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Key to the quantification of rockfall hazard is an understanding of its magnitude-frequency behaviour. Remote sensing has allowed for the accurate observation of rockfall activity, with methods being developed for digitally assembling the monitored occurrences into a rockfall database. A prevalent challenge is the quantification of rockfall volume, whilst fully considering the 3D information stored in each of the extracted rockfall point clouds. Surface reconstruction is utilized to construct a 3D digital surface representation, allowing for an estimation of the volume of space that a point cloud occupies. Given various point cloud imperfections, it is difficult for methods to generate digital surface representations of rockfall with detailed geometry and correct topology. In this study, we tested four different computational geometry-based surface reconstruction methods on a database comprised of 3668 rockfalls. The database was derived from a 5-year LiDAR monitoring campaign of an active rock slope in interior British Columbia, Canada. Each method resulted in a different magnitude-frequency distribution of rockfall. The implications of 3D volume estimation were demonstrated utilizing surface mesh visualization, cumulative magnitude-frequency plots, power-law fitting, and projected annual frequencies of rockfall occurrence. The 3D volume estimation methods caused a notable shift in the magnitude-frequency relations, while the power-law scaling parameters remained relatively similar. We determined that the optimal 3D volume calculation approach is a hybrid methodology comprised of the Power Crust reconstruction and the Alpha Solid reconstruction. The Alpha Solid approach is to be used on small-scale point clouds, characterized with high curvatures relative to their sampling density, which challenge the Power Crust sampling assumptions. [ABSTRACT FROM AUTHOR]

Laser scanning is routinely being used for the characterization and management of rockfall hazards. A key component of many studies is the ability to use the high-resolution topographic datasets for detailed volume estimates. 2.5-Dimensional (2.5D) approaches exist to estimate the volume of rockfall events; however these approaches require rasterization of the point cloud. These 2.5D volume estimates are therefore sensitive to picking an appropriate cell size to preserve resolution while minimizing interpolation, especially for lower volume rockfall events. To overcome the limitations of working with 2.5D raster datasets, surface reconstruction methods originating from the field of computational geometry can be implemented to assess the volume of rockfalls in 3D. In this technical note, the authors address the methods and implications of how the surface of 3D rockfall objects, derived from sequential terrestrial laser scans (TLS), are reconstructed for volumetric analysis. The Power Crust, Convex Hull and Alpha-shape algorithms are implemented to reconstruct a synthetic rockfall object generated in Houdini, a procedural modeling and animation software package. The reconstruction algorithms are also implemented for a selection of three rockfall cases studies which occurred in the White Canyon, British Columbia, Canada. The authors find that there is a trade-off between accurate surface topology reconstruction and ensuring the mesh is watertight manifold; which is required for accurate volumetric estimates. Power Crust is shown to be the most robust algorithm, however, the iterative Alpha-shape approach introduced in the study is also shown to find a balance between hole-filling and loss of detail. [ABSTRACT FROM AUTHOR]