LOW ORDER MODELS OF STORM TRACK VARIABILITY

地球大气中的风暴轨迹是中纬度天气系统的主要轨迹。它们的几何结构是由当地的表面边界条件与平均流相互作用，导致当地的斜压不稳定增长率的变化。斜压不稳定性是引起中纬度天气系统的相关的水动力不稳定性;它的增长时间尺度由平均风的垂直切变确定。观测到的风暴路径在很宽的时间尺度上表现出变率。变异模式的功率谱很宽，变异性很慢。由于斜压不稳定作用于相对较快的时间尺度（约3-5天），风暴路径的非线性特性产生了10天或更长的慢时间尺度，直至气候时间尺度。本项目的目的是更好地了解导致慢变率的潜在非线性动力学。事实上，风暴路径对缓慢气候强迫的响应是未来气候预测中的关键未知因素之一，本项目的目标之一是更好地了解风暴路径的潜在非线性动力学如何对不断变化的外部强迫作出反应。最近的工作，建立在一长串的相关进展，已经证明了低阶捕食者-猎物模型似乎捕捉慢波平均流相互作用的重要属性。有大量的间接证据表明，风暴路径的变化是由低阶动力系统决定的。到目前为止，基本的捕食者-被捕食者模型的推导大多是启发式的，过去从Navier-Stokes方程推导的第一性原理还不能包含当前对风暴轴变化的理解。我们研究风暴轴低阶动力学的最初方法将来自两个不同的方面：第一、利用我们从观察捕食者那里学到的东西对于风暴路径中的猎物型行为，我们将应用模型简化技术，将完整的流体动力学模型简化为包含已知风暴重要动力学特征的低阶模型其次，从已发表的捕食者-被捕食者模型开始，我们将尝试以与时间相关的方式扩展这些系统，以捕获更复杂（可能是混沌）的动态。此类延期的候选人是：与湿度场的相互作用（热力学上是风暴路径的主要能量来源），急流纬度（气候动力学中的“已知未知”），与外加外力的相互作用（周期性、季节性强迫或随机强迫），但也可能有其他的。有几个额外的途径可在这两个方向，并从他们约项目的最后一年。这些途径包括大量的数据分析（最近使用了新的相空间投影）和理想化建模（这种模型存在并广泛用于解决基本的GFD问题，通常围绕射流形成和变化）。

The storm tracks in the Earth's atmosphere are the main locus of midlatitude weather systems. Their geometric structure is determined by local surface boundary conditions interacting with the mean flow which leads to local variations in the growth rate of baroclinic instability. Baroclinic instability is the relevant hydrodynamic instability which gives rise to midlatitude weather systems; its growth time scales are set by the vertical shear of the mean wind.The observed storm track shows variability on a broad range of timescales. The power spectrum of modes of variability is wide with substantial slow variability. Given that baroclinic instability works on relatively fast timescales, of around 3-5 days, it is the non-linear properties of the storm tracks that produce the slow timescales of 10 days or more, up to climate time scales.The aim of this project is to better understand the underlying non-linear dynamics leading to slow variability. In fact, the response of the storm tracks to slow climatic forcings is one of the key unknowns in future climate predictions, and it is one of the aims of this project to understand better how the underlying nonlinear dynamics of the storm track would react to changing external forcings.The main paradigm of understanding non-linear scale interactions in the storm tracks revolves around the idea of wave-mean flow interaction. Recent work, building on a long line of relevant progress, has demonstrated how low-order predator-prey models appear to capture important properties of the slow wave-mean flow interactions. There is substantial, but circumstantial evidence to show that the variability of storm tracks is determined by low-order dynamical systems. The derivations of the underlying predator-prey models has been mostly heuristic up to now, and first-principles derivations from the Navier- Stokes equations in the past have not been able to incorporate current understanding of storm-track variability.The initial approach to our study of the low-order dynamics of the storm track will come from two different sides:Firstly, using what we have learned from observed predator-prey style behaviour in the storm tracks we will apply model reduction techniques to reduce the full hydrodynamic models to low order versions that include known important dynamical features of the storm track (such as downstream jet latitude shifts).Secondly, starting from the published predator-prey models, we will attempt to extend those systems in a geophysically relevant way to capture more complex (likely chaotic) dynamics. Candidates for such extensions are: interactions with the humidity field (ther- modynamically the key source of energy in the storm track), jet latitude (a "known unknown" in climate dynamics), interactions with imposed external forcings (periodic, seasonal forcings, or stochastic forcings), but there may be others.There are several additional avenues available around those two directions and following on from them for approximately the final year of the project. Such avenues include substantial data analysis (where novel phase-space projections have recently been used), and idealised modeling (such models exist and are widely used to address fundamental GFD problems, typically around jet stream formation and variability).