Estimating parameters of the channel width-flow discharge relation using rill and gully channel junction data

Eroding channels can usually be characterized by a power relationship between channel width (W) and channel discharge (Q). This paper examines the WQ relation using a recently developed channel junction approach to extend the validity of the WQ relation and to develop a procedure for estimating the WQ exponent and proportionality coefficient. Rill and gully channel data from the literature, and new data collected in different badland areas and in a few forest mountain streams, are analysed. Analysis shows that the WQ relation for channel width collected in badlands and forests agrees with trends observed for cropland. The exponent increases with increasing channel width in a continuous fashion rather than in a step-like way and tends to a maximum whose value ranges between 0.5 and 0.6. The proportionality coefficient can be split into two terms, one expressing the case in which an eroding channel can broaden, the other reflecting the difficulties in removing the less erodible clods or rock fragments from the channel bed. Its splitting allows the development of a more correct form of the WQ relation in agreement with modern approaches of channel geometry: one part has the dimension of a discharge and makes the power base dimensionless, while the other brings the dimension of a length, needed for the channel width, into the WQ relation. The interpretation of the two constants is Supported by data collected in rainfall-runoff simulation experiments conducted in the field. Values characterizing the two constants in some environments are also given. Nevertheless the approach is not sufficiently parameterized yet to be of practical use (e.g. in models or for estimating peak discharge in areas where rill channels have formed).