Morphodynamic observations in large alluvial rivers show the presence of large dunes which are constantly adjusting to varying flow conditions. This suggests that the bed roughness, in particular its component due to form drag, is as dynamic as the dunes themselves. In this work, the roughness function first defined by Hama (1954) which appears in the velocity profile proposed by Clauser (1954) for boundary-layer flows, is generalized to define the nature of "alluvial roughness" for flows over fully-developed dunes. The method proposed herein is an extension of the one developed by Perry et al. (1969) for pipe flows. When spatiallyaveraged velocity profiles of flow over dunes are available, the method can be used to estimate sand-grain roughness as well as a spatially-averaged composite roughness due to the combined effect of both skin friction and formdrag in large sand-bed rivers.This can facilitate computation of sediment transport aswell the estimation of water temperature effects on flow stage as commonly observed in the Missouri River.