JGR 行星 JGR 行星

研究论文研究文章

10.1029/2021JE006899

特别部分：特别部分：

ExoMars 痕量气体轨道飞行器：One Martian Year of Science
ExoMars 痕量气体轨道飞行器：一个火星年的科学

要点：

介绍了 ExoMars 痕量气体轨道飞行器上大气化学套件仪器对重力波的观测结果
观察到的波活动、势能、动量通量和波阻力的全球分布与模型预测非常吻合
The observed global distribution of wave activity, potential energy, momentum flux, and wave resistance is in good agreement with model predictions
我们发现波幅和浮力频率之间没有相关性，这是以前观察到的与温度反相关的延伸

通信地址：

E. D. 斯塔里琴科，
starichenko.ed@phystech.edu

引文：

Starichenko， ED， Belyaev， DA， Medvedev， AS， Fedorova， AA， Korablev， OI， Trokhimovskiy， A.， et al. （2021）.距离 ACS/TGO 掩星测量的 20-160 km 高度火星大气中的重力波活动。地球物理研究杂志：行星，126，e2021JE006899。https://doi.org/10.1029/2021JE006899

收稿日期 2021 收到 2021 年 3 月 18 日年 3 月 18 日接受日期 2021 年 7 月 15 日接受于 2021 年 7 月 15 日

作者贡献：

概念化：Denis A. Belyaev、Alexander S. Medvedev、Oleg I. Korablev、Erdal Yiğit、Paul Hartogh 数据管理：Alexander Trokhimovskiy
概念化：德尼斯·A·别利亚耶夫，亚历山大·S·梅德韦杰夫，奥列格·I·科拉别夫，埃尔达尔·伊吉特，保罗·哈托赫数据管理：亚历山大·特罗希莫夫斯基正式分析：Ekaterina D.
正式分析：叶卡捷琳娜·D。
Starichenko 资金获取：Oleg I. Korablev 调查：Ekaterina D. Starichenko
资金获取：奥列格·I·科拉别夫调查：叶卡捷琳娜·D·斯塔里琴科
方法：Ekaterina D. Starichenko、Denis A. Belyaev、Alexander S. Medvedev
方法论：叶卡捷琳娜·D·斯塔里琴科，德尼斯·A·别利亚耶夫，亚历山大·S·梅德韦杰夫项目管理：Oleg I. Korablev、Alexander Trokhimovskiy、Franck Montmessin
© 2021 年。美国地球物理联合会。保留所有权利。
© 2021. 美国地球物理联盟。保留所有权利。

距离 ACS/TGO 掩星测量 20-160 km 高度的火星大气中的重力波活动

叶卡捷琳娜 D. 斯塔里琴科 $^{1, 2}^{(D)}$ ， Denis A. Belyaev $^{1, 2}^{(D)}$ ，亚历山大·梅德韦杰夫 $^{3}^{(D)}$ ，安娜 A. 费多罗娃 $^{1}^{(D)}$ ，奥列格·科拉布列夫 $^{1}^{(D)}$ 、亚历山大·特罗希莫夫斯基 $^{1 (D}$ ， Erdal Yiğit $^{3, 4}$ （D），胡安·阿尔代 $^{5}$ 、Franck Montmessin $^{6}$ （D）和 Paul Hartogh $^{3}$ （四） $^{1}$ 俄罗斯科学院（IKI）空间研究所，俄罗斯莫斯科， $^{2}$ 莫斯科物理与技术学院，俄罗斯多尔戈普鲁德尼， $^{3}$ 马克斯·普朗克太阳系研究所，德国哥廷根， $^{4}$ 乔治梅森大学物理与天文学系，美国弗吉尼亚州费尔法克斯， $^{5}$ 牛津大学物理系，英国牛津， $^{6}$ LATMOS/IPSL，UVSQ Université Paris-Saclay，CNRS，圭扬库尔，法国
$^{1}$ 俄罗斯科学院（IKI）空间研究所，俄罗斯莫斯科， $^{2}$ 莫斯科物理与技术学院，俄罗斯多尔戈普鲁德尼， $^{3}$ 马克斯·普朗克太阳系研究所，德国哥廷根， $^{4}$ 乔治梅森大学物理与天文学系，美国弗吉尼亚州费尔法克斯， $^{5}$ 牛津大学物理系，英国牛津， $^{6}$ LATMOS/IPSL，UVSQ 巴黎-萨克雷大学，CNRS，圭扬库尔，法国

抽象摘要

本文介绍了使用中红外（MIR）光谱仪获得的火星大气中重力波诱导温度扰动的观测结果，该光谱仪是痕量气体轨道飞行器（ACS/TGO）上大气化学套件仪器的一个通道。a 的日掩星测量 ${CO}_{2}$ 吸收带 $2.7 μ m$ 用于检索 20 至 160 公里高度之间的密度和温度剖面，垂直分辨率足以推导出与重力波相关的小尺度结构。已经探索和比较了几种将干扰与背景温度区分开来的技术。已经确定了瞬时温度曲线、波包的振幅和势能。已经估计了水平动量通量和相关的波阻力。分析的数据集包含 144 个剖面，包括火星 34 年下半年从太阳经度进行的测量 $165^{\circ}$ 通过 $355^{\circ}$ .我们在 100-130 公里的中层更压区域观察到增强的重力波消散/破裂。我们的分析表明，波幅和 Brunt-Väisälä 频率之间没有直接相关性。这可能表明对流不稳定性可能不是限制火星中层大气中重力波增长的主要机制。
本文介绍了使用中红外（MIR）光谱仪获得的火星大气中重力波诱导温度扰动的观测结果，该光谱仪是痕量气体轨道飞行器（ACS/TGO）上大气化学套件仪器的一个通道。a 的日掩星测量吸收带用于检索 20 至 160 公里高度之间的密度和温度剖面，垂直分辨率足以推导出与重力波相关的小尺度结构。已经探索和比较了几种将干扰与背景温度区分开来的技术。已经确定了瞬时温度曲线、波包的振幅和势能。已经估计了水平动量通量和相关的波阻力。分析的数据集包含 144 个剖面，包括火星 34 年下半年从太阳经度进行的测量通过。我们在 100-130 公里的中层更压区域观察到增强的重力波消散/破裂。我们的分析表明，波幅和 Brunt-Väisälä 频率之间没有直接相关性。这可能表明对流不稳定性可能不是限制火星中层大气中重力波增长的主要机制。

通俗易懂总结低层大气来源的引力波（GW）不断扰乱火星大气。在向上传播的过程中，它们的振幅增加，最终 GW 分解或消散。沉积的动量和能量是驱动 100 公里以上热层环流的主要机制。由于 GW 的空间尺度相对较小，因此难以测量。ExoMars 痕量气体轨道飞行器上的大气化学套件（ACS）仪器允许提取从对流层到热层（

20 - 160 km

）垂直分辨率高，约 2 公里。该仪器测量被大气掩蔽的太阳光谱，二氧化碳吸收处于中间红外波长范围内。这些观测提供了 GW 活动及其在火星上的特征的纬度和季节覆盖范围。我们的结果允许对模型预测进行首次观测验证，量化 GW 的动力学效应并限制火星一般环流模型。
通俗易懂总结低层大气来源的引力波（GW）不断扰乱火星大气。在向上传播的过程中，它们的振幅增加，最终 GW 分解或消散。沉积的动量和能量是驱动 100 公里以上热层环流的主要机制。由于 GW 的空间尺度相对较小，因此难以测量。ExoMars 痕量气体轨道飞行器上的大气化学套件（ACS）仪器允许提取从对流层到热层（）垂直分辨率高，约 2 公里。该仪器测量被大气掩蔽的太阳光谱，二氧化碳吸收处于中间红外波长范围内。这些观测提供了 GW 活动及其在火星上的特征的纬度和季节覆盖范围。我们的结果允许对模型预测进行首次观测验证，量化 GW 的动力学效应并限制火星一般环流模型。

1. 引言

行星大气的结构和环流受到引力波（GW）的强烈影响，引力波在任何对流稳定的大气中都无处不在。它们主要负责从低层大气到高层大气的能量和动量传递。历史上，GW诱导的耦合在地球大气中被广泛研究（例如，参见Fritts和Alexander的评论，2003年;Yiğit & Medvedev， 2015）。随着太空探索的进步，火星大气已成为研究第二好的例子。伴随着数值建模的大量太空任务为火星上 GW 的重要性提供了充分的证据。Medvedev 和 Yiğit （2019）最近的评论总结了一些火星 GW 效应，它们与地球上的共性和具体性。对火星上 GW 活动的观测知识至关重要，但仍然不足以量化其影响和限制火星一般环流模型（MGCM）。我们的论文通过使用高分辨率来解决这个问题
行星大气的结构和环流受到引力波（GW）的强烈影响，引力波在任何对流稳定的大气中都无处不在。它们主要负责从低层大气到高层大气的能量和动量传递。历史上，GW 诱导的耦合在地球大气中被广泛研究（例如，参见 Fritts 和 Alexander 的评论，2003 年；Yiğit & Medvedev，2015）。随着太空探索的进步，火星大气已成为研究第二好的例子。伴随着数值建模的大量太空任务为火星上 GW 的重要性提供了充分的证据。Medvedev 和 Yiğit（2019）最近的评论总结了一些火星 GW 效应，它们与地球上的共性和具体性。对火星上 GW 活动的观测知识至关重要，但仍然不足以量化其影响和限制火星一般环流模型（MGCM）。我们的论文通过使用高分辨率来解决这个问题。

