## 3 Results
### Other Orbit Constellation Scenarios  
In the discussion in Section 3.1, the 3-satellite orbit simulation was done for a non-sun-synchronous orbit with a \(45^{\circ}\) inclination plane. In this section, simulations are carried out with a \(98^{\circ}\) (sun-synchronous) orbit inclination and a \(45^{\circ}\) non-sun-synchronous orbit, each with four receiving satellites, each separated from its neighbor by two minutes. For both cases, the corresponding precession is included. These four satellites have their own location, identified as 1, 2, 3 and 4. To examine the quantity of events that will be obtained meeting the \"at least one RO inside and at least one RO outside\" criteria defined above, different configurations of the four satellites are considered. Figure 10: (**a**) A 2-dimensional (2-D) histogram of the relative angle (\(\alpha\)) between the along-ray direction and the line joining the tangent points, as a function of the associated tangent point separation difference \(d\) (see Figure 8). Only those RO events that had at least one observation that detected precipitation (i.e., \(\Delta\Phi>1.5\) mm, denoted as “inside precipitation”) and at least one observation that did not detect precipitation (i.e., \(\Delta\Phi<1.5\) mm, denoted as “outside precipitation”) are considered. (**b**) An associated 1-D histogram of the tangent point separation difference \(d\). (**c**) An associated 1-D histogram of the distribution of angles between the along-ray direction and the line joining the tangent points. For example, the configuration whereby all four satellites are considered is identified as \"1-2-3-4\" and the separation distance is always two minutes. If only the first and third satellites are considered, the configuration is denoted by \"1-3\" and the separation distance is 2 + 2 = 4 min, etc., Table 1 lists the six scenarios. The total number of cases that have at least one observation crossing detectable precipitation and one crossing undetectable precipitation and the distance between the tangent points \(d\), is computed for six prescribed configurations. These results are depicted in Figure 11 (\(d\) in grey box and \(d_{\textit{eff}}\) as a blue line). The left and right columns refer to the 45- and 98-degree inclination scenarios, respectively, and each of the six rows corresponds to the row in Table 1.  
The first thing to notice is that the total number of cases increases with the number of satellites, but also with the maximum time separation between these satellites. This is a direct consequence of having more chances of hitting precipitation by increasing the number of satellites (i.e., number of observations) and increasing the likelihood of observing _simultaneously_ inside and outside the precipitation structures by increasing the nominal separation. In general, there are more cases of _simultaneous_ inside and outside precipitation observations with the 98\({}^{\circ}\) orbit configuration, since the separation between the observations is larger. It is also noticeable how the distribution of effective distances changes with respect to the distances between the tangent points. However, the cases where \(d_{\textit{eff}}>25\) km is more than the 85% of the total cases for all configurations. The \(d_{\textit{eff}}\) is remarkably similar to the distance between tangent points for the cases with an orbital plane of 98\({}^{\circ}\). The reason is that for this configuration, \(\alpha\) is closer to 90\({}^{\circ}\). This is a consequence of the orbit inclination, and the relative inclination between the GNSS satellites and the receiving satellites. For such a configuration, most of the occultations are collected at the edges of the receiving antenna beam pattern (i.e., away from the velocity or anti-velocity direction of the receiving satellite), while for the 45\({}^{\circ}\) inclination orbit, the observations are more likely to be collected with the central part of the antenna beam pattern (RO geometry more aligned with the velocity or anti-velocity direction of the receiving satellite).