# A System to Improve Port Navigation Safety and Its Use in Italian Harbours
## 2 Materials and Methods
### Forecasting Sea Level in Harbours
The hydrobarometric transfer factor \(\mathrm{J_{ph}}\) [cm\(\cdot\)hPa\({}^{-1}\)] is estimated for each event as:  
\[\mathrm{J_{ph}}=\Delta\mathrm{h}/\Delta\mathrm{p}, \tag{1}\]  
expressed in absolute value, where \(\Delta\mathrm{h}\) and \(\Delta\mathrm{p}\) represent the change in sea level and atmospheric pressure, respectively; in these cases, we obtain a value of about 2.3 cm\(\cdot\)hPa\({}^{-1}\) for the event in Figure 12 and 2.1 cm\(\cdot\)hPa\({}^{-1}\) for the event in Figure 13.  
In the ports of Livorno and Bari and, more in general, in Italian coastal areas, typical values found by means of a multi-year statistical analysis carried out for \(\mathrm{J_{ph}}\) are larger (even more than double) compared to the typical 1 cm\(\cdot\)hPa\({}^{-1}\) of the offshore; this phenomenon, if in phase with astronomical tides, can cause exceptional tide waves. Then, for each event that happened in a given location in the period under consideration, the variation of low frequencies sea level \(\Delta\mathrm{h}\) and the gradient of atmospheric  
Figure 12: Low-frequency components of meteomareographic parameters acquired by ISPRA’s monitoring station in the port of Livorno from 27 November to 13 December 2019: (**a**) atmospheric pressure; (**b**) sea level; solid lines: low-frequency components surviving the filtering; dashed lines: high-frequency components eliminated by the filtering. Figure 13: Low-frequency components of meteo-mareographic parameters acquired by ISPRA’s monitoring station in the port of Bari from 15 to 23 May 2011: (**a**) atmospheric pressure; (**b**) sea level; solid lines: low-frequency components surviving the filtering; dashed lines: high-frequency components eliminated by the filtering. pressure \(\Delta\)p are evaluated, and the calculation of \(J_{\rm ph}\) is repeated. Many pairs (\(\Delta\)p, \(\Delta\)h) and of corresponding values of \(J_{\rm ph}\) are obtained in this way, one for each occurrence of the phenomenon in the time interval examined in a certain basin. In Tables 1 and 2 representative events that occurred since 2010 in Livorno and Bari harbours are listed, together with the estimates of \(J_{\rm ph}\) (data from 21 September 2015 to 24 March 2019 in Bari are not available). The plots of these events are shown in Appendix A, in Figures A1-A20 (except the events already shown in Figures 12 and 13). Starting from this statistic, the mean value (2 cm\(\cdot\)hPa\({}^{-1}\) for Livorno, 2.1 cm\(\cdot\)hPa\({}^{-1}\) for Bari) can be used as an estimate of \(J_{\rm ph}\) (which means to hypothesize a linear dependence of \(\Delta\)h from \(\Delta\)p). Once known, the hydro-barometric transfer factor allows estimating for each basin a future change in sea level based on the measurement or forecasting of atmospheric pressure (it will be sufficient to multiply the variation of atmospheric pressure by the mean \(J_{\rm ph}\) factor and then reverse the sign, taking into account that pressure and level changes have opposite signs: when one increases, the other decreases). By doing so, the average error on the forecasted meteorological tide (difference between the expected value and the measured one) is about 9.6% for Livorno and 8.2% for Bari, that is satisfactory for our purposes; otherwise, a better estimate could consider a non-linear variation of \(\Delta\)h as a function of \(\Delta\)p, at the cost of increased computational burden. Once \(J_{\rm ph}\) has been evaluated, it is possible to estimate the forecasted sea level by means of a simple processing procedure that calculates the sum of two contributions: the astronomical tide (well-known, available from tide charts) and the meteorological one that, as seen, can be found as the product of the average hydrobarometric factor \(J_{\rm ph}\) (with the sign reversed) by the expected (or real-time acquired) atmospheric pressure gradient. Therefore, the knowledge of \(J_{\rm ph}\) is very helpful in harbour waterside management: the effects of pressure variations on seawater depth can be applied to bathymetric maps