# Dynamic Roughness Modeling of Seasonal Vegetation Effect: Case Study of the Nanakita River

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Study Area

^{2}, the average annual discharge is 10 m

^{3}/s, and the flood discharge of a 100-year return period is 1650 m

^{3}/s. The bed slope of the Nanakita River is about 0.0016 in the relatively upstream reach and about 0.0003 in the lower reach [28].

^{3}, with the purpose of flood control, river flow maintenance, and water supply. According to the prefecture’s administration, the dam was not assigned the control of the river discharge at the time of Typhoon Hagibis.

## 3. Methodology

#### 3.1. UAV Observations

^{–2}.

#### 3.2. Hydrologic Model

#### 3.3. Two-Dimensional Hydraulic Model

#### 3.4. Dynamic Roughness

_{water}is the water depth of the section, and h

_{vegetation}is the vegetation height.

^{3}/s. Both simulations were validated by comparing the water level profile in the peak with the floodmark points at specific locations.

#### 3.5. Vegetation Characteristics

## 4. Results and Discussion

#### 4.1. Vegetation Conditions

#### 4.2. Hydrologic Simulation

^{3}s

^{–1}, lower than the 100-year return period of 1650 m

^{3}s

^{–1}affirmed by Tanaka et al. [26]. Figure 7 shows the discharge in each station, in the upstream section of the UAV-observed area and the outlet. The comparison between the observed and simulated water level in each station is shown in Figure 8. Nash–Sutcliffe efficiency and RMSE were calculated for each station to validate the model. Except for the Kawazaki station, all stations showed Nash–Sutcliffe values ranging from 0.62 to 0.88. Because the Nash–Sutcliffe efficiency of most of the gauge stations was close to 1, the model could be considered sufficiently accurate.

#### 4.3. Hydraulic Simulation

#### 4.4. Seasonal Effect of Vegetation on the Water Profile

^{2}) of vegetation average height versus water level were 0.91 and 0.83, respectively, confirming a stronger relationship than that of the vegetation area versus water level, with R of 0.79 and R

^{2}of 0.63. The parameters are dependent on each other, influencing the overall Manning roughness coefficient of the floodplains.

## 5. Conclusions

^{2}of 0.83. Therefore, considering only the vegetation area to estimate the water level, as does the static roughness model, would be less efficient. Considering the distributed vegetation height together with the vegetation area provides a stronger relationship between the riparian vegetation and the water level.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Study area: (

**a**) Location of the Nanakita River basin in Miyagi prefecture; (

**b**) basin map with the topography used as calculation area for the rainfall-runoff inundation model; (

**c**) the 2 km stretch of the Nanakita River obtained from the UAV observation of September 2019 used as calculation area for the 2D hydraulic model.

**Figure 3.**Relationship between the Manning roughness coefficient and the degree of submergence for different types of vegetation hardness and the regression curve.

**Figure 5.**Image of the DEM (

**left**), DSM (

**center**), and vegetation height (

**right**); vegetation height is the result of DSM–DEM for the vegetated grid cells.

**Figure 6.**Vegetated area and vegetation average height in the UAV-observed stretch shown in Figure 1c from April 2020 to March 2021.

**Figure 7.**RRI simulated discharges in all the water level gauge stations shown in Figure 1b, in the UAV upstream section, and in the outlet.

**Figure 9.**RRI-simulated peak inundation caused by the typhoon event in the river basin shown in Figure 1b.

**Figure 10.**Simulated water level profiles of the simple Manning roughness coefficient setting simulation and the dynamic Manning roughness coefficient calculation simulation.

**Figure 11.**Comparison of simulated and observed water level values from the static roughness model using several Manning values.

**Figure 12.**Pixel-level behavior of the Manning roughness coefficient estimation along the simulation time for: (

**a**) the dynamic roughness model in September 2019 at point 1 from Figure 1c, (

**b**) the dynamic roughness model in September 2019 at point 2 from Figure 1c, (

**c**) the static roughness model at point 1 in Figure 1c, and (

**d**) the static roughness model at point 2 in Figure 1c.

**Figure 13.**Water level profiles simulated by the 2D hydraulic model using the dynamic roughness model with: (

**a**) the vegetation average height and (

**b**) vegetation area from April 2020 to March 2021.

**Figure 14.**Linear relationship between the water level in the middle section of the UAV observed area and the vegetation parameters: (

**a**) area; (

**b**) average height.

Parameter | Group 1 | Group 2 |
---|---|---|

Accuracy | 0.99 | 0.96 |

Precision | 0.93 | 0.84 |

Misclassification | 0.01 | 0.04 |

Recall | 0.98 | 0.74 |

Manning | RMSE |
---|---|

0.022 | 0.931 |

0.038 | 0.671 |

0.040 | 0.641 |

0.050 | 0.522 |

0.060 | 0.421 |

0.068 | 0.354 |

0.070 | 0.340 |

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**MDPI and ACS Style**

Araújo Fortes, A.; Hashimoto, M.; Udo, K.; Ichikawa, K.; Sato, S. Dynamic Roughness Modeling of Seasonal Vegetation Effect: Case Study of the Nanakita River. *Water* **2022**, *14*, 3649.
https://doi.org/10.3390/w14223649

**AMA Style**

Araújo Fortes A, Hashimoto M, Udo K, Ichikawa K, Sato S. Dynamic Roughness Modeling of Seasonal Vegetation Effect: Case Study of the Nanakita River. *Water*. 2022; 14(22):3649.
https://doi.org/10.3390/w14223649

**Chicago/Turabian Style**

Araújo Fortes, André, Masakazu Hashimoto, Keiko Udo, Ken Ichikawa, and Shosuke Sato. 2022. "Dynamic Roughness Modeling of Seasonal Vegetation Effect: Case Study of the Nanakita River" *Water* 14, no. 22: 3649.
https://doi.org/10.3390/w14223649