Most downstream hydraulic geometry exponents have been found to be very close to the classic values reported by Leopold and Maddock (1953). These have been viewed as the simplified cases to general trends because the hydraulic geometry of alluvial channels is actually the product of 'multivariate controls' (Richards, 1982). This paper is an attempt to develop a soundly based foundation for the explanation of the physical mechanisms of these controls. A quantitative relationship between channel shape and boundary shear distribution developed from experimental flume results is found to be applicable in some instances to alluvial channels, particularly to stable canals. On the basis of this relationship, it is shown that downstream hydraulic geometry is determined not only by flow discharge, but also by channel slope, channel average roughness and sediment composition of the channel boundary. This is strongly supported by our analysis of 529 observations from both stable canals and natural rivers in the U.S.A. and the U.K.. The difference between regime relations in canals and the hydraulic geometry of rivers appears to be caused mainly by channel slope and average roughness, which can be regarded as constants only in stable canals. The close relationship between discharge and channel average roughness observed in canals is not repeated in natural channels, partly because of the variety of flow values used to define the channel-forming discharge. Furthermore, it is indicated that the effects of the sediment composition of the channel boundary on hydraulic geometry are significant and need further investigation.
