## 3 Observation Sufficiency to Distinguish the Convective Transition Relationship
### Separation Using IMERG Precipitation
This procedure was repeated for the East Pacific, Indian, and Atlantic Ocean domains that lie within this same \(\pm\)20-degree latitude range. For all five regions, the minimum number of observations needed to separate these transition curves for different numbers of temperature ranges was determined. Table 1 tabulates the results, where the number of required observations has been rounded upwards to four values, each indicated with a different color. For example, in the East Pacific Ocean, 5000 observations can distinguish amongst three temperature ranges by 1 K, 10,000 amongst five ranges, and 20,000 amongst six ranges. Since the requirement (discussed below) will be to discriminate the transition curves in each region by at least three temperature bins separated by no more than 1K  
Figure 6: Depiction of the area between adjacent transition curves, used as a metric to separate precipitation-water vapor dependence by different tropospheric temperature ranges. In this depiction the black, orange, blue and red line colors represent a 1-degree different tropospheric temperature range centered at 264, 265, 266 and 267K, respectively. The area between curves for two different temperatures (shown here separating the 264 and 265K range) and between 0.3-0.55 mm h\({}^{-1}\) is used in the statistical significance tests. (0.5 K in the global tropics), analysis was not done for some of the combinations (gray shaded boxes) once this criterion was reached. It is emphasized that even though this temperature separation criterion was defined by the area enclosed within the portion of these transition curves that has substantial conditional-average precipitation, the total number of observations required to separate these curves was drawn from a representative sample that includes all conditions, precipitating or not. This is essential: the increase in the change in precipitation statistics with water vapor reflects a higher probability of precipitation, as well as higher typical intensity [26; 29]. Section 4 will examine the required on-orbit time needed by the PRO satellite constellation in order to meet the required observation count for the different oceanic basin regions. Figure 8: Precipitation rate as a function of 200–850 hPa integrated column water vapor (pickup curves) after (**left**) 50,000 observations, (**center**) 10,000 observations, and (**right**) 2000 observations taken from the COSMIC-IMERG dataset, subsetted into the West Pacific domain. Color scheme otherwise identical to Figure 5.  
Figure 7: Statistical significance test for the number of soundings required to distinguish between precipitation-water vapor curves to determine data sufficiency. The area metric schematized in Figure 6 is applied to a series of bootstrap ensembles similar to those in Figure 5 to provide a significance test from samplings of the data set as a function of number of observations. The zero crossing of the black curve shows the number of soundings required to achieve the 95% confidence level for distinguishing the curves. Results here are for the whole tropics.