Networks analysis of Brazilian climate data based on the DCCA cross-correlation coefficient

Based on the analysis of the detrended fluctuation analysis of all environmental variables in all Brazilian state capitals, it can be concluded that the non-stationary and persistent behavior (αDFA(medium) ffi 1.21; n ⩽ 13), upward and/or downward trends are time dependent. In the long-range persistent behavior (αDFA(medium) ffi 0.87; 13 < n ⩽ 5.625), it is observed that var- iables with closer values remain for a longer time, influencing the memory. As for the anti-per- sistent behavior (αDFA(medium) ffi 0.06; n > 5.625), a more stable behavior is expected as the scale reaches the maximum value. It can be seen that the result of autocorrelation in the state capitals of the Southeast and South regions for humidity (S3 Fig in S1 File) and wind speed (S4 Fig in S1 File) have a differ- ent pattern due of their geographic locations (Table 1). The Southeast, with a tropical climate, has the greatest climate variability in Brazil, and its state capitals are influenced by elements such as altitude and latitude (Table 1) and air masses coming from the ocean. It is located in a transition area between an extremely dry region (Northeast region), with the altitude acting as a climate modeler distributing rainfall of different temperatures, and the South region. The South, on the other hand, with temperatures that are usually lower than the rest of Brazil, has a shorter summer with high temperatures and a rigorous winter, being a region that receives winds from the Southeast region, raising the humidity and heat for the region, increasing the temperature and causing rain.

DCCA cross-correlation coefficient analysis. In this section, to present the analysis of the ρDCCA coefficient, the organization is done by Brazilian region (North, Northeast, Central- West, Southeast, and South) and by environmental variable (radiation, temperature, humidity, and wind speed). A detailed analysis of radiation is presented in this section, while the plots for the remaining variables are presented in the supplementary material: North (S5-S8 Figs in S1 File), Northeast (S8-S10 Figs in S1 File), Central-West (S11-S13 Figs in S1 File), Southeast (S14-S16 Figs in S1 File) and South (S17-S19 Figs in S1 File), for the environmental variables radiation, temperature, humidity and wind speed, respectively. Fig 2 shows the results for global radiation in the North region. We can observe three char- acteristic behaviors, two maximum points at n = 13 (one day of observations—ρDCCAMedium * 0.83) and n = 5625 (430 days of observations—ρDCCAMedium * 0.14) and a minimum point at n = 457 (35 days of observations—ρDCCAMedium * 0.70), showing a variation in the fluctuation with the increase of the scale. With a minimum approaching zero for all correla- tions in six capitals in the North region (Bele´m, Macapa´, Manaus, Palmas, Porto Velho, and Rio Branco), Boa Vista shows a different behavior with a minimum below zero (ρDCCAPalmas x ρDCCABoaVista), that is, a negative cross-correlation (ρDCCA < 0). The temperature (S5 Fig in S1 File) and humidity (S6 Fig in S1 File) show a behavior very similar to radiation. Once again,

Boa Vista stands out in relation to the other capitals when analyzing temperature (Porto Velho, Bele´m, Macapa´, and Palmas) and humidity for all capitals. For wind speed (S7 Fig in S1 File), up to n = 13, the cross-correlation coefficient is very similar, followed by individual varia- tions per capital. The behavior was very similar for Manaus, Porto Velho, and Rio Branco for all scales, whereas Bele´m, Macapa´, and Palmas show variations between −0.73 < ρDCCA < 0.61 for n > 457. These results corroborate with findings of [16, 42, 43]. Fig 3 shows the results for global radiation in the Northeast region. The ρDCCA is positive for all capitals with a variation between 0.21 < ρDCCA < 0.88, and the minimum value between (ρDCCATeresina x ρDCCAMaceio). S8 Fig in S1 File shows a positive cross-correlation for temper- ature between all capitals for n � 135 and with fluctuation between −0.30 < ρDCCA < 0.99 for all capitals after for values of n above 135. Humidity (S9 Fig in S1 File) shows a positive cross- correlation (ρDCCA > 0) for all scales, with the exception of (ρDCCAFortaleza x ρDCCAMaceio) from n > 3328 (256 days) and (ρDCCATeresina x ρDCCAMaceio) to n > 1570 (120 days). The ρDCCA coefficient shows a fluctuating between −0.06 < ρDCCA < 0.91 for all capitals. The wind PLOS ONE Networks analysis of Brazilian climate data based on the DCCA cross-correlation coefficient PLOS ONE | https://doi.org/10.1371/journal.pone.0290838 September 15, 2023 8 / 18