Aquaplanet experiments are used to investigate the physical convergence of a Global Storm-Resolving model (GSRM) under successive, two-fold horizontal grid spacing refinements from 160 km to 1.25 km. A methodology based on the Richardson extrapolation method is used with the aquaplanet hemispherical symmetry to quantify convergence. We use the symmetrical and anti-symmetrical solution components to estimate the asymptotic convergence pattern, the asymptotic estimate, and sampling uncertainty. Based on successive refinements, different climate statistics are explored to evaluate if they enter into a convergent regime and, if so, what their convergent value is. Our analysis focuses on global mean statistics related to the general circulation and aspects that influence the climate: the meridional overturning circulation, the tropical structure (the Inter-Tropical Convergence Zone (ITCZ), and the zonal mean thermodynamic state), and the energy and water budget. Our results show a kilometer and hectometer-scale horizontal grid spacing requirement for physical convergence of the meridional overturning circulation structure and global mean statistics. Distinctively, the tropical structure is estimated to be very near their asymptotic values at km-scale grid spacing, but the circulation intensity appears to converge more slowly, as do the storm track and jet-stream. As we increase the horizontal grid spacing, a better representation of clouds and zonal distribution of water vapor drives convergence in the energy and water budget. We conclude that simulations with a resolution of 2.5 km pose a great candidate for multi-decadal simulations within a compromise of the meridional overturning circulation structure convergence and intensity.