Statistical considerations show that the sediment, solute, or pollutant load of a river is likely to be underestimated by methods in which unmeasured concentrations are estimated from discharge using a least squares regression for the logarithm of concentration. The degree of underestimation increases with the degree of scatter about the rating curve and can reach 50%. A simple correction factor is proposed and tested successfully on simulated and real data sets.

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A numerical model has been developed for the routing of gravel‐sized sediment along a river channel which is free to adjust both its long profile and surface texture. Hydraulic calculations use a step‐backwater approach, and sediment transport is predicted with the method of Parker (1990a), which uses a low degree of size selectivity. Exchange of sediment between the surface and subsurface is described using the modified Exner equation of Parker and Sutherland (1990). The model is applied to an idealized channel based on the highly concave Allt Dubhaig, Scotland, in which fining by particle wear is minor. The rapid downstream fining observed in this river is closely matched by model predictions after a time equivalent to <102 years under the present flow regime of the river. The evolution of the fining pattern during the model run and associated changes in sediment transport and bed aggradation are described. It is concluded that strong profile concavity can force rapid downstream fining even though bed load transport is only slightly size selective. This run of the model serves as a basis for testing of the sensitivity of downstream fining to alternative choices of parameter values and boundary conditions, which are summarized here and will be described in a subsequent paper.

River loads often have to be estimated from continuous discharge data but relatively infrequent sampling of sediment, solute, or pollutant concentrations. Two standard ways of doing this are to multiply mean concentration by mean discharge, and to use a rating curve to predict unmeasured concentrations. Both methods are known from previous empirical studies to underestimate true load. Statistical considerations explain these biases and yield correction factors which can be used to obtain unbiased estimates of load. Simulation experiments with normally‐distributed scatter about log‐linear trends, and sampling experiments using a natural data set, show that the corrected rating curve method has lower sampling variability than other unbiased methods based on average instantaneous load and is thus the recommended procedure when the rating plot is of the assumed form. The precision of all methods increases with sample size and decreases with increasing rating‐curve slope and scatter.

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