Deriving scaling laws for extreme weather events using the Buckingham-PI theorem

Changes in extreme weather events such as heatwaves, droughts, and cold spells under climate change are questions of significant scientific and societal importance. Currently, quantifying changes in such extreme events relies on state-of-the-art climate models; however, model biases and infrequent occurrence of extreme events complicate obtaining conclusive answers. Having scaling laws for how the key characteristics of extreme events, such as their duration, frequency, intensity, and size depend on the mean state can help with constraining the model projections and also learning about future extreme events from paleo data. The Buckingham-PI theorem has a long and successful history in fluid mechanics; however, it is not often used in climate science. Here, we show examples of the successful application of the Buckingham-PI theorem to derive scaling laws for the size and duration of the midlatitude persistent anticyclones, i.e., the extreme-causing blocking events. The scaling laws derived for a simple prototype of the midlatitude circulation (a two-layer QG model) are shown to work in a hierarchy of climate models and explain some of the observed changes in blocking characteristics under climate change in state-of-the-art, CMIP-type, climate models.