# Atmospheric GNSS RO 1D-Var in Use at UCAR: Description and Validation
## 5 Conclusions  
While RO produces a great deal of data, the observations of bending angles and refractivities do not directly satisfy many data users' needs. Thus, efforts have continued from the early days of RO to retrieve atmospheric profiles of temperature and water vapor from RO observations. UCAR has been using an atmospheric 1D-Var for the last twenty years, which recently underwent a significant upgrade. In this paper, we describe the UCAR 1D-Var and present some of our validation results to answer increasing inquiries about the retrieval method and its data product (wetPf2). The findings of this study can be summarized as follows. Tests with observations perturbed at a single level (presented in Section 3.1) show that the 1D-Var response to the pointwise perturbation is highly nonlocal and differs considerably from one state variable to another, clearly illustrating the vertical spread of information by the observation operator and error covariances. The broad and complicated response accentuates the importance of accurate and precise error covariances, which is especially true for 1D-Var, lacking some resources and apparatuses available to multi-dimensional systems. The tests also validate that the 1D-Var works as designed and expected, making suitable corrections to the background, provided with an accurate observation profile containing many independent pieces of information, which is largely true for RO. Tests using synthetic data (Section 3.2) show that the 1D-Var attains a smaller posteriori error than a priori error, given accurate error covariances. In other words, the 1D-Var can produce value-added retrievals that are better than the background. The error reduction (ratio of a posteriori error to a priori error) varies significantly among the state variablesand depends on the atmospheric condition. Overall, temperature (and pressure) error reduction is much greater than humidity error reduction in a dry atmosphere, while moisture error reduction is predominant in humid conditions. This dependence on the atmospheric condition is determined by how the state variables' a priori errors compare when converted into refractivity equivalents. The 1D-Var primarily focuses on improving the largest variable in the refractivity-equivalent a priori error, which usually is temperature (and pressure) in the stratosphere and humidity in the lower troposphere. In contrast, the 1D-Var has difficulty reducing a priori humidity error in the stratosphere, which typically is already small and can easily be overshadowed by minor retrieval errors in temperature and pressure. Likewise, temperature error reduction is also challenging in the tropical lower troposphere. In these challenging cases, the 1D-Var is more receptive to systematic observation error. The results in Sections 3.3 and 3.4 support that the performance of the 1D-Var shown by synthetic data tests remains valid for real-world data sets and confirm that the retrieved profiles are of added value regarding a priori profiles. The 1D-Var shows close agreements with ECMWF analysis in all state variables' mean difference and standard deviation, and the retrieved profiles accord excellently with high vertical resolution profiles of RS92 radiosonde. This comparison to RS92 radiosonde suggests that the random uncertainties of the retrieved profiles are no larger than 1 \({}^{\circ}\)C in temperature, 0.7 hPa in pressure, and 1 g kg\({}^{-1}\) in specific humidity at heights below 25 km. These random uncertainties are exceedingly small considering the differing characteristics of RO and radiosondes. Another finding of this comparison is that the 1D-Var temperature and pressure agree notably better with RS92 observations than the traditional dry retrieval throughout the entire height range of the comparison in both mean difference and standard deviation. The closer agreement shown by the 1D-Var profiles indicates that the 1D-Var is a valuable complement to the dry retrieval.