资源：Denis A. Belyaev、Oleg I. Korablev 软件：Ekaterina D. Starichenko 监督：Denis A. Belyaev、Oleg I. Korablev
验证：Ekaterina D. Starichenko、Anna A. Fedorova、Juan Alday 可视化：Ekaterina D.
Starichenko 写作 - 原始草稿：Ekaterina D. Starichenko、Denis A. Belyaev、Alexander S. Medvedev、Oleg I. Korablev
写作 - 审查和编辑：叶卡捷琳娜D. 斯塔里琴科，丹尼斯· A·别利亚耶夫，亚历山大· S·梅德韦杰夫，安娜· A·费多罗娃，奥列格· I. 科拉布列夫，亚历山大·特罗希莫夫斯基，埃尔达尔·伊伊特，胡安·阿尔代，弗兰克·蒙梅辛，保罗·哈托格从微量气体轨道器（TGO）上的大气化学套件（ACS）仪器获取的掩星数据。
写作 - 审查和编辑：叶卡捷琳娜 D. 斯塔里琴科，丹尼斯· A·别利亚耶夫，亚历山大· S·梅德韦杰夫，安娜· A·费多罗娃，奥列格· I. 科拉布列夫，亚历山大·特罗希莫夫斯基，埃尔达尔·伊伊特，胡安·阿尔代，弗兰克·蒙梅辛，保罗·哈托格从微量气体轨道器（TGO）上的大气化学套件（ACS）仪器获取的掩星数据。
火星 GW 的观测是通过不同的遥感技术和原位方法从轨道飞行器进行的。在空气制动操作期间，包括火星全球勘测者（MGS，火星奥德赛（ODY，火星侦察轨道器（MRO，火星大气和挥发物演化器（MAVEN）和微量气体轨道器（TGO）（Creasey，Forbes，& Keating），2006年）在热层中用加速度计进行了GW诱导的密度波动的原位测量，这些航天器包括火星全球勘测者（MGS，火星奥德赛（ODY，火星侦测轨道器（MRO）火星大气和挥发物演化物（MAVEN）和微量气体轨道器（TGO）（Creasey，Forbes和Keating），2006年;Fritts et al.， 2006;Jesch等人，2019 年;Keating et al.， 1998;Siddle et al.， 2020;Tolson 等人，2005 年、2008 年;Vals等人，2019 年;Withers，2006 年）。上层热层中的GWs也通过MAVEN上的中性气体和离子质谱仪（NGIMS）测量（England等人，2017;Terada等人，2017 年;Yiğit et al.， 2015）。与GWs相关的温度和密度干扰已经从恒星、太阳和射电掩星数据以及肢体观测中远程检索（Ando et al.， 2012;Creasey， Forbes， & Hinson， 2006;Heavens et al.， 2020;Hinson 等人，1999 年;Nakagawa等人，2020 年;Wright，2012 年）。
火星 GW 的观测是通过不同的遥感技术和原位方法从轨道飞行器进行的。在空气制动操作期间，包括火星全球勘测者（MGS）、火星奥德赛（ODY）、火星侦察轨道器（MRO）、火星大气和挥发物演化器（MAVEN）和微量气体轨道器（TGO）（Creasey，Forbes，& Keating，2006 年）在热层中用加速度计进行了 GW 诱导的密度波动的原位测量，这些航天器包括火星全球勘测者（MGS）、火星奥德赛（ODY）、火星侦测轨道器（MRO）、火星大气和挥发物演化物（MAVEN）和微量气体轨道器（TGO）（Creasey，Forbes 和 Keating，2006 年；Fritts et al.，2006；Jesch 等人，2019 年；Keating et al.，1998；Siddle et al.，2020；Tolson 等人，2005 年、2008 年；Vals 等人，2019 年；Withers，2006 年）。上层热层中的 GWs 也通过 MAVEN 上的中性气体和离子质谱仪（NGIMS）测量（England 等人，2017；Terada 等人，2017 年；Yiğit et al.，2015）。与 GWs 相关的温度和密度干扰已经从恒星、太阳和射电掩星数据以及肢体观测中远程检索（Ando et al.，2012；Creasey，Forbes，& Hinson，2006；Heavens et al.，2020；Hinson 等人，1999 年；Nakagawa 等人，2020 年；Wright，2012 年）。
以前许多 GW 观测技术的缺点是高度覆盖范围有限。例如，原位测量局限于热层中相对狭窄的垂直范围，而无线电掩星和红外肢体探测允许研究最低层（

0 - 40 km

）部分。紫外线遥感允许扩展高度覆盖范围。火星快车（MEX）上的火星大气特性研究光谱学（SPICAM）仪器测量了 60 至 130 公里之间的温度和密度分布（Forget 等人，2009 年）。MAVEN 上的成像紫外线光谱仪（IUVS）探索了热球层（100150 公里）（Gröller等人，2018 年;Medvedev et al.， 2016）。最近，Nakagawa 等人（2020 年）从 IUVS 数据中获得了温度曲线，数据范围从 20 公里到 140 公里不等，垂直采样优于 6 公里。ACS/TGO 是第一台允许在太阳掩星模式下测量更广泛高度范围（20-160 km）内温度和密度分布的红外仪器。自 2018 年 4 月以来，ACS 的三台光谱仪之一的中红外（MIR）光谱仪提供了数百张剖面图，其中一些具有垂直分辨率，可用于研究 GW。
以前许多 GW 观测技术的缺点是高度覆盖范围有限。例如，原位测量局限于热层中相对狭窄的垂直范围，而无线电掩星和红外肢体探测允许研究最低层（

0 - 40 km

）部分。紫外线遥感允许扩展高度覆盖范围。火星快车（MEX）上的火星大气特性研究光谱学（SPICAM）仪器测量了 60 至 130 公里之间的温度和密度分布（Forget 等人，2009 年）。MAVEN 上的成像紫外线光谱仪（IUVS）探索了热球层（100150 公里）（Gröller 等人，2018 年;Medvedev et al.， 2016）。最近，Nakagawa 等人（2020 年）从 IUVS 数据中获得了温度曲线，数据范围从 20 公里到 140 公里不等，垂直采样优于 6 公里。ACS/TGO 是第一台允许在太阳掩星模式下测量更广泛高度范围（20-160 km）内温度和密度分布的红外仪器。自 2018 年 4 月以来，ACS 的三台光谱仪之一的中红外（MIR）光谱仪提供了数百张剖面图，其中一些具有垂直分辨率，可用于研究 GW。

必须首先将较小尺度的 GW 引起的温度扰动与大尺度变化相关的背景温度场分开。尽管该程序在地球和火星环境中经常进行，但没有通用的技术可以应用于从不同仪器获得的垂直剖面（Ehard等人，2015 年）。在这项工作中，我们探讨了从 ACS MIR 数据中提取 GW 的几种方法的敏感性，并描述了它们从第一组可用的 ACS/TGO 数据中得出 GW 场的各种特性（振幅、波势能、动量通量和波阻力）的应用。
必须首先将较小尺度的 GW 引起的温度扰动与大尺度变化相关的背景温度场分开。尽管该程序在地球和火星环境中经常进行，但没有通用的技术可以应用于从不同仪器获得的垂直剖面（Ehard 等人，2015 年）。在这项工作中，我们探讨了从 ACS MIR 数据中提取 GW 的几种方法的敏感性，并描述了它们从第一组可用的 ACS/TGO 数据中得出 GW 场的各种特性（振幅、波势能、动量通量和波阻力）的应用。

论文的结构如下。第 2 节概述了 ACS/TGO 实验和仪器本身。第 3 节描述了本研究中使用的方法。特别是，第 3.1 节介绍了从测量光谱中检索温度曲线，提取波干扰的技术在第 3.2 节中给出。第 3.3 节描述了波活动（波包的振幅）和势能的推导，第 3.4 节概述了水平动量的绝对垂直通量和平均流的动量强迫的计算。结果在第 4 节中介绍。它们包括一个案例研究（4.1）、波特性的空间分布（4.2）以及波幅与 Brunt-Väisälä 频率之间的关系（4.3）。结论在第 5 节中给出。

2. Atmospheric Chemistry Suite 机载痕量气体 Orbiter 仪器
2. 大气化学套件机载痕量气体 Orbiter 仪器

ACS 是一组三台红外光谱仪，用于 ExoMars 2016 TGO 任务。自 2018 年 4 月以来，它一直在火星轨道上运行。ACS 由近（NIR）、中（MIR）和热红外（TIRVIM）通道组成，它们共同覆盖了

0.7 - 17 μ m

（Korablev et al.， 2018）。在本文中，我们使用从在太阳掩星模式下工作的交叉色散中阶梯光栅 MIR 光谱仪检索到的数据。

2.3 - 4.2 μ m

范围。这种光谱覆盖是通过二次色散光栅实现的，该光栅可以旋转到 12 个位置之一。在掩星过程中，仪器指向太阳。每次测量都包含一个位于

640 \times 512

像素焦平面阵列（FPA），可容纳多达 20 个通过次光栅在 FPA 上分散的衍射级。1 次掩星

Figure 1. Spectroscopy of

{CO}_{2}

and

H_{2} O

absorption in the diffraction order #223 of ACS-MIR (panel A) and an example of retrieved atmospheric temperature and density vertical profiles (panel B). (a) Transmission spectra measured at tangent altitudes of 150, 90 and 29 km (red dots) on a background of the best-fitted models (black solid lines); (b) Vertical profiles of temperature (left) and atmospheric number density (right) derived from the MCD (black dashed line), from ACS-MIR (red dots), and from ACS-NIR (Fedorova et al., 2020) (green dots). Error bars for the temperature values express 1-

σ

uncertainties of the retrievals.
图 1. ACS-MIR 的衍射级数#223 中

{CO}_{2}

和

H_{2} O

的光谱吸收（面板 A）以及检索的大气温度和密度垂直剖面的示例（面板 B）。(a) 在 150、90 和 29 公里的切线高度测得的传输光谱（红点），背景为最佳拟合模型（黑色实线）；(b) 从 MCD（黑色虚线）、ACS-MIR（红点）和 ACS-NIR（Fedorova 等，2020）（绿色点）得出的温度（左）和大气数密度（右）的垂直剖面。温度值的误差条表示检索的 1-

