## 4 Results and Discussion
### Rain Cell Retrieval by Network of ESLs and HMLs  
The \"rain cell\" is a meteorological term used to represent the distribution of rain rate along the path. By studying the spatial distribution characteristics of rainfall, the exponential rain cell (EXCELL) model, Gaussian model and HYCELL model are mainly used to represent the rain cell at present [47; 48; 49]. In this case, the HYCELL model with better spatial representation, which is based on a combination of the EXCELL model and the Gaussian model [50]. Additionally, the expression of the model is  
\[R(x,y)=\left\{ \begin{array}{l}R_{E}\cdot exp\left[-\left(\frac{x^{2}}{a_{E} ^{2}}+\frac{y^{2}}{b_{E}^{2}}\right)^{\frac{1}{2}}\right],\,(R_{1}\!<R\,<\!\!R_ {2})\\ \\ R_{G}\cdot exp\left[-\left(\frac{x^{2}}{a_{G}^{2}}+\frac{y^{2}}{b_{G}^{2}} \right)\right],\,(R>\!\!R_{2})\end{array} \right. \tag{28}\]  
where \(R_{E}\) and \(R_{G}\) are the peak rain rate in the EXCELL model and Gaussian model, respectively, \(a_{E}\) and \(b_{E}\) are parameters of the EXCELL model, and \(a_{G}\) and \(b_{G}\) are parameters of the Gaussian model. From the model, it can be seen that when the rain rate \(R\) is lower than \(R_{2}\), the rainfall conforms to the EXCELL model. Additionally, when the rain rate is higher than \(R_{2}\), the rainfall conforms to the Gaussian model. To test the performance of rain cell retrieval by the network of ESLs and HMLs, we first designed various kinds of different rain cell samples in the experimental area as the initial rainfall fields according to the HYCELL model. The rain cells consist of 1225 (35 \(\times\) 35) rain rate signals and thus have a spatial resolution of 1 \(\times\) 1 km\({}^{2}\). Then, the sparsely distributed rain cells in the experimental area are retrieved by the joint network of ESLs and HMLs. Finally, the OK algorithm and RBF neural network are used to reconstruct the sparse rain cells, respectively, so as to obtain the complete rain cells in the experimental area. For the RBF neural network, we simulate 100 different rain cells as the training set according to the parameter range in Table 2, so as to determine the parameters of the neural network model. In addition, in order to verify the performance of OK algorithm and RBF neural network for reconstructing rain cells, a set of different rain cells consisting of three rain cells were designed as the validation samples of rainfall field, and their spatial distribution of rainfall is shown in Figure 6. There are significant differences in the range of rain rates and the location of peak rainfall between these rain cells. In the whole retrieval process, the rain rates at the location of the links in the rain cell can first be measured using the joint network of ESLs and HMLs. Then, the OK algorithm and RBF neural network are used to reconstruct the sparse rain rates measured by the network, respectively. The distribution of the complete rain rates of the rain cell is thus obtained, and the retrieval of the rain cell in the area is finally accomplished. Figure 7 shows the results of the joint network of ESLs and HMLs based on the OK algorithm and RBF neural network to retrieve the different rain cells. It can be seen from the figure that the retrieved rain cells of the OK algorithm and RBF neural network show good consistency with the initial rain cells. This indicates that these two methods can both accurately retrieve the distribution of rain rates for each of the rain cells. It should be noted that the rain rates of the rain cells retrieved using the OK algorithm are locally closer to those of the initial \begin{table}
\begin{tabular}{c c c} \hline \hline
**Rain Rate** & **Parameters** & **Range** \\ \hline \multirow{3}{*}{\(R_{1}<R<R_{2}\)} & \(R_{E}\) & 10–100 mm/h \\  & \(a_{E}\) & 0.5–35 km \\  & \(b_{E}\) & 0.5–35 km \\ \hline \multirow{3}{*}{\(R>R_{2}\)} & \(R_{G}\) & 10–80 mm/h \\  & \(a_{G}\) & 0.5–35 km \\ \cline{1-1}  & \(b_{G}\) & 0.5–35 km \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The range of parameters of the HYCELL model. rain cells.