Simulation of the emergent radiation from the top of atmosphere, where the broken cirrus layer is considered

A method of simulation of the upwelling radiation from the atmosphere bounded by the surface is suggested. The semi-infinite thin cloud layer is inserted in the atmosphere. The effects of the atmosphere and semi-infinite cloud layer on the emergent radiation from the top of the atmosphere is discussed with respect to surface observations in the vicinity of cloud. The cloud layer is located normal to the principal plane which is determined by the directions of Sun, nadir and observation. The emergent radiation is then a function of location, nadir angle of observation, optical thicknesses of the atmosphere and cloud, and altitude of cloud. The radiation reflected from the cloud sides is neglected. In the computational procedure, the emergent radiation is expanded into a series of radiative interaction modes with cloud, atmosphere and surface. Then in each mode, a probability of radiation interacting with cloud or atmosphere is first calculated. With the aid of these probabilities, the emergent radiation at the top of the atmosphere is calculated approximately by considering the radiative interact ions among atmosphere, cloud and surface up to twice as large