# A System to Improve Port Navigation Safety and Its Use in Italian Harbours
## 2 Materials and Methods
### Forecasting Sea Level in Harbours  
Meteo-tides are well-known in off-shore areas (the \"inverted barometer\" effect), where 1 hPa of atmospheric pressure change (cause) induces nearly 1 cm of sea-level variation (effect), but they need more study in coastal areas, where the shoreline prevents the displacement of the marine water mass along horizontal directions towards the coastline: the effect of this constraint is to amplify the vertical movement [40; 41; 42; 43; 44; 45; 46; 47; 48; 49; 50; 51; 52; 53; 54; 55; 56; 57; 58; 59; 60; 61; 62]. Moreover, the correlation between atmospheric pressure and sea level (represented by means of the so-called hydrobarometric transfer factor \(\mathrm{J_{ph}}\)) depends on a number of specific parameters for the location examined (overall the topography of the basin), therefore it cannot be described by means of a deterministic law valid everywhere but must be studied through a local observation of the phenomenon and subsequent statistical analysis. Therefore, the study of meteorological tides consists essentially in analysing events (sea-level variations consequent to atmospheric pressure changes) that occur in a given basin during a certain time interval (usually some years), to estimate the hydrobarometric transfer factor \(\mathrm{J_{ph}}\); the starting point is the monitoring of atmospheric pressure and sea level; for example, in Figure 8 parameters observed in the port of Livormo from 27 November to 13 December 2019 are shown, while Figure 9 refers to data acquired in Bari harbour from 15 to 23 May 2011. Sea level acquired includes all the phenomena that contribute to its variations, above all astronomical (in particular diurnal and semidiurnal) and meteorological tides. Other short-term phenomena such as wind effect and storm surges are not taken into consideration in this study (only events occurring in the absence of wind were studied). To remove contributions different from the meteorological one, measurements are filtered appropriately taking advantage of the fact that astronomical tides are characterized by high frequencies; power spectral densities of atmospheric pressure and sea level acquired in the port of Livorno during 2019 are shown in Figure 10: frequency components related to diurnal and semidiurnal tides are at about 1.2 and \(2.3\cdot 10^{-5}\) Hz, respectively; Figure 11 shows the same quantities relating to the port of Bari in 2011. Figure 8: Meteomareographic parameters acquired by ISPRA’s monitoring station in the port of Livorno from 27 November to 13 December 2019. Figure 9: Meteomareographic parameters acquired by ISPRA’s monitoring station in the port of Bari from 15 to 23 May 2011. Data are subjected to a Low Pass filtering that avoids diurnal and semidiurnal tides, which are the spectral components dashed in Figures 10-13: only low-frequency components (slow variations), related to atmospheric pressure, survive the filtering (solid lines). Regarding the period from 27 November to 13 December 2019 in Livorno, the filtered data shown in Figure 12 result, in which 19.5 hPa of atmospheric pressure increase in \(\Delta\)p (cause) induce nearly 45.2 cm of low meteorological tide \(\Delta\)h (height of tide wave, effect). As for filtered data from 15 to 23 May 2011 in Bari, Figure 13 shows that an increase in \(\Delta\)p of 8.1 hPa in atmospheric pressure causes a decrease in \(\Delta\)h of nearly 16.8 cm in sea level. Figure 11: Power spectral densities of meteomareographic parameters acquired by ISPRA’s monitoring station in the port of Bari in 2011: (**a**) atmospheric pressure; (**b**) sea level; solid lines: lowfrequency components surviving the filtering; dashed lines: highfrequency components eliminated by the filtering. Figure 10: Power spectral densities of meteomareographic parameters acquired by ISPRA’s monitoring station in the port of Livorno in 2019: (**a**) atmospheric pressure; (**b**) sea level; solid lines: lowfrequency components surviving the filtering; dashed lines: highfrequency components eliminated by the filtering.