Velocity-discharge relationships in three lowland rivers

The use of different functional forms to describe the variation of velocity with discharge is explored for four cross‐sections, nine short reaches (100‐250 m), and three long reaches (2‐7 km) in three lowland rivers in Lincolnshire. The traditional log‐linear relationship applies to more than half the cases, the degree of correlation never falling below 0‐9. Although probably more valid from a physical standpoint, the log‐quadratic relationship‐is only moderately successful, one problem being the position of the vertex relative to bankfull discharge. Alternative formulations based on a kinematic routing model and a partitioned log‐linear model have restricted application. Rates of change of velocity with discharge are relatively high in these lowland rivers, not only at‐a‐station but also downstream. One explanation is that velocity becomes particularly sensitive to local slope and within‐channel vegetation conditions as discharge decreases, resulting in rather low velocities at small discharges. Cross‐sectional and reach‐based results are compared for neighbouring stretches of river. Velocities in short reaches do not differ appreciably from those at nearby cross‐sections or from those in long reaches with a length of less than 3 km. By integrating within‐reach variability and avoiding the need to chose a representative cross‐section, velocity measurement over short reaches is probably preferable to that at cross‐sections as a basis for at‐a‐station hydraulic geometry.