Comparison of gully initiation thresholds estimation techniques: a case study from India
Authors: Majhi Anindya , Nyssen Jan , Verdoodt Ann 
Published: June 2022

&lt;p&gt;Characterising topographic threshold conditions of existing gullies is pivotal for locating areas that may be at risk of fresh gully head development in a landscape. Expressed as a rather simple equation &lt;em&gt;S = aA&lt;sup&gt;&amp;#8722;b&lt;/sup&gt;&lt;/em&gt;, where &lt;em&gt;S&lt;/em&gt; is the critical slope gradient for gully head development (m m&lt;sup&gt;&amp;#8722;1&lt;/sup&gt;), &lt;em&gt;A&lt;/em&gt; is gully head drainage area (ha) and &lt;em&gt;a&lt;/em&gt; and &lt;em&gt;b&lt;/em&gt; are environment-specific coefficients, it is premised on the concept that in a region of uniform lithology/soil, land cover/use and climate, gully erosion is a threshold phenomenon that initiates when, for a given catchment area, a critical slope gradient has been exceeded or vice versa.&lt;/p&gt;&lt;p&gt;The critical threshold condition is represented by the straight line that passes through the floor of the &lt;em&gt;S-A&lt;/em&gt; scatter upon plotting in logarithmic axes and essentially discriminates between the gullied and ungullied areas of a landscape. A whole host of approaches have been conceived and followed to construct the said threshold line, ranging from manual drawing through lowermost collinear points to applying various statistical methods such as orthogonal regression, quantile regression and nonlinear regression. However, it was found through a literature survey that often a method was chosen and applied without proper justification as regards its pertinence.&lt;/p&gt;&lt;p&gt;Using data collected through field measurements at 110 gully heads across ten sites in eastern India, this study assessed the various methods that have been employed so far to estimate gully initiation thresholds, highlighted their merits and demerits following a rigorous comparative analysis and concluded that the two techniques based on orthogonal regression, coined by Vandekerckhove &lt;em&gt;et al.&lt;/em&gt; (1998) and Vanwalleghem &lt;em&gt;et al.&lt;/em&gt; (2005) are the most appropriate. However, the method of Vandekerckhove &lt;em&gt;et al.&lt;/em&gt; (1998) was observed to be relatively robust to outliers and should thus be the preferred choice in future studies of this type. Albeit it is not recommended to use quantile regression for this purpose, it may be useful to discern if there are significant differences in the &lt;em&gt;S-A&lt;/em&gt; relationship across quantiles and assess the same with respect to changes in environmental factors that are known to exercise utmost control on gully initiation.&lt;/p&gt;&lt;p&gt;&amp;#160;&lt;/p&gt;&lt;p&gt;&lt;strong&gt;References&lt;/strong&gt;&lt;/p&gt;&lt;p&gt;Vanwalleghem, T., Poesen, J., Nachtergaele, J., &amp; Verstraeten, G. (2005). Characteristics, controlling factors and importance of deep gullies under cropland on loess-derived soils. Geomorphology, 69(1&amp;#8211;4), 76&amp;#8211;91.&lt;/p&gt;&lt;p&gt;Vandekerckhove, L., Poesen, J., Oostwoud Wijdenes, D., &amp; de Figueiredo, T. (1998). Topographical thresholds for ephemeral gully initiation in intensively cultivated areas of the Mediterranean. CATENA, 33(3), 271&amp;#8211;292.&lt;/p&gt;