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Abstract:Empirical prediction equations of the form W D aQ b have been reported for rills and rivers, but not for ephemeral gullies. In this study six experimental data sets are used to establish a relationship between channel width (W, m) and flow discharge (Q, m 3 s 1 ) for ephemeral gullies formed on cropland. The resulting regression equation (W D 2Ð51 Q 0Ð412 ; R 2 D 0Ð72; n D 67) predicts observed channel width reasonably well. Owing to logistic limitations related to the respective experimental set ups, only relatively small runoff discharges (i.e. Q < 0Ð02 m 3 s 1 ) were covered. Using field data, where measured ephemeral gully channel width was attributed to a calculated peak runoff discharge on sealed cropland, the application field of the regression equation was extended towards larger discharges (i.e. 5 ð 10 4 m 3 s 1 < Q < 0Ð1 m 3 s 1 ). Comparing W-Q relationships for concentrated flow channels revealed that the discharge exponent (b) varies from 0Ð3 for rills over 0Ð4 for gullies to 0Ð5 for rivers. This shift in b may be the result of: (i) differences in flow shear stress distribution over the wetted perimeter between rills, gullies and rivers, (ii) a decrease in probability of a channel formed in soil material with uniform erosion resistance from rills over gullies to rivers and (iii) a decrease in average surface slope from rills over gullies to rivers.The proposed W-Q equation for ephemeral gullies is valid for (sealed) cropland with no significant change in erosion resistance with depth. Two examples illustrate limitations of the W-Q approach. In a first example, vertical erosion is hindered by a frozen subsoil. The second example relates to a typical summer situation where the soil moisture profile of an agricultural field makes the top 0Ð02 m five times more erodible than the underlying soil material. For both cases observed W values are larger than those predicted by the established channel width equation for concentrated flow on cropland. For the frozen soils the equation W D 3Ð17 Q 0Ð368 R 2 D 0Ð78; n D 617 was established, but for the summer soils no equation could be established.

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