## 3 Results
#### Description of ZPD Values
A quantitative evaluation of the ZPD estimation can be obtained through direct comparison with MERRA-2 values, using as the score parameters, the (Pearson) correlation, the mean square error (MSE), the root mean square error (RMSE) and the mean bias error (MBE). These parameters were computed separately for each station and are shown in Table 2, together with the number of points available for their calculation (during the full three year period) and with the equation of the best-fit line. As expected, the errors from the ship-based receivers were greater than those from the fixed stations, which also showed a higher correlation value. In fact, the motion of the station on the sea decreased the estimation performances, resulting in higher oscillations of the ZPD values, but only slightly. As is evident even just from the scatter plots, for all the stations, the correlation value was rather high, always higher than 0.85, with the exception of the CRRM station, which, as we have shown, had some known problems in the first period of operation. Most stations showed RMSE and MSE values that were rather reduced. Only the CRRM and METH ship stations had higher errors due to the higher number of outliers, but within the acceptance window of our general filtering process (i.e., non-upgraded with seasonal constrains). What happened for the fixed station LAM1 was different, as the correlation was very high, 0.95, equal to the correlation that occurred in the other fixed station (GROS), but the values of RMSE and MSE were close to the METH station. Moreover, in Figures 4 and 6, the values of ZPD computed from the GNSS stations (in particular LAM1) were slightly underestimated (i.e., biased) compared to the reference values. This was also confirmed by the high absolute \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{\
\begin{tabular}{c} **Station** \\ **Name** \\ \end{tabular} } & \multicolumn{1}{c}{
\begin{tabular}{c} **Number of** \\ **Points** \\ \end{tabular} } & \multirow{2}{*}{**Correlation**} & \multirow{2}{*}{**RMSE [mm]**} & \multirow{2}{*}{**MBE [mm]**} & \multirow{2}{*}{**Best Fit Line y = ax + b**} \\ \hline MEAN & 4376 & 0.91 & 24.15 & \(-8.8\) & \(\text{y}=0.90\times 245.13\) \\ LOTA & 3676 & 0.91 & 22.7 & \(-7.9\) & \(\text{y}=0.94\times 147.97\) \\ SMER & 4175 & 0.92 & 22.5 & \(-9.0\) & \(\text{y}=0.93\times 163.63\) \\ MEFO & 3572 & 0.91 & 22.6 & \(-7.5\) & \(\text{y}=0.92\times 201.25\) \\ METH & 4371 & 0.85 & 30.1 & \(-5.8\) & \(\text{y}=0.81\times 463.01\) \\ MEII & 3857 & 0.94 & 18.4 & \(-7.3\) & \(\text{y}=0.98\times 41.1\) \\ MEON & 4033 & 0.93 & 20.3 & \(-8.4\) & \(\text{y}=0.95\times 124.89\) \\ CRRM & 252 & 0.65 & 42.9 & \(-1.1\) & \(\text{y}=0.44\times 1363.61\) \\ _CROS_ & 2549 & 0.95 & 21.2 & \(-12.6\) & \(\text{y}=1.03\times-71.6\) \\ _LAM1_ & 2888 & 0.95 & 30.4 & \(-24.5\) & \(\text{y}=1.07\times-150.48\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Estimation scores. Fixed stations (the two last ones) are labelled in italic. Figure 6: GNSS-ZPD (using MG-APP software) for the two fixed stations. All available data in the period 1 January 2020 and 31 December 2022 are considered. value of MBE, the largest of all. An important bias was also recorded in the second fixed station, GROS.