Cascade processes, emergent turbulent laws and multiscale dynamics in the atmosphere

自20世纪80年代以来，在非线性动力学和湍流方面取得了一些突破。 对这一提议特别重要的是：a）发展了尺度不变性作为一种普遍而有力的非经典对称性; B）发现了多重分形及其与湍流级联过程的关系。 在今后五年中，我建议以几种方式在此基础上再接再厉： a）随机参数化：数值天气模型是确定性的，而现代气象学的目标是预测未来的大气状态及其发生的相对概率，即目标是随机的（概率）。 事实上，随机结构把我们几乎完全预测乘法级联模型打开了大门，包括最后把“随机参数化”程序在一个良好的理论基础上，同时开辟了新的参数化方案的方式快速进步。 这项工作将与NOAA的气候诊断中心合作进行。 B） 天气-气候转换和随机气候预测：天气和气候之间的差异目前是基于主观选择的时空平均尺度。 新的综合方法为这种区分提供了客观的定量基础，将天气-气候变化视为一种“维度转换”。 它进一步准确地预测了延伸到十年周期及更长时间的天气气候光谱平台的统计特性。 这是随机预测的基础，类似于随机线性强迫方法，其业务预测气候变量，如厄尔尼诺和海面温度高达6 - 9个月的尺度。 c）、 辐射传输和云与辐射场之间的尺度关系：全球气候模式将云视为均匀的物质板;然而，到小湍流耗散尺度，云液态水和相应的辐射场是高度可变的;这意味着模式中的系统偏差。这些偏差破坏了包括全球变暖情景在内的模型预测的可信度。 最简单的非均匀性假设是它是级联的结果。 在这里，我们将调查云和辐射之间的详细尺度统计关系，并使用它来改进参数化。

Since the 1980's there have been several breakthroughs in nonlinear dynamics and turbulence. Of particular importance to this proposal are: a) the development of scale invariance as a general and powerful nonclassical symmetry; b) the discovery of multifractals and their relation to turbulent cascade processes. During the next five years I propose to build on this in several ways: a) Stochastic Parametrisations: Numerical weather models are deterministic, yet the aim of modern meteorology is to predict future atmospheric states and their relative probability of occurrence, i.e. the objective is stochastic (probabilistic). The fact that the stochastic structure turns our to be almost exactly as predicted by multiplicative cascade models opens the door for rapid advances including finally placing "stochastic parametrization" procedures on a sound theoretical basis while opening the way to qualitatively new parametrization schemes. This work will be done in collaboration with NOAA's Climate Diagnostic Centre. b) The weather - Climate transition and stochastic climate prediction: The difference between the weather and climate is currently based on subjectively chosen space-time averaging scales. The new synthesis provides an objective quantitative basis for this distinction treating the weather - climate change as a kind of "dimensional transition". It further accurately predicts the statistical properties of a weather-climate spectral plateau that extends to decadal periods and beyond. This is the basis for stochastic forecasting, analogous to the Stochastic Linear Forcing approach which operational forecasts climate variables such as El-Nino and Sea Surface Temperatures up to scales of 6 -9 months. c) Radiative transfer and the scale by scale relation between cloud and radiation fields: Global climate models treat clouds as homogeneous slabs of material; yet down to small turbulent dissipation scales, cloud liquid water and the corresponding radiation fields are highly variable; implying systematic biases in the models. These biases undermine the credibility of the model predictions including global warming scenarios. The simplest heterogeneity assumption is that the it is the consequence of cascades. Here we will investigate the detailed scale by scale statistical relations between clouds and radiation and use this to improve parametrizations.