A Stochastic Description of a Broken Cloud Field

Abstract

The chord length distributions within a cloud and between clouds are considered. Such information is needed as input to certain statistical models of cloud–radiation interaction. Modeling the clouds as azimuthally symmetric ellipsoids, the authors find that the chord length distribution through a cloud of fixed size is proportional to the chord length. The proportionality constant depends upon the semiaxes of the ellipse as well as the angle of incidence of the radiation. This linear behavior is easily convolved over an arbitrary size distribution of the clouds to obtain the chord length distribution through a statistical mixture of different cloud sizes. The chord length distribution between clouds is also considered for an atmospheric layer of finite thickness. In this case, both analytic and numerical methods are needed to obtain results. In the limit of an infinite thickness atmospheric layer described by homogeneous statistics and fixed cloud chord lengths, our considerations reduce to a Mar-kovian (exponentially distributed chord lengths) model for the intercloud spacing.