# PHOTOSED—PHOTOgrammetric Sediment Erosion Detection

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Experiments in the Erosion Flume—SETEG

#### 2.2. PHOTOSED—PHOTOgrammetric SEDiment Erosion Detection

#### 2.3. Calibration and Verification Method

## 3. Results and Discussion

#### 3.1. Calibration and Verification

_{x}= 0.9 μm/px, while in the y-direction the mean calibration factor yields dy = 69.6 μm/px and a standard deviation of σ

_{y}= 1.49 μm/px. Given the symmetry, an equal calibration factor of 69.4 μm/px, with the standard deviation of σ

_{xy}= 1.25 μm/px, was chosen for the following procedure.

_{z}= 10.3 μm. This calibration factor needs to be multiplied with the position-dependent correction factors in Figure 3 to obtain the correct displacement in the z-direction.

#### 3.2. Accuracy of PHOTOSED

#### 3.3. Exemplary Erosion Experiments

_{1}= 7.5 L/s, Q

_{2}= 11.3 L/s), were conducted to demonstrate the spatial resolution of the photogrammetric approach and to show the spatial and temporal heterogeneity of the measured erosion rates. The particle size distribution of the sediment surface consisted of 8% clay, 83% silt and 9% sand, while the wet bulk density was 1.42 g/cm³. The flow rates correspond to Reynolds shear stresses of 0.7 Pa (Re = 64,500) and 1.3 Pa (Re = 97,400), respectively. The sediment surface was exposed to the two flow rates for a total time of 600 s each and consecutive images were captured in a temporal resolution of 1.0 s. Figure 6 shows three dimensional plots of the sediment surface at the end of both erosion experiments (t = 600 s) for a flow of Q

_{1}= 7.5 L/s and Q

_{2}= 11.3 L/s, respectively.

_{1}= 7.5 L/s (Figure 6A) one erosion peak located at the edge of the ROI is observed, indicating a large local erosion. The surrounding smaller erosion peaks are presumably a result of the adjacent erosion peak at the edge of the ROI, which leads to local changes in the topography and roughness. Other areas of the ROI are not eroded at all. For Q

_{2}= 11.3 L/s (Figure 6B) the erosion is further developed, showing a second peak with large erosion and a spatial distribution of medium erosion. However, some areas of the surface remain stable without any erosion. Moreover, it becomes obvious that the roughness of such a structured surface will change compared to the initial surface and, consequently, the local shear stresses to which the sediments are exposed to during the erosion experiment.

^{6}) showing the erosion rates for time intervals of 30 s (Figure 7).

_{1}= 7.5 L/s (Figure 7A), the median of the erosion rates varies between 0.24 × 10

^{−4}mm³/s and 0.46 × 10

^{−4}mm³/s, which represents almost a factor of two. The maximum value yields 4.1 × 10

^{−4}mm³/s during the beginning of the experiment at t = 30 s, when the sediments are first exposed to the flow. However, parts of the sediment surface show no erosion at all. The variability of the erosion rates within each time interval is even higher. Therefore, the median is compared to the maximum values as a criterion for the degree of variability, leading to factors from 2.7 (minimum at t = 540 s) to 11 (maximum at t = 30 s), with a mean value of 5.6, which indicates an extremely high heterogeneity of the obtained erosion rates.

_{2}= 11.3 L/s (Figure 7B) shows, as expected, higher erosion rates with median values ranging from 0.31 × 10

^{−4}to 1.12 × 10

^{−4}mm³/s. The maximum value for the entire experimental duration is 5.84 × 10

^{−4}mm³/s (t = 60 s). The minimum variability within one time interval results in a factor of 4.0 at t = 30 s, while the maximum variability yields a factor of 8.1 at t = 570 s. The mean variability yields a value of 6.1 and is slightly higher compared to the erosion experiment with Q

_{1}= 7.5 L/s.

_{2}= 11.3 L/s.

## 4. Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Image of the CMOS-camera showing the round panel of the calibration setup with three different test areas (

**A**). Exemplary visualization of the DOF algorithm for each test area, the color represents the drop of the test areas (

**B**–

**D**).

**Figure 3.**Calibration factor for the vertical scaling from pixel into metric scale of the distorted camera images. The plotted points (n = 12) represent the measurements while the mesh represents their spatial interpolation.

**Figure 4.**Vertical measuring accuracy of PHOTOSED for given incremental vertical shifts of dz = 0.5 mm (

**A**) and dz = 1.0 mm (

**B**). The dashed lines represent the median ± the doubled standard deviation (± 2σ).

**Figure 5.**Comparison between photogrammetrically determined volumes against predefined volumes using the three different test areas.

**Figure 6.**Three-dimensional plots of the sediment surfaces at the end of the erosion experiments after t = 600 s for Q

_{1}= 7.5 L/s (

**A**) and Q

_{2}= 11.3 L/s (

**B**).

**Figure 7.**Variability of erosion rates for time intervals of t = 30 s throughout the entire erosion experiments for Q

_{1}= 7.5 L/s (

**A**) and Q

_{2}= 11.3 L/s (

**B**).

**Figure 8.**Temporal erosion progress of the erosion experiment with Q

_{2}= 11.3 L/s (x-y-plane) at six selected time-steps (Δt = 100 s).

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**MDPI and ACS Style**

Noack, M.; Schmid, G.; Beckers, F.; Haun, S.; Wieprecht, S.
PHOTOSED—PHOTOgrammetric Sediment Erosion Detection. *Geosciences* **2018**, *8*, 243.
https://doi.org/10.3390/geosciences8070243

**AMA Style**

Noack M, Schmid G, Beckers F, Haun S, Wieprecht S.
PHOTOSED—PHOTOgrammetric Sediment Erosion Detection. *Geosciences*. 2018; 8(7):243.
https://doi.org/10.3390/geosciences8070243

**Chicago/Turabian Style**

Noack, Markus, Gerhard Schmid, Felix Beckers, Stefan Haun, and Silke Wieprecht.
2018. "PHOTOSED—PHOTOgrammetric Sediment Erosion Detection" *Geosciences* 8, no. 7: 243.
https://doi.org/10.3390/geosciences8070243