The variability of the atmospheric power spectrum

大气功率谱的变化

• 批准号: 2440368
• 金额: --
• 依托单位: University of Oxford
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2020
• 资助国家: 英国
• 起止时间: 2020 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2440368
• 关键词: variability; atmospheric; power; spectrum

The kinetic energy spectrum of the atmosphere is a measure of how much energy is at each length scale - It is essentially the spatial Fourier transform of the kinetic energy field. Figure 1 shows the spectrum calculated by Nastrom and Gage (1985) from aircraft data. Motions on the largest length scales contain most of the kinetic energy. Figure 1 is on a log scale, so the gradients of the lines correspond to a power law relationship between spectral density of kinetic energy and wavelength. The spectral gradient is significant due to its link with predictability. Lorenz (1969) showed that, under certain statistical assumptions, the 2D vorticity equations -a good approximation to atmospheric motion on synoptic scales- will have an intrinsically finite range of predictability if the energy of the system has a -3 or shallower spectral gradient. Note that taken with figure 1, that re-ally does imply we will never be able to predict the weather more than 2-3 weeks in advance.A controversial question.The origin of the -3 range of figure 1 was convincingly explained by Charney (1971) as resulting from a large scale quasi-2D flow that is well-mixed via baroclinic in-stability. A similarly convincing explanation for the -5/3 range has not been provided so far. For some intuition, 2D turbulence will display an upscale energy cascade from the energy injection scale that has a -5/3 power law and a downscale enstrophy cascade of -3. 3D turbu-lence will have no transfer of energy upscale, instead it will just have a -5/3 downscale energy cascade (see Val-lis 2017, ch 14).Figure 1: The result of thousands of aircraft measurements, this fig-ure shows the mysterious -5/3 spectral gradient at the mesoscales. [Nastrom 1985]What could be causing the unexpectedly energetic mesoscale? In 1979, Gage suggested that it was the re-sult of 2D upscale energy transfer from small scale mix-ing such as storms. In opposition to this explanation, VanZandt (1982) pointed out a downscale motion of en-ergy associated with gravity waves could produce the observation. Further complicating the issue, the spec-trum is variable. Orographic forcing was shown to have a large effect with mesoscale energy over mountains up to 10 times larger than over ocean (Nastrom et al 1987). Similarly, precipitation has been seen to energize the mesoscales in models, (Selz et al 2019) for example. It has even be suggested that there may be no universal dynamical mechanism that governs the observed spec-trum, the lack of compelling theory simply being due to the statistical assumptions not applying to the highly complex real atmosphere (Selz et al 2019). The answer is likely to be a combination of the above with which cause dominates depending on latitude (Cho et al 1999), and possibly altitude.In the last decade computing power has continued to grow. ECMWF analysis data can now see the -5/3 spec-trum and we are approaching a period where our ques-tions about the cause can be answered in a more direct manner. To provide evidence for the origin of the -5/3, a thorough categorization of the power spectrum in analysis istherefore proposed. A tantalizing question is whether observed variation in the power spectrum correlates with changes in the state-dependent predictability. If this was found to be the case, forecasters could tell in advance how many ensemble members would be needed to sufficiently explore the state-space.

大气的动能谱是对每个长度尺度上有多少能量的测量——它本质上是动能场的空间傅立叶变换。图 1 显示了 Nastrom 和 Gage (1985) 根据飞机数据计算出的频谱。 Motions on the largest length scales contain most of the kinetic energy.图 1 采用对数刻度，因此线条的梯度对应于动能谱密度与波长之间的幂律关系。 The spectral gradient is significant due to its link with predictability. Lorenz (1969) 表明，在某些统计假设下，如果系统的能量具有 -3 或更浅的光谱梯度，二维涡度方程（天气尺度上大气运动的良好近似）将具有本质上有限的可预测性范围。请注意，结合图 1，这确实意味着我们永远无法提前超过 2-3 周预测天气。这是一个有争议的问题。Charney (1971) 令人信服地解释了图 1 的 -3 范围的起源，它是由通过斜压不稳定性充分混合的大规模准二维流产生的。迄今为止，尚未对 -5/3 范围提供类似的令人信服的解释。对于某些直觉来说，二维湍流将显示来自能量注入尺度的高档能量级联，其幂律为 -5/3，而低尺度熵级联为 -3。 3D 湍流不会有向上尺度的能量转移，而是只有 -5/3 向下尺度的能量级联（参见 Val-lis 2017，第 14 章）。图 1：数千次飞机测量的结果，该图显示了中尺度上神秘的 -5/3 光谱梯度。 [Nastrom 1985]是什么导致了意想不到的高能中尺度？ 1979年，盖奇提出这是风暴等小规模混合产生的二维高级能量转移的结果。与这种解释相反，VanZandt（1982）指出，与重力波相关的能量的小尺度运动可以产生观测结果。 Further complicating the issue, the spec-trum is variable.地形强迫被证明对山脉上的中尺度能量有很大的影响，比海洋上的能量大 10 倍（Nastrom 等，1987）。 Similarly, precipitation has been seen to energize the mesoscales in models, (Selz et al 2019) for example.甚至有人认为，可能不存在控制观测到的光谱的通用动力机制，缺乏令人信服的理论仅仅是因为统计假设不适用于高度复杂的真实大气（Selz 等人，2019）。答案可能是上述因素的组合，其原因取决于纬度（Cho et al 1999），也可能取决于海拔高度。在过去十年中，计算能力持续增长。 ECMWF 分析数据现在可以看到 -5/3 频谱，我们正在接近一个可以以更直接的方式回答有关原因的问题的时期。 To provide evidence for the origin of the -5/3, a thorough categorization of the power spectrum in analysis istherefore proposed.一个诱人的问题是观察到的功率谱变化是否与状态相关可预测性的变化相关。如果发现这种情况，预报员可以提前告知需要多少个集合成员才能充分探索状态空间。