Alternative net longwave radiation equation for the FAO Penman–Monteith evapotranspiration equation and the Penman evaporation equation

Net longwave radiation, which is an essential factor in evapotranspiration, is generally estimated by multiplying the net emissivity under clear-sky conditions by the effect of cloudiness. In this study, we proposed a phenomenon-specific daily net longwave radiation function, in the form of a difference between the upward longwave radiation and the downward longwave radiation, for the Penman–Monteith evapotranspiration equation and the Penman evaporation equation. In addition, we verified the net longwave radiation equation by comparing the observed downward longwave radiation with that estimated by the downward longwave radiation equation derived from the well-known net longwave radiation equations in the Penman–Monteith evapotranspiration equation and the Penman evaporation equation. The downward longwave radiation equation constituting the proposed net longwave radiation equation w1ith four calibrated parameters had an RMSE of 8.60 W m−2 and MBE of − 4.37 W m−2 and is more accurate than the downward longwave radiation equations derived from the general net longwave radiation equations at Tateno, Japan.