Using support vector machine to deal with the missing of solar radiation data in daily reference evapotranspiration estimation in China

Accurate estimation of reference evapotranspiration (ET0) is of great importance for regional water resources planning and irrigation scheduling. The FAO56 recommended Penman-Monteith (P-M) model is widely adopted as the standard method for ET0 estimation, but its application is usually restricted by limited meteorological data worldwide, especially global solar radiation (Rs). This study provided two possible solutions to deal with the missing Rs data in ET0 estimation in China mainland. In the first solution, Rs data were estimated with the & ANGS;ngstro & BULL;m-Prescott (A-P) formula and daily sunshine hours. The values of two A-P formula fundamental co-efficients a and b were obtained through three ways: (1) estimated based on limited Rs measurements at 80 solar radiation measurement stations (or site-calibrated); (2) recommended by the FAO-56 manual (or FAO-recommended); and (3) estimated based on the altitude and latitude of each weather station through the sup-port vector machine algorithm (or SVM-estimated). The second solution used the SVM algorithm and available weather variables without Rs. The results showed that the FAO-recommended coefficients a and b were sepa-rately overestimated and underestimated in China mainland, which generated the largest simulation errors of Rs. However, the transfer errors from Rs estimations to ET0 estimations were reduced by using the P-M model for all of the three kinds of coefficients. Compared with the Rs-based models, the estimation accuracy of the SVM-ET0 model yielded the highest accuracy both at the training stage (R2 = 0.979; RMSE = 0.273 mm d-1) and the testing stage (R2 = 0.973; RMSE = 0.302 mm d-1). Generally, both the P-M and the machine-learning-based methods could be used for the ET0 estimation, when only Rs data were missing. However, considering the complexity in the programming, the P-M model combining with the A-P formula with the SVM-estimated A-P coefficients is recommended for daily ET0 estimation in China.