## 3 The PFAC Measurements and the FRM Uncertainty Analysis
### Uncertainty Budget for Sea-Surface Calibration
#### 3.2.1 Sea-Surface Height Constituent  
Measurements obtained by tide gauges are used to determine the sea surface height above a reference ellipsoid at the PFAC Cal/Val sites. According to FRM standards, at least two such instruments of diverse make and operating principle are to operate at each site. This redundant instrumentation permits efficient monitoring of each instrument's performance and inter-validation of their measurements. For example, in Gavdos Cal/Val, there are five continuously operating tide gauges: KVR3 (radar), KVR4 (acoustic), KVR5 (pressure), KVR6 (radar and operating in a stilling well) and KVR7 (radar) (Figure 6). Figure 6: The current set up of the “Karave” Cal/Val site in Gavdos harbor for sea-surface calibrations. Five tide gauges (KVR3-radar, KVR4-acoustic, KVR5-pressure, KVR6-radar in a stilling well, and KVR7-radar), two GNSS receivers (GVD7 and GVD8) and one meteorological station comprise the main scientific instrumentation of the Gavdos Cal/Val site. \begin{table}
\begin{tabular}{c c c c} \hline
**GVDS Station** & **Relative Differential** & **Precise Point Positioning** & **Difference** \\ \hline X [m] & 4,782,603.4086 & 4,782,603.4080 & 0.6 mm \\ \hline Y [m] & 2,141,348.9747 & 2,141,348.9748 & 0.1 mm \\ \hline Z [m] & 3,624,048.9145 & 3,624,048.9142 & 0.3 mm \\ \hline V\({}_{\rm X}\) [m/yr] & 0.0042 & 0.0035 & 0.7 mm/yr \\ \hline V\({}_{\rm Y}\) [m/yr] & 0.0105 & 0.0104 & 0.1 mm/yr \\ \hline V\({}_{\rm Z}\) [m/yr] & \(-\)0.0117 & \(-\)0.0117 & 0.0 mm/yr \\ \hline Time Span [yr] & 2010.4973–2019.1712 & 2011.0060–2019.1743 & \\ \hline \end{tabular}
\end{table} 
Table 3: GNSS processing results (Cartesian coordinates and velocities) for the GVD8 station as derived by the relative differential and precise point positioning techniques. The overall performance of these tide gauges is monitored on a daily and/or monthly basis. A 24-h recording of four of those tide gauges, on 14-Oct-2019, is given in Figure 7.  
A more detailed analysis of water level observations involves, among others, the evaluation of the Van de Casteele diagrams on a daily basis. The shape of the Van de Casteele diagram provides a qualitative illustration of the type of error involved in tide gauge measurements [27]. Simultaneous water level heights of a certain tide gauge are compared against a master reference tide gauge (Figure 8). The x-axis corresponds to the difference between the two tide gauge measurements over a full tidal cycle. The y-axis is the \"true\" sea-surface height as measured by the reference tide gauge. The shape of the diagram may be used to identify the source of any deviation between the measurements obtained by the reference and the tide gauge under investigation [28]. Figure 8: The Van de Casteele diagrams applied for tide gauge records at the Gavdos Cal/Val site on 14 October 2019. The radar KVR3 sensor is considered to be the reference against which the performance of the acoustic KVR4 (upper), and radar KVR7 (lower) tide gauges is evaluated. Each diagram represents the sea level (SSH, y axis) versus the difference between records of the two instruments (\(\Delta\)H, x-axis). The sampling rate is 6 min. Figure 7: Single-day (14-October-2019) water level measurements of the KVR3 (radar), KVR4 (acoustic), KVR6 (radar in a stilling well) and KVR7 (radar) tide gauges operating at the Gavdos Cal/Val site. In Gavdos, the KVR3 radar tide gauge is considered to be the reference water level sensor. The Van de Casteele test is applied and the performance of the remaining tide gauges (i.e., KVR4, KVR6, KVR7) is monitored. Various sampling intervals exist for the different tide gauges. In order to apply the Van de Casteele diagram, the daily tide gauge records are averaged, when needed, to match a 6-min sampling interval. Figure 8 presents an indicative example of such a single day (14-October-2019) monitoring for the KVR4 and the KVR7 sensors. It can be seen that, for this particular day, all tide gauge records agree with an uncertainty of the order of \(\pm 1\)cm.