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This paper describes, along with some validation results, the one-dimensional variational method (1D-Var) that is in use at the University Corporation for Atmospheric Research (UCAR) to retrieve atmospheric profiles of temperature, pressure, and humidity from the observation of the Global Navigation Satellite System (GNSS) radio occultation (RO). The retrieved profiles are physically consistent among the variables and statistically optimal as regards to a priori error statistics. Tests with idealized data demonstrate that the 1D-Var is highly effective in spreading the observational information and confirm that the method works as designed and expected, provided that correct input data are given. Tests for real-world data sets show that the retrieved profiles agree remarkably well with global weather analyses and collocated high vertical resolution radiosonde observations, and that the 1D-Var can produce value-added retrievals with respect to a priori profiles. We also find that the retrieved profiles are of exceptional long-term stability, suggesting that the 1D-Var can provide an excellent climate data record.