# Atmospheric GNSS RO 1D-Var in Use at UCAR: Description and Validation
## 1 Introduction  
The Global Navigation Satellite System (GNSS) Radio Occultation (RO) technique [1; 2; 3] has become established as a climate-quality benchmark observing system for measuring the atmosphere's thermodynamic states [4; 5]. It provides accurate, precise, high-vertical-resolution, globally distributed sounding observations under all weather conditions and regardless of Earth's surface condition. These unique strengths make RO a valuable data source for Numerical Weather Prediction (NWP), as evidenced by routine, operational use of the data at weather forecasting centers worldwide [6; 7; 8]. In addition, RO becomes increasingly relevant for climate studies as its data record lengthens. This stable, drift-free, self-calibrating data record is ideal for monitoring the Earth's changing climate. The data coverage is of good global and temporal coverage, which reduces the sampling error in climate system studies [4]. Aside from weather forecasting and climate change monitoring, there is a considerable body of literature where RO data are utilized to study atmospheric processes, e.g., those related to the tropopause, the planetary boundary layer, atmospheric waves and tides, significant weather events, and so on. RO data also provide unique and valuable information on the ionosphere [9; 10; 11; 12], but these applications are not discussed in this paper. The RO technique is based on the GNSS signal recorded by a receiver onboard a low-Earth orbit (LEO) satellite as the GNSS satellite sets or rises behind the Earth's atmospheric limb. The primary measurement is the signal's phase delay from which the ray's bending angle and atmospheric refractivity can be deduced in sequence. While the bending angle and refractivity profiles can be assimilated into NWP models directly, these data are not convenient for many research studies of atmospheric processes and phenomena. Accordingly, efforts have long been made to provide data products of greater geophysical relevance and, ultimately, to make RO data more useful to the science community. Specifically, theseefforts aim to retrieve atmospheric profiles of temperature, pressure, and water vapor that determine the GNSS signal's refraction. A fundamental difficulty facing these efforts is that the retrieval is an underdetermined problem. The three unknowns (temperature, pressure, and water vapor) must be determined from a single observed physical quantity (bending angle or refractivity). This difficulty can be eased under certain conditions. When the atmosphere is dry, the unknowns are reduced to temperature and pressure, which can be related to each other through hydrostatic balance. This resolves the underdetermination, allowing one to obtain accurate temperature and pressure profiles in the stratosphere [13]. In moist air, however, water vapor effect dominates, e.g., the refractivity of pure water vapor at typical atmospheric temperatures is approximately 17 times greater than that of dry air near the surface in the tropics [14]. In a humid atmosphere, it is thus possible to isolate the water vapor effect to an acceptable degree by approximating the unknown temperature and pressure with a priori values, as demonstrated by [15; 13]. These methods developed in the early days of RO (hereafter referred to as traditional methods) can provide either temperature or moisture (when atmospheric water vapor is either scarce or abundant), but not both together and cannot be applied to general atmospheric conditions. These methods work less well when the water vapor and dry atmospheric effects on refractivity are comparable, as in the middle troposphere. An essential prerequisite for the success of these traditional methods is that the RO refractivity data are of sufficient quality. However, RO data are subject to various error sources [2; 3; 16; 17]. These kinds of uncertainties and errors are ubiquitous in geophysical data inversion, and taking them into account has become a cornerstone of modern geophysical inversion theories, e.g., [18].