An advanced photogrammetric method to measure surface roughness: Application to volcanic terrains in the Piton de la Fournaise, Reunion Island

We present a rapid in situ photogrammetric method to characterize surface roughness by taking overlapping photographs of a scene. The method uses a single digital camera to create a high-resolution digital terrain model (pixel size of ~ 1.32 mm) by means of a free open-source stereovision software. It is based on an auto-calibration process, which calculates the 3D geometry of the images, and an efficient multi-image correlation algorithm. The method is successfully applied to four different volcanic surfaces-namely, a′a lava flows, pahoehoe lava flows, slabby pahoehoe lava flows, and lapilli deposits. These surfaces were sampled in the Piton de la Fournaise volcano (Reunion Island) in October, 2011, and displayed various terrain roughnesses. Our in situ measurements allow deriving digital terrain models that reproduce the millimeter-scale height variations of the surfaces over about 12 m2. Five parameters characterizing surface topography are derived along unidirectional profiles: the root-mean-square height (ξ), the correlation length (Lc), the ratio Zs = ξ2/Lc, the tortuosity index (τ), and the fractal dimension (D). Anisotropy in the surface roughness has been first investigated using 1-m-long profiles circularly arranged around a central point. The results show that Lc, Zs and D effectively catch preferential directions in the structure of bare surfaces. Secondly, we studied the variation of these parameters as a function of the profile length by drawing random profiles from 1 to 12 m in length. We verified that ξ and Lc increase with the profile length and, therefore, are not appropriate to characterize surface roughness variation. We conclude that Zs and D are better suited to extract roughness information for multiple eruptive terrains with complex surface texture.