Numerical investigation of avulsions in gravel-bed braided rivers

Gravel-bed braided rivers are highly energetic fluvial systems characterized by frequent in-channel avulsions, which govern the morphodynamics of such rivers and are essential for them to maintain a braided planform. However, the avulsion mechanisms within natural braided rivers remain unclear due to their complicated hydraulic and morphodynamic processes. Influenced by neighbouring channels, avulsions in braided rivers may differ from those of bifurcations in single-thread rivers, suggesting that avulsions should be studied within the context of the entire braid network. In this study, braiding evolution processes in gravel-bed rivers were simulated using a physics-based numerical model that considers graded bed-load transport by dividing sediment particles into multiple size fractions and vertical sediment sorting by dividing the riverbed into several vertical layers. The numerical model successfully produced braiding processes and avulsion activities similar to those observed in a laboratory river. Results show that bend evolution of the main channel was the fundamental process controlling the occurrence of avulsions in the numerical model, with a cyclic process of channel meandering by lateral migration that transitioned to a straight channel pattern by avulsion. The radius of bend curvature for triggering avulsions in the numerical model was measured and it was found that the highest probability for a channel bend to generate an avulsion occurs when its radius of curvature is approximately 2.0–3.3 times the average anabranch width. Other types of avulsion were also observed that did not occur specifically at meander bends, but upstream meander evolution indirectly influenced such avulsions by altering channel pattern and discharge to those locations. This study explored the processes and mechanisms of several types of avulsion, and proposed factors controlling their occurrence, namely increasing channel curvature, high shear stress, tributary discharge, riverbed gradient and upstream channel pattern, with high shear stress being a direct indicator. Furthermore, avulsions in a typical gravel-bed braided river, the Waimakariri River in New Zealand, were analysed using sequential Google Earth maps, which confirmed the conclusions derived from the numerical simulation.     

DYNAMIC RESOURCES OF RIVER SEDIMENTS

The currently enforced Bulgarian water legislation [the Water Act (1999), the Environmental Protection Act (2002), etc.] requires conducting special studies for accurate assessments of sand and gravel flux along the rivers, prior to the issue of the license for operation of the quarries, where they will be dredged. The activity of a quarry necessitates special investigations because of the large dimensions of the damages inflicted on the environment. Ours studies have shown that there are two types of river reaches, in which abstraction of sand and gravel is performed. The first one refers usually to the plain area river reaches. The other type is mountainous with high rate of sediment load, which consists of coarse solid matter. The “on-the-spot” study on the environmental impact of the sand and gravel dredging has revealed that in the area of the quarry the riverbed cuts into the alluvial sediments to about 6-7 m and this ditch has spread by attenuation at a distance of more than 25 km upstream. Downstream the pit the picture is replicated and at the 8th km a local scour on the riverbed, amounting to more than 1.80-2.00 m, has been measured near the foundation of a massive bridge in the centre of city of Plovdiv. Such assessments of dynamic resources of sand and gravel materials are expected to serve for the purposes of gradual limitation of this activity in river sections close to renewable resources. The amount of sediment load, which may be abstracted in the area of the Orizare quarry in Bulgaria on a yearly basis has been calculated as 6000 m^3/a. It ensures that the resources will not be exhausted and irreversible distortion of the riverbed will be prevented. This is an environmentally safe limit.     

Field application of close‐range digital photogrammetry (CRDP) for grain‐scale fluvial morphology studies

In situ measurement of grain‐scale fluvial morphology is important for studies on grain roughness, sediment transport and the interactions between animals and the geomorphology, topics relevant to many river practitioners. Close‐range digital photogrammetry (CRDP) and terrestrial laser scanning (TLS) are the two most common techniques to obtain high‐resolution digital elevation models (DEMs) from fluvial surfaces. However, field application of topography remote sensing at the grain scale is presently hindered mainly by the tedious workflow challenges that one needs to overcome to obtain high‐accuracy elevation data. A recommended approach for CRDP to collect high‐resolution and high‐accuracy DEMs has been developed for gravel‐bed flume studies. The present paper investigates the deployment of the laboratory technique on three exposed gravel bars in a natural river environment. In contrast to other approaches, having the calibration carried out in the laboratory removes the need for independently surveyed ground‐control targets, and makes for an efficient and effective data collection in the field. Optimization of the gravel‐bed imagery helps DEM collection, without being impacted by variable lighting conditions. The benefit of a light‐weight three‐dimensional printed gravel‐bed model for DEM quality assessment is shown, and confirms the reliability of grain roughness data measured with CRDP. Imagery and DEM analysis evidences sedimentological contrasts between gravel bars within the reach. The analysis of the surface elevations shows the effect variable grain‐size and sediment sorting have on the surface roughness. By plotting the two‐dimensional structure functions and surface slopes and aspects we identify different grain arrangements and surface structures. The calculation of the inclination index allows determining the surface‐forming flow direction(s). We show that progress in topography remote sensing is important to extend our knowledge on fluvial morphology processes at the grain scale, and how a technique customized for use by fluvial geomorphologists in the field benefits this progress. Copyright © 2016 John Wiley & Sons, Ltd.     

