Preliminary research on the relationship between long-range correlations and predictability

By establishing the Markov model for a long-range correlated time series (LRCS) and analysing its evolutionary characteristics, this paper defines a physical effective correlation length (ECL) τ, which reflects the predictability of the LRCS. It also finds that the ECL has a better power law relation with the long-range correlated exponent γ of the LRCS: τ = K exp(−γ/0.3) + Y, (0 < γ < 1) — the predictability of the LRCS decays exponentially with the increase of γ. It is then applied to a daily maximum temperature series (DMTS) recorded at 740 stations in China between the years 1960–2005 and calculates the ECL of the DMTS. The results show the remarkable regional distributive feature that the ECL is about 10–14 days in west, northwest and northern China, and about 5–10 days in east, southeast and southern China. Namely, the predictability of the DMTS is higher in central-west China than in east and southeast China. In addition, the ECL is reduced by 1–8 days in most areas of China after subtracting the seasonal oscillation signal of the DMTS from its original DMTS; however, it is only slightly altered when the decadal linear trend is removed from the original DMTS. Therefore, it is shown that seasonal oscillation is a significant component of daily maximum temperature evolution and may provide a basis for predicting daily maximum temperatures. Seasonal oscillation is also significant for guiding general weather predictions, as well as seasonal weather predictions.