Quantifying Below-Water Fluvial Geomorphic Change: The Implications of Refraction Correction, Water Surface Elevations, and Spatially Variable Error
Abstract
:1. Introduction
- (a)
- Coverage within submerged areas only, for a single point in time. This is particularly applicable in the case of new and emerging technologies, which have not yet progressed much beyond proof of concept. For example, [29] evaluates a range of sensors for deriving fluvial bathymetry data, including a RPAS-mounted hyperspectral sensor with a moderately high spatial resolution of 0.18 m/pixel.
- (b)
- (c)
- Complete fluvial coverage (i.e., both exposed and submerged areas) but only for a single point in time and requiring the use of a combination of survey methods. For example, [35] uses a combination of helicopter-acquired imagery, processed using Structure-from-Motion (SfM) photogrammetry, for exposed areas and bathymetric echo-sounding in submerged areas. In other settings, such as coastal and shallow marine environments, a combination of approaches is also common (e.g., [36]).
- (d)
- Complete fluvial coverage for multiple points in time, but with the need for extensive fieldwork to collect calibration data within the submerged parts of the channel, which can be dangerous or prohibitively time-consuming in some settings. For example, [37] uses an optical bathymetric approach on images acquired by RPAS (remotely piloted aircraft system) to obtain data in submerged areas. This approach requires the associated acquisition of bathymetry elevations using a GNSS to calibrate the relationship between the spectral image data and the water depth (from which elevation can be inferred). Similar workflows are employed by [38].
1.1. Refraction Correction
1.2. Water Surface Elevation
1.3. Spatially Variable Elevation Error
- Topographic complexity: Including slope angle and point cloud roughness.
- Landscape composition: Including presence/absence of dense vegetation and water depth.
- Survey quality: Including image quality, SfM point cloud density, and the precision of SfM tie points. We note the latter two SfM variables here are influenced by image texture, and therefore might also be classified as dependent on the nature of the landscape composition.
- Survey conditions: Including the presence/absence of water surface reflections and roughness and the presence/absence of dark shadows.
2. Materials and Methods
2.1. Site Set-Up
2.2. RPAS Surveys
2.3. SfM Processing
2.4. Validation Data
2.5. Water Surface Elevations
2.6. Refraction Correction
2.7. Small Angle Refraction Correction
2.8. Multi-View Refraction Correction (BathySfM)
2.9. Refraction Correction Validation
- 5.
- Exposed: Exposed areas only, where no refraction correction was necessary.
- 6.
- SmallAngle–Manual: Submerged areas only, using the small angle refraction correction (Equation (1)) and the manually digitised water surface elevations.
- 7.
- SmallAngle–Smooth: Submerged areas only, using the small angle refraction correction (Equation (1)) and the smoothed water surface elevations.
- 8.
- BathySfM–All: Submerged areas only, using the multi-view refraction correction and the smoothed water surface elevations.
- 9.
- BathySfM–Filtered: Submerged areas only, using the angle and distance filtered multi-view angle refraction correction and the smoothed water surface elevations.
