## 5 Conclusions  
In this work, an instrumented particle of 7 cm has been used to investigate the incipient entrainment from a hydraulically rough bed surface. Five runs of a well-controlled laboratory flume experiment were performed for a flowrate range near the critical threshold of motion. ADV was used to record the local flow hydrodynamics from which flow impulses above critical can be estimated, as well as define the quadrant that each reading corresponds to. The critical impulse level herein was defined by stochastically linking the frequency of a coarse instrumented particle entrainment estimated using the sensor readings, to the frequency of the flow impulses above the critical impulse for each corresponding critical impulse level. The main objective of this study was to identify trends in the sequence of flow structures before and after the occurrence of impulses in excess of the critical level, linked to coarse particle entrainment, using quadrant analysis.  
Our results indicate that there is a slight dominance in the \(Q_{4}\) and \(Q_{2}\) quadrant events compared to the \(Q_{1}\) and \(Q_{3}\) quadrant readings, in the flow. Additionally, sweep quadrant readings have occurred more often compared to outward interaction quadrant events during the occurrence of impulses above the critical level. However, given the greater prevalence of \(Q_{2}\) and \(Q_{4}\) events near the bed surface, it is expected that for cases of smaller particle-size-to-flow-depth ratios, these events will contribute even more towards coarse particle entrainment.  
Finally, the results, considering all five runs, indicate the primary contribution of sweep events (\(Q_{4}\) to \(Q_{4}\), \(Q_{1}\) to \(Q_{4}\)) and secondarily the ejection events (\(Q_{1}\) to \(Q_{1}\), for both cases of critical impulse, i.e., \(l_{cr}\) = 0.0445 m\({}^{2}\)/s and \(l_{cr}\) = 0.0063 m\({}^{2}\)/s). In essence, the findings of this study clearly demonstrate that the impulses above the critical impulse, which are responsible for the entrainment of the coarse instrumented particle, predominantly consist of relatively short-lived sweep events and to a lesser extent, relatively short-lived outward interactions. This conclusion is confirmed by the finding that the bulk of quadrant reading transitions take place prior to and following the first and last quadrant readings of the impulses. This is in addition to the transitions between sweeps and outward interactions, i.e., \(Q_{4}\) and \(Q_{1}\).  
**Author Contributions:** Conceptualization, M.V.; methodology, M.V. and K.A.; software, K.A. and M.V.; validation, M.V. and K.A.; formal analysis, K.A.; investigation, K.A.; resources, K.A.; data curation, M.V. and K.A.; writing--original draft preparation, K.A.; writing--review and editing, M.V. and K.A.; visualization, M.V. and K.A.; supervision, M.V.; project administration, M.V.; funding acquisition, M.V. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This work has been supported in part by the Royal Society (Research Grant RG2015 R1 68793/1), the Royal Society of Edinburg (Crucible Award) and the Carnegie Trust for the Universities of Scotland (project 7066215).  
**Data Availability Statement:** All data are available in the main text body and can be made available upon submitting a request to the corresponding author.  
**Acknowledgments:** We are grateful to the University of Glasgow lab technician, [PERSON], and undergraduate research student, [PERSON], for their help in preparing the experimental setup, as well as the editor and the anonymous reviewers for their recommendations.  
**Conflicts of Interest:** The authors declare no conflict of interest.