# Reconstruction of Rainfall Field Using Earth-Space Links Network: A Compressed Sensing Approach
## 5 Conclusions  
In this paper, we have carried out research on reconstructing high-precision rainfall fields using an ESL network with CS in the case of the sparse distribution of the ESLs. First of all, ESL networks with different densities were designed using the K-means clustering algorithm in Jiangning district, Nanjing. We then used the designed ESL networks with the CS method to reconstruct the real rainfall fields from the CMORPH and compared the  
Figure 7: Results of the four designed ESL networks reconstructing the rain rates of rainfall fields. (**a,c,e,g**) are the results of reconstructing the rainfall fields using ESL network 1, ESL network 2, ESL network 3 and ESL network 4 by the IDW algorithm, respectively, and the corresponding (**b,d,f,h**) are the results of reconstructing the rainfall fields using ESL network 1, ESL network 2, ESL network 3 and ESL network 4 with CS, respectively.  
reconstructed results with those of the IDW algorithm. The results show the feasibility of reconstructing rainfall fields using an ESL network, and the performance of reconstructing rainfall fields using the ESL networks with CS is better than that of the IDW algorithm both without and with systematic noise. When the density is 0.05 links per square kilometer, the RMSE and CC of the rainfall fields reconstructed using the ESL network with CS are lower than 0.15 mm/h and higher than 0.999, respectively. It is thus further illustrated that an ESL network with CS is capable of reconstructing high-precision rainfall fields under sparse sampling.  
With the development of satellite constellation communication networks, there is great potential to reconstruct rainfall fields with high precision in large areas by using widely distributed ESL networks. We have only preliminarily verified the feasibility of reconstructing the high-precision rainfall fields using ESL networks with CS through the simulation. Additionally, when reconstructing rainfall fields using the CS method, the prior relationship between the rainfall fields and the sparse signal has to be established first by using a redundant dictionary, which requires sufficient historical data and consumes some computational cost in advance. Also, the same process needs to be carried out for different areas. However, the high-precision reconstruction performance of the CS method under sparse sampling makes it still worthwhile to investigate the method in more depth. Next, we will build a real ESL network and reconstruct the high-precision rainfall fields in the area of the network. Furthermore, the ESL network will be exploited to monitor the rainfall information in the area on a large scale.  
Conceptualization, Y.Z. and X.L.; methodology, Y.Z. and X.L.; software, Y.Z. and K.S.; validation, L.L. and K.P.; formal analysis, X.L. and L.L.; investigation, X.L. and K.P.; resources, Y.Z. and K.S.; data curation, Y.Z. and X.L.; writing--original draft preparation, Y.Z.; writing--review and editing, X.L. and K.P.; visualization, Y.Z. and L.L.; supervision, X.L.; project administration, X.L.; funding acquisition, X.L. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China (Grant No. 41975030), and the Excellent Youth Scholars of Natural Science Foundation of Hunan Province of China (Grant No. 2021 JJ20046).  
The data used in the simulation experiment on rainfall fields retrieved are provided by Climate Prediction Center of NOAA, which can be download from an open-access source: [[https://ftp.cpc.ncep.noaa.gov/precip/CMORPH_V1.0/](https://ftp.cpc.ncep.noaa.gov/precip/CMORPH_V1.0/)]([https://ftp.cpc.ncep.noaa.gov/precip/CMORPH_V1.0/](https://ftp.cpc.ncep.noaa.gov/precip/CMORPH_V1.0/)) (accessed on 22 January 2021). Additionally, the data used in this study can be obtained from the corresponding author of this article.  
The authors thank the editor and anonymous reviewers for providing helpful advice. The authors declare no conflict of interest.