{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,6]],"date-time":"2026-02-06T05:33:40Z","timestamp":1770356020223,"version":"3.49.0"},"reference-count":31,"publisher":"MDPI AG","issue":"18","license":[{"start":{"date-parts":[[2022,9,16]],"date-time":"2022-09-16T00:00:00Z","timestamp":1663286400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Tuscany regional administration (Italy)","award":["101003534"],"award-info":[{"award-number":["101003534"]}]},{"DOI":"10.13039\/501100000780","name":"European Commission\u2019s Horizon 2020 research and innovation programme","doi-asserted-by":"publisher","award":["101003534"],"award-info":[{"award-number":["101003534"]}],"id":[{"id":"10.13039\/501100000780","id-type":"DOI","asserted-by":"publisher"}]},{"name":"COST (European Cooperation in Science and Technology)","award":["101003534"],"award-info":[{"award-number":["101003534"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The demand for accurate rainfall rate maps is growing ever more. This paper proposes a novel algorithm to estimate the rainfall rate map from the attenuation measurements coming from both broadcast satellite links (BSLs) and commercial microwave links (CMLs). The approach we pursue is based on an iterative procedure which extends the well-known GMZ algorithm to fuse the attenuation data coming from different links in a three-dimensional scenario, while also accounting for the virga phenomenon as a rain vertical attenuation model. We experimentally prove the convergence of the procedures, showing how the estimation error decreases for every iteration.\u00a0The numerical results show that adding the BSL links to a pre-existent CML network boosts the accuracy performance of the estimated rainfall map, improving up to 50% the correlation metrics. Moreover, our algorithm is shown to be robust to errors concerning the virga parametrization, proving the possibility of obtaining good estimation performance without the need for precise and real-time estimation of the virga parameters.<\/jats:p>","DOI":"10.3390\/s22187019","type":"journal-article","created":{"date-parts":[[2022,9,19]],"date-time":"2022-09-19T04:49:22Z","timestamp":1663562962000},"page":"7019","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Rainfall Map from Attenuation Data Fusion of Satellite Broadcast and Commercial Microwave Links"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5776-3936","authenticated-orcid":false,"given":"Fabio","family":"Saggese","sequence":"first","affiliation":[{"name":"Department of Electronic System, Aalborg University, 9220 Aalborg, Denmark"}]},{"given":"Vincenzo","family":"Lottici","sequence":"additional","affiliation":[{"name":"Department of Information Engineering, University of Pisa, 56122 Pisa, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0043-4098","authenticated-orcid":false,"given":"Filippo","family":"Giannetti","sequence":"additional","affiliation":[{"name":"Department of Information Engineering, University of Pisa, 56122 Pisa, Italy"}]}],"member":"1968","published-online":{"date-parts":[[2022,9,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1323","DOI":"10.1175\/1520-0450(1991)030<1323:TRORFT>2.0.CO;2","article-title":"Tomographic Reconstruction of Rainfall Fields through Microwave Attenuation Measurements","volume":"30","author":"Giuli","year":"1991","journal-title":"J. Appl. Meteorol. Climatol."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"713","DOI":"10.1126\/science.1120034","article-title":"Environmental Monitoring by Wireless Communication Networks","volume":"312","author":"Messer","year":"2006","journal-title":"Science"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Leijnse, H., Uijlenhoet, R., and Stricker, J.N.M. (2007). Rainfall measurement using radio links from cellular communication networks. Water Resour. Res., 43.","DOI":"10.1029\/2006WR005631"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"991","DOI":"10.5194\/amt-9-991-2016","article-title":"Real-time data acquisition of commercial microwave link networks for hydrometeorological applications","volume":"9","author":"Chwala","year":"2016","journal-title":"Atmos. Meas. Tech."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"6559","DOI":"10.5194\/amt-13-6559-2020","article-title":"Atmospheric observations with E-band microwave links\u2013challenges and opportunities","volume":"13","author":"Fencl","year":"2020","journal-title":"Atmos. Meas. Tech."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Berne, A., and Uijlenhoet, R. (2007). Path-averaged rainfall estimation using microwave links: Uncertainty due to spatial rainfall variability. Geophys. Res. Lett., 34.","DOI":"10.1029\/2007GL029409"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1385","DOI":"10.5194\/amt-3-1385-2010","article-title":"Prediction of rainfall intensity measurement errors using commercial microwave communication links","volume":"3","author":"Zinevich","year":"2010","journal-title":"Atmos. Meas. Tech."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/TGRS.2021.3110004","article-title":"Precipitation Estimates From Commercial Microwave Links: Practical Approaches to Wet-Antenna Correction","volume":"60","author":"Pastorek","year":"2022","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1616","DOI":"10.1109\/TSP.2009.2012554","article-title":"Rain Rate Estimation Using Measurements From Commercial Telecommunications Links","volume":"57","author":"Goldshtein","year":"2009","journal-title":"IEEE Trans. Signal Proc."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"770","DOI":"10.1109\/LGRS.2019.2935348","article-title":"Spatial Reconstruction of Rain Fields From Wireless Telecommunication Networks\u2014Scenario-Dependent Analysis of IDW-Based Algorithms","volume":"17","author":"Eshel","year":"2020","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"831","DOI":"10.1175\/JHM-D-20-0164.1","article-title":"Quantitative Analysis of the Performance of Spatial Interpolation Methods for Rainfall Estimation Using Commercial Microwave Links","volume":"22","author":"Eshel","year":"2021","journal-title":"J. Hydrometeorol."