Advancing gully topographic threshold analysis using an automated algorithm and high-resolution topography

Advances in technology to acquire high-resolution topography (HRT) have enabled increasingly detailed assessments of gully erosion from digital elevation models (DEMs), but also increased the need for reliable and reproducible methods. We developed an automated algorithm for characterising morphological properties of gullies and their surrounding terrain using HRT DEMs. While this concept may seem simple, the absence of an objective and reproducible method has been a key source of error in topographic and morphological studies of gullies. The algorithm constructs a geometric model of the gully head and uses this to estimate the width, depth, and slope of the gully channel as well as slope of the surrounding terrain. This new analysis removes arbitrary decisions regarding the computation of slope for input into topographic models of gully formation and enables consistent estimation of gully head morphology. We tested the algorithm across a similar to 1200 km(2) area in the Fitzroy River basin of north-eastern Australia where gully erosion occurs across a range of lithologies. Results show that topographic thresholds of gully formation are more reliably estimated when slope is computed along natural flow lines upslope of gully heads, not along the sides of gullies where topography is more variable. We used the algorithm to compare gully morphological measurements, finding a statistically significant relationship between gully depth and hillslope gradient. Estimated gully topographic thresholds for our study area indicate high susceptibility to gully erosion (k approximate to 0.021), consistent with previous studies in similar semi-arid Australian landscapes. However, this estimate was larger (k approximate to 0.049) using coarser resolution (>= 10 m) DEMs, indicating that DEM resolution affects modelled susceptibility of a landscape to gully incision. Our automated algorithm supports objective assessments of topographic studies of gullies with potential to improve comparability within and between studies.