Bankfull Shields number versus slope and grain size

Many characteristics of alluvial rivers, including hydraulic geometry and sediment transport during periods of morphological activity, can be related to the bankfull Shields number. Recent papers have used regression analysis on large datasets of bankfull hydraulic geometry to formulate a predictive relation for bankfull Shields number as a function of reach-averaged channel slope and characteristic bed grain size. These results show different regression fits; the relationship for bankfull Shields stress is therefore still ambiguous. We propose a new relation via multivariate major axis regression, a symmetric, error-in-variables regression scheme, which improves on previous attempts by introducing error in both the dependent variable and independent variables. We discuss the use of typical ordinary least squares, Bayesian, and error-in-variables regressions to inform the use of regression statistical methods to quantify hydraulic geometry. The results reported here back previous claims that bankfull shear velocity is rather invariant to median bed material.