2.10. Spatially Variable Errors
2.11. Multiple Regression
2.12. Machine Learning Classification
2.13. Error Propagation and Change Detection
3. Results
3.1. SfM Modelling
3.2. Water Surfaces
3.3. Refraction Corrections
3.4. Spatially Variable Error
3.4.1. Linear Regressions
3.4.2. Multiple Regression
3.5. Machine Learning Classification
3.6. Geomorphic Change
4. Discussion
4.1. Refraction Correction
4.2. Water Surface Elevations
4.3. Spatially Variable Error for Geomorphic Change Detection
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Parameter (Type) | Symbol | Method of Extraction | Type: Range/Units | Sample Size: Count (%) | |
---|---|---|---|---|---|
2016 | 2017 | ||||
Slope angle (topographic complexity) | S | RPAS–SfM DEMs imported to ArcGIS. 3D Analyst extension was used to compute slope angles. Focal (f) statistics for slope within a 0.2 m circular window of each validation point also computed. | Continuous: 0–90° | 1522 (100%) | 2091 (100%) |
Point cloud roughness (topographic complexity) | R | RPAS–SfM point clouds imported to CloudCompare. ‘Compute geometric features’ tool used to compute roughness for each point in the cloud within spherical kernels with a 0.4 m radius. Roughness is defined as the distance between the point and the best fitting plane computing from all the surrounding points which fall within the kernel. Rasterised at 0.1 m pixel size and exported to ArcGIS. Smaller pixel sizes were found to produce too many holes in the resulting raster. Focal statistics for roughness within a 0.2 m circular window of each validation point also computed. | Continuous: 0–0.34 m | 1515 (99.5%) | 2090 (99.9%) |
Point cloud density (survey quality/ landscape composition) | D | RPAS–SfM point clouds imported to CloudCompare and rasterised according to the number of points falling within each 0.05 m grid cell. Raster exported to ArcGIS. | Continuous: 0–64 count | 1522 (100%) | 2091 (100%) |
Water depth (landscape composition) | h | Computed using the multi-view refraction correction process and smoothed water surface, as detailed within this paper (BathySfM–All). | Continuous: 0–1.97 m | 355 (23.3%) | 1170 (56%) |
Image quality (survey quality) | CQ | Image quality estimates are provided by PhotoScan Pro on a scale of 0 to 1 and based on the level of image sharpness in the best focused area of the image. Images with quality values of less than 0.5 are generally not recommended for use in subsequent processing. Image quality data were exported from PhotoScan Pro and the average quality of cameras that ‘see’ each point was appended to that point. Point–camera connections were calculated in the same way as the BathySfM correction. | Continuous: 0–1 | 1522 (100%) | 2086 (99.8%) |
Tie point precision (survey quality/ landscape composition) | P | Computed using the tie point precision method presented by [49]. Tie points are rasterised at 1 m pixel size and exported from CloudCompare to ArcGIS. The tie points form the sparse point cloud from the PhotoScan Pro software, therefore exporting at a finer resolution would lead to large holes in the resulting raster. | Continuous: 0–4.8 m | 1342 (88.2%) | 1884 (90.1%) |
Vegetation presence (landscape composition) | V | RPAS–SfM orthophotos imported to ArcGIS. Editor toolbar used to visually identify and map areas of particularly dense vegetation or tree coverage. | Binary: [0] = Not present [1] = Present | 1522 (100%) [0] = 89.5% [1] = 10.5% | 2091 (100%) [0] = 90.5% [1] = 9.5% |
