## Appendix A
When considering only P/E events (Figure 10(d)), about 44% of these fall within the 50-150-km range with a rather uneven distribution, weighted towards separations \(<100\) km. Figure 11 shows an identical format as Figure 10(a), but for the 98-degree, 800-km sun-synchronous polar orbit. Slightly more events (102,284) were captured. However, this advantage comes at the cost of more orbital time spent at higher latitudes, where heavy precipitation is less frequent. The angle \(\alpha\) is clumped more near 80 degrees (Figure 11(b)), leading to a broader distribution in adjacent effective ray path separation (Figure 11(c)) roughly centered near 80 km. In general, the 98-degree orbit exhibits a larger separation between successive RO ray paths, owing to its more north-to-south descending orbit path. About 50% of the P/E events fall within the 50-150-km separation range (Figure 11(d)) with values weighted past 100 km (opposite of Figure 10). Table 1 summarizes the global simulation results for different numbers of satellites in the constellation (C1) and orbit inclination and altitude (columns C2 and C3). The number of events (C4) does not change significantly, and as one would expect the fraction of these that are P/E events drops off with a smaller number of satellites. The key metric is column C9, the number of P/E events collected per day (C9 = C4 \(\times\) C6 \(\times\) C7). Column C8 presents the fraction of P/E events that fall within the desired 50-150 km ray path spacing between the \"inside\" and \"outside\" precipitation PRO. These findings can be summarized as follows:  
1. The fraction of events that are P/E events quickly drops off as the number of satellites in the constellation is reduced. 2. The effective separation between each of the ray paths tends to decrease as the orbit inclination decreases. For a 30-degree inclination, a spacecraft separation \(\Delta t\) of 4-min increases the number of events with a larger value of \(d_{\mathit{off}}\) and nearly doubles the number of P/E events, compared to the \(\Delta t\) = 2-min separation. 3. A constellation placed into a 60-degree inclination collects slightly more events than one at 30- or 45-degree inclination. This occurs since the GNSS transmitting satellites orbit in a \(\sim\)55-degree inclination, and the transmitting and receiving satellites are in view slightly more often. 4. A polar orbit collects slightly more events than any of the inclined orbits, but also the largest fraction of events whose effective separation exceeds 100 km. Unlike the inclined orbit, these observations would not sample the precipitation diurnal cycle. In Table A1, an idealized data collection was assumed, implying that all available occultation opportunities were captured. In actual operating conditions, this is not the case (further discussed in Section 4.2). At any given time, each PRO receiver will have multiple GNSS occultation opportunities within the broad antenna field of view. Figure A4 shows the cumulative normalized histogram of the number of occultations that occur for different PRO receive capabilities. A PRO receiver capable of only GPS capture is shown in the black line, whereas a PRO receiver capable of all four telemetries is shown in the red line. Note that in this latter case, there can be up to 10 occultations (rising or setting) that are available to be captured, and for a PRO measurement there are two channels (H and V) required. With only two telemetries (GPS and GLONASS), no more than four occultation opportunities occur nearly all of the time. If onboard processing software, antenna, or hardware limitations are a consideration, this factor will need to be taken into consideration.