σ

不确定性。
covers

0.15 - 0.3 μ m

range. The instrument’s resolving power is

λ / Δ λ \sim 25, 000

and the signal-to-noise ratio varies between 1,000 and 10,000. The vertical resolution of MIR depends on the integration time (

\sim 2 s

per image) and ranges from 0.5 to 2.5 km . The transmission is obtained by division of the solar spectrum passed through the atmosphere to the reference one, which is measured above the altitude of 200 km , where the absorption by the atmosphere is negligible.
覆盖

0.15 - 0.3 μ m

范围。仪器的分辨率为

λ / Δ λ \sim 25, 000

，信噪比在 1,000 到 10,000 之间变化。MIR 的垂直分辨率取决于积分时间（

\sim 2 s

每幅图像）并在 0.5 到 2.5 公里之间变化。传输是通过将穿过大气的太阳光谱与在 200 公里以上测量的参考光谱进行除法获得的，在该高度，大气的吸收可以忽略不计。

In this study, we use the

2.66 - 2.68 μ m

portion of the spectrum from the grating position #4, the echelle diffraction order #223, which includes a wing of the

2.7 μ m {CO}_{2}

absorption band (Figure 1a).
在本研究中，我们使用来自光栅位置#4 的

2.66 - 2.68 μ m

光谱部分，埃谢尔衍射级数#223，其中包括

2.7 μ m {CO}_{2}

吸收带的一部分（图 1a）。
Strong absorption lines of

{CO}_{2}

allow for retrieving temperature and density in the Martian atmosphere with good sensitivity.
强吸收线的

{CO}_{2}

允许以良好的灵敏度获取火星大气中的温度和密度。

3. Methods 3. 方法

3.1. Retrieval of Temperature Profiles
3.1. 温度剖面的检索

The retrieval scheme consists of several iterations. On the first step, we retrieve temperature and pressure from the rotational structure of

{CO}_{2}

absorption bands in spectral intervals without

H_{2} O

lines (see Figure 1a). A priori altitude profiles of

T (z)

and

p (z)

as well as one of the

{CO}_{2} VMR

, are taken from the Mars Climate Database (MCD) for a specified occultation in MY34 (Millour et al., 2018). On the second step, we simultaneously retrieve temperature and

{CO}_{2}

concentration, while the pressure profile is kept constant assuming the hydrostatic equilibrium

p_{h y d} (z) = p_{0} (z_{0}) \exp [- \int_{z_{0}}^{z} \frac{g (z^{'}) M (z^{'})}{R T (z^{'})} d z^{'}]

, where

g

is the acceleration of gravity,

M

is the atmospheric molar mass and

R

is the gas constant. The reference pressure

p_{0}

is chosen at an altitude

z_{0}

, usually around

30 - 50 km

, where uncertainties of the fitting are smallest. We repeat the second step 5-7 times until the profiles reach convergence. In each iteration, we apply the Tikhonov regularization (Tikhonov & Arsenin, 1977) for the temperature and concentration altitude profiles with a smoothing coefficient less than 5 km . It defines the shortest wavelength to

5 - 6 km

when analyzing vertical wavy structures. The third step focuses only on

{CO}_{2}

and

H_{2} O

concentration retrievals over the entire wavenumber range in
检索方案由几个迭代组成。在第一步中，我们从

{CO}_{2}

吸收带的旋转结构中检索温度和压力，光谱区间内没有

H_{2} O

线（见图 1a）。

T (z)

和

p (z)

的先验高度剖面以及

{CO}_{2} VMR

之一，均取自火星气候数据库（MCD），用于指定的 MY34（Millour 等，2018）掩蔽。在第二步中，我们同时检索温度和

{CO}_{2}

浓度，同时保持压力剖面不变，假设静水平衡

p_{h y d} (z) = p_{0} (z_{0}) \exp [- \int_{z_{0}}^{z} \frac{g (z^{'}) M (z^{'})}{R T (z^{'})} d z^{'}]

，其中

g

是重力加速度，

M

是大气摩尔质量，

R

是气体常数。参考压力

p_{0}

选择在高度

z_{0}

，通常在

30 - 50 km

附近，此时拟合的不确定性最小。我们重复第二步 5-7 次，直到剖面达到收敛。在每次迭代中，我们对温度和浓度高度剖面应用 Tikhonov 正则化（Tikhonov & Arsenin，1977），平滑系数小于 5 公里。它定义了在分析垂直波状结构时的最短波长

5 - 6 km

。第三步仅关注整个波数范围内的

{CO}_{2}

和

H_{2} O

浓度检索
order #223 (Figure 1a) using the

p (z)

and

T (z)

profiles already found. This step is not a subject of the present paper.
订单 #223 (图 1a) 使用已找到的

p (z)

和

T (z)

配置文件。此步骤不是本论文的主题。

A similar fitting procedure, including the hydrostatic approximation, has been used in the work by Fedorova et al. (2020) (proprietary code) and Alday et al. (2019) (the NEMESIS code (Irwin et al., 2008),) in their retrievals of temperature and pressure from the ACS data. We validated our atmospheric temperature and number density profiles with simultaneous and collocated occultation measurements by ACS-NIR (Fedorova et al., 2020). An example comparison is presented in Figure 1b. A weaker

{CO}_{2}

absorption band at 1.58

μ m

measured by NIR allows for detection up to

110 - 120 km

, or the density of

\sim 10^{12} {cm}^{- 3}

, while the band at

2.7 μ m

observed by MIR is measurable up to

160 - 170 km

, or

\sim 10^{9} {cm}^{- 3}

. The lowermost altitude of the temperature profile retrieval is conditioned by the aerosol opacity and by the saturation of the

{CO}_{2}

absorption lines.
一种类似的拟合程序，包括静水近似，已在 Fedorova 等人（2020 年）（专有代码）和 Alday 等人（2019 年）（NEMESIS 代码（Irwin 等，2008 年））的工作中使用，用于从 ACS 数据中提取温度和压力。我们通过 ACS-NIR 的同时和重叠的掩星测量（Fedorova 等，2020 年）验证了我们的气温和数密度剖面。图 1b 中展示了一个比较示例。NIR 测得的 1.58 的较弱吸收带允许检测到高达

110 - 120 km

，或

\sim 10^{12} {cm}^{- 3}

的密度，而 MIR 观察到的

2.7 μ m

的带可测量高达

160 - 170 km

，或

\sim 10^{9} {cm}^{- 3}

。温度剖面提取的最低高度受气溶胶不透明度和

{CO}_{2}

吸收线的饱和度的限制。

Each temperature value in a vertical profile was retrieved by fitting a modeled transmission spectrum

J_{mod}

to the measured one

J_{mes}

at a specified altitude. We model the spectra by the Beer-Lambert law
每个垂直剖面中的温度值是通过将模型传输光谱拟合到指定高度的测量光谱中获取的。我们通过比尔-朗伯定律对光谱进行建模。

J_{mod} (v, z) = \exp [- \int (σ_{CO 2} (T, p) n_{CO 2} (z^{'}) + σ_{H 2 O} (T, p) n_{H 2 O} (z^{'}) + τ_{a}) d z^{'}]

where

n (z)

are gaseous concentrations,

σ (T, p)

are absorption cross-sections of

{CO}_{2}

and

H_{2} O

correspondingly for specific temperature

T (z)

and pressure

p (z)

at an altitude

z

, and

τ_{a}

is aerosol slant opacity. A transfer between the linear

[{cm}^{- 2}]

and the volume

[{cm}^{- 3}]

concentrations is performed using the well-known “onion-peeling” method with the numeric integration over all altitude layers

z_{i}

above the

i

th one. Molecular cross-sections are calculated line-by-line on a basis of the HITRAN2016 database (Gordon et al., 2017) considering pressure-broadening coefficients of the

H_{2} O

lines suitable for a

{CO}_{2}

-rich atmosphere ( Ga mache et al., 2016) and self-broadening in the case of

{CO}_{2}

. Then we convolve the modeled spectrum by the previously determined instrument line shape (ILS) using wavenumber calibrations (see details in Alday et al., 2019). The fitting procedure is conducted by minimizing the “chi-square” function

χ^{2} = \sum_{i} A^{2} (v_{i})

A (v_{i}) = [J_{mod} (v_{i}) - J_{mes} (v_{i})] / δ J

, where

δ J

are transmittance uncertainties, and the sum is taken over all considered spectral points (pixels). Our optimization algorithm to search for the

χ^{2}

minimum is based on partial derivatives of the Jacobian matrix

\partial A / \partial X

(Marquardt, 1963), where

X

is a vector of free parameters, that is, temperature,

{CO}_{2}

concentration,

H_{2} O

mixing ratio, and aerosol slant opacity. Here, a significant contribution to the Jacobian comes from the rotational absorption lines, which are strongly sensitive to the temperature variability in the spectral range of interest.
其中

n (z)

是气体浓度，

σ (T, p)

是

{CO}_{2}

的吸收截面，

H_{2} O

对应于特定温度

T (z)

和压力

p (z)

在一个高度

z

，并且

τ_{a}

是气溶胶斜率不透明度。通过使用著名的“洋葱剥皮”方法，利用数值积分在所有高度层

[{cm}^{- 2}]

之上进行线性

[{cm}^{- 3}]

和体积

z_{i}

浓度之间的转换

i

。分子截面是基于 HITRAN2016 数据库（Gordon 等，2017）逐行计算的，考虑了适合

H_{2} O

的

{CO}_{2}

-富气氛的压力展宽系数（Ga mache 等，2016）以及在

{CO}_{2}

的情况下的自展宽。然后，我们通过先前确定的仪器线形（ILS）对建模的光谱进行卷积，使用波数校准（详见 Alday 等，2019）。拟合过程是通过最小化“卡方”函数进行的，其中是透射不确定性，求和是在所有考虑的光谱点（像素）上进行的。我们搜索最小值的优化算法基于雅可比矩阵的偏导数，其中是自由参数的向量，即温度、浓度、混合比和气溶胶斜率不透明度。在这里，雅可比矩阵的一个重要贡献来自于旋转吸收线，这些吸收线对感兴趣光谱范围内的温度变化非常敏感。

