Correlations and Cross-Correlations in Temperature and Relative Humidity Temporal Series From Manizales, Colombia

AbstractThe analysis of air temperature and relative humidity is fundamental in several areas of knowledge. For example, they define the climate, establish the population’s development in a region, and be indicators of climate change. Cross-correlation and autocorrelation analysis are well-known tools to characterize data series. However, the traditional statistical methods cannot be appropriately applied to long-term climatological series since they are non-stationary. The Detrended Fluctuation Analysis (DFA) and the Detrended Cross-Correlation Analysis (DCCA) are tools to find relationships within and between non-stationary series. This work analyzes autocorrelations and cross-correlations for relative humidity and air temperature series of four stations in Manizales. First, a windowed detrended fluctuation analysis was applied to the series to identify the yearly persistence of the series. Then, the DFA shows long-term persistence for all the series. Finally, a matrix-based algorithm was implemented to perform the DCCA; this analysis showed negative correlations between the air temperature and relative humidity series, following their physical behavior. Besides, the DCCA analysis showed positive correlations among the humidity series of different stations. Similar results were obtained and among the air temperature series of different locations.KeywordsAir temperatureCorrelationsCross-correlationsDetrended cross-correlation analysis (DCCA)Detrended fluctuation analysis (DFA)Relative humidity