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Oct.  2017

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# Equatorial Wave Expansion of Instantaneous Flows for Diagnosis of Equatorial Waves from Data: Formulation and Illustration

• This paper presents a method for expanding horizontal flow variables in data using the free solutions to the shallow-water system as a basis set. This method for equatorial wave expansion of instantaneous flows (EWEIF) uses dynamic constraints in conjunction with projections of data onto parabolic cylinder functions to determine the amplitude of all equatorial waves. EWEIF allows us to decompose an instantaneous wave flow into individual equatorial waves with a presumed equivalent depth without using temporal or spatial filtering a priori. Three sets of EWEIF analyses are presented. The first set is to confirm that EWEIF is capable of recovering the individual waves constructed from theoretical equatorial wave solutions under various scenarios. The other two sets demonstrate the ability of the EWEIF method to derive time series of individual equatorial waves from instantaneous wave fields without knowing a priori exactly which waves exist in the data as well as their spatial and temporal scales using outputs of an equatorial β-channel shallow-water model and ERA-Interim data. The third set of demonstrations shows, for the first time, the continuous evolutions of individual equatorial waves in the stratosphere whose amplitude is synchronized with the background zonal wind as predicted by quasi-biennial oscillation theory.
摘要: 本文提出EWEIF (Equatorial Wave Expansion of Instantaneous Flows) 方法, 用于将即时气流场以赤道β-平面浅水模式的线性自由波为基函数来展开，从而分析任意时刻所观测到的赤道波水平空间分布。在已知流体等效深度的前提下，EWEIF方法无需事先对气流场进行时间和空间上的滤波，从而保证仅用即时气流场，即可得到该时刻各类赤道波动的水平空间分布。对不同时刻气流场分别做EWEIF分析，便可得到各类赤道波动的时空连续演变特征，包括东西传播，振幅强弱， 发生，发展，和消失等变化。本文用三组示例来演示EWEIF分析。第一组示例用于评估EWEIF是否能够还原按赤道波理论解的时空演变所构造出的理想波场中的赤道波频散关系，同时阐述了使用错误流体等效深度对EWEIF分析结果的影响。后两组示例分别使用赤道β-通道浅水模型结果和ERA-Interim再分析资料，演示EWEIF方法能够在无需假定数据中存在哪些波动的前提下，得到其中各类赤道波的时空演变序列。第二组示例的资料取于赤道β-通道浅水模型结果而第三组取于ERA-Interim再分析资料。需要特别指出的是，第三组示例所演示的结果是首次从观测资料中得到平流层中各类赤道波随时空连续演变，并证实了QBO理论所预测的，平流层中各类赤道波的振幅强弱变化确实与背景纬向风场QBO振荡同步。

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## Manuscript History

Manuscript revised: 17 April 2017
Manuscript accepted: 11 May 2017
###### 通讯作者: 陈斌, bchen63@163.com
• 1.

沈阳化工大学材料科学与工程学院 沈阳 110142

## Equatorial Wave Expansion of Instantaneous Flows for Diagnosis of Equatorial Waves from Data: Formulation and Illustration

• 1. Geophysical Fluid Dynamics Institute, Florida State University, Tallahassee, Florida, 32306, USA
• 2. Department of Earth, Ocean, and Atmospheric Science, Florida State University, Tallahassee, Florida, 32306, USA

Abstract: This paper presents a method for expanding horizontal flow variables in data using the free solutions to the shallow-water system as a basis set. This method for equatorial wave expansion of instantaneous flows (EWEIF) uses dynamic constraints in conjunction with projections of data onto parabolic cylinder functions to determine the amplitude of all equatorial waves. EWEIF allows us to decompose an instantaneous wave flow into individual equatorial waves with a presumed equivalent depth without using temporal or spatial filtering a priori. Three sets of EWEIF analyses are presented. The first set is to confirm that EWEIF is capable of recovering the individual waves constructed from theoretical equatorial wave solutions under various scenarios. The other two sets demonstrate the ability of the EWEIF method to derive time series of individual equatorial waves from instantaneous wave fields without knowing a priori exactly which waves exist in the data as well as their spatial and temporal scales using outputs of an equatorial β-channel shallow-water model and ERA-Interim data. The third set of demonstrations shows, for the first time, the continuous evolutions of individual equatorial waves in the stratosphere whose amplitude is synchronized with the background zonal wind as predicted by quasi-biennial oscillation theory.

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