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Bed load transport is a highly nonlinear phenomenon. Numerous stress-transport power relations, with exponents varying between 1.5 and 16, have been proposed to capture the entire range of solid discharge trends exhibited by experimental data. A physics-based explanation of the variation in exponent values is provided here. The concept of time-resolved local stream power is used to determine the above-threshold energy available for mobilizing bed materials, giving rise to solid discharge estimates. The generated transport capacity records, analyzed by a long-term averaging process, allow for the construction of bed load curves that resemble the trends frequently reported in prior experimental studies. Under such conditions, use of long-term averaged bed shear stress and bed load transport rates provide practical, yet oversimplified accounts of the transport phenomenon. The limitation of this methodology is particularly evident in low-to-moderate transport rates, where the calculated bed shear stress and consequent bed load transport rates are underestimated compared to values based on active periods of sediment movement. As the degree of intermittency in bed load transport increases, so does the exponent to compensate for the inactive periods of bed mobility. Conditionally averaged stress-transport data, based on the active periods of bed load transport alone, however, exhibit a constant trend, reasonably well represented by a 1.5 power formula across the entire transport range. This approach better reflects the prevailing cause and effect relation by properly accounting for varied transport timescales. Furthermore, the resulting transport trend signifies a nearly constant efficiency in entraining and transporting sediment particles.

Plain Language Summary Bed load transport is a complex phenomenon involving nonlinear interactions between the fluid and solid particle dynamics. The conventional quantitative methods, based on a long-term averaging framework, lead to various power regression equations that link the bed load transport rates to the bed shear stress values, with exponents varying from 1.5 to 16, or even higher exponents, over a wide range of transport scenarios. The highly varied exponent values represent uncertainties that will compromise the utility of such empirical regression formulas in assessing bed load transport rates at different flow conditions. The unique contribution of this work is to elaborate on the underlying mechanism responsible for the variation in exponent values. Furthermore, a conditional data treatment is applied to the entire range of solid discharge trends, which appropriately accounts for the varied transport timescales shown at different levels of bed mobilization. This approach gives rise to a reasonably consistent power regression with exponents of 1.5. This 1.5th power relation signifies a nearly constant energy transfer efficiency by which the flow can entrain and transport sediment materials. These findings provide a better understanding of the transport mechanism(s) and facilitate the development of a consistent and physically meaningful bed load transport expression.