Estimating critical stream power for bedload transport calculations in gravel-bed rivers

The physical basis of Bagnold's equation for critical stream power is examined. Although the general approach is well founded, the original equation can be criticised for (1) failing to distinguish between the grain size in transport and the grain size that represents bed roughness; (2) requiring a knowledge of critical flow depth in addition to gross channel properties; (3) failing to allow for hiding and protrusion effects on the mobility of mixed-size stream beds. More general equations are presented which overcome these limitations. They require a knowledge of channel slope, but not depth. The analysis suggests that the presence of form resistance in addition to grain roughness does not affect the calculation of critical power. Critical power is expected to depend more sensitively on grain size between reaches than within reaches.