Cool, low mass stars with a convective envelope have bubbles of hot, bright plasma rising to the surface where they eventually cool, darken and sink. The motions of these plasma bubbles induce stellar line asymmetries since the radial velocity (RV) shift induced from the uprising granules does not completely cancel the shift from the sinking intergranular lanes. Furthermore, these line asymmetries are constantly changing as the ratio of granular to intergranular lane material continues to change due to magnetic field interplay. The net result for Sun-like stars is shifts in the line profiles on the order of several tens of cm/s. Hence an understanding of magneto-convection and its effects is paramount in any high precision RV study. One particular area impacted is the RV confirmation of Earth-analogs; the astrophysical noise from the host star stellar surface magneto-convection completely swamps the 10 cm/s signal induced from the planet. We aim to understand the physical processes involved here so that we may disentangle the effects of magneto-convection from observed stellar lines. To do so, we start with a state-of-the-art 3D magnetohydrodynamic simulation of the solar surface. Motivated by computational constraints and a desire to breakdown the physics, we parameterize the granulation signal from these simulations. This parameterization is then used to construct model Sun-as-a-star observations with a RV precision far beyond current instrumentation. This parameterization across the stellar disc, for a variety of magnetic field strengths, is presented here, alongside the current results from the model star observations. We find several line characteristics to be correlated with the induced RV shifts. Particularly high correlations were found for the velocity asymmetry (comparing the spectral information content of the blue wing to the red wing) and brightness measurements (approximated by integrating under the model observation profiles), allowing significant granulation noise reduction. The results of this campaign can feed directly into future high precision RV studies, such as the search for habitable, rocky worlds, with the forthcoming ESPRESSO and HIRES spectrographs.