Clouds are fractal
Fractal measures provide an elegant mathematical description of cloud structure. Fractals have the same structure at all scales. That may sound exotic, but fractals are actually very common in nature. An instructive example is a photo of a rock, where you cannot see if the rock is 10 cm large or 10 m, without someone or some tool next to it. Other examples of fractals are commodity prices, the branch structure of plants, mountains, coast lines, your lungs and arteries, and of course rain and clouds.The fractal structure of a measurement (time series) of Liquid Water Content (LWC) can be seen by zooming in on the time series. If you zoom in by a factor x, the total variance of this smaller part of the time series will be reduced by a factor y. Each time you again zoom in by factor x, you will find a variance reduction by a factor y, at least on average. This fractal behaviour leads to a power law; the total variance is proportional to the scale (total length of the time series) to the power of a constant; to be precise, this constant is log(x)/log(y). Such power laws can also be seen in the measurements of cloud top height, column integrated cloud liquid water (Liquid Water Path, LWP), the sizes of cumulus clouds, the perimeter of cumulus clouds or showers, and in satellite images of clouds and in other radiative cloud properties.
If you plot such a power law in a graph with logarithmic axis, the power laws looks like a line. Thus, a paper on fractals typically shows a lot of so called log-log-plots and linear fits. To identify scaling you need at least 3 orders of magnitude, thus you need large data sets with little noise.
