Improvement of Makkink model for reference evapotranspiration estimation using temperature data in Northwest China

Reference evapotranspiration (ET0) is an important parameter for climatological and hydrological studies, as well as for agricultural water resources management. In this study, 7 temperature-based solar radiation models were adopted to improve the Makkink model for ET0 estimation in Northwest China. The temperature-based models only require air temperature as input data, which can be easily monitored in most areas around the world. The applicability of the improved Makkink models (M1-M7), the original Makkink (MK) model, the Jensen-Haise (JH) model as well as the Irmak (IK) model were evaluated on different time scales using meteorological data obtained from 12 weather stations in Northwest China. The results showed that the 7 improved Makkink (MKi) models (R2 ranged 0.71-0.86) were more accurate than the 3 physical models (R2 ranged 0.64-0.76) for daily ET0 estimation at the 4 sub-zones of Northwest China, and the M4, M5, M6 and M7 models were superior to the other models. The M5 model had the best estimation accuracy for daily ET0 on daily scale, followed by M7 and M6, with the R2 median of 0.83, 0.83 and 0.82, the RMSE median of 0.86, 0.88 and 0.89 mm/d, and the GPI median of 1.03, 0.90 and 0.87, respectively. On monthly scale, the 7 MKi models (with relative error almost less than 20%) were also better than the 3 physical models (with relative error usually more than 20%) at the 4 sub-zones. The M5 model also showed the best performance for monthly average daily ET0 estimation, followed by M7 and M6, with the R2 median of 1.00, 1.00 and 1.00, the RMSE median of 0.13, 0.16 and 0.19 mm/d, and the GPI median of 0.25, 0.05 and 0.02, respectively. Overall, the estimation accuracy of the Makkink model was much improved by using the temperature-based solar radiation models, and in Northwest China, M5 model which only requires temperature and relative humidity as input data is highly recommended to estimate ET0 on both daily and monthly scales.