Regression residuals and mean profiles in uniform open-channel flows

In spire of the frequent use of regression in hydraulics, the analysis of r egression residuals is often not performed and yet may be important in asse ssing the performance of proposed models. The present work discusses residu als analysis with respect to (1) velocity profiles in clear-water channel f lows; and (2) suspended-sediment concentration profiles in sediment-laden f lows. Three models proposed for the mean velocity profile in turbulent unif orm open-channel clear-water flows, differing only in the treatment of the wake component, are studied. The analysis of residuals from linear regressi on applied to velocity measurements suggests that there are statistical gro unds for believing that these wake-function models are inadequate. The trad itional Rouse suspended-sediment concentration profile provides the context for a comparison of a direct application of non-Linear regression for fitt ing purposes rather than the more traditional linear regression of a transf ormed problem. The importance of the uniform-variance assumption in least-s quares fitting is emphasized. The analysis of residuals indicates that, in spite of smaller residual mean squares, direct nonlinear regression is inap propriate due to the nonuniform variance of the error term. Possibly mislea ding interpretations of high values of the coefficient of determination (R- 2), pointed out, and implications for velocity profiles in sediment-laden f lows and more complicated models of suspended sediment concentration are di scussed.