Presence of water surface reflection (survey conditions) | Rc | RPAS–SfM orthophotos imported to ArcGIS. Editor toolbar used to visually identify and map areas of notable water surface reflections. | Binary: [0] = Not present [1] = Present | 1522 (100%) [0] = 98% [1] = 2% | 2091 (100%) [0] = 94.3% [1] = 5.7% |
Presence of shadows (survey conditions) | Sh | RPAS–SfM orthophotos imported to ArcGIS. Editor toolbar used to visually identify and map areas of dark shadowing. | Binary: [0] = Not present [1] = Present | 1522 (100%) [0] = 99.5% [1] = 0.5% | 2091 (100%) [0] = 98.3% [1] = 1.7% |
Mean | St Dev | 95% Conf. | RMSE | MIN | MAX | ||
---|---|---|---|---|---|---|---|
2016 | X | 0.000 | 0.021 | 0.041 | 0.020 | –0.047 | 0.030 |
Y | 0.000 | 0.027 | 0.052 | 0.026 | –0.046 | 0.047 | |
Z | –0.001 | 0.017 | 0.034 | 0.017 | –0.029 | 0.035 | |
2017 | X | 0.000 | 0.035 | 0.068 | 0.034 | –0.054 | 0.056 |
Y | 0.000 | 0.059 | 0.116 | 0.057 | –0.096 | 0.076 | |
Z | 0.000 | 0.006 | 0.013 | 0.006 | –0.018 | 0.006 |
2016 | 2017 | |||||||||
---|---|---|---|---|---|---|---|---|---|---|
Correction Method | (1) Exposed Only | (2) Small Angle– Manual | (3) Small Angle– Smooth | (4) Bathy SfM–All | (5) Bathy SfM–Filtered | (1) Exposed Only | (2) Small Angle– Manual | (3) Small Angle– Smooth | (4) Bathy SfM–All | (5) Bathy SfM–Filtered |
Mean Error | 0.024 | 0.150 | 0.041 | 0.016 | 0.027 | 0.065 | 0.034 | 0.017 | –0.055 | 0.006 |
St Dev of Error | 0.235 | 0.205 | 0.065 | 0.061 | 0.062 | 0.226 | 0.105 | 0.079 | 0.101 | 0.079 |
Regression Slope | 0.942 | 0.915 | 0.997 | 0.989 | 0.992 | 0.940 | 0.903 | 1.068 | 1.057 | 1.060 |
Min Error | –1.710 | -0.645 | –0.130 | –0.156 | –0.152 | –1.235 | –0.293 | –0.269 | –0.439 | –0.282 |
Max Error | 1.097 | 1.403 | 0.501 | 0.445 | 0.482 | 1.566 | 2.261 | 0.520 | 0.485 | 0.513 |
(a) Elevation Error—Magnitude and Direction | (b) Elevation Error—Magnitude Only | |||||
---|---|---|---|---|---|---|
Variable | Combined | 2016 | 2017 | Combined | 2016 | 2017 |
Slope | –0.10 | –0.20 | 0.00 | 0.50 | 0.47 | 0.56 |
Max. Slope Focal | –0.12 | –0.24 | 0.00 | 0.52 | 0.53 | 0.53 |
Min. Slope Focal | –0.06 | –0.09 | –0.03 | 0.37 | 0.39 | 0.39 |
St. Dev. Slope Focal | –0.12 | –0.25 | 0.04 | 0.44 | 0.44 | 0.45 |
Water Depth (BathySfM–All) | –0.05 | 0.01 | –0.11 | –0.15 | –0.10 | –0.19 |
Point Density | –0.12 | –0.14 | –0.10 | 0.28 | 0.23 | 0.43 |
Image Quality Mean | –0.04 | –0.01 | –0.07 | 0.05 | 0.07 | 0.02 |
Image Quality Mean Focal | –0.04 | –0.01 | –0.07 | 0.06 | 0.07 | 0.02 |
Roughness 40 cm | –0.04 | –0.17 | 0.12 | 0.31 | 0.22 | 0.41 |
Roughness 40 cm Focal | –0.05 | –0.19 | 0.14 | 0.38 | 0.30 | 0.49 |
Tie Point Precision | 0.05 | 0.02 | 0.07 | 0.06 | 0.14 | 0.06 |
(a) Elevation Error—Magnitude and Direction | (b) Elevation Error—Magnitude Only | |||||
---|---|---|---|---|---|---|
Performance Variable | Combined | 2016 | 2017 | Combined | 2016 | 2017 |
Multiple R | 0.47 | 0.54 | 0.53 | 0.61 | 0.65 | 0.63 |
Adjusted R Square | 0.22 | 0.29 | 0.28 | 0.37 | 0.42 | 0.40 |
Standard Error (m) | 0.17 | 0.18 | 0.14 | 0.13 | 0.14 | 0.11 |
Significance (p-value) | <0.01 | <0.01 | <0.01 | <0.01 | <0.01 | <0.01 |
Slope (obs vs. pred) | NC | 0.1666 | 0.1297 | NC | NC | NC |
Mean Residual Error (m) | NC | –0.04 | –0.01 | NC | NC | NC |
