Based on a monthly drought index, the Standardized Precipitation Index (SPI), we investigate the multifractality of monthly drought areas in seven major regions in China from 1961 to 2012 using multifractal detrended fluctuation analysis. The results show that multifractality is evident in the monthly time series for all seven regions, but its strength varies between areas. From the numerical results, we further examine the stationarity and persistence of the time series in the seven drought areas. The characteristics of the variance of big and small fluctuations are also analyzed. The characteristics of multifractal spectra are used to distinguish the features of the singularity of all the data, as well as the large and small fluctuations and the spread of the changes of fractal patterns, and so on, in the monthly drought area time series for the different regions. Finally, we investigate the possible source(s) of multifractality in the drought series by random shuffling as well as surrogating the original series for each region.

At present, high-resolution drought indices are scarce, and this problem has restricted the development of refined drought analysis to some extent. This study explored the possibility of calculating the standardized precipitation index (SPI) with short-term precipitation sequences in China, based on data from 2416 precipitation observation stations covering the time period from 1961 to 2019. The result shows that it is feasible for short-sequence stations to calculate SPI index, based on the spatial interpolation of the precipitation distribution parameters of the long-sequence station. Error analysis denoted that the SPI error was small in east China and large in west China, and the SPI was more accurate when the observation stations were denser. The SPI error of short-sequence sites was mostly less than 0.2 in most areas of eastern China and the consistency rate for the drought categories was larger than 80%, which was lower than the error using the 30-year precipitation samples. Further analysis showed that the estimation error of the distribution parameters $\beta$ and $q$ was the most important cause of SPI error. Two drought monitoring examples show that the SPI of more than 50,000 short-sequence sites can correctly express the spatial distribution of dry and wet and have refined spatial structure characteristics.

Because of the high correlation between random variables of drought duration and severity, their joint distribution is difficult to obtain by traditional mathematical methods. However, the copula method has proved to be a useful tool for analyzing the frequency of drought duration and severity. Most studies have used different marginal distribution functions to fit the drought duration and severity distributions. This requires a great deal of contrast analysis, and sometimes two or more distributions fit the data well. Based on entropy theory, however, a unified probability distribution function is derived which reduces complex contrast analysis and improves the filtering distribution function. Based on monthly precipitation data at 162 stations in China for 1961–2015, the monthly standardized precipitation index was calculated and used to extract drought duration and severity. Then the entropy distribution was used to fit the distributions of drought duration and severity, and to establish the correspondence between them. The probabilities of the interval and return periods were then determined using the copula method. An analysis of the discrepancy between the conventional and entropy-based methods indicated that the entropy distribution showed a better fit than conventional methods for drought duration distribution, although no obvious difference was found in drought severity distribution. The entropy-based results were more consistent with the empirical data, whereas conventional methods showed apparent deviation in some drought types. Hence, the entropy-based method is proposed as an alternative method of deriving the marginal distributions of drought duration and severity, and for analyzing the interval probability and return period in China.

In this study, the standardized precipitation index (SPI) data in Hunan Province from 1961 to 2020 is adopted. Based on the critical slowing down theory, the moving t-test is firstly used to determine the time of drought-flood state transition in the Dongting Lake basin. Afterwards, by means of the variance and autocorrelation coefficient that characterize the phenomenon of critical slowing down, the early-warning signals indicating the drought-flood state in the Dongting Lake basin are explored. The results show that an obvious drought-to-flood (flood-to-drought) event occurred around 1993 (2003) in the Dongting Lake basin in recent 60 years. The critical slowing down phenomena of the increases in the variance and autocorrelation coefficient, which are detected 5–10 years in advance, can be considered as early-warning signals indicating the drought-flood state transition. Through the studies on the drought-flood state and related early-warning signals for the Dongting Lake basin, the reliabilities of the variance and autocorrelation coefficient-based early-warning signals for abrupt changes are demonstrated. It is expected that the wide application of this method could provide important scientific and technological support for disaster prevention and mitigation in the Dongting Lake basin, and even in the middle and lower reaches of the Yangtze River.