## 5 Discussion  
### The Evaluation of Rainfall Inversion from OEL  
In this section, we will evaluate the performance of OEL on rainfall measurement based on a year of statistical rainfall data of our established OEL system, which has been collected since July, 2019. The comparisons of rain intensity between OEL and OTT are presented in Figure 7. Here, each data point denotes the values of rain intensity derived from the two devices at the same time and the corresponding color indicates its absolute error. As can be seen, the rain intensity from OEL is highly correlated with OTT and the correlation coefficient between them is 0.86. The determination coefficient \(\rho^{2}\) is used to evaluate the sensibility of OEL inversed result to the variation of real rain intensity (OTT) and it is defined as:  
\[\rho^{2}=1-\sum_{i=1}^{N}{(R_{OTT}(i)-R_{OEL}(i))^{2}/\sum_{i=1}^{N}{(R_{OTT}(i )-\overline{R}_{OTT})}^{2}} \tag{28}\]  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Heavy Rainfall** & \multicolumn{3}{c}{**Heavy Rainfall Measurement ()**} \\
**Prediction ()** & **Yes** & **No** & **Total ()** \\ \hline
**Yes** & \(TH=15,144\) & \(FH=815\) & 15,959 \\
**No** & \(FN=630\) & \(TN=7911\) & 8541 \\
**Total ()** & 15,774 & 9726 & 24,500 \\ \hline
1  & PC = (\(TH+TN\))/(\(TH+FH+TN\)) = 0.94; POD = \(TH\)/(\(TH+FN\)) = 0.96; FAR = \(FH\)/(\(TH+FH\)) = 0.051; FBI = \((TH+FH)\)/(\(TH+FN\)) = 1.01 \\ \hline \hline \end{tabular}
\end{table}
Table 4: The comparisons of predicted heavy rainfall with measurements for each grid cell in the rainfall field.  
where \(N\) denotes the number of data points shown in Figure 7. In general, a high value of \(\rho^{2}\), equal to 0.73 here, indicates a good ability of OEL to measure rain intensity. The averages of rain intensity from OEL (4.33 mm/h) and OTT (3.95 mm/h) are also close to each other. In total, the OEL can achieve the measurement of rain intensity. However, we can clearly observe that the differences between OTT and OEL become more and more obvious with the increase of rain intensity. As for the extreme rain (50 mm/h-), the estimates from OEL are significantly lower than OTT. Therefore, we will further discuss the performance of OEL on different rainfall categories. The statistical relative errors between OEL and OTT for different rain intensity ranges are given in Figure 8. The medians of relative errors for rain intensity in 0-5 mm/h and 6-15 mm/h are 14.9% and -7.5%, respectively. With the increase of rain intensity, the medians exceed -20% and the worst value reaches to -41.3% for rain intensity in 31-50 mm/h. Above results demonstrate that the inversed rain intensity has better accuracy of light-(0-2.5 mm/h) and moderate-(2.5-10 mm/h) rain than that of heavy-(10-50 mm/h) and extreme rain.  
As for the comparison between OEL and OTT, it should be noted that directly comparing the rain intensity from the two devices may be not reasonable. On the one hand, the observed volumes of atmosphere by OTT and OEL are different. As mentioned above, the inversed rain intensity of OEL represent the average rainfall along the link, but the OTT measures the rain intensity of a single point near the surface. The heavy- and extreme rain event often associates with obvious spatial heterogeneities, which results in the obvious underestimation from OEL. Therefore, several disdrometers will be deployed along the earth-space link in our near future work. On the other hand, as can be seen from Equation (13), the height of 0 \({}^{\circ}\)C isotherm also influences the inversion results. In the above experiment, we use the radiosonde data to estimate the height of 0 \({}^{\circ}\)C isotherm.  
Figure 8: The statistical relative errors between OEL and OTT for different rain intensity ranges.  
Figure 7: The comparisons of rain intensity between OTT and OEL: the color of each square indicates its corresponding absolute error.  
However, the radio sounding is only performed twice a day which is not strictly consistent with OEL measurements so an alternative method is urgently needed.