Abstract: The instantaneous flow field on the axisymmetric plane of an impinging jet is measured using two-dimensional particle image velocimetry (PIV). Utilizing experimental data across varying jet Reynolds numbers and impingement distances, this study investigates the self-similarity of flow statistics in both the impingement region and the wall jet region through various scaling parameters and develops corresponding empirical models. The results indicate that the turbulent quantities (e.g., turbulence intensity and Reynolds shear stress) in the impingement region lack self-similarity when normalized with conventional scaling parameters. To address this, a mixed-length scale derived from the turbulent quantities themselves is proposed as a characteristic length scale for non-dimensionalization. This approach achieves self-similarity of the turbulence quantities in the impingement region. For the wall jet region, the onset of self-similarity of turbulent quantities under radial time-averaged velocity scaling is strongly dependent on both the jet Reynolds number and the impingement distance. This finding clarifies the debate over whether the radial time-averaged velocity is a valid dimensionless scaling parameter for the self-similarity of turbulent statistics. Moreover, further analysis identifies the appropriate dimensionless scaling for turbulence quantities in the wall jet region as their local peak values and outer-layer half-widths. Finally, the empirical models are developed for the time-averaged velocity, axial/radial turbulence intensity and Reynolds shear stress distributions in both the impingement region and the wall jet region, based on the identified self-similarity characteristics. These models achieve prediction accuracies of ±10%, ±15%, ±15% and ±30% in the impingement region, and ±5%, ±15%, ±10% and ±15% in the wall jet region, respectively.