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Proceedings olthe Seventh Federal Interagency Sedimentation Conference, March 25 to 29, 2001, Reno. Nevada . The symbol? in eq (2) applies to a single change in conditions; for results to be representative of a more extensive set of time-series measurements, it is necessary to replace the? with a statistical measure. The approach taken here is to replace? with the standard deviation of a variable, so that 10g.6.Cl1ogAD, is replaced by log6C log6D, a(logC) ~ a(logDJ (3) where o(logC) and o(logD,) represent the standard deviations of loge and 10gD" respectively, This approach of substituting the standard deviation of a variable for a single change (?) in that variable is equivalent to the reduced major axis technique for fitting a line to a scatter plot of x,y data (p, 200,204 in Davis, 1986), Eq (3) predicts the absolute value of log6.Cl1ogADn but not the sign of this quantity. In some cases, the sign can be detennined by inspection; in other cases it may be necessary to determine whether the positive or negative sign gives a better fit to the data (Davis, 1986), Trackinl! I!rain size of bed sediment that is accessible to the flow Once it has been established that grain-size regulation of sediment transport is important in a particular sediment-transport system (p.\ approaches or exceeds 1), it may be desirable to monitor changes in grain size of sediment on the bed. This is useful for at least three goals: (1) quantifying changes dtrough time in the degree of winnowing or annoring downstream from a dam, (2) measuring the extent to which tributaries have contributed fine sediment to the bed of a channel (as is important in determining the timing of artificial floods in the Colorado River in Grand Canyon), and (3) measuring the spatial (depth.related) variation of grain size of sediment on the bed in pools, bars, and floodplains. A dimensionless measure of grain size of sediment on the bed,~, can be defined as f3=~ Dbm (4) . where Db is the median grain diameter of bed sediment at an instant in time. and Dh... is the average of a sequence of median diameters at the same location. Thus, p is a measure of the relative coarseness of sediment at one point on the bed. As Rubin and Topping (in press) showed, P can also be expressed as a function of the dependent variable s C and Dr relative to their mean or median values p "( ~ t'"( ~J'" (5) The exponent of the concentrat ion ratio is negative, whereas the exponent of the grain-size rati 0 is positive (Table 1). As a result, the relative bed coarseness, p, increases as concentration decreases and as grain size increases (as intuition would suggest). Bed-sediment grain size is proportional to p and can be calculated by multiplying P by the time-averaged bed-sediment grain size for a particular reach. The relation between bed sediment and suspended sediment expressed III eq (5) reflects at least three kinds of changes. First, grain size of sediment at a point on the bed (or within a reach) can change through time as a result of deposition of sediment from upstream or tributaries, winnowing of the bed, or erosion and excavation of underlying substrate. Second, the depth to which sediment in the substrate interacts with the flow may vary with flow strength (Wiberg, et a!., 1994). For example, a weak flow that generates ripples on the bed will exchange sediment with the uppennost few centimeters of the sediment substrate. In contrast, a stronger flow that generates large dunes will exchange sediment with a greater depth within the substrate. Third, as stage increases, a river may gain access to finer sediment that occurs on high.elevation channel-margin bars and floodplains. Of these three changes, only the first reflects actual changes on the bed; the latter two changes in grain size reflect lateral or vertical changes in the region of the channel interacting with the flow. Measured changes In P reflect all of these factors. . 1,202