Nogueira Miguel
Instituto Dom Luiz, Faculdade de Ciências da Universidade de Lisboa, Campo Grande, Lisbon, Portugal.
PLoS One. 2017 Mar 23;12(3):e0173994. doi: 10.1371/journal.pone.0173994. eCollection 2017.
The equivalency between the power law behavior of Multiscale Entropy (MSE) and of power spectra opens a promising path for interpretation of complex time-series, which is explored here for the first time for atmospheric fields. Additionally, the present manuscript represents a new independent empirical validation of such relationship, the first one for the atmosphere. The MSE-fractal relationship is verified for synthetic fractal time-series covering the full range of exponents typically observed in the atmosphere. It is also verified for near-surface wind observations from anemometers and CFSR re-analysis product. The results show a ubiquitous β ≈ 5/3 behavior inside the inertial range. A scaling break emerges at scales around a few seconds, with a tendency towards 1/f noise. The presence, extension and fractal exponent of this intermediate range are dependent on the particular surface forcing and atmospheric conditions. MSE shows an identical picture which is consistent with the turbulent energy cascade model: viscous dissipation at the small-scale end of the inertial range works as an information sink, while at the larger (energy-containing) scales the multiple forcings in the boundary layer act as widespread information sources. Another scaling transition occurs at scales around 1-10 days, with an abrupt flattening of the spectrum. MSE shows that this transition corresponds to a maximum of the new information introduced, occurring at the time-scales of the synoptic features that dominate weather patterns. At larger scales, a scaling regime with flatter slopes emerges extending to scales larger than 1 year. MSE analysis shows that the amount of new information created decreases with increasing scale in this low-frequency regime. Additionally, in this region the energy injection is concentrated in two large energy peaks: daily and yearly time-scales. The results demonstrate that the superposition of these periodic signals does not destroy the underlying scaling behavior, with both periodic and fractal terms playing an important role in the observed wind time-series.
多尺度熵（MSE）的幂律行为与功率谱之间的等效性为复杂时间序列的解释开辟了一条充满希望的道路，本文首次针对大气场对此进行了探索。此外，本手稿代表了这种关系的一种新的独立实证验证，是首次针对大气的验证。对于涵盖大气中通常观测到的全指数范围的合成分形时间序列，验证了MSE-分形关系。还对风速仪的近地表风观测数据和CFSR再分析产品进行了验证。结果表明，在惯性范围内普遍存在β≈5/3的行为。在大约几秒的尺度上出现了标度间断，呈现出向1/f噪声的趋势。这个中间范围的存在、范围和分形指数取决于特定的表面强迫和大气条件。MSE呈现出相同的情况，这与湍流能量级联模型一致：惯性范围小尺度端的粘性耗散起到信息汇的作用，而在较大（含能）尺度上，边界层中的多种强迫作用作为广泛的信息源。在大约1 - 10天的尺度上发生了另一种标度转变，频谱突然变平。MSE表明，这种转变对应于引入新信息的最大值，发生在主导天气模式的天气尺度时间尺度上。在更大的尺度上，出现了一个斜率更平缓的标度区域，一直延伸到大于1年的尺度。MSE分析表明，在这个低频区域，随着尺度的增加，产生的新信息量减少。此外，在这个区域，能量注入集中在两个大的能量峰值：日和年时间尺度上。结果表明，这些周期性信号的叠加不会破坏潜在的标度行为，周期性项和分形项在观测到的风时间序列中都起着重要作用。
