Systematic characterisation of cave conduits geometry from dense 3D point clouds

Karst landscapes are characterised by dissolution landforms, including cave conduit networks along which meteoric waters flow. Experimental setups and field monitoring reveal that two main geometric parameters, namely hydraulic diameter and relative roughness, control head losses and flow in a karst conduit. In empirical flow models, the first can be roughly estimated from the topometric data of traditional cave surveys, while the second is usually sampled from a range of plausible values to fit the observed hydraulic signals. A higher resolution representation of cave geometry, in the form of a dense 3D point cloud allows 1) for more complex geometric descriptors and their spatial correlations to be computed, and 2) their impact on hydraulic response to flow conditions to be tested.

We collected field data by mapping the cave passages of interest with a high-resolution dynamic laser scanner in various hydrologically active caves of the European Alps. We modelled the cave walls as triangulated meshes using Poisson reconstruction. We subsequently developed and compared various strategies to automatically extract a cave centreline based on these triangulated meshes. First, we approximated the curve skeleton of the cave conduit by contraction of mesh vertices. Second computed a path supported by a voxel set of the cave interior, maximising clearance to the cave walls. Third we implemented an iterative virtual stepper, finding at each step the next optimal direction of travel based on local cave geometry. We finally confronted these purely geometric approaches to build curvilinear objects with two hydraulic paths from numerical experiments.

Travelling along this 1D object, we implemented an algorithm to find optimal section orientations and compute sequential mesh-plane intersections. We computed a suite of 2D shape descriptors on this family of 2D polylines and analysed the spatial correlation of key descriptors designed to summarise passage size, shape and roughness. Using this newly assembled pipeline for dense point cloud geometric description, we highlight the value of generating new morphometric indicators adapted to the complexity of cave datasets to calculate equivalent hydraulic radii, or along passage roughness, both of which can be used to inform cave-network scale models of flow and transport.