Spatiotemporal Inhomogeneity of Tropical Waves and Their Interactions

热带波，也被称为赤道波，是热带天气的关键组成部分，并且已知在季风变化，厄尔尼诺事件以及飓风和台风的形成中发挥重要作用。热带波的基本特征，包括其大小、形状和频率，可以通过求解其基本动力学的理想化模型来导出。 所得解用正弦波表示，连续的脊和槽在赤道周围均匀重复。 假设这种扩展波列可以检测赤道波的分析方法，这些方法证实了观测到的波在很大程度上与理论预测相符。 但是观测到的波浪通常跨越有限的区域，因此最好使用不假设其全球性质或纵向范围的方法来研究它们。在本项目中，使用多维包络经验模式分解（MEEMD）来识别和研究热带波浪，MEEMD是PI和其他人开创的一种时间序列分析方法（见AGS-1139479）。 MEEMD用于识别沿沿着的每个经度处的频率大致对应于特定波的频率的变化。关于波的预期纬度形状的附加信息用于分离具有相似频率的波类型。 一旦在数据中识别出波浪，就可以使用技术进一步分析它们的行为，以确定诸如等效深度之类的特征，等效深度是对波浪运动深度的测量，可以与云中凝结加热产生的波浪有关。 MEEMD技术在表示不同频率的波的相互作用方面具有一些优势，并且MEEMD技术已被用于开发全息谱分析，这是一种量化波相互作用并研究其能量学的方法。 全息光谱分析的一个应用是研究马登-朱利安振荡对赤道波的调制。马登-朱利安振荡是一种更大的热带变率，在一两个月内缓慢波动。如上所述，由于赤道波对热带天气和气候的重要性，这项工作具有更广泛的影响。 该项目开发的MEEMD和全息光谱分析工具将提供给研究界，以确保该项目产生更广泛的科学影响。 这些工具适用于热带气象学以外的各种研究领域，例如在神经疾病的脑波异常研究中。 此外，该项目将为一名研究生和一名博士后提供支助和培训，从而促进这一研究领域的下一代科学家。

Tropical waves, also referred to as equatorial waves, are a key component of the weather of the tropics, and are known to play important roles in monsoon variability, El Nino events, and the formation of hurricanes and typhoons. The basic characteristics of tropical waves, including their size, shape and frequency, can be derived by solving an idealized model of their fundamental dynamics. The resulting solutions are expressed in terms of sinusoidal waves, with successive ridges and troughs repeating uniformly around the equator. Analysis methods that assume such extended wave trains can detect equatorial waves, and these methods confirm that observed waves largely match theoretical predictions. But observed waves typically span a limited region and it can be desirable to study them using methods which make no assumptions regarding their global nature or longitudinal extent.In this project tropical waves are identified and studied using the Multi-dimensional Ensemble Empirical Mode Decomposition (MEEMD), a time series analysis method pioneered by the PI and others (see AGS-1139479). MEEMD is used to identify variability at each longitude along the equator at frequencies roughly corresponding to frequencies for particular waves. Additional information about the expected latitudinal shape of the waves is used to separate wave types which have similar frequencies. Once the waves are identified in the data their behavior is further analyzed using techniques to determine characteristics such as equivalent depth, a measure of the depth of wave motions that can be related to the generation of waves by condensational heating in clouds. The MEEMD technique has some advantages for representing the interaction of waves of different frequencies, and the MEEMD technique has been used to develop holo-spectral analysis, a method for quantifying wave interactions and studying their energetics. One application of holo-spectral analysis here is to examine the modulation of equatorial waves by the Madden-Julian Oscillation, a much larger form of tropical variability which fluctuates slowly over the course of a month or two.The work has broader impacts due to the importance of equatorial waves for the weather and climate of the tropics, as noted above. The MEEMD and holo-spectral analysis tools developed in the project will be made available to the research community to ensure the scientific broader impacts of the project. These tools have applicability in a variety of research fields beyond tropical meteorology, for example in the study of brain wave anomalies in neural disorders. In addition, the project would provide support and training for a graduate student and a postdoc, thereby promoting the next generation of scientists in this research area.