## 2 Methodology
In this manner, it is secured that there is no interference between the used instrumentation. The ADV is positioned 1 cm upstream of the face of the instrumented particle, and it is configured appropriately to record instantaneously the three components of the local flow field [55]. Flow velocity profiles are then taken after the instrumented particle has been removed, with a vertical resolution of about 7 mm. Likewise, the entrainment record of the instrumented particle is performed after the flow measurement instrumentation has been removed and can be obtained live (via the WiFi protocol) or otherwise saved in the local memory for retrieval after the conclusion of the flow experiment. Five runs were performed, and the flow velocity measurements and the sensor measurements were used to investigate the flow structures that resulted in entraining the instrumented particle stochastically. For the stochastic analysis of particle entrainment, both the flow and particle entrainment time series are required to be long enough so that they have statistics that are representative and independent of the duration of the records. For the typical flow conditions assessed herein, such durations have been experimentally established to be 8 min for the ADV flow hydrodynamic records (12,000 samples at 25 Hz recording rate) and above half an hour for the instrumented particle entrainments records (more than 180,000 samples when recording at 100 Hz). These five runs were used for the analysis of the flow structures that occurred during, before and after the occurrence of impulses above the critical impulse. The acquired instantaneous flow velocity data were de-spiked using the methodology presented by [PERSON] and [PERSON] [56], modified by [PERSON] [57] and [PERSON] et al. [58]. The post-processed velocity measurements were then used to estimate the shear velocity (u\({}_{*}\)) using the Grass method [10] as discussed in [54]. The shear velocity was used to estimate the particle Reynolds number and the Shields parameter for the five runs of the experiment. The results are shown in Section 3, Table 1.  
Figure 1: Illustration of the experimental setup: **(a)** sketch of the side view of the flume, also showing the test section and the relevant instrumentation (acoustic Doppler velocimetry and the instrumented particle), **(b)** the top view and **(c)** photo from the experimental setup, illustrating the use of the instrumented particle sitting on top of a dedicated 3D-printed micro-topography, transferring entrainment data in real time via the WiFi protocol (effective for submergence depths below 13.5 cm—see the WiFi antenna attached on the frame above the target particle), the high-speed video camera (used for visually assessing particle entrainments from the side) and the instrumented particle. The flow direction is also shown. The instantaneous flow velocity measurements 1 cm upstream of the instrumented particle's face, in the longitudinal direction, and in the position in the middle of the top half of the particle's diameter, in the bed-normal direction, were used as the input to the theoretical equations presented in [21; 22], to estimate the flow impulses (as is also shortly illustrated, in Figure 2). This corresponds to point velocimetry taken at a fixed bed-normal distance from the bed surface, which ranges from about 1/3 to 2/5 of the flow depth. This position has been referred to as the position of investigation in this work. The quadrant analysis method was performed using the instantaneous flow velocity measurements at the position of the investigation. As presented in the introduction section, in the quadrant analysis method, the turbulent velocity fluctuations were divided into 4 categories, or quadrants, based on their signs: \(Q_{1}\) (+\(u^{\prime}\), +\(w^{\prime}\)), \(Q_{2}\) (-\(u^{\prime}\), +\(w^{\prime}\)), \(Q_{3}\) (-\(u^{\prime}\), -\(w^{\prime}\)) and \(Q_{4}\) (+\(u^{\prime}\), -\(w^{\prime}\)).