In the L1 Satellite Based Augmentation System (SBAS) Minimum Operational Performance Standard (MOPS) the correlation of the tropospheric model correction error is treated as though it is uncorrelated from one satellite to another when computing the position error bound. This simplification has recently been called into question in Gallon et al. (2021). This paper examines the effect of neglecting this cross-satellite correlation on the protection level computation. We have found the lack of correlation terms to be conservative when generating the Horizontal Protection Level (HPL). However, there are cases where the Vertical Protection Level may be underestimated by neglecting this effect. For current operations where the Vertical Alert Limit (VAL) is 35 m and above, the effect is limited to about 2% of the MOPS VPL value. For smaller VALs, the effect can be much more significant, particularly is VALs below 10 m are considered. We recommend including the correlation term in bounding the tropospheric correction errors for the upcoming dual frequency SBAS MOPS. We examine 10 years of tropospheric delay data collected and processed from hundreds of International GNSS Service (IGS) stations. 3 tropospheric models are used to analyze the residuals between IGS data and model predictions – University of New Brunswick 3 (UNB3), Global Pressure and Temperature 2 Wet (GPT2W) and Global Pressure and Temperature 3 (GPT3). Residuals are analyzed in terms of their probabilistic distribution in each IGS station. Stations are grouped and categorized by years and locations. It is found that residual distributions are most strongly dependent on latitude. In some infrequent cases where the IGS data appear to be anomalous and far from the model values, JPL data and actual weather record are used to evaluate and validate or reject the anomaly data. Finally, Gaussian pair-bounds are established in every station. An overall residual distribution is provided to account for the correction error caused by using the model. Finally, alternate forms for the SBAS VPL are provided to fully account for the cross satellite tropospheric model errors.