A Case for Exponential Cloud Fields?

In a large number of satellite infrared images the proportion of randomly spaced intervals of length p satellite pixels (width, one pixel) that are registered as completely cloudy falls exponentially with increasing interval length. This is exactly to be expected for a one-dimensional exponential cloud field. Further, for rectangular intervals there is also an exponential falloff, as the size of the rectangle increases, in the proportion of completely cloudy intervals. However, the rate of falloff is dependent on the perimeter of the rectangle rather than its area. It is suggested that this can be explained if the length and width of clouds are both exponentially distributed and independent. If this is the case, then the mean horizontal aspect ratio for clouds, defined as the ratio of its semimajor to semiminor axis, is undefined (infinite) even though the ratio of semiminor to semimajor axis has mean 2 ln(2) (≈0.38).