## 2 Materials and Methods
### Principal Component Analysis (PCA)  
Multivariate analysis, as a tool that allows verification of the interrelations with a large number of variables, is known for its varied applications, including studies related to biosolids [32; 33; 34]. According to [35; 36], this technique allows for analyzing sets of complex data without information loss. The interpretation of the analysis occurs via the observation of the angular measure formed between the data, where the weight of the variable lies further from the largest center. The larger an angle a lower correlation and the lower angle formed indicative of a high correlation, as opposite variables, too, are inversely correlated [37]. From linear combinations between variables, it seeks to reduce, as well as to eliminate data for better representativeness, which provides a smaller set of variables that is called components. Quantification of the significance of variables allows for an explanation of the groupings, in which new variables, called orthogonal, are explained by a set of data not correlated with each other and reduced, which are the principal components (PCs). Thus, our focus was to analyze whether there was a significant difference or not, between chemical elements and pH within the categories of seasons of the year in the tropical climate.  
Different from other types of climates, the seasons of the year boil down to two in tropical climates: a rainier and warmer one (summer and spring) and another drier and colder (winter and autumn). Although one usually uses the name \"summer\" and \"winter\", these seasons are broadened and encompass months from \"spring\" and \"autumn\" [38]. Yet, from the practical point of view, there exist only two seasons per year. A rainy season and a dry season, in countries of tropical climates. We include the four seasons matter as  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Culture** & **Quantity of Production** & **Macronutrients** \\ \hline
**Corn** & 5 tons of grains & 106 kgN ha\({}^{-1}\); 45 kg P ha\({}^{-1}\); 106 kg K ha\({}^{-1}\); \\  & & 19 kgCa ha\({}^{-1}\); 26 kgMg ha\({}^{-1}\); 13 kgS ha\({}^{-1}\); \\
**Rice** & 3 tons of grains & 103 kgN ha\({}^{-1}\); 39 kgP ha\({}^{-1}\); 144 kg K ha\({}^{-1}\); \\  & & 27 kgCa ha\({}^{-1}\); 9 kgMg ha\({}^{-1}\); 12 kgS ha\({}^{-1}\); \\
**Wheat** & 3 tons of grains & 56 kgN ha\({}^{-1}\); 21 kgPa\({}^{-1}\); 101 kg K ha\({}^{-1}\); \\  & & 7 kgCa ha\({}^{-1}\); 9 kgMg ha\({}^{-1}\); 8 kgS ha\({}^{-1}\); \\
**Forage grasses** & 1 ton dry matter & 17 kgN ha\({}^{-1}\); 4 kgP ha\({}^{-1}\); 27 kg K ha\({}^{-1}\); \\  & & 5 kgCa ha\({}^{-1}\); 3 kgMg ha\({}^{-1}\); 1 kgS ha\({}^{-1}\); \\
**Sugar cane** & 100 tons of stalks & 150 kgN ha\({}^{-1}\); 46 kgP ha\({}^{-1}\); 201 kg K ha\({}^{-1}\); \\  & & 100 kgCa ha\({}^{-1}\); 52 kgMg ha\({}^{-1}\); 45 kgS ha\({}^{-1}\); \\
**Beans** & 1 ton of grains & 110 kgNa\({}^{-1}\); 22 kgP ha\({}^{-1}\); 119 kg K ha\({}^{-1}\); \\  & & 58 kgCa ha\({}^{-1}\); 19 kgMg ha\({}^{-1}\); 26 kgBa\({}^{-1}\); \\
**Coffee** & 3 tons of grains & 157 kgN ha\({}^{-1}\); 23 kgP ha\({}^{-1}\); 187 kg K ha\({}^{-1}\); \\  & & 63 kgCa ha\({}^{-1}\); 30 kgMg ha\({}^{-1}\); 10 kgS ha\({}^{-1}\); \\
**Cotton** & 750 kg fiber & 90 kgN ha\({}^{-1}\); 32 kgP ha\({}^{-1}\); 42 kg K ha\({}^{-1}\); \\  & & 15 kgCa ha\({}^{-1}\). 12 kgMg ha\({}^{-1}\). 10 kgS ha\({}^{-1}\). \\ \hline \hline \end{tabular}
\end{table}
Table 1: Production expected per 1 ha of cultivation and macronutrients demanded. Source: [29].  
categorical columns in PCA because the biosolids generation occurs in different seasons. In addition, we tested the hypothesis that the chemical elements may differ in sensitivity to the seasons of the year and these environmental conditions may take up the role of variable for changes in the concentrations of the chemical elements.