According to the definition of deuterium excess (d) , its calculation can be seen in the following formula (Dansgaard, 1964).

d =δ D-8×δ 18O (3)

For δ18Opv and δDpv, the hydrogen and oxygen isotopes in precipitating water vapor is difficult to measure directly because of the dynamic nature of the local atmosphere and strong seasonality impact. In this study, this was calculated by means of formula 4 (Xu et al., 2011; Gibson et al., 2008), the vapor–precipitation balance method, which has been successfully employed in many research studies for many districts (Gat et al., 1994; Zuber, 1983; Gonfiantini, 1986; Gibson and Edwards, 2002).