## 2 Methodology
### Applying the TMS Methodology  
The growth and productivity of microalgae is challenged by multiple cultivation parameters, such as pH, nutrients, light, temperature, agitation, cultivation medium, etc. For our case, only physical parameters, solar irradiance (PAR and solar day length), and temperatures are considered in this scientific approach to study the effects of both parameters on microalgae activity. Therefore, the existence of values of these parameters at which the culture is at its optimum level or not leads us to consider different weight factor cases for temperature and irradiance. For this purpose, an approach based on TMY methodologies is used to determine the importance of the meteorological parameters in the growth period of microalgae. Moreover, as these two cultivation parameters change significantly between two meteorological seasons, a seasonal approach is adopted. Each season is examined separately, following a multistage process. Firstly, the whole set of data available (15 years in our case study) has been distributed in the four seasons (E\({}_{\mathrm{w}\,=\,1,\,2,\,3,\,4}\)): 1 = spring (March-May), 2 = summer (June-August), 3 = autumn (September-November), and 4 = winter (December-February) in that order. These seasons are based on the annual temperature cycle and not on the astronomical seasons, so there is a clear transition between them. For each location, there is a time series corresponding to 14 seasons (A\({}_{\mathrm{y}\,=\,1,\,2,\,\ldots,\,14}\)) for each of these four weather seasons. Thereafter, a period of time is identified as follows E\({}_{\mathrm{w}}\)A\({}_{\mathrm{y}}\). For example, E\({}_{1}\)A\({}_{4}\) represents the spring season (E\({}_{1}\)) of 1994 (A\({}_{\mathrm{d}}\)), which is the first spring of the 14 spring seasons that we have between March 1991 and May 2004. Additionally, E\({}_{4}\)A\({}_{14}\) represents the winter season that starts in December 2004 and ends in February 2005. Since it is intended to characterize one week (S\({}_{\mathrm{p}}\)) over a season, and a week is a set of seven consecutive days (not necessarily beginning on Monday and ending on Sunday), the proposal is based on an increase in the available data so that the number of candidate weeks over the study period increases. In addition, for a given season, the weeks are constituted in such a way that there is a discontinuity when passing from one year to the next. In other words, in a sequence (week in our case), we cannot have days that come from two different years. This procedure will generate p weeks from the q available days per meteorological season (d\({}_{\mathrm{q}}\)) in the following way:  
\[ \begin{array}{c}\mathrm{E}_{\mathrm{w}}\mathrm{A}_{\mathrm{y}}=\{\mathrm{d }_{1},\mathrm{d}_{2},\ldots,\mathrm{d}_{\mathrm{q}}\}\\ \mathrm{S}_{1}=\{\mathrm{d}_{1},\mathrm{d}_{2},\ldots,\mathrm{d}_{7}\},\end{array} \]  
where \(p=\mathrm{q}-6\). This represents an increase of nearly 700% in the number of candidate weeks for a season in each year (season) of the time series. The data obtained (all 7-day packages) represent, for example, all candidate weeks for all spring seasons between March 1991 and May 2004. The same has been done for the other meteorological seasons. Therefore, this procedure generated a good number (q) of candidate weeks for each of these four weather seasons: 1204 for spring, 1204 for summer, 1190 for autumn, and finally, 1184 for winter. Thereafter, for the entire dataset corresponding to each season and for each week (of each season), a Cumulative Distribution Function (CDF), Equation (1), is determined for each one of the six selected meteorological parameters: PAR, solar day length, mean, maximum, minimum, and temperature range. The CDF of each meteorological parameter (x) was calculated by classifying the dataset into equally sized intervals, often called lags, because the size of the long-term data is different from that of short-term data. This is why it is interesting to use lags to perform Equation (2).