# Mathematics-Driven Analysis of Offshore Green Hydrogen Stations
## 4 Discussion
### Solar Irradiation and Green Hydrogen Station Capacity  
In Figure 4, the normal solar radiation density received on the surface of the photovoltaic panels is represented, both in its direct component (\(I_{n\_direct}\)) and reflected component (\(I_{n\_reflected}\)), as well as the resulting total contribution (\(I_{n\_total}\)). However, as described in expressions (Equations (15) and (16)), the radiation density received at the Earth's surface is attenuated by the effects of \(M_{air}\) and atmospheric conditions such as those resulting from absorption and scattering processes [46]. These processes define the atmospheric quality between the Sun's position and the photovoltaic station. Figure 11 illustrates the effect of atmospheric attenuation on \(I_{n\_total}\) values received on the panel surfaces. Lower atmospheric quality leads to higher attenuation (higher absorption and scattering coefficients), resulting in lower \(I_{n\_total}\) values. In the case under analysis, the average attenuation of the total irradiance \(I_{n\_total}\) received by the photovoltaic panels is 31.16% when averaged over the hours of a typical day and 25.25% when averaged across all days of the year. Additionally, the presence of small airborne particles--such as dust--not only increases atmospheric pollution levels but also reduces the solar radiation density received on the surface of the panels due to the shading effect they produce, thereby decreasing the panels' operational efficiency. This issue is significantly reduced in offshore installations--such as floating solar energy stations--since the surrounding water helps clean the dust accumulated on the panels' surface [19] and because the distance between the photovoltaic panels' location and the primary sources of particle emissions is typically greater than in equivalent land-based stations. Conversely, higher atmospheric quality results in greater \(I_{n\_total}\) values and reduces the required photovoltaic panel surface area (\(M_{punels}\)) needed to produce the same amount of green hydrogen. This behavior is critical, as it supports the rationale for selecting installation sites in areas far from urban centers with high pollution levels--such as offshore locations. The following figures present only the results for the ALK electrolyzer. This decision was made because the conclusions drawn under the rest of the parameters studied are equivalent to those obtained for the PEM electrolyzer, as long as the relationship between both technologies is maintained. Hydrogen production by the electrolyzer depends on the hydrogen heating value constant (Equation (29)). This constant, in turn, is influenced by the energy recovery capacity integrated into the station's design. Figure 12 illustrates the contribution of both heating value constants to the amount of \(\frac{\mathrm{mol_{H_{2}}}}{\mathrm{s\times m^{2}}}\) produced at the green hydrogen station's output, as well as the photovoltaic panel surface required to produce \(1\)\(\frac{\mathrm{mol_{H_{2}}}}{\mathrm{s}}\). The use of the lower heating value (LHV) constant enables the production of the same amount of hydrogen with lower energy input, thereby reducing the required photovoltaic surface area (\(M_{puncis}\)). In the case under analysis, green hydrogen production increases by 17.69% when the lower heating value (LHV) is used instead of the higher heating value (HHV). This improvement translates into a 15.03% reduction in the photovoltaic surface area required to produce \(1\)\(\frac{\mathrm{mol_{H_{2}}}}{\mathrm{s}}\). Figure 13 illustrates the effect of \(P_{out}\) on the production of \(1\)\(\frac{\mathrm{mol_{H_{2}}}}{\mathrm{s}}\) of hydrogen. As \(P_{out}\) increases, the value of \(\frac{\mathrm{mol_{H_{2}}}}{\mathrm{s}\mathrm{<m^{2}}}\) decreases, while the required \(M_{puncis}\) increases. This occurs because more energy is needed to power the compressor and achieve a higher \(P_{out}\) value.