Measurements of armour layer roughness geometry function and porosity

The roughness geometry function of the interfacial sublayer of a gravel-bed armour layer was measured directly by filling water stepwise into a laboratory flume and indirectly from a digital elevation model (DEM) of the surface. The results of both methods are compared and show that the DEM can be used to reliably estimate the roughness density function for a wide range of the interfacial sublayer. The direct measurements revealed an absolute minimum of porosity at the level of the roughness trough which is significantly smaller than porosity in the undisturbed subsurface and porosity estimates obtained from relationships found in the literature. The significance of the results for hydraulic engineering and ecological applications is highlighted.     

TRANSPORT OF GRAVELS WITH DIFFERENT RANGES OF GRAIN SIZES IN A STEEP CHANNEL

An understanding of the transport mechanism of gravel-bed rivers is very important for the river management and engineering works. The main objective of this study was to conduct a series of laboratory experiment in a steep flume to investigate the particle segregation and the transport rate of nonuniform gravel. Median sizes of 15 mm and 7.5 mm, and gradation coefficients of 1.5 and 2.0 were selected for the particle size distributions of nonuniform gravel. In addition to the 36 sets of data collected in this study, 635 sets of existing data for gravel with both nonuniform and nearly uniform sizes were analyzed. According to the results of the sieve analysis and the related theory, hiding functions for both particle size distributions of this study were derived. An attempt was made to develop an Einstein-type transport relationship for nonuniform gravel using dimensionless parameters with mean size as a representative particle size. A modified Schoklitsch-type sediment transport equation with a critical unit flow discharge was also developed to reasonably predict the transport rate of gravels. In addition, an artificial neural network (ANN) model with a back-propagation network (BPN) algorithm was also applied in this study.     

Inferring sediment transfers and functional connectivity of rivers from repeat topographic surveys

High-resolution topographic models have revolutionized monitoring of river changes by comparing sequential river topographic surveys (i.e. change detection). Nevertheless, much more may be obtained from this innovative quantification of changes. In this paper, we enhance the interpretation of geomorphic processes by presenting a new method for understanding of sources and sinks of sediment, river sediment transfers and functional sediment connectivity. Repeat digital elevation models (DEMs) obtained by photogrammetry were used to quantify topographic change after two floods by creating a DEM of difference (DoD) of a 6.5 km-long reach of Rambla de la Viuda stream, an ephemeral gravel-bed river in eastern Spain. The proposed method involved dividing the channel into 10 m-long longitudinal strips that were used to systematically draw boundaries between the erosional and depositional areas of the DoD. The analysis objectively: (i) drew a series of erosional and depositional segments, from 120 to 1360 m in length; (ii) estimated ranges of source-to-storage sediment transport distances, 320–670 m in the upstream and middle reaches and up to 2030 m in the lower reach; and (iii) obtained values of functional connectivity (i.e. the ratio between the sediment exported (erosion) and retained (deposition), ranging from 10³ to 10⁻³). The variability in these three parameters along the river was found to be related to the level of channel disturbance by in-stream mining during the 1990s and 2000s. Additionally, this method indicates that the main process responsible for self-adjustment of the present morphosedimentary conditions is intra-reach erosion of banks and channel beds. Thus, this study proposes a new methodology to characterize morphological change, sediment transfer and connectivity that may serve as environmental indicators of the hydromorphological integrity of rivers with potential application to the European Water Framework Directive. © 2019 John Wiley & Sons, Ltd.     

