*5.1. Determination of Yang's Formula Independent Variables*

As demonstrated in Section 4.3, in an effort to determine the dimensionless independent variables of Equation (4), a set of supplementary hydraulic parameters, in addition to those displayed in Table 1, had to be calculated. Hence, the following parameters were computed, on the basis of available data: water kinematic viscosity, fall velocity, shear velocity, and the dimensionless critical velocity, *Vcr*/ω.

Fall velocity was deemed to be the most decisive parameter in Yang's formula, as it is the only parameter that appears in all independent variables. For this reason, a special attention was given to fall velocity, which was calculated by two widely used formulas for settling particles, those of Zanke [78] and Rubey [2]. Following the computation of kinematic viscosity and shear velocity, the dimensionless critical velocity, *Vcr*/ω, was calculated, for each set of data, by means of Equations (5) and (6). The ranges of values for all calculated parameters and variables, for each dataset, are provided in Table 2.

In Table 2, *X*1, *X*2, *X*3, *X*4, *X*<sup>5</sup> are the dimensionless variables *log(*ω·*d*50/ν*)*, *log(V*∗/ω*)*, *log(VS*/ω−*VcrS*/ω*)*, *log(*ω·*d50*/ν*)*·*log(VS*/ω−*VcrS*/ω*)*, *log(V*∗/ω*)*·*log(VS*/ω−*VcrS*/ω*)*, respectively, *Ct* is the total measured sediment concentration obtained from the experimental data, and *CF* is the total calculated sediment concentration, as obtained from the unit stream power formula, using Yang's coefficients and by replacing the independent variables with the calculated values of *X*1*, X*2*, X*3*, X*4*, X*5.



As mentioned above, the calculations were carried out two times, one by using the fall velocity obtained by the formula of Zanke [78], and one with the fall velocity from the formula of Rubey [2]. By means of comparison between the 432 values of *logCt* and *logCF*, Nash-Sutcliffe Efficiencies (NSEs) of 0.79 and 0.72 were achieved with Zanke's and Rubey's formulas, respectively. Hence, in Table 2, only the results obtained by the use of Zanke's formula, for fall velocity, are presented.

As a first comment, and by observing both the range values of *logCt* and *logCF*, and the NSE value of 0.79, it can be said that the approximation between the measured and calculated results, as well as the quality of data is deemed satisfactory.
