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Using observed surface temperature data from about 570 meteorological stations in China, the linear temperature trend over the last 50 years (1962–2011) is estimated. Average warming rates at all stations are 0.284 ± 0.142, 0.200 ± 0.163, and 0.392 ± 0.193 °C/10 a for annual, June–July–August (JJA), and December–January–February (DJF) mean temperatures, respectively. The warming rates (°C/a) have a regressed slope of 0.001 with latitude, and their relationship with latitude using data from stations below 1,000 m altitude is estimated at 0.009 °C/(10 a · degree). A k-means clustering is constructed using correlation coefficients to quantify the closeness. The clustering schemes with k = 5 and k = 10 are successfully implemented for annual, DJF, and JJA mean temperatures. The k = 10 scheme showed greater ability to distinguish different locations than the k = 5 clustering. In both schemes, the mean estimated warming rates are averaged over stations in each cluster. The clusters in DJF are much different than those for the entire year and for JJA. The average warming rate in each cluster is estimated and compared. Using stations in the cluster of high-elevation southeast Tibetan Plateau, the relationship between warming rates and altitude is estimated at 1.0 × 10−2 °C/(10 a · 100 m).

Multifractal analysis can provide parameters associated with different scales of rainfall, which may be useful for setting up parsimonious downscaling models of rainfall, or for revealing climate-specific properties. Time series of rain rate with 1-min resolution collected from ten stations over a monsoon watershed in eastern China were used to study the multifractal properties. The power spectra estimated by fast Fourier transform (FFT) and discrete Haar wavelet transform (DWT) showed three scaling regimes: the sub-hourly scaling regime with β ≈ 1.2, the scaling regime from 1 h to 1 day with β close to 0.6, and the low-frequency spectra plateau with β ≈ 0.1. From the hyperbolic tails of exceeding probability distributions, the estimated values of parameter q c are in 2–2.5, which were consistent with the critical order of K(q) curves. The statistical moments display two main scaling regimes: the high-frequency regime from 3 min to 5 days and the scaling regime beyond 5 days. The scales of 5–10 days seem a transitional regime. The reason that the regimes, revealed by the power spectra, disagree with the statistical moments may be that both FFT and DWT power spectra have limited abilities of analyzing low-frequency scaling but are sensitive to the properties in high-frequency scales. The H values estimated for the regime of sub-hourly scales are larger than 0.4, and the values for the regime 1 h–1 day are close to 0.1. For the low-frequency scales beyond 1 day, negative H is obtained by DWT power spectra. The parameters of universal multifractal models were also estimated. The values of α for the scaling range of 1 min–5 days are 0.486 ± 0.047, and for the low-frequency scaling range, its values are 0.808 ± 0.323. For the high- and low-frequency scaling ranges, the values of C 1 are 0.5 and 0.169, respectively, which is different from the values for daily rainfall series collected at the same rain gages.

The multifractal behavior of daily rainfall was investigated for a watershed in Eastern China to better understand the temporal structure of rainfall under monsoonal climate. In this study, over periods of up to 46 years, daily rainfall recorded in 1962 to 2007 at 10 meteorological stations in the administrative area of Lin-Yi City in Shandong province were analyzed with focus on features of power spectra, standard statistical moments, and exceedance probability tails of these daily rainfall time series. Spectral analysis and study of the moments of the rainfall intensity showed that a scaling range from 1 day to 1 year is present. Empirical moment scaling functions of the rainfall intensity calculated for different moments of order suggested that the values of universal multifractal parameters α and C 1 for all stations were approximated to 0.7 and 0.37, respectively. Comparing with the parameters estimated in other literatures, our results showed higher values for α but lower values for C 1 in general, which suggested that the rainfall series in the study watershed influenced by the East-Asia monsoon climate have similarities to that in France, but are spikier and smoother than that in the semi-arid region in Portugal. The parameter H values were estimated as vary from −0.18 to −0.22, which is similar to the result obtained by Tessier et al. (J Geophys Res-Atmos 101:26427–26440, 1996).