Revisiting slope-area thresholds for gully initiation: a systematic review and meta-analysis

Gully erosion is a significant soil erosion process worldwide, especially in semi-arid regions. Representing the most severe erosion phase, gully development poses a major threat to soil quality and land productivity, and to the achievement of multiple sustainable development goals (SDGs). To effectively prevent and control gully erosion, many models have been developed to predict the locations of gully initiation, among which the topographic threshold has been most frequently applied. Approximating the erosive force by a combination of the local slope (S) and upslope drainage area (A), gully erosion is expected to initiate where the erosive force of flowing water exceeds the erosion resistance. This threshold condition can be expressed as SA b = k, in which both b and k are constant coefficients varying with environmental conditions. During recent decades, significant progress has been made in the measurements of both S and A, and the determination of S-A thresholds, resulting in an increased number of S-A datasets and thresholds. The objective of this study was to systematically review and evaluate the existing methods for S-A threshold derivation and data collection, and to assess the effects of climate, lithology, soil texture and land use on gullying threshold based on a total of 127 S-A datasets comprising 5,302 S-A pairs retrieved from 55 publications. In accordance with the geographical distributions of gully erosion, the S-A thresholds were mainly investigated in the temperate climate, sedimentary lithology dominated by marls and loess, and loamy soils, and on the agricultural lands especially croplands. A total of 15 approaches have been developed to determine the S-A threshold, among which the orthogonal regression (OR) method calculating the lower limit of the 95% prediction confidence interval around the OR trendline was believed the optimal in general. Applying this method to all the S-A pairs retrieved, a global threshold was generated as SA 0.269 = 0.014. Working on both the S-A dataset and pair levels, the area exponent b was found to be primarily affected by climate and lithology, and the threshold coefficient k to be strongly influenced by land use. The rapid development of GIS technology has remarkably increased the number of S-A datasets and data pairs, and the traditional field survey techniques have been replaced by high-resolution DEMs obtained from, for example, real-time kinematic (RTK) GPS and unmanned aerial vehicle (UAV) photogrammetry. Future research efforts are still needed to further enrich the S-A data in different environments, to standardize the acquisition procedure for S and A, and to explore advanced methods for S-A threshold determination. • Slope-area (S-A) thresholds were mainly analyzed in temperate climate, sedimentary lithology and loamy soils, and on agricultural lands • A method based on orthogonal regression was generally the optimal one for threshold determination • The area exponent b of the threshold was significantly affected by climate and lithology • The threshold coefficient k was significantly influenced by land use • Recent advances in GIS technology and DEM acquisition have notably increased the numbers of S-A datasets and pairs