Augmenting a satellite's resolution reveals increasingly detailed structures that are found to occupy a decreasing fraction of the image, while simultaneously brightening to compensate. By systematically degrading the resolution of visible and infrared satellite cloud and surface data as well as radar rain data we define resolution-independent co-dimension functions that describe the spatial distribution of image features as well as the resolution dependence of the intensities themselves. The scale invariant functions so obtained fit into theoretically predicted universality classes. These multifractal techniques have implications for our ability to meaningfully estimate cloud brightness fraction, total cloud amount, as well as other remotely sensed quantities. A preliminary account of this work can be found in Gabriel et al., (1988a). See also Gabriel (1988). ¿ American Geophysical Union 1988