In the measurement of Earth radiation budget by satellite radiometers, fields of broken clouds present a special problem. In order to compute the radiant flux from a measured radiance, it is necessary to know the bidirectional reflectance distribution function (BRDF), which desribes the anisotropy of the radiation from the scene. The randomness of the clouds in terms of size, shape, optical depth and spacing causes them to have varying distributions of directional reflectance. Many of the problems of attempting to treat broken cloud fields arise from the three-dimensional characteristics of the clouds. Another aspect of the computation of the BRDF of a broken cloud field is the field of view of the radiometer. This paper discusses the BRDF as a random variable by the use of simple models which incorporate the elements of the problem which are mentioned above. Because the BRDF is a random variable, the flux computed from the measured radiance is in error due to the difference of the model BRDF from the true but unknown BRDF for each realization. The description of the cloud sizes and spacing and their relation to the field of view of the radiometer is an exercize in stochastic geometry.