In this study, we perform a parameter error analysis of the 3D modified Leray- \(\alpha \) model using both analytical and numerical approaches. First, we prove the global well-posedness and continuous dependence on the initial data for the assimilated system. Furthermore, under sufficient conditions on the physical parameters and norms of the true solution, we demonstrate that the true solution can be recovered from the approximate solution, with the error determined by the discrepancy between the true and approximate parameters. Numerical simulations are provided to validate the convergence criteria.
