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In the context of climate change, hydrological processes between surface water and groundwater become increasingly complex, which may aggravate the risk of hydrological drought. As the complexity of factors influencing drought increases, traditional univariate drought indices are likely to be insufficient for accurate drought analysis. Therefore, it is important to develop an appropriate index combining surface water and groundwater for comprehensive monitoring of hydrological drought, and to understand the process of drought propagation to reduce the impact of droughts. This study develops the standardized runoff groundwater drought index (SRGI), which is a multi-variable model based on a combination of the standardized groundwater level drought index (SGI) and the standardized runoff drought index (SRI). The cross-wavelet transforms and correlation coefficient methods are used to reveal the linkages and propagation characteristics between meteorological and hydrological drought. The results indicate that (1) the generalized extreme value (GEV) distribution is generally suitable for the SGI calculation in the midstream of the Heihe River Basin (HHRB); (2) the SRGI, combining the advantages of the SRI and SGI, can detect droughts more accurately and timely than univariate drought indices, and it demonstrates a drought warning capability to some extent; (3) the lag time of the SRI/SRGI responding to the SPI notably varied with seasons, the longer in spring and winter and the shorter in summer and autumn. Additionally, the propagation time from the SRI to the SPI is shorter than that from the SRGI to the SPI in spring and autumn, the opposite is true in summer. (4) Positive correlations exist between the SRI/SRGI and the SPI during the period 1986–2010, which are relatively stable over longer periods, but ambiguous over shorter periods. [ABSTRACT FROM AUTHOR]