3.2. Derivation of Wave Disturbances
3.2. 波动扰动的推导

Gravity wave-induced perturbations of temperature

T^{'}

are sought by separating the mean, or background profile

\bar{T} (z)

from the measured one

T (z)

:
重力波引起的温度扰动

T^{'}

通过将平均值或背景剖面

\bar{T} (z)

与测量值分离来寻找

T (z)

：

T^{'} = T - \bar{T},

where the bar denotes an appropriate averaging. Generally, it implies averaging over wave phases, or spatial and temporal scales that are larger than the periods and wavelengths of contributing GW harmonics. In the case of almost instantaneous (with respect to the periods of GWs) occultation profiles, only separation in vertical scales is possible.
其中的条形表示适当的平均。一般来说，这意味着在波相位或空间和时间尺度上进行平均，这些尺度大于贡献的重力波谐波的周期和波长。在几乎瞬时（相对于重力波的周期）遮蔽轮廓的情况下，仅可能在垂直尺度上进行分离。

John and Kumar (2013) and Ehard et al. (2015) reviewed several common methods of the partition of measured temperature and/or density profiles into the “mean” and wave components. They work well if a clear separation in vertical wavelengths does exist between GWs and large-scale motions belonging to the background. This is not always the case in the Martian atmosphere, because vertical scales of disturbances associated with tides, planetary waves, and other motions may overlap with those due to GWs. It is desirable to retain the former in the background, but one still has to set a vertical scale

Λ_{z}

that separates GWs from the larger-scale features. In the following, we assumed

Λ_{z} = 30 km

. This value may lead to an overestimation of the retrieved wave activity by including non-GW perturbations, but at least no large-scale GW components are missed. Concerning the short-wavelength part of the spectrum, the limited vertical resolution favors detection of larger-scale waves, leaving out harmonics with smaller scales unobserved. Alexander (1998)
约翰和库马尔（2013）以及埃哈德等人（2015）回顾了几种将测量的温度和/或密度剖面划分为“均值”和波动成分的常见方法。如果存在 GWs 与属于背景的大尺度运动之间的清晰垂直波长分离，它们的效果很好。但在火星大气中，这种情况并不总是成立，因为与潮汐、行星波和其他运动相关的扰动的垂直尺度可能与 GWs 的尺度重叠。希望在背景中保留前者，但仍然需要设定一个垂直尺度

Λ_{z}

，以将 GWs 与更大尺度特征分开。在接下来的部分中，我们假设

Λ_{z} = 30 km

。这个值可能会导致通过包括非 GW 扰动而高估检索到的波动活动，但至少不会遗漏大型 GW 成分。关于光谱的短波长部分，有限的垂直分辨率有利于检测更大尺度的波动，未观察到较小尺度的谐波。亚历山大（1998）

Figure 2. Separation of the observed temperature into the mean and wave components for two characteristic profiles: dominated by large vertical-scale (orbit 2892n1, upper row) and small-scale disturbances (orbit 3251n1, lower row). Left column is for the mean temperature

\bar{T} (z)

, the right one is for the relative perturbations

T^{'} (z) / \bar{T} (z)

(in percent). The legend describes the applied methods. Red dashed lines correspond to the Fourier decomposition, green and yellow lines are for the sliding polynomial fit with

2 - km

and 11-km shift steps, correspondingly, and the blue lines are for the 7-th order polynomial fit. The observed temperature profiles are given with the solid black lines. Shaded area denotes the uncertainty of the measurements.
图 2. 将观测温度分离为均值和波动分量的两个特征剖面：由大垂直尺度（轨道 2892n1，上排）和小尺度扰动（轨道 3251n1，下排）主导。左列为均温

\bar{T} (z)

，右列为相对扰动

T^{'} (z) / \bar{T} (z)

（以百分比表示）。图例描述了所应用的方法。红色虚线对应于傅里叶分解，绿色和黄色线分别为滑动多项式拟合，步长为

2 - km

和 11 公里，蓝色线为 7 阶多项式拟合。观测温度剖面用实线黑色表示。阴影区域表示测量的不确定性。
has quantified this “observational filter” and pointed out that some large-scale harmonics refracted by the mean wind beyond the lowest resolution may be missing in observations as well.
已经量化了这种“观察滤波器”，并指出一些被平均风折射的超出最低分辨率的大规模谐波在观测中可能也会缺失。

We explore three methods: spectral filtering, sliding least-square polynomial fit and high-order polynomial fit. The former two have been discussed in relation to lidar and space-based measurements in the atmosphere of Earth (Ehard et al., 2015; John & Kumar, 2013, and the references therein), while the latter was applied to profiles obtained in the terrestrial (e.g., Spiga et al., 2008) and Martian atmosphere (Jesch et al., 2019; Terada et al., 2017; Yiğit et al., 2015). Since the ACS data are distributed irregularly over the altitude, they were first interpolated (oversampled) to an evenly spaced

500 - m

grid. We used only the temperature data with errors

\leq 10 K

. Spectral filtering was performed using Fourier decomposition within sliding 60 - km intervals (

\pm 30 km

around each point), and zero-order Fourier coefficients were used to calculate the background temperature. The examples are shown in Figure 2 for two characteristic profiles

T (z)

. They visibly differ: the profile in Figure 2a (orbit 2892n1) contains large-scale disturbances, while the one in Figure 2c (orbit 3251n1) comprises mostly smaller-scale fluctuations. This method yields smooth mean
我们探讨了三种方法：谱滤波、滑动最小二乘多项式拟合和高阶多项式拟合。前两者已在与激光雷达和地球大气中的空间测量相关的研究中讨论过（Ehard et al., 2015; John & Kumar, 2013，以及其中的参考文献），而后者则应用于在地球（例如，Spiga et al., 2008）和火星大气中获得的剖面（Jesch et al., 2019; Terada et al., 2017; Yiğit et al., 2015）。由于 ACS 数据在高度上分布不规则，因此首先对其进行了插值（过采样），以形成均匀间隔的

500 - m

网格。我们仅使用了误差为

\leq 10 K

的温度数据。谱滤波是通过在滑动 60 公里区间内进行傅里叶分解来执行的（

\pm 30 km

围绕每个点），并使用零阶傅里叶系数计算背景温度。图 2 展示了两个特征剖面的示例

T (z)

。它们明显不同：图 2a（轨道 2892n1）中的剖面包含大规模扰动，而图 2c（轨道 3251n1）中的剖面主要由小规模波动组成。该方法产生平滑的平均值。
temperature profiles and, as a result, large deviations from the mean (Figures 2 b and 2 d ). This is in particular obvious below 60 km and in the upper part of the domain (panels b and d).
温度剖面，因此，与均值存在较大偏差（图 2b 和 2d）。这在 60 公里以下和区域的上部（面板 b 和 d）尤为明显。

For the sliding polynomial fit, we used a procedure described in the work of Whiteway and Carswell (1995). The background profiles are obtained by fitting cubic polynomials within the

60 - km

sliding intervals.

Ob -

servational errors were used as weights that assign a significance to the measurements at each altitude. At first, the intervals were shifted up from the bottom to top by a certain distance (shown in Figures 2a and 2c for 2 and 11 km ), and then the procedure was repeated for the downward shifts starting from the top. The overlapping values of fits from each range were then averaged. Thus obtained profiles were then smoothed using a moving average. At the bottom of the profiles, we had to decrease the width of the sliding windows due to large spurious variations in fitted polynomials and in order to make most of the observational data. The upper and lower 4 km of thus obtained profiles have to be excluded anyway, because of the poor behavior of fitting polynomials, which cannot be averaged with counterparts from other sliding windows. This method occasionally produces disturbances oscillating not around zero. To correct for these numerical biases, we perform detrending by applying the Theil-Sen estimator (Sen, 1968; Theil, 1950) and fitting a linear function to the perturbation profile. The Theil-Sen estimator is a robust method, which is used for determining the linear regression taking the median of the slopes of all lines that can be drawn through the given data set. The linear function is then subtracted from the profile to obtain the corrected temperature.
对于滑动多项式拟合，我们使用了 Whiteway 和 Carswell（1995）工作中描述的程序。背景轮廓是通过在滑动区间内拟合三次多项式获得的。观测误差被用作权重，为每个高度的测量分配重要性。起初，区间从底部向顶部移动一定距离（在图 2a 和 2c 中显示为 2 和 11 公里），然后从顶部开始重复向下移动的过程。然后，将每个范围的拟合重叠值进行平均。这样获得的轮廓随后使用移动平均进行平滑。在轮廓的底部，由于拟合多项式中存在较大的虚假变化，我们必须减小滑动窗口的宽度，以便利用大部分观测数据。由于拟合多项式的表现不佳，上下 4 公里的轮廓必须被排除，因为它们无法与其他滑动窗口的对应值进行平均。该方法偶尔会产生不围绕零波动的干扰。为了纠正这些数值偏差，我们通过应用 Theil-Sen 估计量（Sen, 1968; Theil, 1950）进行去趋势处理，并拟合一个线性函数到扰动轮廓上。Theil-Sen 估计量是一种稳健的方法，用于确定线性回归，取所有可以通过给定数据集绘制的线的斜率的中位数。然后，从轮廓中减去线性函数，以获得校正后的温度。

