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The method improves a recent proposal for unconstrained tomographic inversions and is developed and validated with data from the Manaus dense GNSS network and in\u2010situ radiosondes, covering different seasons and synoptic conditions. The optimization uses a Monte Carlo technique to find the minimum root\u2010mean\u2010square error in a two\u2010dimensional parameter space. A set of fixed parameters, computed by optimizing over a small subset of cases, is found to lead to results that are overall significantly better than those produced by the three more common mapping functions used for geodesy applications. The quality of inversions is, however, found to have significant spread, an indication of the impact of varying GNSS data quality and a reminder of the need of further improvements in the method.<\/jats:p>","DOI":"10.1029\/2022gl100140","type":"journal-article","created":{"date-parts":[[2022,9,22]],"date-time":"2022-09-22T05:56:11Z","timestamp":1663826171000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Improved GNSS Water Vapor Tomography With Modified Mapping Functions"],"prefix":"10.1029","volume":"49","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4288-9456","authenticated-orcid":false,"given":"P. M. 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