Importance of slope gradient and contributing area for optimal prediction of the initiation and trajectory of ephemeral gullies

Ephemeral gully erosion rates are controlled by various factors out of which topography plays an important role. This study investigates the possibility to predict the location of ephemeral gullies using two topographic attributes only: i.e., local slope gradient (S) and upslope contributing area per unit length of contour (As). An inverse relationship between S and As, in which the relative importance of the area exponent was varied, was evaluated as to its performance in predicting the location of ephemeral gullies for three intensively cultivated catchments in the Belgian loess belt. This model is easily applicable as it only uses information on topography, which can be derived from a digital elevation model, and land use. Predicted locations of ephemeral gullies were confronted with the locations recorded over 5 years of field observations. For all catchments a high relative area exponent (relative to the slope exponent) was required to yield good results. The optimal relative area exponent ranged from 0.7 to 1.5; however, the quality of the prediction did not vary significantly when changing the exponent within this range. An average relative area exponent of ca. 1 is appropriate for all three study areas and may therefore be proposed for similar areas under similar conditions. A striking discrepancy was found between the high relative area exponent required to predict optimally the trajectory of the gullies and the low relative area exponent (0.2) required to identify the spots in the landscape where ephemeral gullies begin. This indicates that spots in the landscape where gullies start are more controlled by slope gradient, while the presence of concavities control the trajectory of the gullies until the slope gradient is too low and sediment deposition starts. No relationship was found between the frequency of the occurrence of ephemeral gullies and the percentage of predicted gully pixels for each frequency class. This indicates that frequently occurring gullies at the same location are not easier to predict than accidental gullies.