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Flow accumulation algorithms estimate the steady state of flow on real or modeled topographic surfaces and are crucial for hydrological and geomorphological assessments, including delineation of river networks, drainage basins, and sediment transport processes. Existing flow accumulation algorithms are typically designed to compute flows on regular grids and are not directly applicable to arbitrarily sampled topographic data such as lidar point clouds. In this study we present a random sampling scheme that generates homogeneous point densities, in combination with a novel flow path tracing approach-the Facet-Flow Network (FFN)-that estimates flow accumulation in terms of specific catchment area (SCA) on triangulated surfaces. The random sampling minimizes biases due to spatial sampling and the FFN allows for direct flow estimation from point clouds. We validate our approach on a Gaussian hill surface and study the convergence of its SCA compared to the analytical solution. Here, our algorithm outperforms the multiple flow direction algorithm, which is optimized for divergent surfaces. We also compute the SCA of a 6-km(2)-steep, vegetated catchment on Santa Cruz Island, California, based on airborne lidar point-cloud data. Point-cloud-based SCA values estimated by our method compare well with those estimated by the D-infinity or multiple flow direction algorithm on gridded data. The advantage of computing SCA from point clouds becomes relevant especially for divergent topography and for small drainage areas: These are depicted with much more detail due to the higher sampling density of point clouds.
Skarn deposits are found on every continents and were formed at different times from Precambrian to Tertiary. Typically, the formation of a skarn is induced by a granitic intrusion in carbonates-rich sedimentary rocks. During contact metamorphism, fluids derived from the granite interact with the sedimentary host rocks, which results in the formation of calc-silicate minerals at the expense of carbonates. Those newly formed minerals generally develop in a metamorphic zoned aureole with garnet in the proximal and pyroxene in the distal zone. Ore elements contained in magmatic fluids are precipitated due to the change in fluid composition. The temperature decrease of the entire system, due to the cooling of magmatic fluids and the entering of meteoric water, allows retrogression of some prograde minerals.
The Hämmerlein skarn deposit has a multi-stage history with a skarn formation during regional metamorphism and a retrogression of primary skarn minerals during the granitic intrusion. Tin was mobilized during both events. The 340 Ma old tin-bearing skarn minerals show that tin was present in sediments before the granite intrusion, and that the first Sn enrichment occurred during the skarn formation by regional metamorphism fluids. In a second step at ca. 320 Ma, tin-bearing fluids were produced with the intrusion of the Eibenstock granite. Tin, which has been added by the granite and remobilized from skarn calc-silicates, precipitated as cassiterite.
Compared to clay or marl, the skarn is enriched in Sn, W, In, Zn, and Cu. These metals have been supplied during both regional metamorphism and granite emplacement. In addition, the several isotopic and chemical data of skarn samples show that the granite selectively added elements such as Sn, and that there was no visible granitic contribution to the sedimentary signature of the skarn
The example of Hämmerlein shows that it is possible to form a tin-rich skarn without associated granite when tin has already been transported from tin-bearing sediments during regional metamorphism by aqueous metamorphic fluids. These skarns are economically not interesting if tin is only contained in the skarn minerals. Later alteration of the skarn (the heat and fluid source is not necessarily a granite), however, can lead to the formation of secondary cassiterite (SnO2), with which the skarn can become economically highly interesting.