# Effects of Spatial Data Acquisition on Determination of a Gravel-Bed River Geomorphology

^{*}

## Abstract

**:**

^{3}and 10 m

^{3}over and underestimation, respectively, in a water body area of around 2200 m

^{2}. These findings help to provide more accurate geomorphological data with less effort as inputs for experimental and numerical models to derive better results.

## 1. Introduction

## 2. Materials and Methods

^{2}. Ropes were used along the width of the river to maintain longitudinal intervals. The ropes were marked every 1 m to maintain transverse intervals. It was assumed that the bathymetry obtained from this surveying point cloud represented the riverbed with no error. In this study, 22 different acquisition methods were used in around 10 days. These methods were categorized into 5 groups. The first group included 4 methods in which the dimensions of the measured grids increased from 2 × 2 to 5 × 5 m

^{2}(Figure 1).

## 3. Results

#### 3.1. Different Interpolation Methods

^{2}and 5 × 5 m

^{2}. Figure 5 shows the differences between both interpolation methods. Figure 5a shows that, in a dense measurement survey, there was not a dramatic difference between the TIN and OK. By decreasing the density to 5 × 5 m

^{2}, OK produced smoother DEMs and performed better than the TIN (Figure 5c). Although the smoothness of a DEM is not the governing parameter, resulting in the lowest difference in the DEM of difference (DoD) is the main parameter. Based on Figure 5b,d, DEMs created by TIN resulted in a lower difference than OK. This shows that TIN was better than OK for grids with lower point density. Therefore, further analysis of the surveying methods was conducted using TINs. The created TIN was then converted to a raster with dimensions of 0.25 m

^{2}using the linear method. The bed topography extracted from the 1 × 1 m

^{2}measurement was considered to be the base map and represented the real morphology of the bed.

#### 3.2. Regular Grid Methods

^{2}to the right in the upstream part of the reach with an elevation of 99.1 m—all DEMs showed this area very well. Although more details are presented in the 1 × 1 m

^{2}and 2 × 2 m

^{2}grids, the other grids show the area and depth of these locations. Overall, Figure 5 shows that, in the selected gravel-bed river, by decreasing the point density and using wider measurement grids, the overall shape of the riverbed could be measured and erosion and deposition areas were presented. The average elevation of the riverbed was also calculated with some small percentages of errors. However, the pattern of the riverbed was presented properly. The percentages of the errors will be calculated further. The grids presented in Figure 5 are useful when ground-based measurement devices are used.

#### 3.3. Cross and Longitudinal Section Methods

#### 3.4. Zigzag Methods

#### 3.5. Large-Scale Methods

#### 3.6. Measurement Errors and Durations of Each Method

^{2}measurement method had a point density of 1.14 points per square meter, with a measurement duration of 10 h. Figure 10 shows that, by using the 1 m zigzag method, the fieldwork decreased to around 60 percent (it took 6 h to conduct measurements). The measurement of only three cross-sections also took 30 min. Figure 10 shows that, although the measurement methods were different, for some methods, the measured point density and fieldwork did not change dramatically. For example, 1 × 2 m

^{2}had similar point density and fieldwork to the 2 × 1 m

^{2}method.

^{2}and three cross-sections, the volumes of overestimation were much higher than those of every other method. Figure 10 also shows that the volumes of overestimation were much higher than the volumes of underestimation. On the other hand, the volumes of overestimation in regions near the banks were similar to the volumes in the central region. Although the right and left bank regions occupied 24 and 17 percent of the whole studied area, respectively, the calculated volumes of errors in these regions were similar to those of the central 59 percent of the reach. Figure 10 shows that increasing the measured points did not necessarily increase the accuracy of the DEMs. Comparing cross-sectional and longitudinal grids showed that cross-sectional grids were more accurate than longitudinal grids. Figure 10 also shows that regular grids had better performance than the longitudinal and cross-sectional measurements, although they could decrease the measurement fieldwork to a greater extent than the other methods.

