There are two sources of error involved in using a sampling device to derive bedload discharge estimates [Hubbell, 1964].
Reliable estimates of the streamwide bedload discharge obtained using sampling devices are dependent upon good at-a-point knowledge across the full width of the channel. Any number of random samples may, in theory, provide an estimate of the prevailing mean bed load transport rate, though the magnitude of the errors involved may be expected to decrease as sample size increases. However, it is almost impossible to obtain a truly independent random sequence of at-a-point bedload samples under field conditions, and sequential samples likely will be serially correlated. Each observation in an autocorrelated time series repeats part of the information contained in previous observations. Thus, more sequential samples than independent random samples are required to provide the same information about the true mean.
Gomez et al.  evaluated errors associated with at-a-point sampling where dunes were present. Their analysis suggests that 21 sequential samples are required to obtain an estimate of the mean at-a-point bed load transport rate that falls within Å50% of the true mean relative bedload transport rate, at the 99% confidence level. (The relative transport rate is the instantaneous bed load transport rate divided by the true mean rate.) This assumes that the sampling period is long enough to allow at least one primary bedform to migrate past the sampling point. (The sampling period is the sum of the sampling times and sampling intervals; where the sampling time is the length of time the sampler remains on the bed, and the sampling interval is the length of time that elapses between consecutive samples.) In consequence, sampling periods may be lengthy. When the sampling time is short (¦30 s), independence between samples may be maintained by ensuring that the sampling interval is relatively long (Æ300 s). Effects due to nonstationarity may be minimized by ensuring that the sampling interval does not coincide with the period of the bedforms that are present.
Gomez & Troutman  used field data and information derived from a model, that describes the geometric features of a dune train in terms of a spatial process observed at a fixed point in time, to show that sampling errors decrease as the number of samples collected increases, and the number of traverses of the channel over which the samples are collected increases. If a relatively large number of samples (say 50) are collected in a relatively short period of time (implying a high sampling rate, such as 12 samples per hour), increasing the number of traverses (at-a-point repetitions) initiates a tradeoff between the systematic and random errors associated with the sampling process. This tradeoff is less pronounced at lower sampling rates. However, although one traverse minimizes systematic errors, for a given number of samples and sampling rate, a greater number of traverses (at-a-point repetitions) is necessary to minimize random errors. In many cases the most favorable situation is attained when sampling involves between 4 and 7 traverses. Thus, the combination of a relatively large number of samples and a relatively low sampling rate is preferred since, for a fixed number of samples and sampling rate, although increasing the number of at-a-point repetitions tends to decrease the random error involved, beyond a certain point the effect is offset by an accompanying increase in systematic error.
Gomez, B., & Troutman, B.M., Evaluation of process errors in bed load sampling using a dune model, Water Resour. Res.33, 2387-2398, 1997.
Gomez, B., Hubbell, D.W., & Stevens, H.H., At-a-point bedload sampling in the presence of dunes, Water Resour. Res. 26, 2717-2731, 1990.
Gomez, B., Emmett, W.W., & Hubbell., D.W., Comments on sampling bedload in small rivers, Proc. 5th Fed. Inter-Agency Sedimt. Conf. 2, 65-72, 1991.
Hubbell, D.W., Apparatus and techniques for measuring bedload, U.S. Geol. Survey Water-Supply Paper 1748, 1964.
Hubbell, D.W., Stevens, H.H., Skinner, J.V., & Beverage, J.P., New approach to calibrating bedload samplers, J. Hydraul. Engr., Am. Soc. Civ. Engrs.111, 677-694, 1985.
Thomas, R.B. & Lewis, J., A new model for bed load sampler calibration to replace the probability-matching method, Water Resour. Res. 29, 583-597, 1993.