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2536","DOI":"10.1109\/36.789649","article-title":"Microwave tomographic inversion technique based on stochastic approach for rainfall fields monitoring","volume":"37","author":"Giuli","year":"1999","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"D\u2019Amico, M., Cerea, L., De Michele, C., Nebuloni, R., and Cubaiu, M. (2018, January 10\u201313). Tomographic Reconstruction of Rainfall Fields Using Heterogeneous Frequency Microwave Links. Proceedings of the 2018 IEEE Statistical Signal Processing Workshop (SSP), Freiburg im Breisgau, Germany.","DOI":"10.1109\/SSP.2018.8450723"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Giannetti, F., Reggiannini, R., Moretti, M., Adirosi, E., Baldini, L., Facheris, L., Antonini, A., Melani, S., Bacci, G., and Petrolino, A. (2017). Real-Time Rain Rate Evaluation via Satellite Downlink Signal Attenuation Measurement. Sensors, 17.","DOI":"10.3390\/s17081864"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Gharanjik, A., Mishra, K.V., MR, B.S., and Ottersten, B. (2018, January 10\u201313). Learning-Based Rainfall Estimation via Communication Satellite Links. Proceedings of the 2018 IEEE Statistical Signal Processing Workshop (SSP), Freiburg im Breisgau, Germany.","DOI":"10.1109\/SSP.2018.8450726"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1109\/MAES.2019.2916292","article-title":"The NEFOCAST System for Detection and Estimation of Rainfall Fields by the Opportunistic Use of Broadcast Satellite Signals","volume":"34","author":"Giannetti","year":"2019","journal-title":"IEEE Aerosp. Electron. Syst. Mag."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Csurgai-Horv\u00e1th, L. (2020). Small Scale Rain Field Sensing and Tomographic Reconstruction with Passive Geostationary Satellite Receivers. Remote Sens., 12.","DOI":"10.3390\/rs12244161"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Gragnani, G.L., Colli, M., Tavanti, E., and Caviglia, D.D. (2021). Advanced Real-Time Monitoring of Rainfall Using Commercial Satellite Broadcasting Service: A Case Study. Sensors, 21.","DOI":"10.3390\/s21030691"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Giannetti, F., and Reggiannini, R. (2021). Opportunistic Rain Rate Estimation from Measurements of Satellite Downlink Attenuation: A Survey. Sensors, 21.","DOI":"10.3390\/s21175872"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Pastoriza-Santos, V., Machado, F., Nandi, D., and P\u00e9rez-Font\u00e1n, F. (2022). Low-Cost Ka-Band Satellite Receiver Data Preprocessing for Tropospheric Propagation Studies. Sensors, 22.","DOI":"10.3390\/s22031043"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Saggese, F., Giannetti, F., and Lottici, V. (September, January 29). A Novel Approach to Rainfall Rate Estimation based on Fusing Measurements from Terrestrial Microwave and Satellite Links. Proceedings of the 2020 XXXIIIrd General Assembly and Scientific Symposium of the International Union of Radio Science, Rome, Italy.","DOI":"10.23919\/URSIGASS49373.2020.9232257"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Raich, R., Alpert, P., and Messer, H. (2018). Vertical Precipitation Estimation Using Microwave Links in Conjunction with Weather Radar. Environments, 5.","DOI":"10.3390\/environments5070074"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Lolli, S., D\u2019Adderio, L., Campbell, J., Sicard, M., Welton, E., Binci, A., Rea, A., Tokay, A., Comeron, A., and Barragan, R. (2018). Vertically Resolved Precipitation Intensity Retrieved Through a Synergy Between the Ground-Based NASA MPLNET Lidar Network Measurements, Surface Disdrometer Datasets and an Analytical Model Solution. Remote Sens., 10.","DOI":"10.20944\/preprints201805.0266.v1"},{"key":"ref_24","unstructured":"International Telecommunication Union-Radiocommunication (ITU-R) (2013). Rain Height Model for Prediction Methods, International Telecommunication Union."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"318","DOI":"10.1109\/TAP.1978.1141845","article-title":"The aRb relation in the calculation of rain attenuation","volume":"26","author":"Olsen","year":"1978","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_26","unstructured":"International Telecommunication Union-Radiocommunication (ITU-R) (1997). Specific Attenuation Model for Rain for Use in Prediction Method, International Telecommunication Union."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1023\/A:1010717821659","article-title":"Analytic Specific Attenuation Model for Rain for Use in Prediction Methods","volume":"22","author":"Zhao","year":"2001","journal-title":"Int. J. Infrared Millim. Waves"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Shepard, D. (1968). A Two-Dimensional Interpolation Function for Irregularly-Spaced Data. Proceedings of the ACM \u201968: 1968 23rd ACM National Conference, Association for Computing Machinery.","DOI":"10.1145\/800186.810616"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1007\/s00466-003-0532-2","article-title":"A new concept of probability metric and its applications in approximation of scattered data sets","volume":"33","year":"2004","journal-title":"Comput. Mech."},{"key":"ref_30","first-page":"1888","article-title":"A parameterization of the evaporation of rainfall","volume":"116","author":"Rosenfeld","year":"1988","journal-title":"Mon. Weather Rev."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Boyd, S., and Vandenberghe, L. (2004). Convex Optimization, Cambridge University Press.","DOI":"10.1017\/CBO9780511804441"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/18\/7019\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:32:46Z","timestamp":1760142766000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/18\/7019"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,9,16]]},"references-count":31,"journal-issue":{"issue":"18","published-online":{"date-parts":[[2022,9]]}},"alternative-id":["s22187019"],"URL":"https:\/\/doi.org\/10.3390\/s22187019","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,9,16]]}}}