Lateral and longitudinal flight dispersals of a stonefly,Alloperla ishikariana (Plecoptera,Chloroperlidae), from the hyporheic zone in a gravel-bed river in Japan

The life-history traits of amphibitic insects are not well understood. These insects inhabit saturated interstitial areas below the riverbed (hyporheic zone) at the larval stage, mate in terrestrial habitats, and return to rivers for oviposition, but there is no knowledge concerning their dispersal characteristics. We sought to address this by examining how far amphibitic insects disperse away from the channel (laterally) and along upstream or downstream (longitudinally) in a gravel-bed river. Alloperla ishikariana was selected as the focal species because it numerically dominates other amphibites in an 18-km study segment of a 4th-order gravel-bed river in Hokkaido, Northern Japan. Malaise traps were set at various distances from the channel towards the riparian forest to estimate lateral dispersal distances. An elevated stable nitrogen isotope ratio in downstream larvae, caused by the influence of effluent from a wastewater treatment plant, was used to assess longitudinal dispersal by identifying and tracking adult movements. Laterally, 50th and 90th percentile dispersal distances were 11.66 and 35.09 m for female A. ishikariana and 20.59 and 59.20 m for male, respectively; this overlapped with distances previously estimated for other aquatic benthic taxa. Longitudinally, 50th and 90th percentile dispersal distances were 0.74 and 1.43 km for female and 3.11 and 7.87 km for male, respectively. Alloperla ishikariana had one of the longest upstream traveling distances compared with other aquatic insects, and the longest among Plecoptera taxa known thus far where male exhibited a greater dispersal distance. A higher number of adults demonstrated upstream movement, suggesting an upstream bias in the longitudinal dispersal of A. ishikariana. Overall, amphibitic stoneflies did not exhibit distinct dispersal characteristics compared with the results of previous reports on presumably benthic taxa. Our findings support an improved visualization of a multi-dimensionally connected river ecosystem in terms of material flow, including vertical connectivity.     

Bed-material transport estimated from channel surveys: Vedder River,British Columbia

This study investigates the possibility to estimate bed-material transfer in gravel-bed rivers by analysis of morphological changes along Vedder River, British Columbia. Data from repeated cross-section surveys are used to estimate volume changes along the length of an 8 km reach. Gravel budgets are based on a continuity approach. An error analysis is performed to evaluate the uncertainty in the best estimate of transport rates. The mean annual gravel transport into the reach over a 9 year period was estimated to be 36600 ± 5600 m³ yr^?1. The sediment transport regime along the length of the river is evaluated and examined in relation to peak flood flows. Significant spatial and temporal variability in transport rates is demonstrated, making dubious the generalization of transport estimates from hydraulic calculations, or from sample measurements at a single cross-section. The assumptions, procedures and limitations of the ‘morphological approach’ to sediment transport analysis are discussed. It is concluded that this approach provides information of quality comparable or superior to that of direct measurements of transport, yet requires less field effort. It also provides additional information about river morphological changes, making it a preferred method for geomorphlogical investigations and for many river management concerns.     

Gravel excavation and geomorphic evolution of the mining affected river in the upstream reach of the Yangtze River,China

As economic development upstream in the Yangtze River basin has progressed in recent decades,the demand for sediment has rapidly increased and contributed to an expansion in sediment excavation that may affect the river’s stability and navigation safety.In the current study,the distribution of gravel mining in the upstream reach of the Yangtze River was investigated using field measurements obtained from2008 to 2017.An experimental investigation was then done to analyze the bed load behavior in ...     

Modelling gravel-bed topography from sediment transport

A simple queueing model which generates bed topography consistent with the mechanics of gravel motion is presented. The equations on which it is based are derived from the application of simple theoretical ideas and an analysis of published flume data (Meland and Norrman, 1966; Francis, 1973; Abbott and Francis, 1977). The simulation produces an extremely variable bed topography in which at least two scales of bedform may be identified. Features of 5–10 grain wavelengths, similar to pebble clusters, are superimposed on other forms whose wavelength is up to 30–40 grains and which resemble step-pools systems and antidunes. Sediment transport shows many of the characteristics found in the field and the model is, therefore, thought to provide a useful starting point from which to examine the interaction between flow, sediment transport, and bedforms in gravel-bed and cobble streams.     

