The drought indices are common tools for monitoring and risk assessment of the drought. Based on copula function, this paper proposes a bivariate combined drought index (BCDIbcf) that can comprehensively characterize the meteorological characteristics (precipitation) and hydrological characteristics (runoff). Besides, the cross-wavelet transform (XWT) is introduced to research the relationship of drought, and identifies the lag in the propagation process. Take Huayuankou station as an example, results indicated: (1) The BCDIbcf combines the merit of the standardized precipitation index (SPI) in capturing the onset of drought and that of the standardized runoff index (SRI) in capturing the end of drought, which contains information on both SPI and SRI, can characterize two types droughts of hydrology and meteorology simultaneously. (2) The characteristics of hydrology and meteorology have significantly periodic, the most obvious on the scale of 2-4a. (3) There is the significant positive statistical correlation between precipitation and runoff, and hydrological droughts are lagging behind meteorological droughts by 1–2 months at Huayuankou station. The BCDIbcf can identify drought more comprehensively and provide strong support for drought detection and prevention.
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