## 3 Results and Discussion  
Figure 4 presents a comparison between the annual energy consumption of the backup water heater in a conventional DHW solar system and that in a DHW solar system with an adsorption module for five solar collector slopes in the seven assessed locations. The locations were sorted in descending order of latitude. For each collector inclination, the annual backup energy saving (Q\({}_{\text{saving}}\)) is presented on top of the respective bars in Figure 4, in both absolute (MJ) and percentual values. It should be noted that the scales of the ordinates are not the same for all the locations. Figure 4: Comparison of yearly energy consumption of the backup water heater (Q\({}_{\text{backup}}\)) using a conventional DHW solar system (blue bars) and that using a DHW solar system with an adsorption module (green bars) for different solar collector slopes in the seven assessed locations: (**a**) Beijing; (**b**) Baltimore; (**c**) Lisbon; (**d**) New Delhi; (**e**) Brasilia; (**f**) Cape Town; (**g**) Canberra. The annual backup energy saving Q\({}_{\text{saving}}\) is presented on top of the bars in both absolute (MJ) and percentual (%) values (taking Q\({}_{\text{backup,conv,year}}\) as a reference). A similar evolution is observable in most of the locations: higher collector slopes lead to lower energy consumptions for both the conventional system and the one with an adsorption module and result in higher energy savings (Qsaving). Therefore, the best results were obtained for large solar collector inclinations, thus favoring the system's operation during winter, when the heating needs are higher. The exception is Brasilia (see Figure 4e), where this behavior was only noticed until the collector slope was increased to the intermediate level and was then inverted with further increase of the collector slope. This seems to be related with Brasilia's latitude--15.8\({}^{\circ}\) S, which is lower than that of the remaining locations and between the Tropics (\(\pm\)23.5\({}^{\circ}\)). There, the solar zenith angle is always high, leading to higher solar radiation throughout the year (see Figure 4 in Appendix A). Therefore, there is little gain by varying the solar collectors' slope, as opposed to what happens for locations at higher latitudes (the remaining assessed locations), where the solar zenith angle is considerably lower in winter. It is noticeable that at the warmer locations (New Delhi, Brasilia, and Cape Town), despite the fact that the percentual energy savings are of the same order of magnitude, the absolute values of Qsaving are much lower than in the remaining locations. Therefore, considering a similar investment cost for the adsorption system, there seems to be little advantage in installing such a system at these warmer locations, since the effective energy savings are much lower, within the corresponding massive payback periods. The yearly solar radiation available at different locations and the corresponding minimum values of Qbackup (with and without the adsorption module) and maximum values of Qsaving are displayed in Figure 5. The Qbackup and Qsaving values can present significant differences for locations at similar latitudes: these values are clearly smaller in Lisbon in relation to those in other locations at similar latitudes--Beijing and Baltimore. This is due to the solar radiation availability in Lisbon (5880 MJ/year/m\({}^{2}\) in the horizontal plane), which is higher than in the other locations--5025 MJ/year/m\({}^{2}\) in Beijing and 5358 MJ/year/m\({}^{2}\) in Baltimore--, thus leading to lowering backup energy consumptions. Accordingly, locations with less available solar radiation tend to present higher Qbackup and Qsaving values, i.e., the system with an adsorption module operates with higher performance in these locations. This renders a very strong Pearson correlation coefficient (\(\rho\)) of \(-\)0.94 between the maximum absolute value of Qsaving (Qsaving,max) and the available horizontal solar radiation (Table 2).