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
Figure 1. Spectroscopy of CO_(2)\mathrm{CO}_{2} and H_(2)O\mathrm{H}_{2} \mathrm{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- sigma\sigma uncertainties of the retrievals. 图 1. ACS-MIR 的衍射级数#223 中 CO_(2)\mathrm{CO}_{2} 和 H_(2)O\mathrm{H}_{2} \mathrm{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- sigma\sigma 不确定性。
covers 0.15-0.3 mum0.15-0.3 \mu \mathrm{~m} range. The instrument’s resolving power is lambda//Delta lambda∼25,000\lambda / \Delta \lambda \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 ( ∼2s\sim 2 \mathrm{~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 mum0.15-0.3 \mu \mathrm{~m} 范围。仪器的分辨率为 lambda//Delta lambda∼25,000\lambda / \Delta \lambda \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（ ∼2s\sim 2 \mathrm{~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 mum2.66-2.68 \mu \mathrm{~m} portion of the spectrum from the grating position #4, the echelle diffraction order #223, which includes a wing of the 2.7 mumCO_(2)2.7 \mu \mathrm{~m} \mathrm{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 mum2.66-2.68 \mu \mathrm{~m} 光谱部分，埃谢尔衍射级数#223，其中包括 2.7 mumCO_(2)2.7 \mu \mathrm{~m} \mathrm{CO}_{2} 吸收带的一部分（图 1a）。
Strong absorption lines of CO_(2)\mathrm{CO}_{2} allow for retrieving temperature and density in the Martian atmosphere with good sensitivity. 强吸收线的 CO_(2)\mathrm{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)\mathrm{CO}_{2} absorption bands in spectral intervals without H_(2)O\mathrm{H}_{2} \mathrm{O} lines (see Figure 1a). A priori altitude profiles of T(z)T(z) and p(z)p(z) as well as one of the CO_(2)VMR\mathrm{CO}_{2} \mathrm{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)\mathrm{CO}_{2} concentration, while the pressure profile is kept constant assuming the hydrostatic equilibrium p_(hyd)(z)=p_(0)(z_(0))exp[-int_(z_(0))^(z)(g(z^('))M(z^(')))/(RT(z^(')))dz^(')]p_{h y d}(z)=p_{0}\left(z_{0}\right) \exp \left[-\int_{z_{0}}^{z} \frac{g\left(z^{\prime}\right) M\left(z^{\prime}\right)}{R T\left(z^{\prime}\right)} d z^{\prime}\right], where gg is the acceleration of gravity, MM is the atmospheric molar mass and RR is the gas constant. The reference pressure p_(0)p_{0} is chosen at an altitude z_(0)z_{0}, usually around 30-50km30-50 \mathrm{~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 5-6km5-6 \mathrm{~km} when analyzing vertical wavy structures. The third step focuses only on CO_(2)\mathrm{CO}_{2} and H_(2)O\mathrm{H}_{2} \mathrm{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)\mathrm{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\mathrm{H}_{2} \mathrm{O} 线（见图 1a）。 T(z)T(z) 和 p(z)p(z) 的先验高度剖面以及 CO_(2)VMR\mathrm{CO}_{2} \mathrm{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)\mathrm{CO}_{2} 浓度，同时保持压力剖面不变，假设静水平衡 p_(hyd)(z)=p_(0)(z_(0))exp[-int_(z_(0))^(z)(g(z^('))M(z^(')))/(RT(z^(')))dz^(')]p_{h y d}(z)=p_{0}\left(z_{0}\right) \exp \left[-\int_{z_{0}}^{z} \frac{g\left(z^{\prime}\right) M\left(z^{\prime}\right)}{R T\left(z^{\prime}\right)} d z^{\prime}\right] ，其中 gg 是重力加速度， MM 是大气摩尔质量， RR 是气体常数。参考压力 p_(0)p_{0} 选择在高度 z_(0)z_{0} ，通常在 30-50km30-50 \mathrm{~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 5-6km5-6 \mathrm{~km} 。第三步仅关注整个波数范围内的 CO_(2)\mathrm{CO}_{2} 和 H_(2)O\mathrm{H}_{2} \mathrm{O} 浓度检索