The results for the sliding polynomial fit are plotted in Figure 2 for the 2 and 11 km shift steps with green and yellow lines, correspondingly. It is seen that they are very close and, thus, the background and disturbances depend on the sliding step to a minor degree. The method shows some useful features in comparison with spectral filtering. The fitted mean curves in the regions of large-scale disturbances (Case 1) follow the observed temperature profiles closer (Figure 2a) and are smoother where small-scale structure dominates (Case 2) (Figure 2c, between 70 and 130 km ). This produces smaller wave amplitudes in Case 1, and reveals more wavy structures in Case 2. Especially plausible results are in the bottom of the profiles, where GWs are expected to have smaller amplitudes (due to larger density).
滑动多项式拟合的结果在图 2 中绘制，2 公里和 11 公里的移动步长分别用绿色和黄色线表示。可以看出，它们非常接近，因此背景和干扰在很小程度上依赖于滑动步长。与光谱滤波相比，该方法显示出一些有用的特征。在大尺度干扰区域（案例 1）中，拟合的平均曲线更接近观察到的温度剖面（图 2a），而在小尺度结构主导的区域（案例 2）（图 2c，70 到 130 公里之间）则更平滑。这在案例 1 中产生了较小的波幅，并在案例 2 中揭示了更多的波动结构。特别可信的结果出现在剖面的底部，预计重力波的幅度较小（由于密度较大）。
We next explored the technique of fitting higher-order polynomials in the entire interval of heights. In particular, the seventh-order polynomial fit, which was previously used for extracting GWs on Mars (Jesch et al., 2019; Yiğit et al., 2015), produces most plausible results. They are presented in Figure 2 with dashed and dotted blue lines. It is immediately seen that thus obtained wave disturbances are in a very good agreement with those derived by the sliding polynomial fit method, especially for profiles containing small-scale features (Figure 2d). For profiles dominated by large-scale perturbations, the agreement is also good in terms of the determined vertical structure of the wave, although the magnitudes are often exaggerated (Figure 2 b ). The weak point of the method is that it occasionally produces spurious disturbances near the edges of the vertical domain with vertical gradients of the mean temperature directed opposite to the measured profiles. After careful consideration of the three methods applied to the available measurements, we selected the sliding third-order polynomial fit as the most appropriate and robust.
我们接下来探讨了在整个高度区间内拟合高阶多项式的技术。特别是，第七阶多项式拟合，之前用于提取火星上的重力波（Jesch et al., 2019; Yiğit et al., 2015），产生了最可信的结果。它们以虚线和点线蓝色线条的形式呈现在图 2 中。可以立即看出，这样获得的波动与通过滑动多项式拟合方法得出的结果非常一致，特别是对于包含小尺度特征的剖面（图 2d）。对于以大尺度扰动为主的剖面，尽管幅度往往被夸大，但在确定波的垂直结构方面也有良好的一致性（图 2b）。该方法的弱点在于，它偶尔会在垂直域的边缘产生虚假扰动，且平均温度的垂直梯度与测量剖面相反。在对三种应用于可用测量的方法进行仔细考虑后，我们选择了滑动三阶多项式拟合作为最合适和稳健的方法。

3.3. Wave Activity and Potential Energy
3.3. 波动活动和潜在能量

The GW field is often characterized by the magnitude of fluctuations

| T^{'} | = {(\overset{―}{T^{' 2}})}^{1 / 2}

and wave potential energy (per unit mass)
GW 场通常以波动的幅度

| T^{'} | = {(\overset{―}{T^{' 2}})}^{1 / 2}

和波动势能（每单位质量）

E_{p} = \frac{1}{2} {(\frac{g}{N})}^{2} \overset{―}{{(\frac{T^{'}}{\bar{T}})}^{2}}

where

N

is the Brunt-Väisäla frequency
哪里

N

是布伦特-维萨拉频率

N = \sqrt{\frac{g}{\bar{T}} (\frac{d \bar{T}}{d z} + \frac{g}{c_{p}})}

g

is the acceleration of gravity and

c_{p}

is the specific heat capacity at constant pressure. The amplitude of the wave packet at a given height |

T^{'} (z) ∣

(hereafter called “wave activity”) represents an envelope of the measured profile

T^{'} (z)

. We calculated it by performing Fourier decomposition in each sliding

60 - km

vertical

g

是重力加速度，

c_{p}

是定压下的比热容。给定高度处波包的振幅 |

T^{'} (z) ∣

（以下简称“波动活动”）表示测量轮廓的包络

T^{'} (z)

。我们通过在每个滑动

60 - km

垂直进行傅里叶分解来计算它。

Figure 3. Wave activity |

T^{'} ∣

(left column) and potential energy (per unit mass, right column) for the same as in Figure 2 representative profiles. Dashed blue lines indicate quantities calculated for the entire spectrum, dashed red lines are for accounting two longest harmonics only. Shaded areas denote observational errors.
图 3. 波动活动 |

T^{'} ∣

（左列）和潜在能量（每单位质量，右列）与图 2 中代表性剖面相同。虚线蓝线表示为整个谱计算的量，虚线红线仅用于考虑两个最长的谐波。阴影区域表示观测误差。
interval and, based on Parceval’s identity, summing up contributions of all harmonics. Examples of thus obtained envelopes and potential energy for the same selected profiles as in Section 3.2 are presented in Figure 3.
基于帕尔塞瓦尔定理的间隔，并汇总所有谐波的贡献。图 3 中展示了与第 3.2 节中选择的相同轮廓所获得的包络和潜在能量的示例。

Blue and red dashed lines denote the quantities calculated from the entire spectrum and by accounting for contributions of only two largest harmonics. It is seen that the neglect of shorter-scale harmonics, as was occasionally done in analyses of satellite observations (e.g., Ern et al., 2004), introduces little error to the estimated GW activity. However, the neglect of short-scale harmonics may lead to a noticeable underestimation of wave potential energy (cf. Figures 3b and 3d).
蓝色和红色虚线表示从整个光谱计算的量，以及仅考虑两个最大谐波的贡献。可以看出，忽略短尺度谐波（如在卫星观测分析中偶尔进行的那样，参见 Ern 等，2004）对估计的重力波活动引入的误差很小。然而，忽略短尺度谐波可能会导致波动势能的明显低估（参见图 3b 和 3d）。

3.4. Momentum Flux and Momentum Deposition
3.4. 动量通量和动量沉积

Another useful characteristic of the GW field is the vertical flux of horizontal momentum, or “momentum flux” for brevity,

F = (F_{x}, F_{y}, 0) = ρ_{0} (\overset{―}{u^{'} w^{'}}, \overset{―}{v^{'} w^{'}}, 0)

, where

ρ_{0}

is the mean density and (

u^{'}, v^{'}, w^{'})

are the components of wave-induced perturbations of wind velocity

u^{'}

along with the two horizontal and the vertical axis, correspondingly. Momentum flux is constant for conservatively propagating waves. Breaking/dissipating GWs deposit their momentum to the mean flow, thus inducing an acceleration or deceleration (depending on the sign) of the horizontal flow.
GW 场的另一个有用特征是水平动量的垂直通量，或简而言之的“动量通量”，

F = (F_{x}, F_{y}, 0) = ρ_{0} (\overset{―}{u^{'} w^{'}}, \overset{―}{v^{'} w^{'}}, 0)

，其中

ρ_{0}

是平均密度，(

u^{'}, v^{'}, w^{'})

是风速波动的分量

u^{'}

，分别沿着两个水平轴和垂直轴。动量通量对于保守传播的波是恒定的。破裂/耗散的重力波将其动量传递给平均流，从而引起水平流的加速或减速（取决于符号）。

(a_{x}, a_{y}) = - \frac{1}{ρ_{0}} \frac{d F}{d z}

The direction of the flux cannot be determined from the occultation measurements, however total (or absolute) momentum fluxes for a harmonic

F_{k, m} = \sqrt{F_{x, k, m}^{2} + F_{y, k, m}^{2}}

can be estimated (e.g., Ern et al., 2004, sect. 4):
通量的方向无法从掩星测量中确定，但可以估计谐波的总（或绝对）动量通量

F_{k, m} = \sqrt{F_{x, k, m}^{2} + F_{y, k, m}^{2}}

（例如，Ern 等，2004 年，第 4 节）：

F_{k, m} = \frac{1}{2} ρ_{0} \frac{k_{h}}{m} {(\frac{g}{N})}^{2} {(\frac{| T_{k, m}^{'} |}{\bar{T}})}^{2},

where

k_{h}

and

m

are the horizontal and vertical wavenumbers, correspondingly, and

| T_{k, m}^{'} |

is the amplitude. The latter two are found from the Fourier decomposition, whereas

k_{h}

cannot be derived from our measurements.
其中

k_{h}

和

m

分别是水平和垂直波数，

| T_{k, m}^{'} |

是振幅。后两个是通过傅里叶分解得到的，而

k_{h}

不能从我们的测量中推导出来。

The total flux

F

is the sum of contributions of individual harmonics

F = \sum_{m} F_{k, m}

. Since the horizontal wavenumber

k_{h}

cannot be obtained from the measurements, it, therefore, serves as a scaling factor for the derived profiles of

F

and momentum forcing (5). The densest atmospheric footprint at a target point in occultation geometry is

400 - 500 km

horizontally, depending on the height. This constrains the upper limit for unresolved wavelengths. In our calculations, we assumed a representative horizontal wavelength

λ_{h} = 2 π / k_{h} = 300 km

, the value typically used in numerical general circulation models (Yiğit et al., 2018), and allowing for more direct comparison with simulations. The results for two representative profiles, same as in Figures 2 and 3, are given in Figure 4.
总通量

F

是各个谐波贡献的总和

F = \sum_{m} F_{k, m}

。由于无法从测量中获得水平波数，因此它作为推导的

F

和动量强迫（5）的缩放因子。目标点在掩蔽几何中的最密集大气足迹是

400 - 500 km

水平的，取决于高度。这限制了未解析波长的上限。在我们的计算中，我们假设一个代表性的水平波长

λ_{h} = 2 π / k_{h} = 300 km

，这是数值一般环流模型中通常使用的值（Yiğit 等，2018），并允许与模拟进行更直接的比较。两个代表性剖面的结果，与图 2 和图 3 相同，见图 4。

To demonstrate the sensitivity of the calculations to the used parameters of the technique, we plotted with different colors the profiles of momentum fluxes (per unit mass)

