The downward long-wave radiation has an important impact on the surface energy balance and surface evaporation.This paper compares six methods for estimating the downward long-wave radiation.These formulae modify the atmospheric emissivity for clear skies for cloudy skies according to the daily solar radiation ratio (defined as the ratio of the measured incoming solar radiation to the solar radiation received with clear skies).The estimates from these methods are compared with measurements from the Weishan Echo-Hydrology Experimental Station in Shandong Province and the Luancheng Agro-Ecosystem Experimental Station in Hebei Province in the North China Plain.The results show that the Marshunova equation gives the best estimates with a correlation coefficient(R~2) larger than 0.97,a mean bias error(MBE)less than 4W/m~2,and a root mean square error(RMSE)less than 11W/m~2.The correlation slope is 1.000.05and the intercept is less than 15W/m~2.Thus, this equation can accurately estimate the downward long-wave radiation for climate change models.