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Statistical metrics can be used to analyse the morphology of natural or simulated karst systems; they allow describing, comparing, and quantifying their geometry and topology. In this paper, we present and discuss a set of such metrics. We study their properties and their usefulness based on a set of more than 30 karstic networks mapped by speleologists. The data set includes some of the largest explored cave systems in the world and represents a broad range of geological and speleogenetic conditions allowing us to test the proposed metrics, their variability, and their usefulness for the discrimination of different morphologies. All the proposed metrics require that the topographical survey of the caves are first converted to graphs consisting of vertices and edges. This data preprocessing includes several quality check operations and some corrections to ensure that the karst is represented as accurately as possible. The statistical parameters relating to the geometry of the system are then directly computed on the graphs, while the topological parameters are computed on a reduced version of the network focusing only on its structure. Among the tested metrics, we include some that were previously proposed such as tortuosity or the Howard's coefficients. We also investigate the possibility to use new metrics derived from graph theory. In total, 21 metrics are introduced, discussed in detail, and compared on the basis of our data set. This work shows that orientation analysis and, in particular, the entropy of the orientation data can help to detect the existence of inception features. The statistics on branch length are useful to describe the extension of the conduits within the network. Rather surprisingly, the tortuosity does not vary very significantly. It could be heavily influenced by the survey methodology. The degree of interconnectivity of the network, related to the presence of maze patterns, can be measured using different metrics such as the How

The eastern coast of the Yucatan Peninsula, Mexico, contains one of the most developed karst systems in the world. This natural wonder is undergoing increasing pollution threat due to rapid economic development in the region of Tulum, together with a lack of wastewater treatment facilities. A preliminary numerical model has been developed to assess the vulnerability of the resource. Maps of explored caves have been completed using data from two airborne geophysical campaigns. These electromagnetic measurements allow for the mapping of unexplored karstic conduits. The completion of the network map is achieved through a stochastic pseudo-genetic karst simulator, previously developed but adapted as part of this study to account for the geophysical data. Together with the cave mapping by speleologists, the simulated networks are integrated into the finite-element flow-model mesh as pipe networks where turbulent flow is modeled. The calibration of the karstic network parameters (density, radius of the conduits) is conducted through a comparison with measured piezometric levels. Although the proposed model shows great uncertainty, it reproduces realistically the heterogeneous flow of the aquifer. Simulated velocities in conduits are greater than 1cm s−1, suggesting that the reinjection of Tulum wastewater constitutes a pollution risk for the nearby ecosystems

Statistical metrics can be used to analyse the morphology of natural or simulated karst systems; they allow describing, comparing, and quantifying their geometry and topology. In this paper, we present and discuss a set of such metrics. We study their properties and their usefulness based on a set of more than 30 karstic networks mapped by speleologists. The data set includes some of the largest explored cave systems in the world and represents a broad range of geological and speleogenetic conditions allowing us to test the proposed metrics, their variability, and their usefulness for the discrimination of different morphologies. All the proposed metrics require that the topographical survey of the caves are first converted to graphs consisting of vertices and edges. This data preprocessing includes several quality check operations and some corrections to ensure that the karst is represented as accurately as possible. The statistical parameters relating to the geometry of the system are then directly computed on the graphs, while the topological parameters are computed on a reduced version of the network focusing only on its structure. Among the tested metrics, we include some that were previously proposed such as tortuosity or the Howard's coefficients. We also investigate the possibility to use new metrics derived from graph theory. In total, 21 metrics are introduced, discussed in detail, and compared on the basis of our data set. This work shows that orientation analysis and, in particular, the entropy of the orientation data can help to detect the existence of inception features. The statistics on branch length are useful to describe the extension of the conduits within the network. Rather surprisingly, the tortuosity does not vary very significantly. It could be heavily influenced by the survey methodology. The degree of interconnectivity of the network, related to the presence of maze patterns, can be measured using different metrics such as the How

The eastern coast of the Yucatan Peninsula, Mexico, contains one of the most developed karst systems in the world. This natural wonder is undergoing increasing pollution threat due to rapid economic development in the region of Tulum, together with a lack of wastewater treatment facilities. A preliminary numerical model has been developed to assess the vulnerability of the resource. Maps of explored caves have been completed using data from two airborne geophysical campaigns. These electromagnetic measurements allow for the mapping of unexplored karstic conduits. The completion of the network map is achieved through a stochastic pseudo-genetic karst simulator, previously developed but adapted as part of this study to account for the geophysical data. Together with the cave mapping by speleologists, the simulated networks are integrated into the finite-element flow-model mesh as pipe networks where turbulent flow is modeled. The calibration of the karstic network parameters (density, radius of the conduits) is conducted through a comparison with measured piezometric levels. Although the proposed model shows great uncertainty, it reproduces realistically the heterogeneous flow of the aquifer. Simulated velocities in conduits are greater than 1cm s−1, suggesting that the reinjection of Tulum wastewater constitutes a pollution risk for the nearby ecosystems