# Development of RiverBox—An ArcGIS Toolbox for River Bathymetry Reconstruction

## Abstract

**:**

## 1. Introduction

## 2. Materials

#### 2.1. Chosen Case Study

^{3}/s. For the determination of inundation areas and flood hazard maps the extreme discharges representing 10-, 100- and 500-year floods were used. Their values are 560 m

^{3}/s, 928 m

^{3}/s, and 1211 m

^{3}/s, respectively. In 2016 these data were bought from the Polish Institute of Meteorology and Water Management (IMGW—Polish Instytut Meteorologii i Gospodarki Wodnej). All quoted hydrological characteristics are estimated on the basis of observations and data measured in the period 1971–2014. The whole reach is denoted with a blue line in Figure 1. The pink area represents the inundation area for a 100-year flood.

^{3}/s. The extreme values are as follows: for a 10-year flood 129.72 m

^{3}/s, for a 100-year flood 191.73 m

^{3}/s, and for a 500-year flood 230.93 m

^{3}/s [20]. All these values are assessed on the basis of data observed during the period 1961–2013. The modeled reach is presented as a blue line in Figure 2. As before, the pink areas denote the flood inundation for a 100-year event.

#### 2.2. Available Data for Bathymetry Reconstruction

^{2}and 359 km

^{2}, respectively. The nonempty areas are smaller, equaling 78 km

^{2}and 297 km

^{2}, respectively.

^{2}for bed interpolation. The average and the longest distance between interpolated cells and measurements are 160 m and 730 m, respectively.

^{2}. The reason for such differences in interpolation areas is the much smaller width of the channel in the second case. The estimated average distance between cells and measurements is smaller than before and equals 136 m, but the estimated maximum is 1283 m, which is about twice that in the previous case.

#### 2.3. Data for Validation Tests

## 3. Methods

#### 3.1. Basic Elements of the Algorithm

- The point denoted as a blue dot is projected on the river centerline. The coordinates are determined in the following manner. The longitudinal one is calculated on the basis of linear referencing assigned to the centerline vertexes. The transversal coordinate is calculated as the relative distance of the point from the left bank measured along the projection direction.
- If the longitudinal coordinate is known, the two closest cross-sections with measurements can be found. One of them has to be located upstream and the second is found downstream of the river. As this stage, the measurements are represented by three-dimensional polylines of cross-sections. The vertexes of lines have four coordinates: namely spatial coordinates X and Y, elevation Z, and linear referencing along the cross-section M. The latter, M, is a transversal coordinate calculated as the relative distance from the left bank. In each selected cross-section the elevation is determined for the value of the transversal coordinate at the point projected previously (blue dot).
- The elevations determined in upstream and downstream cross-sections are used to linearly interpolate the elevation along the channel centerline. Finally, the elevation at the projected point is known.

- For each vertex of the river centerline the cross-section is determined. The cross-section is perpendicular to the line connecting vertexes located upstream and downstream from the analyzed one. The longitudinal coordinate of this cross-section is the same as the coordinate determined for the analyzed vertex.
- The point located in the “no valid projection” or “double projection” zone is projected to the cross-section determined in step 1. For each such point the longitudinal coordinate is the same as the coordinate of the centerline node. Next, the transversal coordinate is calculated along this cross-section. The rule for calculation of the transversal is the same as shown previously.

#### 3.2. Applied Computational Schemes

#### 3.3. Available Tools at the Current State of Development

- Create Axis—a tool used for processing of the river centerline and setting linear referencing along it;
- Create Bed Polygon—the tool creates the bed polygon from the bank lines. Such a polygon has linear referencing along its perimeter;
- Select Points ISOK/GPS/XS—three tools applied for selection of points located in the bed polygon. The use of the tool depends on the format of stored points. The formats are described in the Materials section;
- Create Cross-Sections 3D—a tool used for preparation of the 3D lines representing measurement cross-sections.

- 8.
- Single Bed From ISOK/GPS/XS points—these tools are prepared for processing the particular format of points and all other necessary procedures. At the present state these tools cooperate only with the first scheme of the bathymetry interpolation.

