Testing GIS-morphometric analysis of some Sicilian badlands

•Eroded volumes of calanchi landforms can be predicted by measuring their length.•The calanchi behave similarly to rills, ephemeral and permanent gullies.•The Hack's law is also applicable to calanchi badlands.•Calanchi become wider, and not more elongate, when increasing their drainage area.

Calanchi badlands are erosion landforms characterized by areas with scarce or absent vegetation, steep slopes, knife-edge divides and high erosion rates. They are originated by a combination of morphogenetic processes, partly similar to those shaping bigger fluvial landforms, and therefore can be considered as field “laboratories.” This paper presents the results of an investigation carried out in two badland sites located in Sicily, where the geometry of 25 calanchi has been characterized using Digital Elevation Models having a mesh size equal to 2 m. For each landform, a power length–volume relationship is established. This relationship demonstrates that length of calanchi channels can be used as a reliable predictor of eroded volume, as already verified for smaller linear erosion landforms such as rills, ephemeral and permanent gullies. Moreover, length, volume, width and depth of calanchi are combined into two dimensionless groups, allowing to establish a morphological similarity between rills, ephemeral, permanent gullies and the studied badlands. Furthermore the Hack's law, which relates channel length to drainage basin area, is applied to the 25 calanchi basins obtaining an exponent of this power law smaller than 0.5; this result indicates that basins do not become necessarily more elongate with increasing size. Finally the relationships between maximum length and width of the landforms are analyzed demonstrating that calanchi basins become wider, and not longer and narrower, when evolving and increasing their size.