F / ρ_{0}

and GW momentum deposition, that is, wave drag

a

obtained from the full spectrum and taking account of only two major harmonics. In addition, the results are shown for the interval shifts 2 and 7 km . It is immediately seen that these details play little role, and the calculations of fluxes and wave drag are very robust when the measured temperature profile is dominated by large-scale features (Figure 4, the upper row). It is different for profiles containing smaller vertical-scale disturbances (Figure 4, the lower row): their neglect leads to an underestimation of the fluxes and wave drag, and the smaller vertical shifts reveal finer structure associated with dissipation of individual spectral harmonics.
为了演示计算对所用技术参数的敏感性，我们用不同的颜色绘制了动量通量（每单位质量）和重力波动量沉积，即波阻力的剖面，这些数据是从全谱中获得的，并仅考虑了两个主要谐波。此外，结果显示在 2 公里和 7 公里的间隔变化中。可以立即看出，这些细节作用不大，当测量的温度剖面主要由大尺度特征主导时，通量和波阻力的计算非常稳健（图 4，上排）。对于包含较小垂直尺度扰动的剖面（图 4，下排），情况则不同：忽略它们会导致通量和波阻力的低估，而较小的垂直变化揭示了与单个谱谐波耗散相关的更精细结构。

4. Results and Discussions
4. 结果与讨论

4.1. Case Study 4.1. 案例研究

Spectral analysis of the obtained set of profiles (described in the next subsection) has demonstrated greater contribution of larger-scale disturbances in all cases. However, each individual profile was unique. Two examples with and without small vertical-scale components have been presented above. We next consider a case with a relatively broad spectrum of wave-like perturbations with large amplitudes (about twice as large as those in orbit 3251 n 1 ). The retrieved temperature for the orbit 4926 n 1 along with the fitted background profile are plotted in Figure 5a. The envelope in Figure 5b clearly shows that the amplitude gradually ceases its exponential growth with height and becomes nearly constant above

\sim 110 km

.
所获得的剖面的光谱分析（在下一小节中描述）表明，在所有情况下，大尺度扰动的贡献更大。然而，每个单独的剖面都是独特的。上面展示了两个例子，一个有小的垂直尺度分量，一个没有。接下来，我们考虑一个具有相对宽广波动谱的案例，波动幅度较大（约为轨道 3251 n 1 的两倍）。轨道 4926 n 1 的检索温度以及拟合的背景剖面绘制在图 5a 中。图 5b 中的包络线清楚地显示，幅度随着高度的增加逐渐停止其指数增长，并在

\sim 110 km

.以上几乎保持不变。

The reason for this so-called wave “saturation” can be seen from the behavior of the squared Brunt-Väisälä frequency

N^{2} (z)

(Figure 5c, black).

N^{2}

calculated from the background profiles (Figure 5c) remains relatively constant with height (up to about 120 km ) suggesting convective stability of the mean state.

N^{2}

from the original profiles (see Figure 5c, red-dashed) shows large swings associated with temperature disturbances. Near

110 km, N^{2}

drops almost to zero as the result of the temperature gradient (associated with a large amplitude of the disturbances) approaching the adiabatic lapse rate. Enhanced wave dissipation due to a combination of physical processes (Yiğit et al., 2018) in the vicinity of the convective instability severely limits the GW amplitude, leading to the decrease of the momentum flux above this altitude and peaking of the mean flow acceleration (Figure 5d) at almost

2, 000 m s^{- 1} {sol}^{- 1}

. In the analyzed data set, such large numbers are not common and occur only occasionally. Application of a smaller vertical shift of sliding intervals shows finer structure of the GW momentum flux and drag, but do not significantly modify the magnitudes.
这种所谓的波“饱和”现象的原因可以从平方布伦特-维萨拉频率的行为中看出（图 5c，黑色）。从背景剖面（图 5c）计算得出的频率在高度上保持相对恒定（最高约 120 公里），这表明平均状态的对流稳定性。来自原始剖面（见图 5c，红色虚线）显示出与温度扰动相关的大幅波动。由于温度梯度（与扰动的大幅度相关）接近绝热递减率，几乎降到零。由于物理过程的组合（Yiğit 等，2018）在对流不稳定性附近增强了波的耗散，严重限制了重力波的幅度，导致该高度以上的动量通量减少，并且平均流加速度在几乎达到峰值（图 5d）。在分析的数据集中，这样的大数字并不常见，仅偶尔出现。较小的垂直位移滑动区间的应用显示了重力波动量通量和阻力的更精细结构，但并未显著改变其大小。

Figure 4. Absolute momentum flux (per unit mass) and the momentum forcing for two representative profiles (orbits 2892n1 and 3251n1, upper and lower rows, correspondingly). The legend describes the profiles calculated using the full spectrum and only two major harmonics along with sliding interval steps 2 and 7 km .
图 4. 绝对动量通量（每单位质量）和两个代表性剖面的动量强迫（轨道 2892n1 和 3251n1，上下行，分别）。图例描述了使用全谱和仅使用两个主要谐波计算的剖面，以及滑动间隔步长为 2 和 7 公里。

4.2. Spatial Distribution of Gravity Wave Activity
4.2. 重力波活动的空间分布

In this section, we use the data obtained by the ACS instrument in MY34, at solar longitudes from

L_{s} = 164^{\circ}

354^{\circ}

. The data set contains altogether 144 occultation profiles: 84 in the northern hemisphere and 60 in the southern one. The latitude-solar longitude coverage is shown in Figure 6 with red and blue dots representing morning and evening occultation measurements, correspondingly. The longitudinal orbit coverage was fairly uniform, and is not discussed here.
在本节中，我们使用在 MY34 由 ACS 仪器获得的数据，太阳经度范围从

L_{s} = 164^{\circ}

到

354^{\circ}

。数据集总共包含 144 个掩星剖面：北半球 84 个，南半球 60 个。纬度-太阳经度覆盖范围如图 6 所示，红点和蓝点分别代表早晨和晚上的掩星测量。经度轨道覆盖相当均匀，这里不作讨论。

A significant portion of observations were made during the global dust storm of MY34, which started between

L_{s} = 185^{\circ}

and

190^{\circ}

, attained its maximum around

L_{s} = 220^{\circ}

, and gradually decreased until

L_{s} \approx 290^{\circ}

. A regional storm occurred at the end of MY34 between approximately

L_{s} = 325^{\circ}

and

345^{\circ}

. Figure 7 presents latitude-altitude distribution of the derived GW parameters averaged over the entire period of observations depicted in Figure 6.
在 MY34 全球沙尘暴期间，观察的一个重要部分是在

L_{s} = 185^{\circ}

和

190^{\circ}

之间进行的，达到最大值是在

L_{s} = 220^{\circ}

，并逐渐减少直到

L_{s} \approx 290^{\circ}

。在 MY34 结束时，发生了一场区域性风暴，大约在

L_{s} = 325^{\circ}

和

345^{\circ}

之间。图 7 展示了在图 6 所示的整个观察期间平均的派生 GW 参数的纬度-高度分布。

It shows that the mean amplitude of GW-induced temperature fluctuations (

| T^{'} |

, Figure 7a) grows with height reaching up to

\sim 10 K

near the top of the domain. At higher altitudes (

170 - 220 km

), the in situ measurements with Neutral Gas and Ion Mass Spectrometer (NGIMS) on board MAVEN revealed even larger GW magnitudes over the same time (Leelavathi et al., 2020; Yiğit et al., 2021). The latitudinal structure of the GW activity in the mesosphere and lower thermosphere is not uniform. For comparison, we overplotted the zonal wind simulated with the Max Planck Institute (MAOAM) MGCM https://mars.mipt.ru/ for
这表明 GW 引起的温度波动的平均幅度（

| T^{'} |

，图 7a）随着高度的增加而增长，达到

\sim 10 K

，接近区域的顶部。在更高的高度（

170 - 220 km

），搭载在 MAVEN 上的中性气体和离子质谱仪（NGIMS）的原位测量显示，在相同时间内 GW 的幅度甚至更大（Leelavathi 等，2020；Yiğit 等，2021）。中层大气和下热层中 GW 活动的纬向结构并不均匀。为了比较，我们叠加了由马克斯·普朗克研究所（MAOAM）MGCM 模拟的纬向风https://mars.mipt.ru/。

ADVANCING EARTH 推进地球

Figure 5. Vertical profiles for the orbit 4926n1. (a) The measured (solid black) and fitted mean temperature (red dashed); (b) wave temperature disturbance (solid black) and envelope (red dashed); © Brunt-Väisälä frequency calculated for the mean (black) and net temperature (red dashed); (d) momentum flux calculated using 2- and 7-km sliding window shifts (bottom axis, red dashed and solid black lines, correspondingly, and mean flow acceleration (“wave drag,” upper axis, yellow dashed and solid blue for the 2- and 7-km steps, respectively). Shading denote observational uncertainties.
图 5. 轨道 4926n1 的垂直剖面。(a) 测量的（实线黑色）和拟合的平均温度（红色虚线）；(b) 波动温度扰动（实线黑色）和包络线（红色虚线）；(c) 计算的布伦特-维萨拉频率，针对平均（黑色）和净温度（红色虚线）；(d) 使用 2 公里和 7 公里滑动窗口偏移计算的动量通量（底部坐标轴，红色虚线和实线黑色线，分别对应，平均流加速度（“波阻力”，上部坐标轴，黄色虚线和实线蓝色，分别对应于 2 公里和 7 公里步骤）。阴影表示观测不确定性。

