**2. Experimental Set-Up and Methods**

The experiments were carried out in a 12 m long, 0.3 m deep, and 0.44 m wide glass-sided, tilting flume in the Hydraulic Laboratory at the University of Auckland. The schematic of the flume is shown in Figure 1a and the detailed description of the flume can be found in [3]. The sediment used in the experiments was a uniform coarse sand with median diameter, *d*50 = 0.85 mm, and relative submerged particle density, Δ = 1.65. The weir used in the experiments was a 10 mm thick rectangular plastic plate, with the same width as the flume. A constant flow depth, *h* = 150 mm, was maintained for all the experiments, and three weir heights, *z* = 30 mm, 40 mm, and 50 mm, were used, which resulted in three different overtopping ratios *z*/*h* = 0.20, 0.27, and 0.33, respectively. In total, five clear-water scour tests were conducted. The detailed experimental conditions are shown in Table 1. For all the tests, the velocity profiles of the approach flow upstream of the weir were measured by using a three-component, downward-looking Nortek Vectrino+ acoustic velocimeter on the centerline of the flume (see Figure 1b). For each point measurement, two minute samples were collected with a sampling rate of 200 Hz. After the flow measurements, all the raw velocity data from the velocimeter were filtered by using WinADV [26], so that low quality data that had spikes, SNR (signal-noise ratio) < 15 or COR (correlation) < 70, were removed [27]. The average approach velocities, *U*0, were estimated from the processed velocity profiles. The critical average approach velocities for bed sediment entrainment, *U*c, were calculated from the logarithmic mean velocity equation for a rough bed [28]. Since the flow intensities used, which is defined as *U*0/*U*c, are quite small (0.73–0.92), the local water level rise at the weir for all the tests is negligible.

**Figure 1.** Experimental set-up and definition of experiential parameters: (**a**) schematic of experimental flume, reproduced from [3]; (**b**) experimental flume and measurement devices; (**c**) definition of experimental parameters in 2D.

All the experiments were started with a flat bed. The three-dimensional scour geometry downstream of the weirs was measured by using a Seatek Multiple Transducer Array (MTA) system as a function of time for each clear-water scour test. The MTA system comprises 32 transducers, which can be used to detect the distance from the transducers' surface to a reflective object (bed surface) under the water. The measuring accuracy of the MTA is ±1 mm. In this study, a total of 25 transducers were used to measure the scour profiles. As shown in Figure 1, the transducers were mounted in a rectangular grid on a moving carriage on the top rail of the flume. For each scour profile measurement, the MTA was operated at 5 Hz and could scan the whole scour region within one minute. The detailed arrangemen<sup>t</sup> of the transducers and bed profile contouring method can be found in [3]. After the 3D bed profile contouring, the maximum scour depth *ds*, scour length *ls*, and scour volume *Vs* were obtained from the processed 3D scour geometry by using a compiled MATLAB code [3].



For all the runs: *h* = 150 mm, *d*50 = 0.85 mm, *Uc* = 0.362 m/s.
