## Processing Setup and Description
### Uncertainty Modeling
#### 3.5.1 LEO Systematic Uncertainty Estimates  
LEO satellite orbits with derived systematic uncertainties within a 3D root-mean-squared (RMS) \(u_{\rm CB}^{\rm Rx}\) of 5 cm (position) and 0.05 mm/s (velocity) threshold promote negligible errors into the final atmospheric variables derived from RO. Furthermore, this threshold is regarded as conservative, since it fulfils the RO quality requirement of an error not higher than about 0.05 mm/s in along-occultation-path velocity [3; 29], which is the most critical POD variable for RO retrieval quality.  
In our approach several sources are exploited for the estimation of the LEO orbit uncertainties. First, the inter-comparison of different orbit products routinely calculated (Section 3.3) allows for an assessment of the generic consistency between the individual orbit solutions. Since the employed POD software packages, processing setup, parametrization, models, and GNSS data used are regarded as sufficiently independent, possible systematic errors are considered plausibly estimated. In addition, independent SLR tracking can also reveal systematic deficiencies in the orbit determination and help identify the most accurate solution. The following three measures are derived on a daily basis for checking the WEGC-BC primary solution:  
1. WEGC-BC vs. WEGC-NC difference (_LEO POD cross-check_): Based on GNSS orbit input from CODE the orbit differences are driven by computational setup and model considerations of the different LEO POD software packages employed.
2. WEGC-BC vs. WEGC-BI difference (_GNSS input sanity-check_): The orbit computations are carried out by Bernese with different GNSS orbit, clock, and EOP data and might reveal deficiencies in the transmitter orbit modeling.
3. WEGC-BC vs. SLR difference (_SLR validation cross-check_): Analysis of SLR residuals for missions equipped with an LRR. This validation represents snapshots because of the limited number of available SLR measurement sequences per day.  
The overall 3D-RMS estimate is calculated from epoch-wise differences in radial, along-track, and cross-track components as well as the RMS from the 1D SLR residuals, resulting in one daily scalar estimate per measure. From these three scalar uncertainty measures for (a), (b), and (c), termed\(u_{\text{(a)}}\), \(u_{\text{(b)}}\), \(u_{\text{(c)}}\) hereafter, the final systematic uncertainty estimate \(u_{s}^{\text{Rx}}\) for the primary orbit solution is derived as follows:  
\[u_{s}^{\text{Rx}}=\max\left(u_{\text{CB}}^{\text{Rx}},\ \sqrt{u_{\text{(a)}}^{2}+u_{ \text{(b)}}^{2}+u_{\text{(c)}}^{2}}\right)\,;\ \text{if}\ u_{\text{(x)}}<u_{\text{CB}}^{\text{Rx}}\ \text{then}\ u_{\text{(x)}}=0,\ \ \text{x}\in\{\text{a,b,c}\}. \tag{3}\]  
Such a variance combination of the uncertainty measures ensures a reasonable RMS estimate even if the individual components are not fully independent (according to the Guide to the Expression of Uncertainty in Measurement by the Joint Committee for Guides in Metrology (JCGM) [98]; see also [99] (pp. 29-44 therein)). Note that laser ranging residuals only contribute their measure \(u_{\text{(c)}}\) to the calculation if available. The position uncertainties (in units cm) are empirically found (cf. Figure 2) to map with a factor around \(1/1000\) to the velocity uncertainties (in units mm/s); hence we adopted a conversion factor of \(1/1000\) for this mapping.