MY34 and averaged over the same interval of

L_{s}

as in the observations. The wind distribution varied during this time from the equinoctial to solstitial and back to the equinoctial types. The result reflects the largest contribution of the prograde and retrograde jets during the perihelion solstice. It is seen that the regions with large wave amplitudes encircle the upper edges of two midlatitude jets. This is the result of intensive filtering of individual harmonics by strong background winds. For the wave potential energy, which is a quadratic function of wave amplitudes, this pattern is even more obvious (Figure 7b).
MY34 和在观察中相同时间间隔的平均值。此期间的风分布从春分型变化到夏至型，再回到春分型。结果反映了在近日点夏至期间，顺行和逆行喷流的最大贡献。可以看到，大波幅区域环绕着两个中纬度喷流的上缘。这是强背景风对个别谐波进行强烈过滤的结果。对于波动势能，它是波幅的二次函数，这种模式更加明显（图 7b）。

Figure 7 c shows that GW momentum fluxes reach local maxima near the mesopause (

100 - 125 km

) giving evidence of very intensive wave breakdown/dissipation in this region. The peaks of the associated momentum deposition approximately coincide (Figure 7d). They too wrap around the edges of the jets in the middle atmosphere. It is noteworthy that such distribution of the GW drag is
图 7c 显示，重力波动量通量在中间大气的中层边缘附近达到局部最大值（

100 - 125 km

），这表明该区域存在非常强烈的波动破裂/耗散。相关动量沉积的峰值大致重合（图 7d）。它们也环绕在中层大气的喷流边缘。值得注意的是，重力波阻力的这种分布是

Figure 6. Latitude-solar longitude (

L_{s}

) distribution of the ACS MIR occultation profiles used in this study. Morning and evening measurements are shown in red and blue, correspondingly.
图 6. 本研究中使用的 ACS MIR 掩蔽剖面的纬度-太阳经度（

L_{s}

）分布。早晨和晚上的测量分别用红色和蓝色表示。
very similar to that predicted by a Martian GCM (Medvedev et al., 2011, Figures 3 and 7) for the solstice and equinox, respectively, and represents the first (to the best of our knowledge) observational validation of the model predictions. The magnitudes of the GW drag, although defined up to the constant

k_{h}

, agree with the simulations (using a similar

k_{h}

) as well.
与火星 GCM（Medvedev 等，2011 年，图 3 和图 7）对至日和春分的预测非常相似，并且代表了我们所知的模型预测的首次观测验证。GW 拖曳的大小，尽管定义为常数

k_{h}

，也与模拟结果（使用类似的

k_{h}

）一致。

4.3. Amplitude Dependence on Mean Temperature and BruntVäisälä Frequency
4.3. 振幅对平均温度和布伦特-维萨拉频率的依赖

In situ measurements with NGIMS on board MAVEN showed a clear anti-correlation between relative density fluctuations in the upper thermosphere and the ambient temperature (England et al., 2017; Terada et al., 2017; Vals et al., 2019; Yiğit et al., 2015). It was linked to convective instability as a dominant mechanism that limits growth of GW
在 MAVEN 上搭载的 NGIMS 进行的原位测量显示，上层热层中相对密度波动与环境温度之间存在明显的反相关关系（England 等，2017；Terada 等，2017；Vals 等，2019；Yiğit 等，2015）。这与对流不稳定性相关，作为限制重力波增长的主要机制。

Figure 7. Latitude-altitude cross-sections of the retrieved GW (a) amplitudes (in K), (b) potential energy (per unit mass), © vertical fluxes of absolute horizontal momentum (per unit mass) and (d) associated momentum forcing ( GW drag). The size of the employed latitudinal bins is

10^{\circ}

. Contour lines present the zonal wind (in

m s^{- 1}

) simulated with the MAOAM MGCM for MY34 (https://mars.mipt.ru/data.php) and averaged over the same as in Figure 7 period of observations.
图 7. 检索到的重力波的纬度-高度横截面 (a) 振幅 (以 K 为单位)，(b) 潜在能量 (每单位质量)，(c) 绝对水平动量的垂直通量 (每单位质量) 和 (d) 相关动量强迫 (重力波阻力)。所用的纬度区间大小为

10^{\circ}

。等高线表示使用 MAOAM MGCM 模拟的 MY34 的纬向风 (以

m s^{- 1}

为单位)，并在与图 7 相同的观测期内取平均。
amplitudes with height (wave saturation). The arguments were based on the relation for a single harmonic (e.g., Fritts et al., 1988; Equation 6)
幅度与高度（波饱和度）。论点基于单一谐波的关系（例如，Fritts 等，1988；方程 6）

\frac{| T^{'} |}{\bar{T}} = \frac{| u^{'} |}{| c - \bar{u} |} \frac{N^{2}}{m g}

where

| u^{'} |

is the amplitude of fluctuations of horizontal velocity in the wave,

c

is its horizontal phase velocity and

\bar{u}

is the background wind. When

| u^{'} |

approaches

| c - \bar{u} |

, increasing dissipation limits

| u^{'} |

thus that the ratio

| u^{'} | / | c - \bar{u} |

becomes constant. The linear convective instability threshold demands a unit ratio, however observations suggested a ratio of 0.7 (Fritts et al., 1988; Equation 2), and the theoretical consideration of the nonlinear diffusion mechanism yielded

1 / \sqrt{2} \approx 0.707

(Medvedev & Klaassen, 2000, Section 7). Regardless of the precise number, Equation 7 establishes proportionality between the amplitude of relative temperature/density perturbations and squared mean Brunt-Väisälä frequency under the saturation condition. Near the exobase, where the majority of NGIMS/MAVEN observations were taken, the vertical gradient

d \bar{T} / d z

is small and can be neglected in Equation 4, thus giving the inverse proportionality of relative perturbation amplitudes and

\bar{T}

.
其中

| u^{'} |

是波中水平速度波动的幅度，

c

是其水平相速度，

\bar{u}

是背景风。当

| u^{'} |

接近

| c - \bar{u} |

时，增加的耗散限制了

| u^{'} |

，使得比率

| u^{'} | / | c - \bar{u} |

变得恒定。线性对流不稳定性阈值要求单位比率，然而观察结果表明比率为 0.7（Fritts 等，1988；方程 2），而非线性扩散机制的理论考虑得出了

1 / \sqrt{2} \approx 0.707

（Medvedev & Klaassen，2000，第 7 节）。无论精确数字如何，方程 7 确立了相对温度/密度扰动幅度与饱和条件下的平方平均 Brunt-Väisälä 频率之间的比例关系。在外层大气基底附近，大多数 NGIMS/MAVEN 观测数据是在此处获得的，垂直梯度

d \bar{T} / d z

较小，可以在方程 4 中忽略，从而给出了相对扰动幅度与

\bar{T}

的反比例关系。
ACS/TGO occultation data cover altitudes below the exobase, where

d \bar{T} / d z

can no longer be neglected. Therefore, we plotted in Figure 8a the amplitudes of relative temperature perturbations for all orbits as functions of

N^{2}

.
ACS/TGO 消失数据覆盖了低于外逸层的高度，在这里

d \bar{T} / d z

不再可以忽略。因此，我们在图 8a 中绘制了所有轨道的相对温度扰动幅度作为

N^{2}

. 的函数。

It is seen that red and blue dots corresponding to morning and evening measurements show no clear dependence on

N^{2}

at all altitudes. To explore this further, we over-plotted the linear regression of the form

| T^{'} | / \bar{T} = α N^{2} + β

and put the values of

α

and

β

in the legend. The coefficients

α

are far less than those expected from Equation 7, that is, several tens or hundreds, depending on the characteristic vertical wavenumber

m

. The distinction between morning and evening amplitudes is also insignificant, except above 100 km , where morning values are slightly larger.
可以看出，早晨和晚上的测量对应的红点和蓝点在所有高度上都没有明显的依赖关系。

N^{2}

为了进一步探讨这一点，我们叠加了形式为

| T^{'} | / \bar{T} = α N^{2} + β

的线性回归，并在图例中放置了

α

和

β

的值。

α

系数

m

远低于方程 7 所预期的值，即几十或几百，具体取决于特征垂直波数。{{6}} 早晨和晚上的幅度差异也不显著，除了在 100 公里以上，早晨的值略大一些。

Figure 8. Amplitudes of relative temperature disturbances as functions of the squared Brunt-Väisälä frequency (a) and mean temperature (b) at different heights. Red and blue dots are for the morning and evening measurements, correspondingly. Linear regressions of the form (a)।

T^{'} ∣ / \bar{T} = α N^{2} + β

and (b)

| T^{'} | / \bar{T} = α \bar{T} + β

are shown with thin solid lines, and the values of the respective coefficients are given in the legends.
图 8. 不同高度下相对温度扰动的幅度与平方布伦特-维萨拉频率(a)和平均温度(b)的关系。红点和蓝点分别代表早晨和晚上的测量。线性回归形式为(a)。

T^{'} ∣ / \bar{T} = α N^{2} + β

和(b)

| T^{'} | / \bar{T} = α \bar{T} + β

以细实线表示，相应系数的值在图例中给出。

Figure 8 b presents the dependencies of amplitudes of relative temperature disturbances as functions of the mean temperature. They are nearly uniform. Although regression coefficients show a weak negative trends at all altitudes, their magnitudes are much smaller than to those observed previously (of the order of 0.5-1) near the exobase (England et al., 2017; Terada et al., 2017; Vals et al., 2019; Yiğit et al., 2015). A similar lack of correlation between GW amplitudes and atmospheric temperature was found from TGO aerobraking measurements at altitudes between 100 and 130 km (Jesch et al., 2019, Figure 12). The atmospheric drag data were collected between

