Drought is an abnormal and prolonged deficit in available water. Possible drought impacts are crop losses, famine, fatalities, power blackouts and degraded ecosystems. These severe socio-economic and environmental impacts show the need to carefully monitor drought conditions using a suitable index. Our objective is to provide an intercomparison of frequently used physical drought indices to show to which degree they are interchangeable for monitoring drought in precipitation, soil moisture, groundwater and streamflow. Physical indices are commonly introduced to predict drought impacts, because appropriate drought impact indices are still missing. Correlations (R) between frequently used indices for different drought types were calculated at the global scale. We have made the index timeseries available to the community for future studies. Precipitation drought indices show low to intermediate correlations (ranging from R = 0.1 to 0.75), soil moisture drought indices show an even lower similarity (R = 0.25). Indices for streamflow drought show the highest correlation (R = 0.5 to 0.95). Additionally, meteorological drought indices do not capture the soil moisture drought correctly (R = 0.0 to 0.6) nor streamflow drought (R = 0.0 to 0.7). These findings have implications for drought monitoring systems: (i) for each drought type, a different index should carefully be identified; (ii) drought indices that are designed to monitor the same drought type show large discrepancies in their anomalies and hence drought detection; (iii) there is no single superior physical drought index that is capable of accurately capturing the diverse set of drought impacts in all parts of the hydrological cycle.