Drought indices have been widely used in climate classification. However, there is not enough evidence for their ability in identifying the multiple climate types in areas with complex topography and landscape, especially in those areas with a transition climate. This study compares a meteorological drought index, the aridity index (<i>AI</i>) defined as the ratio of precipitation (<i>P</i>) to potential evapotranspiration (<i>PET</i>), with a hydrological drought index, the evaporative stress index (<i>ESI</i>) defined as the ratio of actual evapotranspiration (<i>AET</i>) to <i>PET</i>. We conducted this study using modeled high resolution climate data for period of 1980–2010 in the Heihe River Basin (HRB) in the arid northwestern China. <i>PET</i> was estimated using the Penman–Monteith and Hamon methods. The climate classified by <i>AI</i> shows two distinct climate types for the upper and the middle and lower basin reaches, while three types were found if <i>ESI</i> was used. This difference indicates that only <i>ESI</i> is able to identify a transition climate zone in the middle basin. This contrast between the two indices is also seen in the inter-annual variability and extreme dry/wet events. The magnitude of variability in the middle basin is close to that in the lower basin for <i>AI</i>, but different for <i>ESI</i>. <i>AI</i> has larger magnitude of the relative inter-annual variability and greater decreasing rate from 1980–2010 than <i>ESI</i>, suggesting the role of local hydrological processes in moderating extreme climate events. Thus, the hydrological drought index is better than the meteorological drought index for climate classification in the arid Heihe River Basin where local climate is largely determined by topography and landscape. We conclude that the land–surface processes and human disturbances play an important role in altering hydrological drought conditions and their spatial and temporal variability.