## 3 Results and Discussion
### Comparative Analysis of Algae Production  
In this section, the PDF of the microalgal productivity for each day that forms each GMS for the summer season is represented for the study location. The spring, autumn, and winter figures are in Appendix A. In Figure 5 (and the figures included in Appendix A), the asterisk symbol represents the biomass concentration obtained for each day of TMS and was placed in the middle of the corresponding biomass concentration bin. Figure 4: Seasonal variation in the concentration of algal biomass as a function of meteorological parameters (typical meteorological sequence, TMS) from the northern region of Madrid (Riosequillo). These curves were derived by applying, as input data to the model, the average daily temperature (\(T_{me}\)) and \(PAR\) values of selected TMS, Figure 3 [2]. Figure 5: Probability distribution function (PDF) of the sequence of day-by-day biomass concentrations using PAR and temperature data from each GMS input for the model of the summer season at Riosequillo (Madrid). (**a–f**) Represent the PDF of the biomass concentration of each dataset from days D2, D3, D4, D5, D6, and D7, respectively. In summer, the biomass concentration estimates by TMS coincide with the most probable values obtained with the proposed methodology, as Figure 5 shows. The same was observed with data from the spring season, except for the case of days D2 and D7, Figure A1. The position of the biomass concentration, for D5 in the summer (Figure 5) and for D2 and D7 in the spring TMS (Figure A1), is in the concentration bin with a relatively high probability and is directly preceded or followed by the bin with the highest PDF value. The methodology seems to confirm the representativeness of the TMS for the summer and spring seasons in the location studied. In fact, in these two seasons, almost all of the days of TMS already selected are in one of the ranges of biomass concentration that have the highest PDFs. However, the PDF is more distributed for the autumn season (see Figure A2). In this case, the biomass concentration position of each of the TMS days is not within the bin with the highest PDFs or within the bins near the latter. In Figure A3, in addition to day D2, the biomass concentration for each of the other days of TMS representing winter is far from being among those with the highest probability of distribution, despite the low dispersion of the results. Furthermore, the concentration hardly increases during this period. Consequently, most of the concentrations with the highest probability of distribution are below the initial biomass concentration. The non-growth of the biomass concentration can be explained by the fact that the PAR and temperature values are relatively low during these periods of the year and are unfavorable to the proliferation of these microorganisms. For example, according to Figure 3, average daily temperatures are below the minimum required for the growth of _Chlorella vulgaris_. The best results, in terms of productivity, were obtained for the summer and spring. The explanation may lie in the fact that certain values of the model parameter were taken from references that worked in conditions with the presence of light and an adequate temperature almost similar to those of these two periods of the year. As Figures 2 and 3 show, the other two seasons, autumn and winter, offer unsuitable conditions for microalgae cultivation. Figure 6 shows four box plots for the different seasons, grouping the daily average biomass concentrations obtained from the simulation by day. This allows one to evaluate the ranges within which daily biomass production is recorded. It can be observed that the results are almost similar in spring and autumn with more spread boxes between the 25 th and 75 th percentiles for the latter. However, daily production is less dispersed during summer and winter, clearly showing optimal performance during summer and negligible production levels during winter.