# Atmospheric GNSS RO 1D-Var in Use at UCAR: Description and Validation
## 1 Introduction
Two popular uncertainty-based approaches in geophysical data inversion are the optimal interpolation (often referred to as the optimal estimation) method and the variational method. These methods are commonly based on [PERSON] theorem and are equivalent when certain conditions are met. These inversion methods have their roots in data assimilation. Historically, variational data assimilation underwent rapid development in the 1980s, e.g., ref. [19; 20; 21] and showed many practical advantages over the optimal interpolation method. Hence, weather forecasting centers around the world quickly started adopting the variational method switching from the optimal interpolation following the first operational use of three-dimensional variational data assimilation (3D-Var) by the National Centers for Environment Prediction (NCEP) [22; 23]. Regarding RO, [PERSON] [24] pioneered the idea of assimilating the observation into NWP models. [PERSON] et al. [25] explored the possibility by assimilating synthetic refractivity profiles into a limited-area model. [PERSON] et al. [26] are the first who assimilated real observations of RO. They assimilated 30 bending angle profiles obtained from the GPS/MET (Global Positioning System/Meteorology) experiment [27] into an NCEP global analysis system using a ray-tracing observation operator. The number of RO profiles available daily has increased over time. In particular, the number soared after the launch of six satellites of the Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC) [28] in April 2006. This, along with the advance of the RO technique, allowed many data assimilation experiments, e.g., ref. [6; 7; 8] to show the beneficial impact of RO data on weather forecasting. Today RO is widely accepted as an essential observation for NWP and atmospheric reanalysis projects [29; 30; 31]. In parallel with these data assimilation efforts, there were studies of uncertainty-based RO retrieval. One-dimensional variational methods (1D-Var) were applied to simulated [32] and GPS/MET [33] refractivity profiles. Direct algebraic inversion methods (1D equivalent of the optimal interpolation) were also tested with simulated [34; 35] and GPS/MET [36] bending angles. These studies have demonstrated that uncertainty-based retrieval methods--specifically, those based on the optimal estimation theory [37]--can provide realistic profiles of atmospheric temperature, humidity, and pressure under general atmospheric conditions. The COSMIC Data Analysis and Archive Center (CDAAC) at the University Corporation for Atmospheric Research (UCAR) has been using a 1D-Var software for the past two decades to produce RO-based profiles of temperature, moisture, and pressure [38]. These 1D-Var profiles show good agreement with radiosonde observations [39; 40; 41; 42; 43] and have been used by numerous researchers around the world for many research problems, e.g., investigation of atmospheric processes and structures [44; 45; 46], validation of other observing systems [47; 48], and testing of physical models and retrieval algorithms [49; 50]. As the 1D-Var profiles are increasingly being used, many data users request information regarding the retrieval method and the data it produces. Recently, CDAAC started producing \"wetPf2\" data with an updated 1D-Var algorithm [51]. Hence, it is an opportune time to introduce data users to the atmospheric 1D-Var used by CDAAC for data production. This paper describes the 1D-Var algorithm and presents some validation results. The description here is not intended to provide an in-depth theoretical treatise, but the central ideas and some specific implementation details on which most of the data users' inquiries were focused.