Max Residual Error (m) | NC | 1.48 | 1.09 | NC | NC | NC |
Min Residual Error (m) | NC | –4.48 | –1.23 | NC | NC | NC |
St Dev Residual Error (m) | NC | 0.22 | 0.16 | NC | NC | NC |
Variable | Standard Deviation | Multiple Regression Co-Efficients/Intercept | |
---|---|---|---|
Epochs Combined | 2016 | 2017 | |
Maximum Slope Focal (MaxSf) | 20.3411 | –0.0674 | –0.0281 |
Minimum Slope Focal (MinSf) | 5.4814 | –0.0059 | –0.0034 |
Refraction Corrected Water Depth (h) | 0.2061 | 0.0140 | –0.0228 |
Point Cloud Density (D) | 4.1113 | –0.0071 | –0.0747 |
Mean Image Quality Focal (MeanCQf) | 1.9848 | –0.0010 | –0.0266 |
Mean Roughness Focal (MeanRf) | 0.0150 | –0.0212 | 0.0333 |
Point Cloud Precision (P) | 0.3863 | 0.0437 | 0.0019 |
Presence of Vegetation (V) | N/A | 0.2604 | 0.2354 |
Presence of Shadows (Sh) | N/A | –0.4588 | 0.0616 |
Presence of Reflections (Rc) | N/A | 0.0511 | 0.0084 |
Intercept (θ) | N/A | 0.1533 | 1.1812 |
Classes | Epoch | Accuracy | F1 Score |
---|---|---|---|
3 classes | 2016 | 78% | 0.83 |
2017 | 76% | 0.81 | |
Both | 74% | 0.80 | |
10 classes | 2016 | 26% | 0.22 |
2017 | 31% | 0.30 | |
Both | 29% | 0.27 |
This Paper | Flener et al. [37] | Tamminga et al. [38] | Shintani and Fonstad [42] | |
---|---|---|---|---|
Refraction correction approach | Co-efficient for clear water (1.34): Small angle & multiview | Optical calibration | Optical calibration | Site specific co-efficient |
Calibration data needed? | No | Yes | Yes | Yes |
Validation points | 1522–2093 | 197 GPS points + extra ADCP points (not reported) | 76–82 | 167 |
Survey size | 600 m reach | ca. 150 m reach (20–30 m wide) | 800 m reach | 140 m reach |
Validation survey type | Differential GNSS + total station | RTK GPS + ADCP | RTK GPS | RTK GPS |
Validation point layout | Random distribution over a range of water depths | Zig-zag pattern along channel over range of water depths | Not reported | 12 evenly spaced channel cross sections |
Maximum water depth (m) | 1.43 | 1.50 | Not reported | 1.25 |
Mean error (m) | 0.006–0.041 | 0.117–0.1196 | 0.0001–0.0007 | 0.009 |
RMSE (m) | 0.063–0.115 | 0.163–0.221 | 0.095–0.098 | Not reported |
Standard deviation (m) | 0.061–0.101 | Not reported | 0.009–0.023 | 0.172 |
© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
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Woodget, A.S.; Dietrich, J.T.; Wilson, R.T. Quantifying Below-Water Fluvial Geomorphic Change: The Implications of Refraction Correction, Water Surface Elevations, and Spatially Variable Error. Remote Sens. 2019, 11, 2415. https://doi.org/10.3390/rs11202415
Woodget AS, Dietrich JT, Wilson RT. Quantifying Below-Water Fluvial Geomorphic Change: The Implications of Refraction Correction, Water Surface Elevations, and Spatially Variable Error. Remote Sensing. 2019; 11(20):2415. https://doi.org/10.3390/rs11202415
Chicago/Turabian StyleWoodget, Amy S., James T. Dietrich, and Robin T. Wilson. 2019. "Quantifying Below-Water Fluvial Geomorphic Change: The Implications of Refraction Correction, Water Surface Elevations, and Spatially Variable Error" Remote Sensing 11, no. 20: 2415. https://doi.org/10.3390/rs11202415
APA StyleWoodget, A. S., Dietrich, J. T., & Wilson, R. T. (2019). Quantifying Below-Water Fluvial Geomorphic Change: The Implications of Refraction Correction, Water Surface Elevations, and Spatially Variable Error. Remote Sensing, 11(20), 2415. https://doi.org/10.3390/rs11202415