Half-Yield Discharge: Process-Based Predictor of Bankfull Discharge

The river management and restoration community has devoted much effort to predicting the bankfull discharge, $Q_{\mathrm{bf}}$, and associated channel geometry at $Q_{\mathrm{bf}}$ for the purposes of channel study, classification, and design. Four types $Q_{\mathrm{bf}}$ prediction methods predominate: (1) direct estimation based on field indicators of bankfull stage, (2) downstream hydraulic geometry equations, (3) a flood peak discharge with a specified return interval based on the annual maximum flood series (e.g., the 1.5- to 2-year flood) or regional flood peak statistical relations, and (4) process-based approaches that incorporate the magnitude and frequency of sediment transport such as the most effective discharge $Q_{\mathrm{eff}}$. Process-based $Q_{\mathrm{bf}}$ predictors are calculated using sediment transport data from 95 gauged sites across the United States including coarse, bed load–dominated channels and fine, suspended load–dominated channels with drainage areas ranging from 6 to $1.4\times {10}^5{\mathrm{km}}^2$. These values are compared with observations of $Q_{\mathrm{bf}}$ made from field measurements of bankfull indicators. It was found that the discharge associated with 50% of cumulative sediment yield based on the flow record—$Q_h$, the half-yield discharge—predicts $Q_{\mathrm{bf}}$ well. When compared with $Q_{\mathrm{eff}}$ and the 1.5- and 2-year floods ($Q_{1.5}$ and $Q_2$), $Q_h$ has the lowest relative error in predicting $Q_{\mathrm{bf}}$ for coarse and fine bed sites. Log-log regression models of observed–predicted data pairs indicate that $Q_h$ and $Q_{1.5}$ calculated for fine bed sites are the only $Q_{\mathrm{bf}}$ predictor models whose slopes are not significantly different from unity and whose intercepts are not significantly different from zero. The most effective discharge, $Q_{\mathrm{eff}}$, and $Q_h$ both perform well in predicting $Q_{\mathrm{bf}}$ in coarse bed sites, followed by $Q_{1.5}$, whereas $Q_{\mathrm{eff}}$ uniformly underpredicts $Q_{\mathrm{bf}}$ in fine bed sites. The behavior of $Q_h$, a process-based predictor of $Q_{\mathrm{bf}}$, is characterized to highlight circumstances in which sediment yield analysis may be important in estimating the bankfull discharge. The half-yield discharge represents a novel estimator of $Q_{\mathrm{bf}}$ in rivers not previously discussed in this context.