Detailed hydraulic measurements were made in nine step-pool, fi ve cascade and one plane-bed reach in Fraser Experimental Forest, Colorado to better understand at-a-station hydraulic geometry (AHG) relations in these channel types. Average values for AHG exponents, m (0·49), f (0·39), and b (0·16), were well within the range found by other researchers working in steep gradient channels. A principal component analysis (PCA) was used to compare the combined variations in all three exponents against fi ve potential control variables: wood, D 84 , grain-size distribution (σ), coeffi cient of variation of pool volume, average roughness-area (projected wetted area) and bed gradient. The gradient and average roughness-area were found to be signifi cantly related to the PCA axis scores, indicating that both driving and resisting forces infl uence the rates of change of velocity, depth and width with discharge. Further analysis of the exponents showed that reaches with m > b + f are most likely dominated by grain resistance and reaches below this value (m < b + f) are dominated by form resistance. Copyright © 2010 John Wiley & Sons, Ltd.KEYWORDS: at-a-station hydraulic geometry (AHG); hydraulic measurements; principal component analysis (PCA); channels
At-a-station Hydraulic Geometry and Flow ResistanceAt-a-station hydraulic geometry (AHG) characterizes how changes in discharge affect specifi c hydraulic variables such as width, depth, velocity and friction. Leopold and Maddock (1953) fi rst coined the term 'hydraulic geometry' to describe systematic changes both downstream and at a cross-section for each of the above hydraulic variables. They proposed three power relations to describe how width (w = aQ b ), depth (d = cQ f ) and velocity (v = kQ m ) vary with discharge both downstream and at a given cross-section in a channel, where Q is discharge; w is water-surface width, d is mean depth; and v is velocity. These power relations are bound by the continuity equation (Q = wdv), so that the coeffi cients a, c, and k have a product equal to one and the exponents b, f, and m sum to one. Leopold and Maddock (1953) found that the rates of change of width, depth and velocity with discharge were related to the shape of the channel, the slope of the watersurface and the roughness of the wetted perimeter. They also found the sediment load to be an important control on the rates of change of both velocity and depth (Leopold and Maddock, 1953).Few studies have reported AHG values for steep mountain channels (Lee and Ferguson, 2002;Reid, 2005;Comiti et al., 2007). A better understanding of at-a-station changes in each of the above hydraulic variables can improve our understanding of the sources and magnitude of hydraulic roughness in these channels, which tend to have values of fl ow resistance as refl ected in Manning's n or Darcy-Weisbach friction factor (ff) that are much higher than values for channel reaches with gradient <1% (Jarrett, 1984;Bathurst, 1985Bathurst, , 1993.Steep mountain channels are divided into cascad...