The Fractional Energy Balance Equation, macroweather forecasts and climate projections

人们日益认识到，需要采取新的方法进行月度和季度预报以及进行多年气候预测。建议是继续一个几十年的研究计划，我在20世纪70年代末发起的目的是应用和发展随机，缩放，（湍流，多重分形）大气建模的方法。在过去的几年里，它催生了最先进的月度、季节性预测和（低不确定性）数十年预测。在今后十年中，这一新模式将以各种方式得到发展和推广。 目前，超级计算机大气模型（GCM）-扩展的天气模型-是进行月度和季节（宏观天气）预测和多年气候预测的唯一工具。它们的持续发展假定现实主义要求尽可能多地包括细节和过程。然而，任何小于模型分辨率（目前为数十公里）的结构都可能爆炸性地增长（“蝴蝶效应”），因此超过十天，GCM输出实际上是随机的。其结果是预测的不确定性大得令人无法接受，例如，著名的CO2加倍的1.5至4.5 oC范围。GCM使用连续介质力学，假设分子水平的细节是不相关的，但再一次，大量相互作用的漩涡的集体行为的大部分细节是不相关的，新的，甚至更高层次的湍流定律出现。该研究计划使用尺度不变性和能量守恒的物理原理直接在宏观天气（例如月）尺度上建立模型，这是可能的，因为新发现，当一个著名的能量平衡模型被更新时，它会产生一个基于新的分数能量平衡方程（FEBE）的统一模型。FEBE是更多的物理基础，并产生缩放宏观天气和气候模式，分别为高频和低频近似。对于温度，这些月尺度模型已经证明与GCM相当或更熟练，而多年代预测的不确定性不到GCM集合的一半（[1]，[2];它需要的计算量减少了一百万倍。当直接用于气候预测时，FEBE完全支持IPCC的最新预测，同时将不确定性降低了50%以上。 该研究计划将开发和扩展FEBE，用于区域预测和预测以及了解过去（古）气候。挑战包括理论和数学问题需要解决新的（分数）运营商以及巩固理论的物理基础。它涉及开发新的数值技术和模型。它的基础将通过使用卫星和其他对地球辐射交换的观测来研究。如果成功，它可以改变我们对大气过程的看法，同时提供更好的预测和预测，影响人类避免气候灾难的努力。

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.