WATER RESOURCES RESEARCH, VOL. 26, NO. 11, PAGES 2717-2731, NOVEMBER 1990 At-a-Point Bed Load Sampling in the Presence of Dunes BASIL GOMEZ Department of Geography and Geology, Indiana State University, Terre Haute D. W. HUBBELL U.S. Geological Survey, Cascades Volcano Observatory, Vancouver, Washington H. H. STEVENS, JR U.S. Geological Survey, Denver Federal Center, Lakewood, Colorado Even during constant, or virtually constant, flow conditions,bed load transport rates are known to vary over a range of temporal scales. Previous studieshave emphasizedthat, in order to provide an accurate estimate of the mean bed load transport rate at a given point, either many samples must be collected repeatedly or the sampling time must be long. We systematically evaluate errors associated with at-a-point bed load sampling during steadyflow conditions in the presence of dunesand provide an indication of the way in which sampling shouldproceed in order to minimize samplingerrors. The analysis is undertaken using laboratory data and a theoretical probability distribution function. It is assumed that bed load samplers have an efficiency of 100% and that the flow conditions and the configuration of the primary bedforms remain constant during the sampling period.In the presence of dunes, sampling should be accomplished using (1) the shortest practicable sampling time for each sample, (2) short, equally spaced time intervals between samples,and (3) as long a sampling period as is necessary to ensure that at least one primary bed form has passed the sampling point. Such procedures will provide informationabout high- and low-frequencyfluctuations in at-a-point bed load transport rates and a reasonably reliable estimate of the mean bed load transportrate. Only about 21 sequentialsamplesare required to estimate the mean bed load transport rate at any given point. However, because•the sampling time generally is shortin comparison with the time that it takes a dune to pass the sampling point, between 50 and 100 samples are needed to define both high- and low-frequency at-a-point rate variations. A knowledgeof the prevailing bed configuration is necessary in order to ensure that samplingproceedsin accordance with these requirements. INTRODUCTION Background One of the most prominent features associatedwith the movement of bed load is its pronouncedtemporal variability even under constant, or virtually constant, flow conditions [Gomez et al., 1989]. This variability is manifest at a variety of time scales and arises from a number of sources that are associated either with the availability of bed material for transport or with the manner in which sediment is mobilized and transported. First, structured variations in bed load yield, that commonly appear to be reflected in the wavelike translation of bed material downstreamor processes suchas scour and fill, result from long- to intermediate-term varia- tions in the rate at which sediment is suppliedto or distrib- uted within a channel or reach. Second, short-term, quasi- cyclical variations in bed load transport rates occur in response to the temporary exhaustion of the supply of transportable material in a channelor reach, the migrationof bed forms or groups of particles, and processes such as armoring. Third, instantaneous fluctuations in bed load transport rates result from the inherently stochastic nature of the physical processes that govern the entrainment and transport of bed load. Copyfight 1990 by the American Geophysical Union. Paper number 90WR01417. 0043-1397/90/90WR-01417505.00 Short-term temporal variations in bed load transport rates are important to the elucidation of bed load transport pro- cesses.For example, functional relations between bed load discharge and water dischargemay not exist where bed load is supply limited [Nordin, 1985]. At a more fundamental level, if bed load transport rates vary under constant-flow conditions, single or short-term at-a-point measurementsare unlikely to represent the mean bed load discharge at that point [Einstein, 1948; Hubbell, 1964, 1987; de Vries, 1973]. Each point either must be sampled repeatedly over an extended period of time, or the sampling time must be protracted enough to average out fluctuations in bed load transport rates to achieve reasonable accuracy. Previous Attempts To Estimate Errors Involved In Bed Load Sampling Errors in bed load sampling principally arise from two sources [Hubbell, 1964]. One source is instrumentally ori- ented and results from the tendency of a given sampling device to underrepresent or overrepresent the quantity of material in transport. The secondsource is processoriented and arises from random or short-term, often quasi-cyclic, variations in bedloadtransport rates. Many attempts to account for instrument errors have been made [e.g., Einstein, 1948; Novak, 1957; Emmett, 1980; Engel,1983; Hubbeliet al., 1981]. Pit-type bed load traps are considered to be consistently accurate [Hubbell, 1964; 2717