## 3 The PFAC Measurements and the FRM Uncertainty Analysis
### Uncertainty Budget for Transponder Calibration
#### 3.3.1 Atmospheric Propagation Delay Constituent  
Determination of the signal delays caused by the atmosphere constitutes the most challenging task in transponder calibration. This is because the radiometer on-board the satellite does not operate properly over land. Thus, other means have to be figured out to correct signal propagation delays when the altimeter flies over a transponder land site. In the PFAC, this is carried out using GNSS-derived corrections for the atmospheric delays. The GNSS-derived delays refer to both the ionospheric and the zenith tropospheric (wet and dry component) delays at the transponder Cal/Val site. The ionosphere delays over the PFAC are regularly stable. They do not change rapidly and can be accurately determined via GNSS processing with an uncertainty of the order of \(\pm 1\) mm [24]. The dry (or hydrostatic) troposphere delay is also stable. It can also be accurately modeled using in-situ surface pressure measurements made by meteorological sensors. The wet component of the troposphere is dynamic, presents unstable variability rapidly changing over time, and cannot be easily modeled. In GNSS processing, this wet troposphere delay is estimated as the remaining part of the total delay minus the dry troposphere delay. Different GNSS processing methodologies generate diverse atmospheric propagation delays (Figure 10). \begin{table}
\begin{tabular}{c c c c} \hline
**Error Constituent** & **Type** & **Uncertainty Estimate** &
\begin{tabular}{c} **Standard Uncertainty** \\ **(Confidence 68\%)** \\ \end{tabular} \\ \hline GNSS Height Repeatability 1  & A & 0.10 mm & \(\pm 0.10\) mm \\ GNSS Receiver 2  & B & 6.00 mm & \(\pm 3.50\) mm \\ GNSS Antenna Reference Point 1  & B & 2.00 mm & \(\pm 2.00\) mm \\ Water Level 1  & B & 1.30 mm & \(\pm 1.30\) mm \\ Tide-Gauge Zero Reference 1  & A & 0.15 mm & \(\pm 0.15\) mm \\ Tide Gauge Vertical Alignment 2  & B & 2.40 mm & \(\pm 1.39\) mm \\ Tide-Gauge Sensor Certificate 1  & B & 5.50 mm & \(\pm 5.50\) mm \\ Leveling Repeatability 1  & A & 0.11 mm & \(\pm 0.11\) mm \\ Monumentation 2  & B & 1.10 mm & \(\pm 0.64\) mm \\ Vertical Misalignment 2  & B & 1.00 mm & \(\pm 0.60\) mm \\ Leveling Observer 2  & B & 1.00 mm & \(\pm 0.60\) mm \\ Leveling Instrument/Method 2  & B & 1.00 mm & \(\pm 0.60\) mm \\ Tide Pole Reading During Calibration 2  & B & 1.00 mm & \(\pm 0.60\) mm \\ Geoid and Mean Dynamic Topography 1  & B & 30.00 mm & \(\pm 30.00\) mm \\ Processing and Approximations 2  & B & 0.50 mm & \(\pm 0.30\) mm \\ Geoid Slope/Offshore Transfer 2  & B & 10.00 mm & \(\pm 5.80\) mm \\ Unaccounted effects 2  & B & 20.00 mm & \(\pm 11.55\) mm \\ Root-Sum-Squared Uncertainty & & & \(\pm 31.91\) mm \\ \hline \end{tabular}
\end{table} 
Table 4: Uncertainty budget for the sea-surface calibration. The final standardized uncertainty (at 68% confidence level), described by a Root-Sum-Square value, has been computed as: \(FRM_{SSH}(Uncertainty)=\pm 31.91\,mm=\sqrt{(0.10)^{2}+(3.50)^{2}+(2.00)^{2}+\cdots+(0.30)^ {2}+(5.80)^{2}+(11.55)^{2}}\). The difference observed in Figure 10 may be attributed to various models applied to determine the dry troposphere delay in their derivation, the means implemented to estimate surface pressure (i.e., models or in-situ measurements), as well as to the sampling rate used for GNSS data processing (Figure 11). In order to be FRM-compliant, the PFAC should verify the GNSS-derived wet tropospheric delays at the time of satellite overpass using an independent technique. A ground microwave radiometer, provided on loan from the European Space Agency, has been installed in 2019 at the CDN1  
Figure 11: Hourly zenith wet delays as estimated by GNSS processing using relative differential positioning (left) and precise point positioning (right) for the Sentinel-3A transponder calibration, on 27-October-2019 at the CDN1 transponder Cal/Val site.