STEP-POOL MORPHOLOGY IN HIGH-GRADIENT STREAMS

l 1NTRODUCTIONGravel bed rivers are found in man parts of the worid, mpically in moUntainous regions with highgradients and seasonally high flows. These rivers are imPotalt in contrlling flood waters from sPringrunoff in regions such as the Pacific Northwest, Where heaVy snowfall can be followed by equally heaVyranfall. The combination of high stream gradient and high discharge causes significant erosion of thebed and bank of the strCam, in some cases moving large boulders with ease.It…     

The zoogeomorphology of case-building caddisfly: Quantifying sediment use

Caddisfly (Trichoptera) larvae are an abundant and widespread aquatic insect group characterized by the construction of silk structures, including nets and cases. Case-building caddisfly have the potential to modify the sorting and mobility of sand and fine gravel via: (1) case construction, resulting in altered sediment properties; (2) transporting sediment incorporated into cases over the river bed; and (3) changing the structure of river beds via burrowing activity. To investigate these mechanisms, it is necessary to understand the mass, size distribution and spatial variability of sediment use by case-building caddisfly larvae. We quantified the mineral sediment used by individuals and communities of case-building caddisfly in 27 samples, from three sites on a gravel-bed stream. The mass and size distribution of sediment in individual cases varied between taxa (mass = 0.001–0.83 g, D₅₀ = 0.17–4 mm). The mean mass of sediment used by the caddisfly community was 38 g m⁻² and varied locally. Sediment use was predominantly coarse sand (D₅₀ = 1 mm). 64% of sediment use was attributable to Agapetus fuscipes (Glossosomatidae). Due to within-species variability in case mass, the abundance of most taxa, including A. fuscipes, was only weakly associated with the mass of sediment used by this species, at the river scale. Whilst the caddisfly community used a small percentage of the total sediment available (average 2.99% of the 1–1.4 mm size fraction), A. fuscipes used more fine sediment in their cases at sites where it was more available. Despite variability in local habitat, all sites supported diverse case-building caddisfly communities utilizing mineral sediment. Consequently, geomorphological effects of case-building caddisfly are potentially widespread. The results provide novel insights into the specific grain sizes and quantities of fine sediment used by caddisfly larvae, which represents an important step towards understanding their zoogeomorphic activities. © 2019 The Authors. Earth Surface Processes and Landforms Published by John Wiley & Sons Ltd.     

Combining suspended sediment monitoring and fingerprinting to determine the spatial origin of fine sediment in a mountainous river catchment

An excess of fine sediment (grain size <2 mm) supply to rivers leads to reservoir siltation, water contamination and operational problems for hydroelectric power plants in many catchments of the world, such as in the French Alps. These problems are exacerbated in mountainous environments characterized by large sediment exports during very short periods. This study combined river flow records, sediment geochemistry and associated radionuclide concentrations as input properties to a Monte Carlo mixing model to quantify the contribution of different geologic sources to river sediment. Overall, between 2007 and 2009, erosion rates reached 249 ± 75 t km^?2 yr^?1 at the outlet of the Bléone catchment, but this mean value masked important spatial variations of erosion intensity within the catchment (85–5000 t km^?2 yr^?1). Quantifying the contribution of different potential sources to river sediment required the application of sediment fingerprinting using a Monte Carlo mixing model. This model allowed the specific contributions of different geological sub‐types (i.e. black marls, marly limestones, conglomerates and Quaternary deposits) to be determined. Even though they generate locally very high erosion rates, black marls supplied only a minor fraction (5–20%) of the fine sediment collected on the riverbed in the vicinity of the 907 km² catchment outlet. The bulk of sediment was provided by Quaternary deposits (21–66%), conglomerates (3–44%) and limestones (9–27%). Even though bioengineering works conducted currently to stabilize gullies in black marl terrains are undoubtedly useful to limit sediment supply to the Bléone river, erosion generated by other substrate sources dominated between 2007 and 2009 in this catchment. Copyright © 2011 John Wiley & Sons, Ltd.     

Climate-change driven increased flood magnitudes and frequency in the British uplands: Geomorphologically informed scientific underpinning for upland flood-risk management

Upland river systems in the UK are predicted to be prone to the effects of increased flood magnitudes and frequency, driven by climate change. It is clear from recent events that some headwater catchments can be very sensitive to large floods, activating the full sediment system, with implications for flood risk management further down the catchment. We provide a 15-year record of detailed morphological change on a 500-m reach of upland gravel-bed river, focusing upon the geomorphic response to an extreme event in 2007, and the recovery in the decade following. Through novel application of two-dimensional (2D) hydrodynamic modelling we evaluate the different energy states of pre- and post-flood morphologies of the river reach, exploring how energy state adjusts with recovery following the event. Following the 2007 flood, morphological adjustments resulted in changes to the shear stress population over the reach, resulting in higher shear stresses. Although the proportion of shear stresses in excess of those experienced using the pre-flood digital elevation model (DEM) varied over the recovery period, they remained substantially in excess of those experienced pre-2007, suggesting that there is still potential for enhanced bedload transport and morphological adjustment within the reach. Although volumetric change calculated from DEM differencing does indicate a reduction in erosion and deposition volumes in the decade following the flood, we argue that the system still has not fully recovered to the pre-flood state. We further argue that Thinhope Burn, and other similarly impacted catchments in upland environments, may not recover under the wet climatic phase currently being experienced. Hence systems like Thinhope Burn will continue to deliver large volumes of sediment further down river catchments, providing new challenges for flood risk management into the future.     

