] [Green Version] - Dunn, C.J.; López, F.; García, M.H. Mean Flow and Turbulence in a Laboratory Channel with Simulated Vegetation; Hydrosystems Laboratory, Department of Civil Engineering, University of Illinois at Urbana-Champaign: Champaign, IL, USA, 1996. [Google Scholar]
- Meijer, D.G.; Van Velzen, E.H. Prototype-scale flume experiments on hydraulic roughness of submerged vegetation. In Proceedings of the 28th International IAHR Conference, Graz, Austria, 22–27 August 1999. [Google Scholar]
- Lopez, F.; Garcia, M.H. Mean flow and turbulence structure of open-channel flow through non-emergent vegetation. J. Hydrol. Eng.
**2001**, 127, 392–402. [Google Scholar] [CrossRef] - Ghisalberti, M.; Nepf, H.M. The limited growth of vegetated shear layers. Water Resour. Res.
**2004**, 40, 196–212. [Google Scholar] [CrossRef] - Murphy, E.; Ghisalberti, M.; Nepf, H. Model and laboratory study of dispersion in flows with submerged vegetation. Water Resour. Res.
**2007**, 43, 687–696. [Google Scholar] [CrossRef] - Nezu, I.; Sanjou, M. Turbulence structure and coherent motion in vegetated canopy open-channel flows. J. Hydro-Environ. Res.
**2008**, 2, 62–90. [Google Scholar] [CrossRef] - Yan, J. Experimental Study of Flow Resistance and Turbulence Characteristics of Open Channel Flow with Vegetation. Ph.D. Thesis, Hohai University, Nanjing, China, 2008. [Google Scholar]
- Yang, W. Experimental Study of Turbulent Open-Channel Flows with Submerged Vegetation. Ph.D. Thesis, Yonsei University, Seoul, Republic of Korea, 2008. [Google Scholar]
- Gao, X.; Lu, J.; Sun, B.; Liu, Y. Experimental study on equivalent bed resistance of river containing vegetation. J. Hydraul. Eng.
**2021**, 52, 1024–1035. (In Chinese) [Google Scholar] - Sun, X.; Zhang, H.; Zhong, M.; Wang, Z.; Liang, X.; Huang, T.; Huang, H. Analyses on the Temporal and Spatial Characteristics of Water Quality in a Seagoing River Using Multivariate Statistical Techniques: A Case Study in the Duliujian River, China. Int. J. Environ. Res. Public Health
**2019**, 16, 1020. [Google Scholar] [CrossRef] [Green Version] - Chai, Y.; Yang, Y.; Deng, J.; Sun, Z.; Li, Y.; Zhu, L. Evolution characteristics and drivers of the water level at an identical discharge in the Jingjiang reaches of the Yangtze River. J. Geogr. Sci.
**2020**, 30, 1633–1648. [Google Scholar] [CrossRef]

**Figure 5.**Variation in the Manning coefficient with the vegetation density and floodplain water depth for the emerged vegetation flow.

**Figure 6.**Variation in the Manning coefficient with the vegetation density and floodplain water depth for submerged vegetation flow (vegetation height h = 0.5 m).

**Figure 7.**Variation in the Manning coefficient with vegetation height and floodplain water depth for submerged vegetation flow (vegetation density a = 1 m

^{−1}).

**Figure 8.**Schematic of the Duliujian River, revised based on Sun et al. [29].

**Figure 9.**Schematic of the middle reaches of Yangtze River from Chai et al. [30]. The study area is between Chenglingji and Luoshan.

Researcher | Vegetation Diameter (mm) | Vegetation Height (m) | Volume Fraction (%) | Vegetation Shape | Pattern | Number of Runs |
---|---|---|---|---|---|---|

Shimizu et al. [19] | 1–1.5 | 0.041–0.046 | 0.44–0.79 | Cylinder | Linear | 28 |

Dunn et al. [20] | 6.35 | 0.118 | 0.14–1.23 | Cylinder | Staggered | 12 |

Meijer and van Velzen [21] | 8 | 0.45–1.5 | 0.32–1.29 | Cylinder | Staggered | 48 |

Lopez and Garcia [22] | 6.4 | 0.12 | 0.55–1.24 | Cylinder | Staggered | 8 |

Ghisalberti and Nepf [23] | 6.4 | 0.138 | 1.26–4.02 | Cylinder | Staggered | 11 |

Murphy et al. [24] | 6.4 | 0.07–0.14 | 1.18–3.77 | Cylinder | Random | 24 |

Nezu and Sanjou [25] | 8 | 0.05 | Flat strip | Linear | 9 | |

Yan [26] | 6 | 0.06 | 1.41–5.66 | Cylinder | Linear | 12 |

Yang [27] | 2 | 0.035 | 0.44 | Cylinder | Staggered | 2 |

Cheng [16] | 3.2–8.3 | 0.1 | 0.41–11.9 | Cylinder | Staggered | 23 |

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**MDPI and ACS Style**

Chen, Z.; Zhou, J.; Chen, Q.
Research and Application of the Calculation Method of River Roughness Coefficient with Vegetation. *Water* **2023**, *15*, 2638.
https://doi.org/10.3390/w15142638

**AMA Style**

Chen Z, Zhou J, Chen Q.
Research and Application of the Calculation Method of River Roughness Coefficient with Vegetation. *Water*. 2023; 15(14):2638.
https://doi.org/10.3390/w15142638

**Chicago/Turabian Style**

Chen, Zhengbing, Jianyin Zhou, and Qianhai Chen.
2023. "Research and Application of the Calculation Method of River Roughness Coefficient with Vegetation" *Water* 15, no. 14: 2638.
https://doi.org/10.3390/w15142638