Correction of Refraction Effects on Unmanned Aerial Vehicle Structure-from-Motion Bathymetric Survey for Coral Reef Roughness Characterisation

Abstract

Highlights: What are the main findings? Both analytical (Snell’s law) and empirical (regression) methods for correcting refraction at the water/air interface drastically improve the quality of UAV-derived bathymetry. Empirical (regression) methods are more efficient to reduce roughness errors and are fairly robust in terms of the choice of calibration points, as long as they cover a range of depths that is representative of the area. What are the implications of the main findings? Refraction corrections enable accurate, low-cost and large-scale coral reef mapping by UAV over shallow areas—reducing the need for extensive in-water measurements and supporting better assessments of wave dissipation, habitat complexity and reef health. Even after correction, the 2.5D raster format of UAV DEM tends to smooth the bed 3D complexity, altering the roughness metrics. Three-dimensional mapping formats should be considered. Coral reefs play a crucial role in tropical coastal ecosystems, even though these environments are difficult to monitor due to their diversity and morphological complexity and due to their shallowness in some cases. This study used two approaches for acquiring very-high-resolution bathymetric data: underwater structure-from-motion (SfM) photogrammetry collected from a low-cost platform and unmanned/uncrewed aerial vehicle (UAV)-based SfM photogrammetry. While underwater photogrammetry avoids the distortions caused by refraction at air/water interface, it remains limited in spatial coverage (about 0.04 ha in 1 h of survey). In contrast, UAV photogrammetry allows for covering extensive areas (more than 20 ha/h) but requires applying refraction correction in order to accurately compute bathymetry and roughness values. An analytical approach based on Snell laws and an empirical approach based on linear regression (calibrated using a batch of points whose depths are representative of the depth range of the surveyed areas) are tested to correct the apparent depth on the raw UAV digital elevation model (DEM). Comparison to underwater photogrammetry shows that correcting refraction reduces the root mean square error (RMSE) by more than 50% (up to 62%) on bathymetric models, with RMSE lower than 0.13 m for the analytical approach and down to 0.09 m for the regression method. The linear-regression-based refraction correction proved most effective in restoring accurate seabed roughness, with a mean error on roughness lower than 17% (vs. 30% for analytical refraction correction and 48% for apparent bathymetry).