order #223 (Figure 1a) using the p(z)p(z) and T(z)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)p(z) 和 T(z)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)\mathrm{CO}_{2} absorption band at 1.58 mum\mu \mathrm{m} measured by NIR allows for detection up to 110-120km110-120 \mathrm{~km}, or the density of ∼10^(12)cm^(-3)\sim 10^{12} \mathrm{~cm}^{-3}, while the band at 2.7 mum2.7 \mu \mathrm{~m} observed by MIR is measurable up to 160-170km160-170 \mathrm{~km}, or ∼10^(9)cm^(-3)\sim 10^{9} \mathrm{~cm}^{-3}. The lowermost altitude of the temperature profile retrieval is conditioned by the aerosol opacity and by the saturation of the CO_(2)\mathrm{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 110-120km110-120 \mathrm{~km} ，或 ∼10^(12)cm^(-3)\sim 10^{12} \mathrm{~cm}^{-3} 的密度，而 MIR 观察到的 2.7 mum2.7 \mu \mathrm{~m} 的带可测量高达 160-170km160-170 \mathrm{~km} ，或 ∼10^(9)cm^(-3)\sim 10^{9} \mathrm{~cm}^{-3} 。温度剖面提取的最低高度受气溶胶不透明度和 CO_(2)\mathrm{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 ")J_{\text {mod }} to the measured one J_("mes ")J_{\text {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。
where n(z)n(z) are gaseous concentrations, sigma(T,p)\sigma(T, p) are absorption cross-sections of CO_(2)\mathrm{CO}_{2} and H_(2)O\mathrm{H}_{2} \mathrm{O} correspondingly for specific temperature T(z)T(z) and pressure p(z)p(z) at an altitude zz, and tau_(a)\tau_{a} is aerosol slant opacity. A transfer between the linear [cm^(-2)]\left[\mathrm{cm}^{-2}\right] and the volume [cm^(-3)]\left[\mathrm{cm}^{-3}\right] concentrations is performed using the well-known “onion-peeling” method with the numeric integration over all altitude layers z_(i)z_{i} above the ii 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\mathrm{H}_{2} \mathrm{O} lines suitable for a CO_(2)\mathrm{CO}_{2}-rich atmosphere ( Ga mache et al., 2016) and self-broadening in the case of CO_(2)\mathrm{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 chi^(2)=sum_(i)A^(2)(v_(i))\chi^{2}=\sum_{i} A^{2}\left(v_{i}\right), A(v_(i))=[J_("mod ")(v_(i))-J_("mes ")(v_(i))]//delta JA\left(v_{i}\right)=\left[J_{\text {mod }}\left(v_{i}\right)-J_{\text {mes }}\left(v_{i}\right)\right] / \delta J, where delta J\delta J are transmittance uncertainties, and the sum is taken over all considered spectral points (pixels). Our optimization algorithm to search for the chi^(2)\chi^{2} minimum is based on partial derivatives of the Jacobian matrix del A//del X\partial A / \partial X (Marquardt, 1963), where XX is a vector of free parameters, that is, temperature, CO_(2)\mathrm{CO}_{2} concentration, H_(2)O\mathrm{H}_{2} \mathrm{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)n(z) 是气体浓度， sigma(T,p)\sigma(T, p) 是 CO_(2)\mathrm{CO}_{2} 的吸收截面， H_(2)O\mathrm{H}_{2} \mathrm{O} 对应于特定温度 T(z)T(z) 和压力 p(z)p(z) 在一个高度 zz ，并且 tau_(a)\tau_{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)]\left[\mathrm{cm}^{-2}\right] 之上进行线性 [cm^(-3)]\left[\mathrm{cm}^{-3}\right] 和体积 z_(i)z_{i} 浓度之间的转换 ii 。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\mathrm{H}_{2} \mathrm{O} 的 CO_(2)\mathrm{CO}_{2} -富气氛的压力展宽系数（Ga mache 等，2016）以及在 CO_(2)\mathrm{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^(')T^{\prime} are sought by separating the mean, or background profile bar(T)(z)\bar{T}(z) from the measured one T(z)T(z) : 重力波引起的温度扰动 T^(')T^{\prime} 通过将平均值或背景剖面 bar(T)(z)\bar{T}(z) 与测量值分离来寻找 T(z)T(z) ：
T^(')=T- bar(T),T^{\prime}=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 Lambda_(z)\Lambda_{z} that separates GWs from the larger-scale features. In the following, we assumed Lambda_(z)=30km\Lambda_{z}=30 \mathrm{~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 Lambda_(z)\Lambda_{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 Lambda_(z)=30km\Lambda_{z}=30 \mathrm{~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)\bar{T}(z), the right one is for the relative perturbations