Co-evolution of coarse grain structuring and bed roughness in response to episodic sediment supply in an experimental aggrading channel

We use flume experiments to better understand how gravel-bed channels maintain bed surface stability in response to pulses of sediment supply. Bed elevations and surface imagery at high spatial resolutions were used to quantify the co-evolution of surface grain-size distribution (GSD), bed roughness statistics, and bed surface structures (clusters, cells and transverse features). Using a new semi-automated method, we identified individual stone structures over a 2 m × 1 m area throughout the experiments. After an initial coarsening, surface GSD and armouring ratio remained nearly stable as sediment pulses caused net bed aggradation. In contrast, individual grain structures continued to form, increase or decrease in size, and disappear throughout the experiments. The response of the bed to sediment pulses depended on the history of surface roughness evolution and bed surface structure development, as these factors changed much more in response to supply perturbations earlier in the experiments compared to later, even as the bed continued to aggrade. We interpret that the dynamic production and destruction of bed surface structures can act as a ‘buffer’ to sediment supply pulses, maintaining a stable bed surface during aggradation with minimal change in grain size or armouring. © 2019 John Wiley & Sons, Ltd.     

Interactions between sediment delivery,channel change,climate change and flood risk in a temperate upland environment

This paper uses numerical simulation of flood inundation based on a coupled one‐dimensional–two‐dimensional treatment to explore the impacts upon flood extent of both long‐term climate changes, predicted to the 2050s and 2080s, and short‐term river channel changes in response to sediment delivery, for a temperate upland gravel‐bed river. Results show that 16 months of measured in‐channel sedimentation in an upland gravel‐bed river cause about half of the increase in inundation extent that was simulated to arise from climate change. Consideration of the joint impacts of climate change and sedimentation emphasized the non‐linear nature of system response, and the possibly severe and synergistic effects that come from combined direct effects of climate change and sediment delivery. Such effects are likely to be exacerbated further as a result of the impacts of climate change upon coarse sediment delivery. In generic terms, these processes are commonly overlooked in flood risk mapping exercises and are likely to be important in any river system where there are high rates of sediment delivery and long‐term transfer of sediment to floodplain storage (i.e. alluviation involving active channel aggradation and migration). Similarly, attempts to reduce channel migration through river bank stabilization are likely to exacerbate this process as without bank erosion, channel capacity cannot be maintained. Finally, many flood risk mapping studies rely upon calibration based upon combining contemporary bed surveys with historical flood outlines, and this will lead to underestimation of the magnitude and frequency of floodplain inundation in an aggrading system for a flood of a given magnitude. Copyright © 2006 John Wiley & Sons, Ltd.     

Three-dimensional flow patterns at the river–aquifer interface — a case study at the Danube

The three-dimensional groundwater flow patterns in a gravel bar at the Danube east of Vienna were investigated and are discussed in this paper. The observed groundwater level gradients are highly dynamic and respond very quickly to changes in the river water levels. A variably saturated groundwater model was calibrated to the data to describe the complex dynamics of flow in the gravel bar. The model results suggest that short-term (6–48 h) fluctuations of river water levels cause variations in the exchange flow rates from − 35 l/s to 82 l/s. The highest rates occur during brief infiltration after rapidly rising river water levels. Simulations of different scenarios indicate that riverbank clogging will decrease the exchange fluxes by up to 80%, while clogging of both riverbank and riverbed essentially stops the flow exchange. The groundwater model is also used to simulate the transport of a conservative tracer. The variation of river water levels over time is shown to increase the extent of the active river–aquifer mixing zone in the gravel bar. These dynamic factors significantly enhance the dilution of conservative tracer concentrations in this zone.     

