Detecting nonlinear information about drought propagation time and rate with nonlinear dynamic system and chaos theory

•Nonlinear Dynamic System (NDS) in phase domain is applied in drought propagation.•Nonlinear information about drought propagation can be detected by NDS.•The propagation time and rate between two types of drought can be calculated by NDS. Current approaches for calculating propagation time and rate from meteorological to hydrological drought mainly focus on the time series of SPI and SRI, and most of these methods are conducted in time domain (e.g., correlation analysis) and frequency domain (e.g., wavelet analysis), which are regarded as linear statistic methods. Inaccuracy could emerge when the complexity and nonlinearity of drought propagation is addressed by such linear methods. In light of this problem, this research adopts Nonlinear Dynamic System (NDS) conducted in phase domain, which provides a nonlinear and systematic perspective on drought propagation. NDS may conditionally generate chaos (commonly known as “butterfly” phenomenon), which was not covered by previous studies on drought propagation. Assuming an underlying NDS for drought events, we demonstrate the NDS of drought propagation could generate chaos, and the nonlinear information about the propagation from meteorological to hydrological droughts can be detected within such chaotic NDS. The propagation time of 1–5 months and the propagation rate of 0.686 were found in the Pearl River Basin. In addition, the propagation time of 3, 7 and 11 months was also found in the Wei River Basin, to prove the broad applicability of our method. The results for these two basins are verified by previous studies.