## 4 Sampling of Precipitation Conditions for the Constellation Simulation
A \"precipitation/environment event\" (hereafter denoted by the term P/E event for brevity) is defined as an event that contains at least one PRO that intersects heavy precipitation (\(\Delta\phi>\) 2 mm) and at least one RO with no precipitation (\(\Delta\varphi=\) 0), thereby sampling the water vapor profile inside of and in the environment surrounding the heavy precipitation, respectively. The P/E events are the observations that are to be counted towards meeting the requirement from Section 3. In Table 3, the sampling statistics for the same five regions are presented for a baseline constellation. This baseline constellation is configured with four satellites separated by 2 min, placed into an orbit with an inclination of 45\({}^{\circ}\) at a 475-km altitude. To obtain samples representative of the annual cycle, the 10-day simulation was flown in each of December, March, June, and September (40 days total), for a total of 95,212 PRO events. Each satellite assumes a PRO receiver capable of collecting four GNSS telemetries (GPS, GLONASS, Galileo, and BeiDou), for RO events that occur within \(\pm\)55\({}^{\circ}\) antenna azimuth. \begin{table}
\begin{tabular}{c c c c} \hline  & & **Ratio of Events in** & **Fraction Events in Region That Are** \\
**Region** & **Events in Region** & **Region Relative to** & **P/E Events** \\  & & **Total Constellation Coverage** & **(\(\Delta\phi>\) 2)** \\ \hline Global Tropics & 33,564 & 0.352 & 0.0380 \\ West Pacific & 5648 & 0.059 & 0.0524 \\ East Pacific & 9200 & 0.097 & 0.0253 \\ Indian Ocean & 5056 & 0.053 & 0.0411 \\ Atlantic Ocean & 5384 & 0.057 & 0.0208 \\ \hline \end{tabular}
\end{table} 
Table 3: Number of simulated PRO events for the baseline constellation dataset, for the \(\pm\)20-degree global tropical latitudes as well as four oceanic basins contained in the same latitude band. The right-most column indicates the fraction of the total events in each region that qualified as P/E events (with at least one occultation inside and outside precipitation), where the precipitation conditions were such that the simulated \(\Delta\phi\) exceeded a threshold of 2 mm. An example is provided to explain the procedure. Table 1 indicates that in the global tropics, 20,000 observations are needed to distinguish five temperature ranges by 0.5 K. From Table 2, this implies that (20,000 \(\times\) 0.01335) = 267 of these observations are required to exceed the \(\Delta\phi>\) 2-mm threshold. In the constellation terminology, each event is one observation. Moving to the constellation in Table 3, the fraction of events that are P/E events is 0.038. Therefore, to meet this requirement, the constellation needs to orbit long enough to collect (267/0.038) = 7024 events in this region. Since the total events listed in Table 3 encompass a 40-day orbit period, this number will be reached after 40 \(\times\) (7024/33564) = 9 days (rounded up). Since the fraction of the events collected by the constellation in this region is 0.352 (Table 3), after this amount of time the four-satellite constellation will have collected (7024/0.352) = 19925 total observations. Table 4 tabulates this same procedure for the other regions and different numbers of tropospheric temperature ranges that can be distinguished, using the same \(\Delta\phi>\) 2-mm threshold. The number in parentheses indicates the number of on-orbit days (rounded up) needed to meet the N of the required total (i.e., collected by the entire constellation) observations. For clarification, bold font specifies requirements that were obtained from the analysis in Section 3, and normal font specifies the required number using the constellation analysis. Figure 9: Close-up to the 20 S–20 N, 0–40 E area, showing the TP locations (points) and an associated 200-km ray path segment (lines) for the case when the eight constellation satellites are separated by 2 min, in a 60-degree inclined orbit, 475-km altitude. Each “event” of the 8 satellites is assigned a unique color.