## 3 Results
#### Description of ZPD Values  
In Figures 3 and 4, the density scatter plots provide an overview of the performance of the ZPD estimation. For all considered stations, a strong linear relationship between the estimated ZPD values and corresponding MERRA-2 ones was clearly found. Moreover, the areas of higher density were very near to the perfect accordance line. The dispersion varied sometimes significantly from ship to ship; this can be reasonably ascribed to a restricted number of causes, such as the adopted installation solutions, interference with other onboard equipment, and ship movements. The number of persisting outliers was also rather high for a few stations (e.g., CRRM, METH, MEAN), where the best-fit line, i.e., the straight line fitted to the data through the least square regression approach, deviated from the perfect accordance line. As expected, the higher was the number of outliers and their scatter, the wider was the deviation of the best-fit line from the perfect one. As also expected, the dispersion was strongly reduced for fixed stations, reported as reference (Figure 4). Note that data for the fixed stations are available for a shorter period (years 2021 and 2022) than for the ships. Figures 5 and 6 allow a further understanding of the behaviour of the different systems. For example, in the case of CRRM, there are two distinct periods with different performances. In the first data sequence, during July 2022, the ZPD was estimated very often to be quite different from the MERRA-2 reference values. This was probably due to an installation issue; in fact, during the receiver stop period (corresponding to the no data in the plot), some interventions because of malfunctioning were carried out, including a new set up of the system, that solved the problem, as is clearly visible by the behaviour for the following period. With regard to the data for the other ships, the following considerations are relevant. These graphs show ZPD values at only four time points of each day (00, 06, 12, and 18 UTC), due to the already mentioned limited occurrence of MERRA-2 data, so a more accurate reconstruction of the time patterns of the ZPD cannot be provided. However, intra- and inter-daily fluctuations are evident, that overlapped with longer, seasonal, periodic trends. The seasonal pattern of ZPD is in good accordance for all ship measurements, showing maxima during the summer season and minima during the winter one, reflecting a combination of both atmospheric total pressure trends and water vapour concentration variations. The physical origin of this behaviour is known and is primarily due to the trend of the zenith wet delay (ZWD), as highlighted in several works, such as [47], showing the climatology of  
Figure 4: Density scatter plots for GNSS-ZPD (using MG-APP software) vs. ZPD retrieved from MERRA-2 reanalysis data for the two fixed stations. All available data in the period 1 January 2021 and 31 December 2022 are considered (i.e., one year less than for the ship data of Figure 3). Figure 3: Density scatter plots of GNSS-ZPD (using MG-APP software) vs. ZPD retrieved from MERRA-2 reanalysis data. Only data from ship stations are included in this figure. All available data in the period 1 January 2020 and 31 December 2022 are considered. integrated water vapour in the European regions, or as in [48], investigating the characterisation of seasonal and diurnal cycles of ZPD at the global level. Figure 5: GNSS-ZPD (using MG-APP software). Only ship stations are considered in this figure. All available data in the period 1 January 2020 and 31 December 2022 are considered. We can note that in this context the outliers are quite evident, as almost all of them are outside the main \"stripe\" of values (i.e., from the variance of the seasonal climatology), and, thus, could be easily identified for removal using additional filters with relatively simple rules.