Analytical estimation of effective discharge for small southern Ontario streams

The effective discharge (Q e ) of a channel reach may be analytically determined by fitting the flow–duration relationship with a distribution model and representing the bed-material transport with a power function. Analysis of streamflow data from small southern Ontario streams showed that the commonly used lognormal distribution does not provide a good fit to many streamflow records. A mixed exponential distribution model is proposed and a formula for computing the resulting Q e is derived. The results from this new Q e formula were compared with those obtained using other analytical distribution functions and those from empirical sediment transport effectiveness curves. These comparisons indicate that the new analytical solution provides on average the most accurate estimates of Q e when the exponent β of the power function describing sediment transport at the channel reach is not more than 2; when β > 2, a gamma distribution provides the most accurate estimates followed closely by the mixed exponential distribution.