## 5 Discussion
### The Stability of Reconstruction Method  
In this section, we will discuss the stability of our method on the reconstruction of rainfall field. Here, the OELs network is used to reconstruct the rainfall fields of the Jiangning district in plum rain season (June, July) of 2016, 2017, 2018 and 2019 by numerical simulation. The number of reconstructed fields during these periods is 1376 and the corresponding results are shown as accumulated rainfall fields in Figure 9. As for the calculation of accumulated rainfall field, it is equal to the sum of all rain intensity fields and meanwhile multiplies the temporal resolution of CMORPH that is equal to 0.5h. It can be seen from the comparisons that the important characteristics of accumulated rainfall field are inversed accurately, such as the increasing (or decreasing) trend of accumulated rain and the maximum (or minimum) position. Table 5 presents four metrics to quantitatively evaluate the reconstructed results. The values of \(CC\) between the OELs network and CMORPH are higher than 0.97 which shows a strong spatial correlation. The values of \(RMSE\) that are lower than 4.1 mm indicate the accuracy of our reconstruction method. Furthermore, the absolute relative errors of maximum and average values in accumulated rainfall fields do not exceed 1.5% and 0.5%, respectively. Moreover, the values of \(RMSE\) of 1376 reconstructed rain intensity fields are lower than 3.4 mm/h and \(CC\) are higher than 0.80. In this simulation, we use the OELs network to inverse rain intensity of approximately \(1.7\times 10^{6}\) grid cells. The comparison between inversed- and original rain intensity is presented in Figure 10. It can be seen that the rain intensity from both sources show a good consistency, with \(CC\) and \(\rho^{2}\) equal to 0.995 and 0.989, respectively. The relative error of average rain intensity is 0.28%. In addition, we can clearly observe from the color bar in Figure 10 that the absolute error of inversed rain intensity \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \(CC\) & \(RMSE\) & \multicolumn{2}{c}{**Maximum (mm)**} & \multicolumn{2}{c}{**Average (mm)**} \\
**Year** & **(\(\backslash\))** & **(mm)** & **CMORPH** & **OELs** & **CMORPH** & **OELs** \\ \hline
2016 & 0.993 & 8.321 & 860.07 & 853.46 & 785.23 & 788.89 \\
2017 & 0.988 & 3.851 & 355.42 & 352.16 & 292.87 & 292.73 \\
2018 & 0.988 & 3.983 & 481.72 & 474.98 & 377.59 & 377.18 \\
2019 & 0.975 & 4.073 & 425.74 & 419.56 & 384.85 & 386.56 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The evaluation metrics of accumulated rainfall field from OELs network during plum rain season (June, July) of 2016, 2017, 2018 and 2019 in Jiangning district of Nanjing. Figure 9: The accumulated rainfall from Climate Prediction Center morphing method (CMORPH) and OELs network during plum rain season (June, July) of 2016, 2017, 2018 and 2019 in Jiangning district of Nanjing. is significantly lower than that in Figure 7, which indicates a better accuracy of the reconstruction method. According to the result of linear regression in Figure 10 (black line: \(y=0.9793x+0.0622\)), there still are slight underestimations for high rain intensity. To quantitatively assess the accuracy of OELs network estimations for different rainfall categories, Figure 11 gives the statistical relative errors between OELs network and CMORPH. In total, the medians of each box are close to zero, and the corresponding values from left to right are \(-0.13\%\), \(-0.60\%\), \(-0.59\%\), \(-0.58\%\) and \(-0.72\%\), respectively, showing an obvious improvement to the results in Figure 8. This is because the representativeness of inversed rain intensity is different and our simulation is performed under some ideal assumptions such as knowing the height of 0 \({}^{\circ}\)C isotherm well and ignoring the variation of rainfall in vertical direction.