Approximate solutions of the radiation budget equation in complex terrain

A theoretical investigation is presented on the approximate solutions of the radiation budget equation in complex terrain. A method of calculating an exact solution to the net radiation balance is also developed and compared to the commonly used approximations. The suggested procedure adopts the effects of multiple reflections of the longwave radiation by evaluating an infinite convergent geometric series in terms of the surface emissivity and sky view factor. The exact solution varies significantly from the approximate methods, and the need for a full solution of the radiation budget equation becomes more critical as the sky view factors or the surface emissivities decrease. A simple semi-empirical scheme based on the exact solution of the radiation budget equation is also presented, which gives estimates of the net all-wave radiation avoiding the use of surface radiation temperature.