# Reconstruction of Rainfall Field Using Earth-Space Links Network: A Compressed Sensing Approach
## 4 Results and Discussion
On the whole, the consistency between the rainfall fields reconstructed by CS and the real rainfall fields in terms of structural distribution is better than that of the IDW algorithm. The results of the quantitative evaluation with RMSE, MB and CC of using ESL network 1 to reconstruct the real rainfall fields of that rainfall event are given in Table 1. It can be seen that the MB of the rainfall fields reconstructed using ESL network 1 are essentially unbiased except for the fact that the IDW algorithm underestimates the rainfall fields 4. By comparing the quantitative reconstruction results in the case of no noise and with systematic noise, it can be found that systematic noise, which follows the normal distribution, has essentially no effect on the reconstruction results of the IDW algorithm, while the accuracy of the reconstruction results of the CS method is decreased. Additionally, when considering systematic noise, the RMSE and CC of the rainfall fields reconstructed by the IDW algorithm are lower than 1.21 mm/h and higher than 0.934, respectively, and the RMSE and CC of the results reconstructed by CS are lower than 0.25 mm/h and higher than 0.997, respectively. Therefore, the performance of reconstructing the rainfall fields by CS is better than that of the IDW algorithm in terms of reconstructing the rainfall fields of the individual rainfall event both without and with systematic noise. Figure 4: Rainfall fields for the rainfall event with intervals of 1 h during 01:00–04:00 on 10 August 2019 in Jiangning district, Nanjing. (**a**) is the rainfall field 1 at 01:00, (**b**) is the rainfall field 2 at 02:00, (**c**) is the rainfall field 3 at 03:00, and (**d**) is the rainfall field 4 at 04:00. Figure 5: Results of reconstructing the rainfall fields of the rainfall event with ESL network 1 for the case of no noise. (**a–d**) represent the rainfall fields reconstructed by the IDW algorithm, and (**e–h**) represent the rainfall fields reconstructed by CS. Figure 6: Results of reconstructing the rainfall fields of the rainfall event with ESL network 1 for the case of systematic noise. (**a–d**) represent the rainfall fields reconstructed by the IDW algorithm, and (**e–h**) represent the rainfall fields reconstructed by CS. To further examine the performance of the ESL networks in reconstructing the rainfall fields, the four designed ESL networks have been used to reconstruct the rainfall fields from May to September each year during the period of 2017 to 2019 in Jiangning district, Nanjing, considering systematic noise. Figure 7 shows the results of the four designed ESL networks reconstructing the rain rates of all rainfall fields. The MB of the results of the four ESL networks reconstructing the rainfall fields shows that the rain rates of the rainfall fields reconstructed by the IDW algorithm and the CS method are essentially unbiased regarding the rain rates of the real rainfall fields, which means that the two reconstruction methods both do not overestimate or underestimate the rainfall fields. Additionally, the accuracy of reconstructing the rainfall fields by the IDW algorithm and CS improves sequentially as the density of the links in the ESL network increases, and the performance of reconstructing the rainfall fields using the four ESL networks with the CS method is superior to the results of the IDW algorithm. Moreover, the reconstructed rainfall fields using an ESL network with CS have been closely approximated to the real rainfall fields when the number of links in the ESL network increases from 20 to 80 in the experimental area of almost 1581 km\({}^{2}\). Specifically, the RMSE and CC of the reconstructed rainfall fields using ESL network 4 with a link density of 0.05 links per square kilometer are lower than 0.15 mm/h and higher than 0.999, respectively. This illustrates that an ESL network with CS is capable of reconstructing high-precision rainfall fields under sparse sampling.