Abstract: Using the 10-day precipitation data of 107 meteorological stations in Henan Province from 1961 to 2012, the variability on temporal-spatial characteristics of mean 10-day precipitation and its standard error among meteorological stations, and the variability on cumulative difference of the mean 10-day precipitation and its standard error among meteorological stations were analyzed with mathematical statistical methods. At the same time, the scale invariance of mean 10-day precipitation were studied with the detrended fluctuation analysis(DFA) method. The results showed that:the mean 10-day rainfall and its standard errors among meteorological stations were 20.6 mm and 15.4 mm, respectively; the skewness coefficients were 2.2 and 2.4, respectively; the sharpness coefficients were 6.1 and 9.8, respectively; the stand error of skewness coefficient and sharp sharpness were 0.06 and 0.11, respectively; therefore, the probability distributions of mean 10-day precipitation and its stand error among meteorological stations were not subject to normal distribution, and subject to positively skew distribution. The cumulative difference of precipitation and its mean standard error among the meteorological stations had the same phase characteristics, and all the stages had the extremely significant linear trends at the 0.001 significant level. The trend rate of mean 10-day precipitation and its standard error among meteorological stations were 49.2 mm·10 d^-1 and 18.7 mm·10 d^-1, respectively. The mean of the scale index in Henan Province were 0.34, and the variability of scale index among meteorological stations was very small, which skewness coefficient and sharpness were 0.26 and 0.43, respectively, which standard error of skewness coefficient and sharpness coefficient were 0.23 and 0.46, respectively, thus, the spatial distribution of scale index was in accord with the normal distribution. The scale index of mean 10-day precipitation of meteorological stations in Henan Province were all below 0.5, showed that time series of mean 10-day precipitation had no persistent and the original sequence were inversely related, i.e., if there was an upward trend in the previous sequence, then it had a downward trend in the future, and vice versa. This also indicated that the inversion frequency of the 10-day precipitation sequence was higher than that of the random process.

Key words: Detrended Fluctuation Analysis(DFA), decadal Precipitation, Henan Province