Clouds come in all sizes, from millimetric wisps up to planetary undulations: a casual glance discloses structures within structures within structures that are constantly changing, evolving from milliseconds to the age of the earth. The structures’ collective behaviour results in variability that is so large that standard methods are utterly inadequate: in 2015, it was found that they had underestimated the variability by the factor of a million billion.
Taming such extreme variability requires physical laws that operate over enormous ranges of scales from small to large, from fast to slow. These scaling laws answer the question: “how big is a cloud?”, and they explain the origin of events that are so extreme that they have been termed “black swans”. They define a new “macroweather” regime that sits in between the weather and climate, finally settling the question: “What is Climate”? while posing another: is agriculture and hence civilization itself, the result of freak macroweather?
Scaling laws are often “universal”, so it isn’t surprising that the red planet turns out to be the statistical twin of our blue one. This new understanding of the statistics - including the black swans – enables us to close the scientific part of climate debate by statistically testing and rejecting the skeptics’ Giant Natural Fluctuation hypothesis. The scaling laws can also be used to make accurate monthly to decadal (macroweather) forecasts by exploiting an unsuspected but huge memory in the atmosphere-ocean system itself. The same scaling approach significantly reduces the large uncertainties in our current climate projections to 2050 and 2100.
This short course reviews the nonlinear geoscience behind this new understanding. This includes multifractals, generalized scale invariance, fluctuation analysis, intermittency, spectra and stochastic macroweather predictions and climate projections [Lovejoy, 2018].

Reference:

Lovejoy, S. (2018), Weather, Macroweather and Climate: our random yet predictable atmosphere, Oxford U. Press, Oxford.