*2.5. Uncertainty Estimation*

The TWSC estimates used in the estimate of ETWB are from CSR-M. Hence, we only estimate the uncertainty of TWSC based on CSR-M. The uncertainty estimate followed the method used in Landerer and Swenson [43] and Scanlon et al. [53]. Details about the method can be found in the supporting information of Scanlon et al. [53]. As the TWSC is the differential of two consecutive months, the uncertainty of TWSC is √2 of the uncertainty of TWSA. The uncertainties of monthly precipitation and runoff data collected by gauge are estimated to 10% and 5%, respectively [2,4,13]. The uncertainty of monthly ETWB is estimated by uncertainties of TWSC, precipitation, runoff based on error propagation law.

The monthly mean ET is the mean values of 13 months for the study period of 2003–2015, from the error propagation law, the uncertainty of monthly mean ET can be calculated as the uncertainty in monthly ETWB divided by √13. The uncertainty of annual ETWB is estimated from the uncertainty of annual *P*, *Q*, and TWSC based on error propagation law. Since the annual TWSC is estimated from the difference of the TWSA at the beginning month in one year and the next year, we estimate the uncertainty of annual TWSC equal to monthly TWSC.