## 4. Discussion

#### 4.1. Interpolation Methods

^{2}grid indicated the better performance of TINs. These observations are consistent with those of Puente and Bras (1986) [40] and Bengora et al., 2018 [7], who showed that kriging may result in important under or overestimation of the prediction error when the size of a dataset decreases. Other studies also found TINs to be more reliable and well-suited to discontinuous shapes and breaks in slope [41,42]. Figure 5 also shows that TINs performed better than OK for banks with steep slopes. The results support the findings of Heritage et al., 2009 [13] regarding the use of TINs as the best interpolator in fluvial environments. The TIN itself is particularly prone to misrepresenting surface topography when low point density and greater topographic complexity combine [17]. Figure 5 also shows that, for lower density and near banks, TINs did not display the bed very well, but the amount of over/underprediction was less than that of OK. Therefore, the interpolation method affected the accuracy of the results, especially for scattered point densities, which is the opposite of the findings of Heritage et al., 2009 [13], which indicated that the choice of the interpolation algorithm is not as important as the survey strategy, but similar to those of Chaplot et al., 2006 [43] and Yue et al., 2007 [44], which indicated that the interpolation methods influence the accuracy and quality of the produced DEMs.

#### 4.2. Measurement Methods

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Regular measurement grids with dimensions of 1 m

^{2}, 4 m

^{2}, 9 m

^{2}, 16 m

^{2}, and 25 m

^{2}from left to right.

**Figure 2.**(

**a**) Cross-sectional measurements with a point interval of 1 m along the path for cross-sectional intervals of 1 m, 2 m, 3 m, 4 m, and 5 m; (

**b**) longitudinal measurements with a point interval of 1 m along the longitudinal path and transverse intervals of 2 m, 3 m, 4 m, 5 m, and 6 m.

**Figure 3.**Zigzag measurement methods with different side intervals of 2 m, 4 m, 6 m, 8 m, and 10 m. The bottom-right scheme is for half of the reach length’s zigzag movement.

**Figure 4.**Quick measurements where cross sections were measured with a very long interval in addition to one central and three longitudinal profiles.

**Figure 5.**Evaluating the accuracy of different interpolation methods for different point density measurements (

**a**–

**d**).

**Figure 10.**The volumes of under/overestimation of the riverbed by different methods of surveying, in addition to measured point density and fieldwork (black line).

**Figure 12.**Depths of under/overestimation of (

**a**) longitudinal and (

**b**) cross-sectional surveying methods.

**Figure 13.**Depths of under/overestimation of different (

**a**) zigzag and (

**b**) combined surveying methods.

**Figure 14.**Real bed elevation of a cross section (black line) and the effects of the distance between two repeated measurement points on the overestimation volumes (orange and red zones).

**Figure 15.**(

**a**) The initial triangulations and (

**b**) manual triangulations for interpolating unmeasured areas for the measurements with three cross sections and one longitudinal section.

**Figure 16.**Depths of under/overestimation of the (

**a**) initial triangulation for three cross sections and one longitudinal section, (

**b**) manual triangulation for three cross sections and one longitudinal section, (

**c**) initial triangulation for 5 m zigzag, and (

**d**) manual triangulation for 5 m zigzag surveying methods.

L ^{1} (m) | W ^{2} (m) | h ^{3} (m) | U ^{4} (m/s) | Q ^{5} (m^{3}/s) | d_{50} ^{6} (mm) |
---|---|---|---|---|---|

90 | 24 | 0.3 | 0.8 | 5 | 30 |

^{1}Length of the reach;

^{2}average width of the reach;

^{3}average water depth;

^{4}average flow velocity;

^{5}discharge during measurements;

^{6}median size of bed materials for which 50% are larger than it.

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**MDPI and ACS Style**

Maddahi, M.; Rahimpour, M.
Effects of Spatial Data Acquisition on Determination of a Gravel-Bed River Geomorphology. *Water* **2023**, *15*, 1719.
https://doi.org/10.3390/w15091719

**AMA Style**

Maddahi M, Rahimpour M.
Effects of Spatial Data Acquisition on Determination of a Gravel-Bed River Geomorphology. *Water*. 2023; 15(9):1719.
https://doi.org/10.3390/w15091719

**Chicago/Turabian Style**

Maddahi, Mohammadreza, and Majid Rahimpour.
2023. "Effects of Spatial Data Acquisition on Determination of a Gravel-Bed River Geomorphology" *Water* 15, no. 9: 1719.
https://doi.org/10.3390/w15091719