Evaluation of structure from motion (SfM) photogrammetry on the measurement of rill and interrill erosion in a typical loess

Structure from motion (SfM) photogrammetry is a cost-effective topographic survey tool capable of producing high-quality 3-dimensional structure of a landform. Yet its application has rarely been reported in rill and interrill erosion at the relatively small spatial scales, especially when taking place in the loess that is vulnerable to erosion. The objective was to examine the accuracy and limits of SfM in quantifying rill and interrill erosion occurring in a typical loess during consecutive rainfall simulations. The loess collected from the plough layer of a cropland in the Loess Plateau of China was packed into a 200 × 100 × 35 cm runoff plot and received simulated rainfall at the intensity of 90 mm h−1 on three slopes of 10°, 15° and 20°. A portable laser scanner (LS) and SfM were used to measure soil surface at every 30 min until rill emergence and after another 30-min rainfall aiming to study rill development. Meanwhile, runoff and sediment samples were collected at the plot outlet and oven-dried to calculate the soil loss. The results showed that the elevation differences calculated by subtracting digital elevation models (DEMs) derived by SfM and LS mainly fell between −2 and 2 mm. Moreover, the root mean square error (RMSE) and mean absolute error (MAE) were mostly smaller than 3 mm, suggesting accurate soil erosion measurement made by SfM at the plot scale. Considering the surface variations, the relative RMSE and MAE, i.e., dividing over the mean elevations measured by LS, were found to decrease as soil erosion proceeded and rills emerged. The rill morphology comparison, however, suggested a better fit of SfM for rills larger than 9 cm in maximum surface width, 6.0 × 10−2 m2 in area and 0.9 × 10−3 m3 in volume. In accordance with DEM comparisons, the soil losses estimated by SfM and LS were statistically similar. Nevertheless, these values were much greater than the amount of sediments collected for the early simulation runs, which might be explained primarily by the settling of loess when subject to heavy rainfall. But as rainfall continued and rills further developed, the misestimations made by LS and SfM remarkably dropped, i.e., from −17.8% to 4.9% and from −18.1% to 4.3%, respectively. These findings suggest a generally higher accuracy of SfM in quantifying rill erosion with more fluctuating soil surface than in interrill erosion measurement.