# An Improved Method Constructing 3D River Channel for Flood Modeling

^{1}

^{2}

^{3}

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## Abstract

**:**

## 1. Introduction

## 2. Constructing Method for River Bed Terrain from Available Cross Sections

#### 2.1. Procedure for River Terrain Model Construction

_{i}and S

_{i}

_{+1}have 3 and 7 points with the same planar distance respectively at the left and right banks (Figure 4). The basic point clouds are generated according to the reconstructed points;

#### 2.2. River Terrain Model Construction in the Planar Coordinate System

_{j}between the nth points of the sections S

_{i}and S

_{i}

_{+1}. The x

_{j}coordinate of the P

_{j}is defined by equally dividing the straight line connecting the points of P

_{i,n}and P

_{i+1,n}, e.g., the line is divided into 7 segments in Figure 4. The interpolating formula for the considered point P

_{j}using the QHSP method can be expressed as:

_{i}and tanθ

_{i}

_{+1}are the tangent of the main flow direction at the cross section S

_{i}and S

_{i}

_{+1}. The coefficients of ${a}_{0}$, ${a}_{1}$, ${b}_{0}$ and ${b}_{1}$ can be evaluated from:

_{i}and S

_{i}

_{+1}. This procedure is repeated for all cross sections to produce the continuous and reliable river channel point cloud.

#### 2.3. Constructing Error Treatment

_{j}using the QHSP method is

#### 2.4. Elevation Interpolation of River Channel

_{j}of the considered point P

_{j}is linearly interpolated from the corresponding given data in the sections S

_{i}and S

_{i}

_{+1}. In other words, the z

_{j}can be computed by interpolating the elevation at P

_{i,n}and P

_{i+1,n}as plotted in Figure 4 in a linear way as

_{i,n}and P

_{i+1,n}.

_{j}are known. In a sum, Equation (1) is used to determine the y valued of the considered point P

_{j}whose x value of x

_{j}is a given one linear interpolated between sections S

_{i}and S

_{i}

_{+1}. I. The parameters applied in Equation (1) are computed by Equations (2) and (3), while when Equation (6) is utilized to compute the z value of the point P

_{j}. Other inserted points can be interpolated in the same way and terrain point clouds between the given sections can be generated.

## 3. Channel Construction for a Synthetic Sinusoidal River

#### 3.1. Benchmark Introduction

#### 3.2. Channel Terrain Construction for the Synthetic Sinusoidal River

#### 3.2.1. River Thalweg Construction

#### 3.2.2. Cross-Section Construction

#### 3.2.3. Error Assessment for the Interpolating Method

## 4. Channel Construction for a Realistic River

#### 4.1. River Channel Construction

#### 4.2. Flood Process Simulation on the Constructed River Bed

## 5. Conclusions

- The QHSP method can effectively resolve the unrealistic oscillations in the plane interpolation process by modifying the reversing tendency of x and y coordinates.
- Comparing to the CHS method, the proposed QHSP method can produce a more accurate river channel by using the same amount of the cross sections. The accuracy of the constructed river bed terrain can be improved by higher than 15% in terms of ME for the two test cases.
- On the constructed river channel by using the QHSP method, the computed hydrograph of flood process is more reliable than that employing the CHS methods, e.g., the former can improve the simulating accuracy by at least 18.5% in all cross sections in the Wangmaogou catchment.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Meandering river channel and (

