## 2 Methodology  
Before investigating the flow structures that have occurred during, before and after the occurrence of impulses above the critical impulse using a well-controlled flume experiment, the sensors of the instrumented particle were calibrated separately using simple and easy to validate theoretically physical motions (see [52] and Appendix 1 in [54]) to quantify the uncertainties in their readings. The casing of the instrumented particle is designed to accommodate different quantities of weighted lead strips, thus offering an adjustable density, which ranges from 1200 to 2900 kg/m\({}^{3}\), when the embedded sensors are also considered. A 2023 kg/m\({}^{3}\) solid particle density is used for this study, which is not far from the natural density of quartz pebbles, but it allows rendering the flow conditions used in the flume, close to the incipient motion threshold. The instrumented particle's calibration process consisted of calibrating the accelerometer and gyroscope separately. For the accelerometer's calibration, a free fall from a known height experiment was performed. The free fall height estimated using the accelerometer's reading was compared to the theoretical height estimated using [PERSON]'s Second Law of Motion and the uncertainty in the accelerometer's reading was quantified. As for the gyroscope's calibration, the rolling down an inclined plane experiment was performed. The total angular velocity down the inclined plane estimated using the gyroscope's readings was compared to the theoretical total angular velocity estimated using the law of conservation of energy. The uncertainty in the gyroscope's reading was quantified. The error values provided the inertial sensor fusion filter's input to achieve the uncertainty reduction. The final error in the sensor's readings only reached 1.1%, which is considered to be a very small value. The sensors were then inserted into the instrumented particle, which was used to conduct the flume experiment. The experiments in this work took place in a tilting and water recirculating flume in the Water Engineering Laboratory at the University of Glasgow. The flume was 8 m in length and 0.9 m in width with a water capacity of 0.2 m\({}^{3}\)/s and a carry flow up to 0.4 m deep was used (Figure 1). The bed was covered with water-worked uniform-sized gravel (d\({}_{50}\) = 25 mm) to achieve an adequate hydraulic roughness. The 1 m test section was located approximately 5.25 m downstream from the flume inlet and 1.75 m upstream from the flume outlet to ensure that the hydraulically rough turbulent flow was fully developed, as shown in Figure 1.  
Each run of the experiment consisted of performing the sensor measurements and flow velocity measurements. In general, there are two main approaches in assessing the relationship between the instantaneous flow hydrodynamic forcing (cause) and resulting particle entrainments (effect). This can be done deterministically, if the flow and particle instrumentation are synchronously taking records, or stochastically, by means of cross-examining the trends between these records, especially useful if these records have been taken separately but refer to the same particle and flow conditions. The use of the former deterministic in-synch records obtaining approach is only possible via the employment of non-intrusive velocimetry methods (such as laser Doppler velocimetry or particle image velocimetry). Given that the experiments carried herein use ADV, which can locally interfere with the particle, the latter stochastic assessment approach is used herein. This involves using the particle movement records towards indirectly inferring the flow impulses that are effective in entraining the instrumented particle, which are then stochastically compared to the directly measured flow hydrodynamics of the same flow. The particle entrainment and flow velocimetry records are obtained separately, having only one piece of instrumentation at a time to avoid either interfering with the other.