The phrase "compelling evidence" means having very strong and convincing proof or information that supports a particular claim or argument. Full definition
The candidate gives plenty of compelling evidence of her experience and suitability for a job as a fitness model. (resume-now.com)
The findings provide compelling evidence for the benefits of more bullying prevention in primary schools. (educationmattersmag.com.au)
Thus the historical tropical storm count record does not provide compelling evidence for a greenhouse warming induced long - term increase. (gfdl.noaa.gov)