- 9.
- Link Channel and Terrain—applied to link the raster of the bed elevations with the basic DEM.

## 4. Results and Discussion

#### 4.1. Validation Tests of Basic Algorithm

#### 4.2. Comparison of Tested Algorithms

^{2}for one point. The measure of density expressed as average area assigned to single points is easier to use than density itself. The boundary points were generated with average density equaling the square root of 40 m

^{2}, which is about 6.32 m.

#### 4.3. Efficiency and Accuracy Analysis

^{2}to 400 m

^{2}for one point. The tested densities are listed in third line of Table 2. If the square root of the area is a side of the equivalent square, the average spatial resolution changes from 4 m to 20 m. For the tested case it means that the number of points generated in the bed polygon ranges from 41,357 to 1654, as listed in line 4 of Table 2. Because the third algorithm is random, the reconstruction of the bed bathymetry was calculated 10 times for each density. The computations, for which parameters are shown in the first line of Table 2, were performed on the computer. For each run the time of computations was recorded. Finally, the differences in bed elevations between particular runs and the bed reconstructed with the first algorithm were analyzed at 100 independently generated points (line 6).

#### 4.4. Discussion

## 5. Conclusions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Example of required data: digital elevation model (DEM), polyline layers (river centerline, banks), and measurement points.

**Figure 5.**Interpretation of basic implemented algorithms: (

**a**) interpolation in channel-oriented coordinates; (

**b**) empty and double projection zones.

**Figure 6.**Tested computational schemes: (

**a**) the first approach based on NumPy array transformation; (

**b**) the second approach based on point–raster transformation; (

**c**) the third approach based on random points.

**Figure 7.**RiverBox presentation: (

**a**) view of the toolbox in the Catalog Tree; (

**b**) example of the tool interface with basic help.

**Figure 8.**Comparison of the bathymetry interpolated with the first algorithm and control cross-sections: (

**a**) location of control cross-sections; (

**b**–

**d**) results of comparison.

**Figure 9.**Comparison of selected cross-sections for the Warta river: (

**a**) Map with locations of the cross-sections used for comparison; (

**b**–

**d**) Compared cross-sections.

**Figure 10.**Comparison of selected cross-sections for the Ner river: (

**a**) Map with locations of the cross-sections used for comparison; (

**b**–

**d**) compared cross-sections.

**Figure 11.**Results of efficiency tests: (

**a**) Dependency of computational time on density of points in the third algorithm; (

**b**) Dependency of difference between the first and third algorithm on density of points.

Error Statistics (cm) | Cross-Section | ||
---|---|---|---|

No.1 | No.4 | No.7 | |

Max | 123 | 168 | 267 |

Mean | 18 | 28 | 52 |

Standard Deviation | 33 | 44 | 83 |

Computer | Processor i7-7820HQ, RAM 16 GB, Disk SSD 512 GB | |||||

Case Study | Warta river near the town of Wronki (7.6 km) | |||||

Average Density of Points (m^{2}/point) | 16 | 25 | 36 | 50 | 100 | 400 |

Number of Bed Points | 41,357 | 26,468 | 18,380 | 13,234 | 6617 | 1654 |

Number of Runs | 10 runs for each density | |||||

Verification | 100 control points |

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**MDPI and ACS Style**

Dysarz, T.
Development of RiverBox—An ArcGIS Toolbox for River Bathymetry Reconstruction. *Water* **2018**, *10*, 1266.
https://doi.org/10.3390/w10091266

**AMA Style**

Dysarz T.
Development of RiverBox—An ArcGIS Toolbox for River Bathymetry Reconstruction. *Water*. 2018; 10(9):1266.
https://doi.org/10.3390/w10091266

**Chicago/Turabian Style**

Dysarz, Tomasz.
2018. "Development of RiverBox—An ArcGIS Toolbox for River Bathymetry Reconstruction" *Water* 10, no. 9: 1266.
https://doi.org/10.3390/w10091266