Spatiotemporal Inhomogeneity of Tropical Waves and Their Interactions

热带波，也被称为赤道波，是热带天气的一个关键组成部分，众所周知，它在季风变化、厄尔尼诺事件以及飓风和台风的形成中发挥着重要作用。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推导。得到的解以正弦波的形式表示，连续的脊线和波谷在赤道周围均匀重复。假设这种扩展的波列可以探测到赤道波的分析方法，这些方法证实了观测到的波与理论预测基本一致。在这个项目中，热带波被识别和研究使用多维集合经验模式分解(多维集合经验模式分解)，这是由PI等人开创的一种时间序列分析方法(见AGS-1139479)。MEEMD用于确定赤道沿线每个经度的可变性，其频率大致对应于特定波的频率。关于预期的波的纬度形状的附加信息被用来区分具有相似频率的波类型。一旦在数据中确定了波浪，就会使用技术进一步分析它们的行为，以确定等效深度等特征，等效深度是一种衡量波浪运动深度的指标，这种深度可能与云中凝结加热产生波浪有关。MEEMD技术在描述不同频率的波相互作用方面具有一定的优势，而MEEMD技术已被用于发展全息谱分析，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可变性形式，在一两个月的过程中缓慢波动。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。将向研究界提供在该项目中开发的MEEMD和全息光谱分析工具，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，例如研究神经障碍中的脑波异常。此外，该项目将为研究生和博士后提供支持和培训，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.