Autocorrelation in ultraviolet radiation measured at ground level using detrended fluctuation analysis

Abstract

In this study, we analyzed the autocorrelation among four ultraviolet (UV) radiation data sets obtained at 305 nm, 320 nm, 340 nm, and 380 nm. The data were recorded at ground level at the INPE climate station in Natal, RN, Brazil, which is a site close to the equator. The autocorrelations were computed by detrended fluctuation analysis (DFA) to estimate the index α. We found that the ​fluctuations in the UV radiation data were fractal, with scale-free behavior at a DFA index α≃0.7. In addition, we performed a power law spectral analysis, which showed that the power spectrum exhibited a power law behavior with an exponent of β≃0.45. Given that the theoretical result is β=2α−1, these two results are in good agreement. Moreover, the application of the DFA ​method to the UV radiation data required detrending using a polynomial with an order of at least eight, which was related to the complex daily solar radiation curve obtained at ground level in a tropical region. The results indicated that the α exponent of UV radiation is similar to other climatic records such as air temperature, wind, or rain, but not solar activity.