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.