# Atmospheric GNSS RO 1D-Var in Use at UCAR: Description and Validation
## 3 Results
### Validation Using NWP Model Data
#### 3.3.3 Dependence on the Background  
1D-Var uses background profiles to enhance the RO observations that are neither perfect nor complete. However, a concern arising in this regard is that the 1D-Var solution is affected by the imperfect background. To investigate this effect, we carried out a statistical analysis using two sets of NEW, one of which (denoted COSMICERA) uses the ECMWF's interim reanalysis (ERA) [79] as the source of a priori profiles and the other (COSMICGFS) uses the Global Forecast System (GFS) analysis of the NCEP. Figure 11 compares the RMS difference between GFS and ERA analyses in parallel with the difference between COSMICERA and COSMICGFS. The two separate 1D-Var retrievals, COSMICGFS and COSMICERA, are much closer to each other than GFS and ERA are, indicating that the 1D-Var solution is constrained well by the observation and does not strongly depend on the background. We observed the same from the recently launched COSMIC-2 [80, 81] (not shown). The little dependence on backgrounds closely relates to the long-term stability of 1D-Var retrieval, which is one of the essential requirements to enable RO-based climate studies. Figure 10: Comparison of 1 DVAR observation operators, for which 1 DVAR temperatures (**upper panels**; \({}^{\circ}\)C) and specific humidities (**lower**; g kg\({}^{-1}\)) produced with different observation operators are compared to ECMWF analysis in the tropics (0–30\({}^{\circ}\); denoted as T at the top right corner of each panel), middle latitudes (30–60\({}^{\circ}\); M), and polar latitudes (60–90\({}^{\circ}\); H). Left panels show differences in the mean and right panels present the standard deviations. See text for the description of the observation operators. Figure 12 compares COSMIC specific humidities with corresponding GFS and ERA at the height of 2.5 km (shown are RMSDs) from January 2008 to August 2014. The RMS difference between GFS and ERA (GFS-ERA; upper left panel) exhibits two sudden changes (marked **A** and **B**), which coincide with the times that NCEP made major changes in their forecasting system [82, 83]. The ECMWF reanalysis (ERA) uses a frozen analysis system and is thus unlikely to cause these sudden changes. When GFS is used as the background (denoted COSMICGFS), the 1D-Var departure from the background (GFS-COSMICGFS; upper right) resembles GFS-ERA. Thus, the 1D-Var produces a temporally continuous solution even though discontinuous background is given. While using ERA as the background (COSMICERA), on the other hand, the background departure (COSMICERA; lower left) does not show any abrupt changes, confirming that neither COSMIC nor ERA but GFS is the cause of the sudden changes. The RMSD between COSMICGFS and COSMICERA (lower right) is remarkably small, indicating that the 1D-Var produces almost identical humidity values regardless of the source of the background. The minor break appearing in COSMICERA-ERA at the end of 2013 seems to be caused by ERA, e.g., a change made to the observing systems used by the reanalysis. Figure 11: Root-mean-square differences for the years 2008–2014. Left panels are between the Global Forecast System (GFS) analysis of NCEP and the interim reanalysis (ERA) in: (**a**) pressure (hPa), (**b**) temperature (\({}^{\circ}\)C), and (**c**) specific humidity (g kg\({}^{-1}\)). (**d–f**) are the same as in (**a–c**) but for between COSMICGFS and COSMICERA, which, respectively, use GFS and ERA as the background. As shown in Figures 6 and 8, 1D-Var can retrieve value-added profiles compared to the background. Real-world data tests also confirmed this point. Figure 13 shows an example where COSMIC-2 humidities (marked COSMIC2) are compared against short-term GFS forecasts (marked GFS\({}_{\text{FCTST}}\)), which served as the background. We made the comparison by taking ECMWF analysis (ECMWF\({}_{\text{ANAL}}\)) as the reference data for the period from 16 July 2019 to 1 February 2020.