## 2 Methods
### Practical Case Study
The results were tested with real values from Las Palmas port (an average loading/unloading time of 3.5 and 2.3 h for feeder and Ro-Pax, respectively, and 30 minutes for the maneuvering stage). Additionally, a hoteling time of 8 h per day (from 23 p.m. to 7 a.m.) was assumed for each shipping line. Despite some of the study ports being involved in CI projects (like the Core LNGs have project, 2020 [22]) none of them has currently permanent on-shore supply facilities for SSS traffic. Thus, 1 hour as a connection/disconnection lag time (\(CT\)) was assumed for all cases. The emission factors for the vessels (\(EF_{\text{M}up}\); \(\forall u\)\(\in\)U \(\land\)\(\forall q\)\(\in\)Q see Equation (2) and \(EF_{\text{B}uq}\); \(\forall u\)\(\in\)U \(\land\)\(\forall q\)\(\in\)Q see Equation (4)) have been obtained through the calculation tools developed by [PERSON] and [PERSON] [23] for container vessels and Ro-Pax vessels [24]. Moreover, the emission factors for CH\({}_{4}\) (\(EF_{\text{c}}\); \(\forall e\)\(\in\)EE) have been assumed with the following values \(EF_{\text{T}}\) = 0.040 g/kWh for fuel-based engines and \(EF_{\text{2}}\) = 5.79 g/kWh dual engines operating with LNG [12]. The electricity grids' emissions (\(EF_{\text{M}u}\); \(\forall u\)\(\in\)U \(\land\)\(\forall k\)\(\in\)K) for the European application cases can be obtained, per country and year, through the European Pollutant Release and Transfer Register -E-PTR- (Regulation (EC) No 166/2006) along with the Energy Statistics published by EUROSTAT (EU Commission, DG Energy, Unit A4,2020) [25]. Despite the E-PTRT providing a register for 91 different pollutants, the particulate matters PM\({}_{\text{2,5}}\) are not specifically given. Due to the significant impact of this pollutant on human health (there were an estimated 412,000 premature deaths in Europe through long-term exposure to this pollutant in 2016 [26]), the PM\({}_{\text{2,5}}\) amount can be estimated through its relationship with the PM\({}_{\text{10}}\) (see Table 2), since the latter is offered by E-PTRT [27]. EUROSTAT (EU Commission, DG Energy, Unit A4, 2020) [25] collects information about gross electricity generation, by fuel or product, as well as by type of generation. In such a case, the calculation of the weighting factor of the source in an electricity grid can be  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline _Hard Coal_ & \begin{tabular}{c} _Brown_ \\ _Coal_ \\ \end{tabular}  & \begin{tabular}{c} _Natural_ \\ _Gas_ \\ \end{tabular}  & \begin{tabular}{c} _Derived_ \\ _Gases_ \\ \end{tabular}  & \ \begin{tabular}{c} _Heavy fuel_ \\ _Oil_ \\ \end{tabular}  & \begin{tabular}{c} _Other_ \\ _Liquefied fuels_ \\ \end{tabular}  & _Biomass_ \\ \hline \text  
calculated for each country and year by making it possible to estimate the PM\({}_{2.5}\) amount from PM\({}_{10}\) information. However, this information is not available for smaller geographical levels in EUROSTAT; for these application cases the official data from regional institutions must be consulted. The European Pollutant Release and Transfer Register (E-PRTR) (Regulation (EC) No 166/2006) not only offers information per kind of economic sector (NACE) and industrial activity, but also desegregates information beyond the national level [27]. Finally, Table 3 provides the air pollutant costs where metropolitan or urban areas are related to the port hinterland population: larger than 0.5 million or less than this population, respectively.