Conclusions: Richardson’s dreams

From big to small, from fast to slow, we traveled through scales— through magnifications of billions in space and billions of billions in time. We looked at how the traditional scalebound approach singles out specific phenomena: structures at specific spatial scales with specific lifetimes. The approach attempts to understand each in a (scale) reductionist and (usually) deterministic manner. Yet it fails miserably to describe more than tiny portions of the actual variability, giving— at best— some qualitative insights. Viewing the big picture with the help of modern data, we saw that, quantitatively, the scalebound approach underestimates the variability by a factor of a million billion (Fig. 2.3A). The alternative is the scaling approach, which attempts to understand and model the atmosphere over wide ranges of scale. This approach is based on space– time scale symmetry principles. It describes statistically the synergy of nonlinear processes that act collectively over wide ranges of scale. To apply the idea in space, we needed to generalize the notion of scale itself (Chapter 3)— notably, to be able to account for the stratification caused by gravity. The appropriate notion of scale is one that emerges as a consequence of strong nonlinear dynamics, rather than being imposed a priori from without. Applying scaling in time, we found that the familiar weather– climate dichotomy was missing a key middle regime: from ten days to twenty years. It is a weather, macroweather, climate trichotomy. When it comes to real atmospheric modeling, scientists have long realized the limits of the scalebound approach. When they “really need to know,” they defer to NWP or GCMs, the embodiment of Richardson’s dream of “weather prediction by numerical process.” This is fortunate, because the NWPs and GCMs respect space– time scaling symmetries; without them, they would be hopelessly unrealistic. At least when used for their original purpose— weather prediction up to the ten- day deterministic predictability limit— respecting scaling allows them to be reasonably accurate.