Data obtained method and application for topographic threshold theory calculation of gully initiation

Gully initiation topographic threshold theory describes gully initiation condition, and is represented by the size of catchment that controls discharge, and local slope at the channel head that controls the velocity of runoff. The main cause of gully formation is excessive (sub) surface runoff, a condition that might be brought about by either climate change or alternations in land use. In this study, this theory was reviewed from the following aspects: theory development, data sources, threshold value calculating methods, influencing factors and applications. The gully initiation threshold concept was originally developed to explain the onset of instability in 1 gully while its neighbours remained stable. The relative area (or shear stress) exponent was generally interpreted in relation to the gully erosion process in the catchment. Values higher than 0.2 were associated with erosion by surface runoff and those lower than 0.2 indicated subsurface processes or mass movement. The threshold coefficient reflected the resistance of the site to gully head development, affected by rainfall, land use, etc. The threshold values variation also depended on the methodology, including field reconnaissance survey and high-resolution remote sensing images as well as digital elevation model. The latter were more convenient for data acquisition, although field reconnaissance survey data would be more accurate. With fast development of unmanned aerial vehicles, high spatial resolution orthophotos derived from structure-from-motion photography could be used to identify the location of gully heads and corresponding catchment size and local slope values. In the early research, the topographic threshold straight line was eye-fitted through the "lower-most" points in a log-log scatter plot. The negative slope of that line was equal to relative area exponent value. Then the threshold value could be obtained as the intercept. Since this threshold line was manually drawn, it did not have statistical meaning. This method might also be problematic as multiple thresholds could exist, and the threshold line was very sensitive to extreme values. Based on orthogonal regression, the mean threshold line was fitted through the data-points. Then the minimum threshold line was defined either by the lower limit of the 95% prediction confidence interval around the mean threshold line, or parallel line below the lower limit of the scatter of the data. Quantile regression was recommended because it was statistically-based and robust to outliers. Since the domination mechanisms of gully initiation would not change within decades in a certain region, the relative area exponent could be fixed as a constant value. According to this hypothesis, the threshold coefficient of muti-periods could be used to investigate human effect on gully initiation. In China, about 70% of the research was carried out in the Loess Plateau region. The 1:10 000 topographic map was widely used to obtain local slope and catchment size, since this was the most extensive and detailed topographic map currently available. Most studies extracted the threshold conditions by using the eye-fitted line through the "lower-most" points, and few consideration was carried out for the potential errors between different calculation methods. Road construction altered the surface hydrology, and the road surface condition reduced the critical slope for a given drainage area required for gullying. Agricultural reclamation was the main reason for gully development in the Northeastern China, where ridge tillage was widely applied. Contour ridge changed runoff pathways and rearranged drainage networks, and longitudinal ridge accelerated flow concentration. Consideration of ridge-direction effect was important for gully initiation topographic threshold theory applications in this region. Using high-resolution topographic maps and adding the parameters that characterized the human activities effect on concentrated surface runoff could enrich the gully initiation topographic threshold theory. Current gully erosion model could simulate gully development while gully head needed to be mannually located. Hence gully initiation topographic threshold theory could be promoted by combining with such models, since this theory could predict where gully initiated.