Two-dimensional modelling of the within-field variation in rill and gully geometry and location related to topography

The topography, rill pattern and geometry were surveyed within a small agricultural field. The rill network and dimensions were converted to a grid-based system and used to calculate the slope gradient and contributing area for each grid cell. A strong correlation was found between the rill cross-sections and a power function of slope gradient and contributing area. The slope and area exponents were 1.28 and 0.89, respectively, for all rill points, and 1.02 and 0.87, respectively, for the rill points not lying in the depositional area. These exponents are within the range reported for field studies in a one-dimensional context. Our data confirmed the potential of an inverse slope-area relationship with an area exponent of 0.5 to predict areas prone to rilling and the location of ephemeral gullies. However, the prediction of individual rill starting points was not possible because of the major influence of small local variations in topography on overland flow discharge. Both the prediction of the rill cross-sections and the prediction of the location of the two ephemeral gullies in the field were significantly improved when the tillage direction was taken into account in calculating the contributing area. Therefore, tillage patterns should be given more attention when developing routing procedures for hydrological and erosion models.