Medium-term gully headcut retreat rates in Southeast Spain determined from aerial photographs and ground measurements

This paper deals with gully retreat rates at different time scales, whereby the short-term time scale may span a time interval of 1–5 years, the medium-term time scale a time interval of 5–50 years, and the long-term time scale a time interval of more than 50 years. An analysis of high-altitude aerial photographs in combination with ground measurements allowed us to quantify volumetric gully-head retreat rates for 12 permanent gullies in Southeast Spain (Guadalentin and Guadix study areas) over a 40–43 year time interval (medium-term time scale). This resulted in an average retreat rate (V_e) of 17.4 m³ year⁻¹. A power relationship between drainage-basin area (A) and medium-term volumetric gully-head retreat rate, V_e=0.069A^0.380 (R²=0.51, n=21), was found by combining the gully-head retreat rates obtained in this study with those obtained by a dendrochronological method. The exponent (b) and the coefficient of determination (R²) of the power relationships V_e=aA^b increases from the short-term to the long-term time scale, expressing the increasing importance of drainage-basin area in gully development with time. Considerable differences between gully-head retreat rates measured at the short and medium-term time scales at individual gullies showed the importance of land-use changes and unsuccessful management practices on gully-head retreat, and the episodic nature of gully-head retreat when piping and tension cracking are involved. Higher gully-head retreat rates are obtained at the medium-term time scale compared to the short-term time scale but the differences are not significantly different at α=10%. The medium-term methods tend to measure proportionally more high gully retreat rates, but less extreme values compared to the short-term method. This is explained by a more equal distribution of extreme rainfall events both in space and time at a longer-term time scale, and hence a higher probability of measuring the average effect of both small and extreme rainfall events at each gully.