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The Fortuna geological formation dated from the late Oligocene to early Miocene is mainly composed of friable sandstone. Gully erosion on this substratum is developing complex shaped gullies where bank processes are as important as head advance by cutting and bed deepening by vertical incision. For irregularly shaped gullies quantitative information on gully erosion rates as related to gully head extension are scarce because bank active sides take many forms presumably depending on topography, climate and lithology. Our field cross section measurements of 4 gullies developed in the Fortuna Formation, (2 located on a steep slope area (> 15%) and the other two on a gentle slope (<9%)), have shown that the geometry of these gullies is far from a conical gully shape. These field measurements were used to calculate gully reaches geometry and volume variation. No direct relationships between gully volume and length could be established for these gullies in the Fortuna formation. Nevertheless, since both gully top view area and maximum top width are increasing, as the gully reach length increases, relationships could be established between maximum top width and their equivalent width defined as the ratio between gully reach top view area and its length. Then, gully volume-length relationships could be established for each of the 5 maximum bank-full widths studied on the two gentle and two steep slope gullies. For any maximum top width, the gully volume-length relationship was found to be not unique but the volume is increasing linearly up to the 15 m and 45 m distance from the gully head and then logarithmically for steep and gentle slope gullies, respectively. The linear and logarithmic equations’ coefficients were also found to be a function of gully maximum top width. These equations were then used to quantify gully sediment yields related to gully shape evolution for eight gullies tributaries of As Sahsafa wadis. For this purpose the top view areas and lengths of these eight gullies were digitized and monitored on rectified air photographs of 1962, 1974 and 2000 using a Geographic Information System (Arc View). Half of these gullies were located in an area with a gentle slope gradient and the other half with steep slope gradient.

The average gullies length variation for the whole study period (1962-2000) were 11.74% and 10.32% whereas the average top view areas variation was 23.57% and 29.4% for gentle and steep slope gullies, respectively. Gullies volume changes during the periods 1962-1974 and 1974-2000 were then derived from the variation of gullies length and top view areas photo-measurements on these 8 tributaries using the relationships established from the four measured gullies. On gentle slopes, the average gully sediment yields during 1962-1974 and 1974-2000 periods were 3.98 and 2.28 m(3) ha(-1) year(-1), respectively. On steep slopes, these values are 4.82 and 2.47 m(3) ha(-1) year(-1). (C) 2012 Elsevier B.V. All rights reserved.