A conceptual model of the relationship between channel characteristics and discharge

Regression equations with the form y = f(q), where y is a channel characteristic and q is a discharge of a particular frequency are widely used in fluvial geomorphology. They imply that channel geometry is related to a dominant discharge. For this to be so, the river must be ‘in regime’ i.e. its characteristics must fluctuate about a mean condition which is effectively stationary at the time scale considered. The static regression-dominant discharge approach does not fully describe the relationship between channel characteristics and discharge and an alternative model is proposed with the form y(t) = ∞ h(u)- q(t-u)du. This model states that channel form is a product of the whole series of discharges experienced by the channel. The dominant discharge-static regression approach provides a working approximation of the relationship between channel characteristics and discharge only when temporal variations in q are small or when y is insensitive to variations in q.