Capturing gypsum rillenkarren morphometry by a 3D-photo reconstruction (3D-PR) technique

Abstract

Rillenkarren are small scale, straight, narrow solution channels that head at the crest of a bare rock slope and are extinguished downslope. In this paper the applicability of 3D-photo reconstruction technique of the rock surface is proposed for capturing the rillenkarren morphometry on gypsum. At first, the measurements are used to assess a relationship between the width/depth ratio and the depth of the rillenkarren. The exponent of this power relationship resulted different from the theoretical value - 0.5, confirming that the cross-section profiles of a rillenkarren can have a shape different from parabolic. The analysis developed for the cross-section area, the perimeter and the hydraulic radius established that the formation process is able to deep and enlarge the channel. The proposed model of the measured longitudinal profiles confirmed that the profile shape can be characterized by a flex point which divide the upstream concave part from the downstream convex one. According to previous studies on soil erosion features (rills, ephemeral gullies and gullies) the relationship between the rillenkarren length and its volume was expressed by a power equation. The comparison between rillenkarren and soil erosion features allowed to conclude that a single exponent (equal to 1.1) can be applied while the coefficient is characteristic of the feature and represents the influence of channel depth and width. Finally a model of rillenkarren morphometry, deduced applying the dimensional analysis and self-similarity, was applied to the measurements. This analysis demonstrated that a single dimensionless relationship is applicable to rillenkarren and rills, ephemeral gullies and gullies, assessing that a morphometric similarity exists between these different erosion features.