## Appendix A  
The design and configuration for the polarimetric RO constellation simulations is described in [PERSON] et al. (2019). In this appendix, a brief summary is provided for reference. A constellation of eight satellites, separated by 2 min, run for a 10-day simulation, sampling 10-day precipitation at 3-month intervals throughout one year (2018) to capture seasonal variability. Each simulation captures the fore (rising) and aft (setting) RO opportunities that occur between each constellation satellite and the GNSS transmitting satellites (telemetries transmitted by each of the GPS, GLONASS, Galileo, and BeiDou satellites). The propagation path (i.e., the line between the transmitting and receiving satellite) are sampled once per second from which the trace of the on-Earth tangent points (TP) and the resulting ray path coordinates and orientation (i.e., the azimuth angle of the ray path relative to the antenna boresight) are derived. From this eight-satellite simulation, selected satellites can be \"omitted\" in order to evaluate how PRO sampling of precipitation conditions varies with a smaller number of constellation satellites or a longer time separation. The procedure described in Section 3.2 is used to calculate the \(\Delta\phi\) that would occur from the sampling of precipitation conditions provided by the nearest 30-min IMERG precipitation dataset. Figure 11 shows a pictorial of one \"event\", an event being defined as all when all satellites are considered to collect a PRO from the same transmitting GNSS satellite. This example is an event from eight satellites. The closest-to-Earth TP locations are shown from each of the eight receiving satellites (each with a different color), and the corresponding receiving satellite ground track (same color as the TP). A \"precipitation + environment\" event (P/E event) occurs when one or more satellites detects heavy precipitation (\(\Delta\phi>2\)) and another detects no-precipitation (\(\Delta\phi=0\)). The TP locations are separated by a distance \(d\). However, the actual propagation ray paths associated with each RO in general lie in a different direction depending upon the position of the transmitting and receiving satellites during the RO duration, given by the angle \(\alpha\). Therefore, the \"effective\" separation between the ray paths (\(d_{\mathit{eff}}\)) is smaller, given by \(d_{\mathit{eff}}\ =\ d\cos(90^{\circ}-\alpha)\). The ray path lines represent the path upon which the corresponding air mass thermodynamics would be sampled from each constellation satellite. For convective science purposes, what is important is the value of \(d_{\mathit{eff}}\) since it determines the ray spacing. For example, if the angle \(\alpha\) approaches zero, the ray paths become packed closer together. If one of the RO captured a heavy rain event, the remaining RO ray paths are too close by and will not adequately sample the horizontal water vapor gradient, capturing the environmental air mass external to the heavy precipitation. While there is no specific value of \(d_{\mathit{eff}}\) that captures the moisture variability surrounding convective precipitation, a desired 50-150 km range of \(d_{\mathit{eff}}\) is considered for this investigation. As one example, Figure 12 summarizes the global statistics for an eight-satellite constellation at a 475-km altitude, 30-degree inclination orbital plane, 2-min satellite spacing and a PRO receiving capable of collecting rising and setting occultations from four GNSS, telemetries, over the 40-day period. Assuming a maximum antenna azimuth angle of 55 degrees, a total of 93,108 events were collected. Figure 10(a),b present the histogram of the separation distance (\(d\)) and angle \(\alpha\), respectively. The separation distance peaks near 70 km, and the relative angle peaks near 5 degrees and slowly drops off. When the resulting effective separation (\(d_{\mathit{eff}}\)) is considered (Figure 10(c)), the peak near 70-km shifts to separate clumps near 10, 40, and 70 km (i.e., ray paths are closer to each other).