## 3 Design of the Joint Network of ESLs and HMLs  
To verify the feasibility of combining ESLs and HMLs for rainfall field retrieval in the area, a joint network design of combining ESLs and HMLs in Xiamen, China, is carried out in this paper through simulation experiment. The latitude and longitude ranges of the experimental area are 118 \({}^{\circ}\)E-118.35 \({}^{\circ}\)E and 24.35 \({}^{\circ}\)N-24.7 \({}^{\circ}\)N. In addition, the whole experimental area is divided into a grid of 35 km \(\times\) 35 km. It is assumed that the rainfall distribution within each grid point is uniform, so the spatial resolution of the rainfall field is 1 \(\times\) 1 km\({}^{2}\). The annual average of the local atmospheric 0\({}^{\circ}\)C-Layer height is 4.476 km [41]. For the design of the link network, we made use of the communication links between the satellite antennas on the ground and the geostationary satellites to build ESLs, and the communication links between the microwave transmitters and the receivers on the ground to build HMLs. Additionally, the parameters of the five geostationary satellites selected for building the ESLs are shown in Table 1.  
In the previous study [34], we only randomly designed the ESLs without considering the impact of a more realistic environment. Obviously, it is impossible to install the ESL antennas for measuring rainfall on the surface of the river and the sea. Therefore, the following guidelines need to be followed in the design of the joint network of ESLs and HMLs in this paper.  
1. The links for ESLs and HMLs should be spread as evenly as possible across the area.
2. The rain rate measured by the link represents the average rain rate over the path and can be considered as the rain rate at the location of the midpoint of the link.
3. Although rain attenuation is more likely to occur for ESLs and HMLs with long distances, the distribution of real rainfall over the area is not uniform. Thus, the long links have poor spatial representation. To improve the spatial representation of rainfall retrieved by ESLs and HMLs, it is necessary to build short links (the link lengths in this experiment are in the range of 2.8-7.6 km).
4. The antennas of ESLs, transmitters and receivers of HMLs cannot be installed on the water surface. However, the links can pass above the water surface.  
In Figure 5, we combined ESLs and HMLs to build a link network for rainfall observation, which consists of 40 links. Specifically, the 20 purple lines represent the HMLs, and the blue \"0\" indicates the location of the satellite antennas, which connect the communication satellites in Table 1 to form the 20 ESLs. The transmitters and receivers of the HMLs are located across the shore in order to monitor the rainfall on the water surface. In addition,  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Satellites** & **Longitude** & **Elevation (\({}^{\circ}\))** & **Azimuth (\({}^{\circ}\))** & **Frequency (GHz)** \\ \hline Apstar9 & 142.0\({}^{\circ}\)E & 50.86 & 133.13 & 11.154 \\ Apstar6C & 134.0\({}^{\circ}\)E & 56.28 & 145.56 & 12.323 \\ AsiaSat9 & 122.0\({}^{\circ}\)E & 61.04 & 170.75 & 12.726 \\ ChinaSat10 & 110.5\({}^{\circ}\)E & 60.10 & 197.94 & 12.309 \\ AsiaSat5 & 100.5\({}^{\circ}\)E & 55.19 & 217.51 & 12.460 \\ \hline \hline \end{tabular}
\end{table}
Table 1: The parameters of the geostationary satellites for building the ESLs.  
the rainfall retrieved by the link can be considered as the rainfall at the red midpoint due to the fact that it only reflects the path-averaged rainfall. To avoid excessive differences in each ESL, the ESLs were built at the Ku band and with horizontal polarization. Moreover, the electromagnetic wave signals of the HMLs are all at 20 GHz with horizontal polarization.