A general power equation for predicting bed load transport rates in gravel bed rivers

Abstract

[1] A variety of formulae has been developed to predict bed load transport in gravel bed rivers, ranging from simple regressions to complex multiparameter formulations. The ability to test these formulae across numerous field sites has, until recently, been hampered by a paucity of bed load transport data for gravel bed rivers. We use 2104 bed load transport observations in 24 gravel bed rivers in Idaho to assess the performance of eight different formulations of four bed load transport equations. Results show substantial differences in performance but no consistent relationship between formula performance and degree of calibration or complexity. However, formulae containing a transport threshold typically exhibit poor performance. Furthermore, we find that the transport data are best described by a simple power function of discharge. From this we propose a new bed load transport equation and identify channel and watershed characteristics that control the exponent and coefficient of the proposed power function. We find that the exponent is principally a factor of supply-related channel armoring (transport capacity in excess of sediment supply), whereas the coefficient is related to drainage area (a surrogate for absolute sediment supply). We evaluate the accuracy of the proposed power function at 17 independent test sites.

Performance of Bed-Load Transport Equations Relative to Geomorphic Significance: Predicting Effective Discharge and Its Transport Rate

“…͑1͔͒, but rather are expressed in complex terms of excess shear stress or excess stream power ͑e.g., Appendix A of Barry et al 2004͒. Therefore, in our analysis we predict total bed-load transport rates and consequent effective discharges in terms of the original formulations specified for each transport equation examined here.…”

“…Local discharge records were combined with the above equations to predict the effective discharge and its associated transport rate at each site, and then compared to observed values determined from site-specific bed-load rating curves. To improve the accuracy of our analysis, we have only included those sites from Barry et al ͑2004͒ where: ͑1͒ the observed record of daily mean discharge covers at least 10 years ͑Biedenharn et al 2001͒; ͑2͒ the bed-load transport observations were made over a wide range of low to high flows; and ͑3͒ the observed bed-load transport data were adequately described by Eq. ͑1͒ ͓i.e., where the correlation coefficient ͑r 2 ͒ of the rating curve is greater than 0.70 and there is no obvious nonlinearity to the observed transport data in log space͔ ͑Nash 1994͒.…”

“…Predicted values of unit bed-load transport rate for each discharge bin ͑q bi ͒ were multiplied by flow width ͑w͒ to determine Q bi , with w estimated from site-specific hydraulic geometry relationships. Shear stress and other necessary equation parameters for making these predictions were determined for each discharge following an approach similar to that used by Barry et al ͑2004͒.…”

“…1͒, and because equation performance can vary with discharge ͑Fig. 2 of Barry et al 2004Barry et al , 2007 , it is unclear whether previous assessments of performance apply to higher, geomorphically significant flows ͑e.g., the bankfull or effective discharges͒. Nor is it clear whether these equations can predict the effective discharge, which depends on the accuracy of the bed-load transport equation across a range of flows.…”

“…Previous studies assessing the accuracy of bed-load transport equations have considered equation performance statistically based on paired observations of measured and predicted bed-load transport rates ͑e.g., Gomez and Church 1989;Yang and Huang 2001;Bravo-Espinosa et al 2003;Barry et al 2004͒. However, transport measurements were typically taken during low flows, biasing the assessment of equation performance toward low discharges ͑Fig.…”