A review of topographic threshold conditions for gully head development in different environments Dino Torri a, ⁎, Jean Poesen b a CNR-IRPI, Perugia, Italy b Division of Geography, Department of Earth and Environmental Sciences, KU Leuven, Belgium abstract article info Article history: Received 12 March 2013 Accepted 16 December 2013 Available online 3 January 2014 Keywords: Catchment area Slope gradient Rock fragment CN-method Climate Gully density Gully head development represents a significant geomorphic process in a wide range of environments. Several studies investigated the critical topographic conditions, expressed by local slope gradient (s) and drainage area (A), controlling the development and position of gully heads in various landscapes. This review examines over 39 publications. After critically analysing the reported threshold data and after standardisation of the procedure to determine the critical topographic conditions for gully head development, i.e., sA b N k or s N kA -b some data sets were discarded because they were not compatible with the standard presentation of data as reported by the majority of studies. Hence, a detailed analysis was made of 63 reported s–A relationships for overland-flow induced gully-heads extracted from data sets collected in various parts of the world. A first examination of the behaviour of both the exponent b and the threshold coefficient k, which reflects the resistance of the site to gully head development, shows clear effects of land use on the value of k whereas the value of b does not seem to be affected. Further analyses are conducted of the recalculated threshold coefficients k, for two predefined constant values of the exponent b. The lowest k-values were observed for cropland followed by values for rangeland, pasture and forest. Effects of climate, rock fragment cover at the soil surface and water storage ca- pacity of the gully catchment on k-values were also shown. The most interesting result is that for a given and con- stant b-value, the threshold coefficient k can be predicted using soil and vegetation characteristics, based on the NRCS Runoff Curve Number values and on surface rock fragment cover. Furthermore, the underlying physical processes explaining the value of the exponent b were analysed. Finally, a physically-based model, well anchored in the established theories, is proposed as a first step to predict gully head development in various landscapes and under changing environmental conditions. The results of this review clearly show that better and more reliable models can be built, including effects of land use, climate changes and natural disasters. © 2013 Elsevier B.V. All rights reserved. Contents 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 1.1. Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 1.2. Theoretical approach to describe gully head development by runoff . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 1.3. Interactions between vegetation, soil, soil surface characteristics, sediment load and resistance to soil erosion by concentrated flow . . . . . 75 1.4. NRCS Curve number method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 1.5. Empirical equations governing concentrated flow erosion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 2. Materials and methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 3. Data analysis and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 3.1. Critical review of literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 3.2. Data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 3.3. The overall effects of vegetation, land management and soil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 3.4. Tangent or sinus? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 4. Towards an explanation of the b-value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 Earth-Science Reviews 130 (2014) 73–85 ⁎ Corresponding author. Tel.: +39 0755014421; fax: +39 0755014420. E-mail address: dino.torri@cnr.it (D. Torri). 0012-8252/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.earscirev.2013.12.006 Contents lists available at ScienceDirect Earth-Science Reviews journal homepage: www.elsevier.com/locate/earscirev