Objectives:

The objectives of this study are to analyze how erosion models different lithologies, and to calculate the erosion rate in volume (m3/area) and mass (ton/area) in three different lithologies in the valley of Yanhuitlán (Oaxaca). To this end, a high-resolution (10 cm) digital terrain model was constructed of a 200-m long hillside showing homogeneous features in terms of length, slope, orientation, climate, and vegetation cover, on which we analyzed the morphometry of the terrain and the erosion rate (volume and mass) before and after rains. The three lithologies are the following.

Yanhuitan Formation: poorly consolidated clayey-silty layers with the lowest hardness, category 1 (USDA, 2012). Erosion type: ravines

Llano de Lobos Tuff: Riodacitic and andesitic tuffs interbedded with limestone in a sandy matrix; hardness category 3 (USDA, 2012). Erosion type: laminar

Yucudaac Andesite: Andesitic lava spills with a high degree of weathering through its cracks; hardness category 5(USDA, 2012). Erosion type: gullies.

Materials and Methods:

Photogrammetric survey with a high-resolution (10 cm) Digital Surface Model (DSM) drone (DSM).

Surface water analysis of the DSM in shape format with the WATERSHED tool in GLOBALMAPPER 16, both of runoff and the respective catchment area; these were analyzed by lithology in 50x50-m plots placed in areas with no vegetation.

Four morphometric parameters were analyzed In the software ARCGIS 10.2: runoff or channel length, runoff catchment area, vertical dissection and dissection density, as well as the ranks of drainage formed by lithology.

Calculation of loss of soil by erosion, in volume and mass, through the overlapping of the models in two dates: 16 May 2016 and 25 September 2016, with a precipitation of 532 mm.

Results:

Clays from the Yanhuitlán formation are the most friable (erosion prone) material due to their poor consolidation, with higher dissection density and vertical dissection rates. For this reason, it also has the largest number of catchments of minimum size. It differs broadly from all other lithologies, with a volume loss rate of 380-492 m3/ha and a mass loss rate of 532-689 ton/ha.

The tuff shows the largest runoff catchment area and the lowest dissection density. Its erosion rate ranges between 100-128m3/ha and 110-141 ton/ha.

Andesite -- the hardest rock -- has the lowest vertical dissection, with an erosion rate of 37.48-48 m3/ha and 92-118 ton/ha/year.

The extrapolation of these data to obtain annual data based on total precipitation in 2016 (699 mm) yields rates of 701-898 ton/ha/year for the Yanhuitlán formation, 143.4-183.9 t/ha/year for tuff, and 128.4-164.6 t/ha/year for andesite.

Conclusions:

Multi-temporal surveys by digital photogrammetry with drones allow the quantification actual (not estimated) erosion of a lithological unit, in volume and mass, and the analysis of the geomorfometric dynamics of erosion. Therefore, this method contributes to conduct more comprehensive, accurate and realistic studies on erosion, including the analysis of the evolution of hillsides, which are valid for risk analysis.