L_{s} = 332^{\circ}

of MY33 and

L_{s} = 132^{\circ}

of MY34. The ACS observations after the aerobraking cover the dusty second half of MY34. Thus, the absence of correlation between GW amplitudes and the background temperature in the lower thermosphere appear to be independent of the season and dust conditions. In the upper thermosphere (Leelavathi et al., 2020, Figure 10d), found a positive correlation during the same second half of MY34, instead of a clear negative correlation over the first (“non-dusty”) half of the year. Our results in the adjacent region (around 140 km ) show no visible change, neither strong negative trend previously found in the MAVEN/NGIMS observations, nor indication of a positive trend. This means that convective instability may not be the main mechanism responsible for damping GWs in the thermosphere, at least during dust storms.
图 8b 展示了相对温度扰动幅度与平均温度的依赖关系。它们几乎是均匀的。尽管回归系数在所有高度上显示出微弱的负趋势，但其幅度远小于之前观察到的（约为 0.5-1）在外气层附近（England 等，2017；Terada 等，2017；Vals 等，2019；Yiğit 等，2015）。在 100 到 130 公里的高度上，从 TGO 气动制动测量中发现 GW 幅度与大气温度之间的相关性也很弱（Jesch 等，2019，图 12）。大气阻力数据是在 MY33 的

L_{s} = 332^{\circ}

和

L_{s} = 132^{\circ}

的 MY34 之间收集的。气动制动后的 ACS 观测覆盖了 MY34 的多尘后半段。因此，GW 幅度与下热层背景温度之间缺乏相关性似乎与季节和尘埃条件无关。在上热层（Leelavathi 等，2020，图 10d），在 MY34 的同一后半段发现了正相关，而不是在第一半段（“无尘”）的明显负相关。我们在相邻区域（约 140 公里）的结果显示没有明显变化，既没有在 MAVEN/NGIMS 观测中发现的强负趋势，也没有正趋势的迹象。这意味着对流不稳定性可能不是在热层中抑制重力波的主要机制，至少在沙尘暴期间不是。

5. Summary and Conclusions
5. 摘要和结论

We have presented the results of gravity wave (GW) retrievals obtained from the Atmospheric Chemistry Suite instrument on board the ExoMars Trace Gas Orbiter (ACS/TGO), which observed solar occultation spectra. GW disturbances are derived from the vertical temperature profiles retrieved from one of the three instrument channels - the mid-infrared ACS/MIR. The uniqueness of the data is that they continuously cover a broad range of altitudes from the Martian troposphere to the thermosphere (

20 - 160 km

) and have a relatively high (

0.5 - 2.5 km

) vertical resolution.
我们展示了从火星探测器（ExoMars Trace Gas Orbiter，ACS/TGO）上的大气化学套件仪器获得的重力波（GW）检索结果，该仪器观察了太阳掩蔽光谱。GW 扰动是从三个仪器通道之一的垂直温度剖面中提取的 - 中红外 ACS/MIR。数据的独特之处在于它们持续覆盖从火星对流层到热层的广泛高度范围（

20 - 160 km

），并具有相对较高的（

0.5 - 2.5 km

）垂直分辨率。
Several techniques of separating GW components from the background temperature have been studied. The sliding-window least squares polynomial fitting method have demonstrated to be the most robust and
已经研究了几种将 GW 成分与背景温度分离的技术。滑动窗口最小二乘多项式拟合方法已被证明是最稳健的。
effective. The procedure was applied to 144 measurements collected over the second half of MY34 to derive vertical profiles of GW disturbances as well as further wave characteristics: amplitude, wave potential energy, absolute vertical flux of horizontal momentum and absolute momentum forcing produced by breaking/ dissipating GWs (“GW drag”). The main results are listed below.
有效的。该程序应用于在 MY34 下半年收集的 144 个测量数据，以推导出 GW 扰动的垂直剖面以及进一步的波动特征：振幅、波动势能、水平动量的绝对垂直通量和由破裂/消散的 GW 产生的绝对动量强迫（“GW 拖曳”）。主要结果如下。

Amplitudes of GW-induced temperature fluctuations, generally, grow with height, while breaking/saturation processes often limit the wave amplitude growth at higher altitudes. Based on a half-year average, wave amplitudes are around $8 - 14 K$ near the mesopause, and often exceed these values in individual profiles.
引起的温度波动的幅度通常随着高度的增加而增加，而破裂/饱和过程往往限制了高海拔地区波幅的增长。基于半年的平均值，波幅在中间层附近约为 $8 - 14 K$ ，并且在个别剖面中通常超过这些值。
The mesopause ( $100 - 120 km$ ) is the region of the strongest GW breaking/dissipation, which is evidenced by a local maximum of momentum fluxes and their vertical divergence, that is, GW drag. Similarly, a large GW drag of hundreds of $m s^{- 1}$ sol $^{- 1}$ in the mesopause region has been demonstrated by MGCMs (e.g., Yiğit et al., 2018).
中间层顶 ( $100 - 120 km$ ) 是重力波破裂/耗散最强的区域，这通过动量通量及其垂直散度的局部最大值得以证明，即重力波拖曳。同样，MGCMs（例如，Yiğit 等，2018）已证明中间层顶区域的重力波拖曳可达数百 $m s^{- 1}$ 太阳 $^{- 1}$ 。
The spatial (altitude-latitude) distribution of the wave drag also agrees well with modeling results (e.g., Medvedev et al., 2011). This is the first direct observational validation of model predictions.
波阻力的空间（高度-纬度）分布与模型结果（例如，Medvedev 等，2011）也很好地一致。这是对模型预测的第一次直接观测验证。
We did not find positive correlation between amplitudes of relative temperature perturbations and the Brunt-Väisälä frequency at all heights. This correlation is a more general formulation of the anti-correlation found near the exobase (England et al., 2017; Terada et al., 2017; Vals et al., 2019; Yiğit et al., 2015) that accounts for vertically varying mean temperature.
我们没有发现相对温度扰动幅度与所有高度的布伦特-维萨拉频率之间的正相关。这种相关性是对在外层大气基线附近发现的反相关性（England et al., 2017; Terada et al., 2017; Vals et al., 2019; Yiğit et al., 2015）的更一般的表述，考虑了垂直变化的平均温度。

The presented GW activity retrievals extending from the middle troposphere to the thermosphere, as derived from the ExoMars data, highlight the role of atmospheric gravity waves as a whole atmosphere phenomenon on Mars. Mars’ thin and windy atmosphere favors strong gravity wave generation, thus an accurate characterization of gravity waves is absolutely essential for a better understanding of the Martian climate (Yiğit & Medvedev, 2019).
从 ExoMars 数据得出的中层对流层到热层的 GW 活动检索，突显了大气重力波作为火星整体大气现象的作用。火星稀薄而多风的大气有利于强重力波的产生，因此准确表征重力波对于更好地理解火星气候至关重要（Yiğit & Medvedev, 2019）。

Data Availability Statement
数据可用性声明

The ACS data are available from ESA’s Planetary Science Archive at https://archives.esac.esa.int/psa/#!Table

∖ % 20 View / ACS =

instrument. The data for latitude-altitude cross-sections of GW characteristics such as amplitudes, potential energy, fluxes, accelerations and zonal wind are available at the Mendeley database (Starichenko, 2021).
ACS 数据可从 ESA 的行星科学档案馆获取，网址为 https://archives.esac.esa.int/psa/#!Table

∖ % 20 View / ACS =

仪器。关于 GW 特征的纬度-高度截面数据，如振幅、势能、通量、加速度和纬向风，可在 Mendeley 数据库中获取（Starichenko, 2021）。

Acknowledgments 致谢
ExoMars is the space mission of ESA and Roscosmos. The ACS experiment is led by IKI Space Research Institute in Moscow. Science operations of ACS are funded by Roscosmos and ESA. The analyses of temperature profiles and wave structures at IKI are funded by the grant #20-42-09035 of the Russian Science Foundation.
ExoMars 是欧洲航天局和俄罗斯航天局的太空任务。ACS 实验由莫斯科的 IKI 空间研究所领导。ACS 的科学操作由俄罗斯航天局和欧洲航天局资助。IKI 对温度剖面和波动结构的分析由俄罗斯科学基金会的资助#20-42-09035 提供资金。

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JGR 行星 JGR 行星

特别部分： 特别部分：

通信地址：

引文：

作者贡献：

距离 ACS/TGO 掩星测量 20-160 km 高度的火星大气中的重力波活动

抽象 摘要

1. 引言

2. Atmospheric Chemistry Suite 机载痕量气体 Orbiter 仪器2. 大气化学套件 机载痕量气体 Orbiter 仪器

3. Methods 3. 方法

3.1. Retrieval of Temperature Profiles3.1. 温度剖面的检索

3.2. Derivation of Wave Disturbances3.2. 波动扰动的推导

3.3. Wave Activity and Potential Energy3.3. 波动活动和潜在能量

3.4. Momentum Flux and Momentum Deposition3.4. 动量通量和动量沉积

4. Results and Discussions4. 结果与讨论

4.1. Case Study 4.1. 案例研究

4.2. Spatial Distribution of Gravity Wave Activity4.2. 重力波活动的空间分布

4.3. Amplitude Dependence on Mean Temperature and BruntVäisälä Frequency4.3. 振幅对平均温度和布伦特-维萨拉频率的依赖

5. Summary and Conclusions5. 摘要和结论

Data Availability Statement数据可用性声明

References 参考文献

特别部分：特别部分：

抽象摘要

2. Atmospheric Chemistry Suite 机载痕量气体 Orbiter 仪器
2. 大气化学套件机载痕量气体 Orbiter 仪器

3.1. Retrieval of Temperature Profiles
3.1. 温度剖面的检索

3.2. Derivation of Wave Disturbances
3.2. 波动扰动的推导

3.3. Wave Activity and Potential Energy
3.3. 波动活动和潜在能量

3.4. Momentum Flux and Momentum Deposition
3.4. 动量通量和动量沉积

4. Results and Discussions
4. 结果与讨论

4.2. Spatial Distribution of Gravity Wave Activity
4.2. 重力波活动的空间分布

4.3. Amplitude Dependence on Mean Temperature and BruntVäisälä Frequency
4.3. 振幅对平均温度和布伦特-维萨拉频率的依赖

5. Summary and Conclusions
5. 摘要和结论

Data Availability Statement
数据可用性声明