Trends in the Air Temperature: A Practical Approach for Auto- and Cross-Correlation Analysis

Abstract

We study the air temperature with 10 years of hourly measured in 12 automatic weather stations, located in the State of Bahia (Brazil), considering mainly its auto- and cross-correlation. We found that, in general, there is a positive linear trend, indicating warming in this variable for all stations. Also, we observe that the probability distribution function clearly exhibits a bimodal distribution, meaning that there are two main seasonal cycles (the largest relating to winter, the other to summer). In order to have a more robust statistical analysis, detrended fluctuation analysis (DFA) method was applied in these time-series to analyzing data where traditional methods might struggle due to nonstationary. In this case, DFA was useful in identifying long-range autocorrelations in these time-series (with persistent and antipersistent behavior) with specific seasonal time-scales (1 day and 1 year). However, if we quantify the cross-correlations between the air temperature in Salvador and the other stations, by ρDCCA, we found that detrended cross-correlation analysis cross-correlation coefficient is always positive with two peaks, the first is located at n=24 (1 day) and the second at n=8766 (1 year). In this sense, ρDCCA coefficient provides insights how air temperature in Salvador is correlated with air temperature in other weather stations over different time-scales, helping to understand their long-term interactions. These results, for example, allow us to identify temporal scales that may be useful to better understand trends in the air temperature and that can help us further answer global warming questions.