**b**) erroneous river trend constructed by using the Cubic Hermite Spline (CHS) method.

**Figure 6.**Constructing error and the treatment. (

**a**) Constructing errors occurring by using the existing method; (

**b**) the corrected river trend construction using the proposed QHSP method.

**Figure 8.**Constructed river thalweg in Case (

**a**) A, (

**b**) B, (

**c**) C, and (

**d**) D with the amplitude of 600 m.

**Figure 9.**Constructed cross section (

**a**) S1, (

**b**) S2, and (

**c**) S3 for the river with the amplitude of 600 m.

**Figure 11.**Computed hydrograph for test case (

**a**) A, (

**b**) B, (

**c**) C, and (

**d**) D at Section S1 in the constructed river with the amplitude of 600 m.

**Figure 12.**Computed hydrograph for test case (

**a**) A, (

**b**) B, (

**c**) C, and (

**d**) D at Section S2 in the constructed river with the amplitude of 600 m.

**Figure 13.**Computed hydrograph for test case and (

**d**) D at Section S3 in the constructed river with the amplitude of 600 m. (

**a**) case A; (

**b**) B, (

**c**) C.

**Figure 14.**DEM (Digital Elevation Model) and available cross sections for Wangmaogou catchment. Unit: m.

**Figure 15.**Constructed river channel at Wangmaogou catchment by using (

**a**) CHS and (

**b**) QHSP methods. Unit: m.

**Figure 17.**Comparison between the computed hydrographs at considered cross sections in Wangmaogou catchment. (

**a**) Section S1; (

**b**) Section S2; (

**c**) Section S3; (

**d**) Section S4; (

**e**) Section S5; (

**f**) Section S6; (

**g**) Section S7; (

**h**) Section S8.

Amplitude | 400 | 600 | 800 | |||
---|---|---|---|---|---|---|

Errors | ME (m) | RMSE (m) | ME (m) | RMSE (m) | ME (m) | RMSE (m) |

CHS_A | 0.16 | 0.49 | 0.15 | 0.48 | 0.16 | 0.51 |

QHSP_A | 0.11 | 0.29 | 0.07 | 0.23 | 0.09 | 0.28 |

CHS_B | 1.24 | 2.60 | 1.24 | 2.62 | 1.27 | 2.64 |

QHSP_B | 0.10 | 0.32 | 0.20 | 0.67 | 0.25 | 0.87 |

CHS_C | 0.51 | 1.44 | 0.61 | 1.70 | 0.72 | 1.91 |

QHSP_C | 0.36 | 1.07 | 0.46 | 1.37 | 0.56 | 1.60 |

CHS_D | 0.46 | 1.36 | 0.54 | 1.56 | 0.61 | 1.69 |

QHSP_D | 0.09 | 0.30 | 0.11 | 0.37 | 0.16 | 0.52 |

**Table 2.**Mean Error (ME) and Root Mean Square Error (RMSE) of the computed hydrograph on the constructed river bed by CHS and QHSP method.

Test Cases | Sections | ME_CHS (m^{3}/s) | ME_QHSP (m^{3}/s) | RMSE_CHS (m^{3}/s) | RMSE_QHSP (m^{3}/s) |
---|---|---|---|---|---|

