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arXiv 2102.07760physics.ao-phmath.DSphysics.data-an
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从短期模拟中学习罕见平流层转变的预报

Learning forecasts of rare stratospheric transitions from short simulations

Justin Finkel, Robert J. Webber, Dorian S. Abbot, Edwin P. Gerber, Jonathan Weare

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26 pages, 7 figures, major revision after original. Accepted to Monthly Weather Review, American Meteorological Society
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摘要：

在非线性大气动力学中出现的罕见事件仍然难以预测和归因。我们解决的问题，预测罕见的事件在一个典型的例子，突然平流层变暖（SSW）。大约每隔一个冬天，北方平流层极涡就会迅速瓦解，从而在数月内改变中纬度地面的天气类型。我们专注于两个关键量的兴趣：发生的概率，和预期的提前期，如果它确实发生，作为初始条件的函数。这些\emph{optimal forecasts}具体衡量事件的进展。直接数值模拟在原则上可以估计它们，但在实践中成本过高：每个罕见事件需要长时间的积分来观察，并且每次积分的成本随着模型的复杂性而增加。我们描述了一种替代方法，使用集成相比，变暖事件的时间尺度是\emph{short}。我们通过求解涉及转换算子的方程来有效地计算概率和提前期，转换算子编码了有关动态的所有信息。我们将这些最佳预测与少量可解释的物理变量联系起来，提出了预测的最佳测量方法。我们用Holton和Mass（1976）发展的SSW原型模式并用随机强迫进行修正来说明这种方法。虽然高度理想化，这个模型捕捉到了SSW的基本非线性动力学，并表现出关键的预测挑战：单个事件之间的时间尺度和连续事件之间的返回时间的戏剧性分离。我们的方法旨在充分利用模型和观测的高维数据，并有可能确定许多复杂的气象罕见事件的详细预测。

英文摘要：

Rare events arising in nonlinear atmospheric dynamics remain hard to predict and attribute. We address the problem of forecasting rare events in a prototypical example, Sudden Stratospheric Warmings (SSWs). Approximately once every other winter, the boreal stratospheric polar vortex rapidly breaks down, shifting midlatitude surface weather patterns for months. We focus on two key quantities of interest: the probability of an SSW occurring, and the expected lead time if it does occur, as functions of initial condition. These \emph{optimal forecasts} concretely measure the event's progress. Direct numerical simulation can estimate them in principle, but is prohibitively expensive in practice: each rare event requires a long integration to observe, and the cost of each integration grows with model complexity. We describe an alternative approach using integrations that are \emph{short} compared to the timescale of the warming event. We compute the probability and lead time efficiently by solving equations involving the transition operator, which encodes all information about the dynamics. We relate these optimal forecasts to a small number of interpretable physical variables, suggesting optimal measurements for forecasting. We illustrate the methodology on a prototype SSW model developed by Holton and Mass (1976) and modified by stochastic forcing. While highly idealized, this model captures the essential nonlinear dynamics of SSWs and exhibits the key forecasting challenge: the dramatic separation in timescales between a single event and the return time between successive events. Our methodology is designed to fully exploit high-dimensional data from models and observations, and has the potential to identify detailed predictors of many complex rare events in meteorology.

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