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

• Two solutions were established with or without R s inputs for daily ET 0 estimation. • FAO56 recommended larger coefficient a but smaller b of the A-P formula in China. • The transfer error from estimated R s to ET 0 was reduced by using the P-M model. • SVM-ET 0 model obtained larger errors than P-M model with estimated R s at test stages. Accurate estimation of reference evapotranspiration (ET 0) 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 ET 0 estimation, but its application is usually restricted by limited meteorological data worldwide, especially global solar radiation (R s). This study provided two possible solutions to deal with the missing R s data in ET 0 estimation in China mainland. In the first solution, R s data were estimated with the Ångström-Prescott (A-P) formula and daily sunshine hours. The values of two A-P formula fundamental coefficients a and b were obtained through three ways: (1) estimated based on limited R s 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 support vector machine algorithm (or SVM-estimated). The second solution used the SVM algorithm and available weather variables without R s. The results showed that the FAO-recommended coefficients a and b were separately overestimated and underestimated in China mainland, which generated the largest simulation errors of R s. However, the transfer errors from R s estimations to ET 0 estimations were reduced by using the P-M model for all of the three kinds of coefficients. Compared with the R s -based models, the estimation accuracy of the SVM-ET 0 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 ET 0 estimation, when only R s 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 ET 0 estimation in China. [ABSTRACT FROM AUTHOR]