(a) Amplitude 400 m | |||||

A | Section S1 | 0.102 | 0.045 | 0.027 | 0.027 |

Section S2 | 0.013 | 0.009 | 0.007 | 0.022 | |

Section S3 | 0.339 | 0.140 | 0.102 | 0.039 | |

B | Section S1 | 0.166 | 0.162 | 0.066 | 0.051 |

Section S2 | 0.226 | 0.118 | 0.082 | 0.042 | |

Section S3 | 0.114 | 0.102 | 0.224 | 0.034 | |

C | Section S1 | 0.115 | 0.072 | 0.105 | 0.061 |

Section S2 | 0.253 | 0.094 | 0.096 | 0.041 | |

Section S3 | 0.146 | 0.143 | 0.164 | 0.151 | |

D | Section S1 | 0.037 | 0.160 | 0.049 | 0.076 |

Section S2 | 0.024 | 0.011 | 0.018 | 0.009 | |

Section S3 | 0.359 | 0.336 | 0.147 | 0.094 | |

(b) Amplitude 600 m | |||||

A | Section S1 | 0.061 | 0.021 | 0.034 | 0.013 |

Section S2 | 0.033 | 0.064 | 0.010 | 0.023 | |

Section S3 | 0.087 | 0.056 | 0.037 | 0.029 | |

B | Section S1 | 0.280 | 0.024 | 0.102 | 0.017 |

Section S2 | 0.218 | 0.070 | 0.079 | 0.037 | |

Section S3 | 0.220 | 0.144 | 0.246 | 0.042 | |

C | Section S1 | 0.129 | 0.100 | 0.152 | 0.166 |

Section S2 | 0.139 | 0.243 | 0.164 | 0.127 | |

Section S3 | 0.316 | 0.004 | 0.123 | 0.074 | |

D | Section S1 | 0.188 | 0.037 | 0.082 | 0.059 |

Section S2 | 0.061 | 0.099 | 0.025 | 0.038 | |

Section S3 | 0.193 | 0.091 | 0.054 | 0.024 | |

(c) Amplitude 800 m | |||||

A | Section S1 | 0.005 | 0.028 | 0.023 | 0.017 |

Section S2 | 0.184 | 0.004 | 0.046 | 0.012 | |

Section S3 | 0.037 | 0.002 | 0.019 | 0.012 | |

B | Section S1 | 0.377 | 0.129 | 0.106 | 0.050 |

Section S2 | 0.179 | 0.202 | 0.275 | 0.062 | |

Section S3 | 0.320 | 0.254 | 0.219 | 0.096 | |

C | Section S1 | 0.028 | 0.181 | 0.275 | 0.217 |

Section S2 | 0.345 | 0.019 | 0.267 | 0.210 | |

Section S3 | 0.108 | 0.346 | 0.196 | 0.219 | |

D | Section S1 | 0.007 | 0.030 | 0.063 | 0.051 |

Section S2 | 0.107 | 0.085 | 0.029 | 0.023 | |

Section S3 | 0.242 | 0.002 | 0.068 | 0.011 |

Method | ME (m) | RMSE (m) |
---|---|---|

CHS | 0.58 | 0.98 |

QHSP | 0.49 | 0.82 |

Time (h) | 1 h | 2 h | 3 h | 4 h | 5 h | 6 h |
---|---|---|---|---|---|---|

Net rainfall (mm/h) | 4.04 | 41.75 | 16.87 | 7.81 | 3.14 | 5.37 |

**Table 5.**Simulating errors of hydrographs at considered cross sections on the DEM constructed by using CHS and QHSP methods.

Sections | S1 | S2 | S3 | S4 | S5 | S6 | S7 | S8 |
---|---|---|---|---|---|---|---|---|

ME_CHS (m^{3}/s) | 1.171 | 0.498 | 0.374 | 0.840 | 0.986 | 0.707 | 0.342 | 0.940 |

ME_QHSP (m^{3}/s) | 0.005 | 0.271 | 0.145 | 0.460 | 0.540 | 0.576 | 0.230 | 0.423 |

RMSE_CHS (m^{3}/s) | 0.316 | 0.162 | 0.227 | 0.239 | 0.195 | 0.143 | 0.083 | 0.183 |

RMSE_QHSP (m^{3}/s) | 0.157 | 0.163 | 0.163 | 0.177 | 0.140 | 0.125 | 0.059 | 0.088 |

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**MDPI and ACS Style**

Hu, P.; Hou, J.; Zhi, Z.; Li, B.; Guo, K.
An Improved Method Constructing 3D River Channel for Flood Modeling. *Water* **2019**, *11*, 403.
https://doi.org/10.3390/w11030403

**AMA Style**

Hu P, Hou J, Zhi Z, Li B, Guo K.
An Improved Method Constructing 3D River Channel for Flood Modeling. *Water*. 2019; 11(3):403.
https://doi.org/10.3390/w11030403

**Chicago/Turabian Style**

Hu, Pengbo, Jingming Hou, Zaixing Zhi, Bingyao Li, and Kaihua Guo.
2019. "An Improved Method Constructing 3D River Channel for Flood Modeling" *Water* 11, no. 3: 403.
https://doi.org/10.3390/w11030403