## 4 Sampling of Precipitation Conditions for the Constellation Simulation  
In this section, various simulated low-Earth orbiting satellite constellation configurations are examined to determine the required orbit time needed to reach the required number of observations determined above. Each constellation is flown over actual IMERG precipitation encompassing the simulation time duration, and the procedure in Section 3.2 is carried out to determine \(\Delta\phi\) for each constellation satellite. The \(\Delta\phi\) fraction determined from the representative dataset in Section 3.1 is used to estimate the required number of constellation observations needed, and the on-orbit time needed to obtain this number. It is emphasized that the on-orbit time considers idealized data collection and processing yields, whereas actual spacecraft operations and science data quality processing will provide some fraction of this number. This fraction will depend upon the specific spacecraft design and processing algorithms. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Region** & **Total N RO** & **(\(\Delta\phi\) > 1.5)/Total** & **(\(\Delta\phi\) > 2)/Total** \\ \hline Global Tropics & 402,549 & 0.018120 & 0.013350 \\ West Pacific & 59,991 & 0.027687 & 0.020320 \\ East Pacific & 99,633 & 0.016802 & 0.012436 \\ Indian Ocean & 61,768 & 0.018569 & 0.013583 \\ Atlantic Ocean & 55,964 & 0.009721 & 0.007469 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Total number (N) of joint COSMIC-IMERG RO observations in the representative dataset for the global tropical latitudes, as well as four sub-basins contained in the same latitudes. The last two columns indicate the fraction of the total observations where the precipitation conditions were such that the simulated \(\Delta\phi\) exceeded a threshold of 1.5 and 2 mm. The design and sampling characteristics of the PRO constellation simulation have been previously described by the authors of [21], who considered a four-satellite constellation, with the satellites separated by 2 min. Here, constellations of 2, 3, 4, and 8 satellites are considered, at inclinations of 30, 45, and 60 degrees, and orbit altitudes of 475 and 600 km. While a lower inclination orbit concentrates the observations in the desired tropical latitudes, a 98-degree, 800-km sun-synchronous polar orbit was also evaluated, since it is a common orbit for operational weather satellites. A summary of the simulation details is provided in Appendix A. To show the geographical sampling from this PRO constellation, Figure 9 depicts the projection of the eight PRO ray paths in central Africa for the specific case of the eight-satellite, 60-degree orbit inclination, and 475-km altitude. The sequence of PRO's that result from the satellites receiving the GNSS signal from the same transmitting satellite is denoted as an \"event\". In this example, the corresponding events cluster together and are assigned a unique color in Figure 9 (the color has no interpretation otherwise). Once the occultation from the first satellite in the constellation initiates, about 2-3 min elapse until the occultation terminates, depending upon the orientation of the occultation ray path relative to the receiving antenna boresight. Several minutes later, the occultation between the second satellite and the same GNSS transmitting satellite starts. This sequence of occultation opportunities then arises for the remaining satellites in the constellation, such that the PRO ray paths are oriented approximately \"parallel\" to each other (the Earth has rotated underneath the satellites in the intervening time). Such a configuration would capture a time sequence of closely spaced moisture profiles when the constellation flew near and across precipitating weather systems.