## 4 Sampling of Precipitation Conditions for the Constellation Simulation
### Constellation Design Considerations  
As mentioned earlier, the results in Table 5 assume an idealized collection of all occultations arising from all transmitting satellites of the four GNSS satellite systems. Overall net yield fraction was not considered, since these characteristics are unique to a specific spacecraft and PRO receiver design, and data processing algorithms. Here, a set of reasonable assumptions are made to provide a realistic duration of the constellation data collection period. A conservative estimate for net yield from both satellite operations and data processing of 50% is assumed, where each RO needs to provide data to at least the 850 hPa level. This consideration would extend the required four-satellite baseline constellation collection period to (14/0.5) = 28 days (assume one month). At any given time, each PRO receiver is tracking multiple occultations from the GNSS satellites that are within its antenna field of view. If all four telemetries are tracked, this number can be as high as 10 at any one time (Figure A4 in Appendix A), and each PRO requires two (H and V) receive channels. Assuming the PRO receiver on each of the constellation satellites can track up to four PROs at any one time, only 70% of the total would be collected. Another option is to track only two GNSS telemetries (GPS + GLONASS) instead of all four, which would capture nearly all (95%) of the available occultations. These receiver characteristics would double the overall collection period to 2 months. Lastly, it is important to add an overall margin on top of this analysis, to account for unexpected conditions leading to missing data. Assuming a conservative 50% margin, this leads to an overall collection period of 3 months. If a three-satellite constellation at the same \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline  & & \multicolumn{3}{c}{**Global**} & \multicolumn{2}{c}{**Western**} & \multicolumn{2}{c}{**Eastern**} & \multicolumn{2}{c}{**Indian**} & \multicolumn{2}{c}{**Atlantic**} \\  & & \multicolumn{3}{c}{**Tropics**} & \multicolumn{2}{c}{**Pacific Ocean**} & \multicolumn{2}{c}{**Pacific Ocean**} & \multicolumn{2}{c}{**Ocean**} & \multicolumn{2}{c}{**Ocean**} \\ \hline \multirow{2}{*}{S} & \multirow{2}{*}{\(\boldsymbol{\phi}\)} & \multirow{2}{*}{**Alt**} & \multicolumn{2}{c}{**Total**} & \multirow{2}{*}{**Days**} & \multicolumn{2}{c}{**Total**} & \multirow{2}{*}{**Days**} & \multicolumn{2}{c}{**Total**} & \multirow{2}{*}{**Days**} & \multicolumn{2}{c}{**Total**} & \multirow{2}{*}{**Days**} & \multicolumn{2}{c}{**Total**} \\  & & & & & & & & & & & & & & \\ \hline
8 & 30 & 475 & 5325 & 3 & 7705 & 4 & 5749 & 3 & 8237 & 4 & 7847 & 4 \\
8 & 45 & 475 & 7811 & 4 & 11,177 & 5 & 9063 & 4 & 13,149 & 6 & 11,326 & 5 \\
8 & 60 & 475 & 8660 & 4 & 12,508 & 6 & 9376 & 4 & 15,165 & 7 & 11,880 & 5 \\
8 & 98 & 800 & 6956 & 3 & 10,385 & 5 & 7183 & 3 & 12,285 & 5 & 7744 & 4 \\ \hline
4 & 30 & 475 & 14,740 & 7 & 23,283 & 10 & 17,186 & 8 & 23,204 & 10 & 24,120 & 11 \\
4 & 45 & 475 & 19925 & 9 & 32,501 & 14 & 25,345 & 11 & 30,676 & 13 & 31,460 & 14 \\
4 & 60 & 475 & 20,930 & 9 & 32,622 & 14 & 23,082 & 10 & 36,268 & 15 & 39,840 & 16 \\
4 & 98 & 800 & 15,224 & 6 & 23,993 & 10 & 15,402 & 6 & 27,859 & 11 & 22,160 & 9 \\ \hline
3 & 30 & 475 & 27,338 & 12 & 43,778 & 19 & 32,695 & 14 & 44,786 & 19 & 46,835 & 20 \\
3 & 45 & 475 & 34,504 & 15 & 55,835 & 24 & 45,967 & 20 & 51,263 & 22 & 65,526 & 28 \\
3 & 60 & 475 & 35,297 & 15 & 62,723 & 25 & 38,274 & 16 & 68,089 & 28 & 60,044 & 24 \\
3 & 98 & 800 & 24,058 & 10 & 36,322 & 14 & 25,469 & 10 & 51,195 & 20 & 35,935 & 14 \\ \hline
2 & 30 & 475 & 95,947 & 41 & 139,400 & 59 & 120,492 & 51 & 182,302 & 77 & 352,345 & 149 \\
2 & 45 & 475 & 107,677 & 45 & 176,270 & 74 & 156,607 & 66 & 169,235 & 71 & 236,753 & 74 \\
2 & 60 & 475 & 93,939 & 38 & 178,946 & 71 & 102,635 & 41 & 250,580 & 100 & 143,702 & 57 \\
2 & 98 & 800 & 58,948 & 23 & 97,450 & 38 & 58,120 & 23 & 131,733 & 51 & 96,391 & 38 \\ \hline \hline \end{tabular}
\end{table}