Channel width–flow discharge relationships for rills and gullies

Abstract

Research conducted during the first half of the last century has shown that a strong power relationship exists between channel width and total flow discharge in streams. Recent studies have shown that this power relationship can be theoretically derived for bankfull discharge in channels. The relationship has been extended empirically to rills and gullies, revealing that the discharge exponent for rills and gullies is significantly smaller than that for rivers. However, water flow in rills and gullies is only rarely bankfull, indicating that the theoretical explanation for the power relationship found for rivers does not apply to rills and gullies. In order to investigate the width−discharge relationships for rills and gullies, a new method is proposed based on field measurements of widths of concentrated-flow erosion channels both upstream and downstream of channel junctions. Although the method only allows the determination of the exponent of the power relationship, it is easy and inexpensive to apply. A total of 322 rill and gully channel junctions with various soils and land use types were investigated in Belgium, Italy and Spain. The obtained data confirmed the existence of the power relationship for rills and gullies, with the exponent varying from 0.43 for small rills (about 3 cm in width) to 0.5 for gullies (about 50 to 100 cm in width). The data did not allow deciding whether the exponent varies consistently with channel width or in a step-wise fashion. The exponent values obtained in this study are larger than those reported in previous studies, but this may result from differences in the definition of the discharge that eroded the channel to its current width.