## 2 Methods  
In order to accurately assess the impact of port mitigation solutions on SSS activity, the following paragraphs introduce a calculation model able to quantify in monetary terms the performance of these measures, with special attention being paid to CI and LNG alternatives. Appendix A provides the detailed nomenclature used in this section for the variables involved. The calculation procedure assumes two circumstances: on-board electricity supply and off-shore electricity supply. The former offers two possibilities: the conventional generation of electricity on board through Low Sulfur Marine Gas Oil (LMGO) (0.5% sulfur content) and the use of on-board generating sets driven by LNG dual engines; while the latter involves CI use (see Figure 1). Even though CI is just an alternative for the berthing time of the vessels (see Figure 1), in order to offer greater knowledge of port pollution, the air emissions generated during vessel maneuvers are also evaluated. Figure 1: Dependences of the variables involved in the calculation model for port emissions costs. Thus, Equations (1) and (3) provide the yearly environmental cost (EUR/year) for on-board electricity generation, during the maneuvering stage (ECM\({}_{\rm q}\), \(\forall\)q\(\in\)Q) and berthing stage (ECB\({}_{\rm q}\), \(\forall\)q\(\in\)Q) on a SSS line. \[\rm{ECM_{q}}=N\cdot\sum_{k=1}^{2}(ECMqk);\ \forall q\in Q \tag{1}\]  
\[\rm{ECM_{q,k}}=\sum_{u=1}^{5}(EFMuq\cdot(MT)\cdot UCukv)+IPBq\cdot EFe\cdot LFMq \cdot MT\cdot UC6 kv; \tag{2}\]  
\[\rm{\forall q\in Q\ \wedge\ \forall k\in K\ \wedge\ \forall v\in V\ \wedge\ \forall e\in EE}\]  
\[\rm{ECB_{q}}=N\cdot\sum_{k=1}^{2}(ECBqk);\ \forall q\in Q \tag{3}\]  
\[\rm{ECB_{q,k}}=\sum_{u=1}^{5}(EFBuq\cdot(BTq)\cdot UCukv)+IPBq\cdot EFe\cdot LFBq \cdot BTq\cdot UC6 kv; \tag{4}\]  
\[\rm{\forall q\in Q\ \wedge\ \forall k\in K\ \wedge\ \forall v\in V\ \wedge\ \forall e\in EE}\]  
Likewise, Equation (5) (\(ECG_{q}\), \(\forall q\)\(\in\)Q) offers information about the yearly environmental costs during berthing when the vessel is plugged into the electricity grid (CI option). \[\rm{ECG_{q}}=N\cdot\sum_{k=1}^{2}(ECG_{q}k);\ \forall q\in Q \tag{5}\]  
\[\rm{ECG_{q,k}}=\sum_{u=1}^{5}(EFGuk\cdot(BTq+CT)\cdot PBq\cdot UCukv)+PBq\cdot EFG 6k\cdot(BTq+CT)\cdot UC6 kv; \tag{6}\]  
\[\rm{\forall q\in Q\ \wedge\ \forall k\in K\ \wedge\ \forall v\in V\ \wedge\ \forall e\in EE}\]  
These Equations (1)-(6) quantify in monetary terms the impact of the pollutants (U = {1,..., _u_}): NO\({}_{\rm x}\) (ozone precursors), SO\({}_{2}\) (acidifying substances), PM\({}_{2.5}\), PM\({}_{10}\) (particular matter mass), and the greenhouse gases (CO\({}_{2}\)) that are emitted to the air by vessels that are suitable for SSS (Q = {1,..., _q_}, container and roll-on, roll-off vessels) by operating in several ports (K = {1,..., _k_}). Additionally, the methane impact (CH\({}_{4}\) pollutant) is also integrated into the assessment by considering its emission factor (\(EF_{e}\); \(\forall e\)\(\in\)EE) for the different kinds of engines (EE = {1,..., _e_}) and their load factor (\(LFM_{q}\)-maneuvering-\(LFB_{q}\)-berthing-, \(\forall q\)\(\in\)Q). The calculation of the environmental costs (Equations (1)-(6)) also considers the yearly trips of the shipping lines (N), the times (hours) invested in the stages (\(MT\)-maneuvering time-, \(BTq\); \(\forall q\)\(\in\)Q -berthing time-), emission factors, unitary costs for the pollutants and the installed power-MCR- for operations during every operational stage (\(IPB_{q}\); \(\forall q\)\(\in\)Q). This power is only the auxiliary engines' power for the berthing whereas, in the maneuvering stage propulsion power (main engine power) is also considered. Due to the features of the electricity grid, equation 6 additionally integrates the connection lag time (\(CT\)) and the required power for the berthing operations (\(PB_{q}\); \(\forall q\)\(\in\)Q).