The Fractional Energy Balance Equation, macroweather forecasts and climate projections

点击翻译按钮获取中文摘要

It is increasingly recognized that new approaches to monthly and seasonal forecasting and to multidecadal climate projections are needed. The proposed is to continue a multidecadal research program that I initiated at the end of the 1970's aiming to apply and develop stochastic, scaling, (turbulent, multifractal) approaches to atmospheric modelling. Over the last years, it has spawned state-of-the-art monthly, seasonal forecasts and (low uncertainty) multidecadal projections. In the next decade, this new paradigm will be developed and extended in various ways. At the moment, supercomputer atmospheric models (GCMs) - extended weather models - are the only tools for making monthly and seasonal (macroweather) forecasts and multidecadal climate projections. Their continued development assumes that realism requires the inclusion of as many details and processes as possible. Yet, any structures smaller than the model resolution (currently tens of kilometers) may grow explosively (the "butterfly effect") so that beyond ten days, GCM outputs become effectively random. A consequence is unacceptably large projection uncertainties, e.g. the famous 1.5 to 4.5 oC range for CO2 doubling. GCMs use continuum mechanics that assume molecular level details are irrelevant yet once again, most of the details of the collective behavior of a huge number of interacting vortices are irrelevant and new, even higher level turbulent laws emerge. This research program builds models directly at macroweather (e.g. monthly) scales using the physical principles of scale invariance and energy conservation that is possible due to the new discovery that when a famous energy balance model is updated it yields a unified model based on the new fractional energy balance equation (FEBE). The FEBE is both more physically based and yields the scaling macroweather and climate models as respectively high and low frequency approximations. For temperatures, these monthly scale models already prove to be comparable or more skillful than GCMs while multidecadal projections have less than half the uncertainties of the GCM ensemble ([1], [2]; it requires a million times fewer computations. When used directly for climate projections, the FEBE fully supports the latest IPCC projections while reducing the uncertainty by over 50%. This research program will develop and extend the FEBE for regional forecasts and projections and for understanding past (paleo) climates. Challenges include theoretical, and mathematical issues needed to resolve new (fractional) operators as well as to consolidate the physical basis of the theory. It involves developing new numerical techniques and models. Its foundations will be studied by using satellite and other observations of the earth's radiative exchanges. If successful, it could change the way we think about atmospheric processes while providing better forecasts and projections, impacting humanities efforts to avoid climate catastrophe.