[5] The bed load experiment used in this Technical Note has been conducted at the Hydraulic Engineering Laboratory of the Politecnico di Milano. We used a pressurized, transparent duct whose cross section is 0.40 m wide and 0.16 m deep; the duct length is almost 6 m. Approximately midway along the duct, a recess section is installed, which is filled with uniform plastic cylindrical particles of a density equal to 1.43 times that of water. Median equivalent size of the particles (i.e., diameter of a sphere of an equal volume) is *d*_{50} = 3.6 mm. In the remaining parts of the duct, the plastic particles were glued to the bed surface to ensure homogeneity in bed roughness.

[6] The described experimental setup differs, owing to flow pressurization, from those typically used in sediment transport research. In this respect it is useful to note that the literature on sediment transport in covered flows [e.g., *Lau and Krishnappan*, 1985; *Smith and Ettema*, 1997] indicates that sediment transport dynamics is not significantly different from that for free-surface flows. For both flow types, definitions of the threshold condition are conceptually the same. In our study, we defined the critical condition as described by *Radice and Ballio* [2008]; that is, we associated the incipient motion with the dimensionless solid discharge per unit width predicted by the Meyer-Peter and Müller (presented paper, 1948) equation for the Shields parameter (ratio of the Shields number to the threshold one) of 1.01. The threshold solid discharge was 6·10^{−5}, and the corresponding water discharge was 18.95 l/s.

[7] We performed a sediment transport experiment with a water discharge of 21.0 l/s. Thus, the corresponding Shields parameter can be estimated, approximately, as 1.2, assuming that for no-bed form conditions it is equal to the squared ratio of the acting flow rate to the critical flow rate. As the bed load was low, bed degradation during experimental runs was negligible and thus no sediment circulation was implemented. The sediment motion was filmed from the top to cover the bed area 20 × 35 cm^{2} (referred below as a measurement window). The instantaneous velocity profiles were measured at a single location using an Ultrasonic Doppler Profiler (UDP) positioned at an angle of 75° to the upper duct wall, oriented upstream. The UDP provided along-beam velocity data, that is, along the inclined coordinate aligned with the UDP. Both bed images and velocity profiles were sampled at 25 Hz frequency. The experiment duration, under constant background conditions, was 20 min, thus providing 30,000 instantaneous values of stationary data for each measured quantity. The measurement duration was chosen to secure sufficient data sets for estimating spectra and higher-order statistics. The period of prevailing velocity fluctuations (i.e., “bursting period”) can be estimated as *T*_{B} = *k*·*δ*/*U*_{max}, with *k* ranging from 2 to 5 [*Nezu and Hakagawa*, 1993]. These fluctuations have been well resolved in our measurements, which were made with 0.04 s sampling intervals (25 Hz). Indeed, with *U*_{max} = 37 cm/s and *δ* = *h*/2 = 8 cm (half the duct height), we obtain *T*_{B} = 0.4–1.1 s. However, particular turbulent events such as ejections or sweeps have been only partially resolved. According to *Nikora and Goring* [2000], the ratio of the event duration to the bursting period is approximately 0.07–0.09 near the bed, so that the event duration should be, in our case, around 0.03–0.08 s. Thus, the sampling frequency and duration in our measurements were appropriate to capture large-scale turbulence structures and their variability while smaller-scale short-lived events have been only partially measured. The bulk flow conditions can be characterized as steady, subcritical, fully turbulent and hydraulically rough; that is, *Re* = *Uh*/*ν* = 52,500, *Re*_{p} = *u*d*_{50}/*ν* ≈ 100, and *Fr* = *U*/(*gh*)^{0.5} = 0.27, where *Re*, *Re*_{p}, and *Fr* are the Reynolds, particulate Reynolds and Froude numbers, respectively, *U* is cross-sectional mean velocity, *h* is depth, *ν* is fluid viscosity, *u** is shear velocity, and *g* is the acceleration due to gravity.

[8] The areal concentration of moving sediments *C* was measured as proposed by *Radice et al.* [2006]. Sediment concentration is defined as a spatially averaged quantity over an averaging area *A*, being *C* = *W*/(*A*·*d*_{50}), where *W* is the total volume of the moving particles. The number of moving grains, which is easily convertible to the corresponding solid volume, was measured by identification of the moving particles through subtraction of consecutive frames and suitable filtering of the obtained difference images. The particle diameter is used as a characteristic height of the moving layer as at low bed load intensity the particle motion occurred in a single-particle layer. Note that this selection has no effect on the statistics reported in this paper.

[9] We explored a range of averaging areas, from 1 cm^{2} to 64 cm^{2}. An example of a studied sediment field with an averaging area of 4 × 4 cm^{2} is shown in Figure 1. The double-averaged (i.e., space-time-averaged [*Nikora et al.*, 2007]) values of the sediment concentration and particle velocity were used to check homogeneity of the sediment transport within the measurement window. The first- and second-order statistics of the sediment concentration are depicted in Figure 2, where the coefficient of variation is defined as the ratio of the standard deviation to the mean. The data show that the sediment transport is fairly uniform in the longitudinal direction, with some heterogeneity in the transverse direction (across the flow). Such heterogeneity could be expected owing to sidewall effects.