Sediment transport at the network scale and its link to channel morphology in the braided Vjosa River system

In this article we apply the CASCADE network-scale sediment connectivity model to the Vjosa River in Albania. The Vjosa is one of the last unimpaired braided rivers in Europe and, at the same time, a data scarce environment, which limits our ability to model how this pristine river might respond to future human disturbance. To initialize the model, we use remotely sensed data and modeled hydrology from a regional model. We perform a reach-by-reach optimization of surface grain size distribution (GSD) and bedload transport capacity to ensure equilibrium conditions throughout the network. In order to account for the various sources of uncertainty in the calculation of transport capacity, we performed a global sensitivity analysis. The modeled GSD distributions generated by the sensitivity analysis generally match the six GSDs measured at different locations within the network. The modeled bedload sediment fluxes increase systematically downstream, and annual fluxes at the outlet of the Vjosa are well within an order of magnitude of fluxes derived from previous estimates of the annual suspended sediment load. We then use the modeled sediment fluxes as input to a set of theoretically derived functions that successfully discriminate between multi-thread and single-thread channel patterns. This finding provides additional validation of the model results by showing a clear connection between modeled sediment concentrations and observed river morphology. Finally, we observe that a reduction in sediment flux of about 50% (e.g., due to dams) would likely cause existing braided reaches to shift toward single thread morphology. The proposed method is widely applicable and opens a new avenue for application of network-scale sediment models that aid in the exploration of river stability to changes in water and sediment fluxes.     

Monitoring gravel augmentation in a large regulated river and implications for process‐based restoration

The artificial gravel augmentation of river channels is increasingly being used to mitigate the adverse effects of river regulation and sediment starvation. A systematic framework for designing and assessing such gravel augmentations is still lacking, notably on large rivers. Monitoring is required to quantify the movement of augmented gravel, measure bedform changes, assess potential habitat enhancement, and reduce the uncertainty in sediment management. Here we present the results of an experiment conducted in the Rhine River (French and German border). In 2010, 23 000 m³ of sediments (approximately the mean annual bedload transport capacity) were supplied in a by‐passed reach downstream of the Kembs dam to test the feasibility of enhancing sediment transport and bedform changes. A 620‐m‐long and 12‐m‐wide gravel deposit was created 8 km downstream from the dam. Monitoring included topo‐bathymetric surveys, radio‐frequency particle tracking using passive integrated transponder (PIT) tags, bed grain size measurement, and airborne imagery. Six surveys performed since 2009 have been described (before and after gravel augmentation, and after Q₂ and Q₁₅ floods). The key findings are that (i) the augmented gravel was partially dispersed by the first flood event of December 2010 (Q₁); (ii) PIT tags were found up to 3200 m downstream of the gravel augmentation site after four years, but the effects of gravel augmentation could not be clearly distinguished from the effects of floods and internal remobilization on more than 3500 m downstream; (iii) linear and log‐linear relationships linking bedload transport, particle mobility, and grain size were established; and (iv) combined bathymetry and PIT tag surveys were useful for evaluating potential environmental risks and the first morpho‐ecological responses. This confirmed the complementary nature of such techniques in the monitoring of gravel augmentation in large rivers. Copyright © 2017 John Wiley & Sons, Ltd.     

Bias and precision of percentiles of bulk grain size distributions

Percentiles such as D₅₀ and D₈₄, calculated from weights retained on different sieves, are widely used to characterize grain size distributions (GSDs) of bulk samples of sedimentary deposits or sediment fluxes. The sampling variability of such percentiles is not well known, and few sampling guidelines exist for reliable characterization of GSDs. We report results from computer sampling experiments on the variability of sample percentiles in different-sized samples from populations with a log-normal GSD by weight and different sorting coefficients. Sample sizes are scaled by the volume of a median-sized grain so that results can be applied to any log-normal GSD. Sampling is random for the GSD by number that is equivalent to a specified GSD by weight. Results show important differences from standard sampling theory applicable to pebble-count GSDs. In small bulk samples all percentiles, including the median, are underestimated (more so for smaller samples, coarser percentiles and poorer sorting), and precision does not improve with the square root of sample size until fairly large sample sizes are exceeded. Non-dimensional equations fitted by eye to the results give good approximations to expected bias and precision in any percentile from 50 to 95 for any given sample size and population sorting coefficient. They are inverted to estimate the sample size required to avoid significant bias, or achieve specified precision, in any percentile of interest given estimates of the population D₅₀ and sorting coefficient. Target sample sizes are sometimes considerably smaller, but in other circumstances larger, than suggested by previous guidelines relating to estimation of the entire grain size distribution. Bias is likely in small samples of river bedload and good precision requires very large samples of poorly sorted gravel deposits. © 1997 John Wiley & Sons, Ltd.