# Atmospheric GNSS RO 1D-Var in Use at UCAR: Description and Validation
## 3 Results
### Tests Using Synthetic Data
The noise added to the \"perfect\" a priori profiles tends to incur numerous super-refraction layers. The occurrence frequency and location of the super-refraction layers are so erratic that it was difficult for us to use bending angle as the observation type. Besides, the refractivity observation operator is local, allowing straightforward interpretation of the testing results. Thus, we chose to use refractivity as the observation. We carried out 10,000 1D-Var retrievals by alternating the combination of observed and a priori profiles, which is analogous to testing the 1D-Var under varying atmospheric conditions and various realizations of weather forecasting. Furthermore, the known true atmosphere permits straightforward evaluation of the retrieval error, freeing us from the uncertainty of real-world data. Figure 6 compares a priori profiles (black dashed lines) and 1D-Var retrievals (red solid lines) in random error, i.e., the standard deviation from the true atmosphere. Small-scale undulations, which are more pronounced in a priori error, are primarily due to the limited vertical resolution of a priori profiles. Since the observation and a priori profile are unbiased, systematic error is irrelevant and not shown here. The 1D-Var shows a remarkable reduction of the temperature error (Figure 6a) at heights above 10 km. Here, the error reduction means comparing retrieval error to a priori error. While still discernible, the temperature error reduction is minor at lower heights. The reduced temperature error accompanies a significant reduction of pressure error (Figure 6b), which is the hydrostatic response to the temperature change, even at the lowest height where the temperature error reduction is relatively small. The specific humidity error is reduced dramatically below 10 km (Figure 6c), where water vapor is abundant. In contrast, it is hardly discernible above 8 km, although the relative humidity shows some error reduction there (Figure 6d). The relatively small temperature error reduction in the lower troposphere is due to the dominance of a priori humidity error. Figure 6: Errors of a priori profile (black dashed lines) and 1D-Var retrieval (red solid) for the subtropical case in Figure 5 in terms of: (**a**) temperature (\({}^{\circ}\)C), (**b**) pressure (hPa), (**c**) specific humidity (g kg\({}^{-1}\)), and (**d**) relative humidity (%). The error is defined as the standard deviation from the known truth. We considered an Arctic case to substantiate this last point. We used the GRUAN observation taken place at the Barrow station (71.32\({}^{\circ}\)N, 156.62\({}^{\circ}\)W) at 18:00 UT on 22 January 2011 (ID: BAR-RS-01_2_RS92-GDP_002_20110122T180000), which is collocated with a COSMIC profile (ID: C004.2011.022.18.00.G31). Figure 7 shows the true and observed refractivity and a priori profiles. Limited by the low temperature, the amount of atmospheric water vapor is small, even in the lower troposphere. Under this atmospheric condition, the 1D-Var reduces the temperature error almost by half throughout the atmosphere (Figure 8a). The diminished temperature error induces a great deal of pressure error reduction, about 80% at the surface (Figure 8b). The substantial error reductions in temperature and pressure contrast with the smaller error reductions in a wet atmosphere (Figure 6). The dry Arctic air restricts a priori humidity error to be small in terms of water vapor pressure and specific humidity, leaving little room for error reduction (Figure 8c,d). The synthetic data tests show that the 1D-Var produces high-quality retrievals whose error is considerably smaller than a priori error. The tests also indicate that the relative error reduction among the state variables depends on the atmospheric condition and respective a priori errors.