“…Based on the ternary feature of ‘nature–artificiality–virtual water’ in the water cycle, for the first time, the ‘nature–society–trade’ ternary water cycle model driven commonly by the three forces of nature, artificiality and economy was proposed by Deng et al (2020), but not much has been done in terms of model empirical research. In summary, there are many studies on natural water cycle (Berghuijs et al, 2017; Chandanpurkar et al, 2021; Godoy et al, 2021; Zhan et al, 2019), ‘nature–artificiality’ binary water cycle, social water cycle and virtual water trade (Liu et al, 2021; Wang et al, 2014; Yang et al, 2012), but few researchers take the ‘nature–society–trade’ ternary water cycle as a system to conduct empirical studies on the formation of regional water resources and its cyclic transformation process (Deng et al, 2020). In addition, at present, many studies on the water cycle in arid inland river basin areas are mostly at the aspect of natural water cycle (Kulaixi et al, 2023; Wang et al, 2023; Xie et al, 2022), and our study is also instructive for water resources management in arid inland river basin areas.…”