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

details of the detrended fluctuation analysis, DCCA cross-correlation coefficient, and network analysis. Then, the results for the detrended fluctuation analysis, DCCA cross-correlation anal- ysis, and network analysis are discussed. The paper ends with some concluding remarks. Materials and methods Data collection and data organization The data about the four environmental and atmospheric variables (global radiation, tempera- ture, humidity, and wind speed) for all 27 Brazilian environmental stations (26 state capitals plus the federal district; Table 1) was extracted from the database of the Instituto Nacional de Pesquisas Espaciais—INPE (https://www.gov.br/inpe/pt-br). In this study, 13 hourly observations (daily local time between 6 am to 6 pm; UTC 9 am to 9 pm), between January 1, 2010, and December 31, 2020 (4018 days; 52234 observations) were considered. Knowing that the original data is available per hour and per year for each of the variables studied, we joined the databases to compile the final time series data. The percentages of missing values in all 112 time series varied between 0.19% and 47.77%, being the missing values imputed by the mean of that hour along the days. However, [24] demonstrated that the DFA and DCCA methods are robust for these time series with missing values. The complete list of percentages of missing values is available in Table 1. Detrended fluctuation analysis Peng et al. (1994) [22] developed the detrended fluctuation analysis (DFA) to analyze the exis-

tence of serial dependence (the statistical self-affinity of a signal), with the advantage of being also possible to be used in non-stationary data. Its main advantage is to avoid spurious detec- tion of long-range dependence due to non-stationary data [25–29]. For a given “Y” time series, the algorithm is described as follows: 1. Define the cumulative sum (XN) of the original signal fluctuations around its mean �Y ): XN ¼ X N i¼1 ðYi �Y Þ ð1Þ 2. Divide XN into boxes of equal length n. 3. In each box, fit the local trend of Xn by a polynomial fit of degree (n), which represents the local trend of the box. 4. For the given n box size, compute the detrended fluctuation function (root-mean-squared) of the signal XN as: FðnÞ ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 N X N i¼1 ðXi PðnÞÞ2 s ð2Þ 5. Step two is repeated for each of the available τ scales (box size) to obtain the empirical rela- tionship between the overall fluctuation F(n) and the box size n: FðnÞ / naDFA ð3Þ 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 3 / 18