T^(')(z)// bar(T)(z)T^{\prime}(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-km2-\mathrm{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)\bar{T}(z) ，右列为相对扰动 T^(')(z)// bar(T)(z)T^{\prime}(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-km2-\mathrm{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-m500-\mathrm{m} grid. We used only the temperature data with errors <= 10K\leq 10 \mathrm{~K}. Spectral filtering was performed using Fourier decomposition within sliding 60 - km intervals ( +-30km\pm 30 \mathrm{~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)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-m500-\mathrm{m} 网格。我们仅使用了误差为 <= 10K\leq 10 \mathrm{~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（ +-30km\pm 30 \mathrm{~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)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-km60-\mathrm{km} sliding intervals. Ob-\mathrm{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^(')|=( bar(T^('2)))^(1//2)\left|T^{\prime}\right|=\left(\overline{T^{\prime 2}}\right)^{1 / 2} and wave potential energy (per unit mass) GW 场通常以波动的幅度 |T^(')|=( bar(T^('2)))^(1//2)\left|T^{\prime}\right|=\left(\overline{T^{\prime 2}}\right)^{1 / 2} 和波动势能（每单位质量）
gg is the acceleration of gravity and c_(p)c_{p} is the specific heat capacity at constant pressure. The amplitude of the wave packet at a given height | T^(')(z)∣T^{\prime}(z) \mid (hereafter called “wave activity”) represents an envelope of the measured profile T^(')(z)T^{\prime}(z). We calculated it by performing Fourier decomposition in each sliding 60-km60-\mathrm{km} vertical gg 是重力加速度， c_(p)c_{p} 是定压下的比热容。给定高度处波包的振幅 | T^(')(z)∣T^{\prime}(z) \mid （以下简称“波动活动”）表示测量轮廓的包络 T^(')(z)T^{\prime}(z) 。我们通过在每个滑动 60-km60-\mathrm{km} 垂直 进行傅里叶分解来计算它。
Figure 3. Wave activity | T^(')∣T^{\prime} \mid (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^(')∣T^{\prime} \mid （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)=rho_(0)( bar(u^(')w^(')), bar(v^(')w^(')),0)\mathbf{F}=\left(F_{x}, F_{y}, 0\right)=\rho_{0}\left(\overline{u^{\prime} w^{\prime}}, \overline{v^{\prime} w^{\prime}}, 0\right), where rho_(0)\rho_{0} is the mean density and ( {:u^('),v^('),w^('))\left.u^{\prime}, v^{\prime}, w^{\prime}\right) are the components of wave-induced perturbations of wind velocity u^(')\mathbf{u}^{\prime} 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)=rho_(0)( bar(u^(')w^(')), bar(v^(')w^(')),0)\mathbf{F}=\left(F_{x}, F_{y}, 0\right)=\rho_{0}\left(\overline{u^{\prime} w^{\prime}}, \overline{v^{\prime} w^{\prime}}, 0\right) ，其中 rho_(0)\rho_{0} 是平均密度，( {:u^('),v^('),w^('))\left.u^{\prime}, v^{\prime}, w^{\prime}\right) 是风速波动的分量 u^(')\mathbf{u}^{\prime} ，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）。
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))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))F_{k, m}=\sqrt{F_{x, k, m}^{2}+F_{y, k, m}^{2}} （例如，Ern 等，2004 年，第 4 节）：
where k_(h)k_{h} and mm are the horizontal and vertical wavenumbers, correspondingly, and |T_(k,m)^(')|\left|T_{k, m}^{\prime}\right| is the amplitude. The latter two are found from the Fourier decomposition, whereas k_(h)k_{h} cannot be derived from our measurements. 其中 k_(h)k_{h} 和 mm 分别是水平和垂直波数， |T_(k,m)^(')|\left|T_{k, m}^{\prime}\right| 是振幅。后两个是通过傅里叶分解得到的，而 k_(h)k_{h} 不能从我们的测量中推导出来。
The total flux FF is the sum of contributions of individual harmonics F=sum_(m)F_(k,m)F=\sum_{m} F_{k, m}. Since the horizontal wavenumber k_(h)k_{h} cannot be obtained from the measurements, it, therefore, serves as a scaling factor for the derived profiles of FF and momentum forcing (5). The densest atmospheric footprint at a target point in occultation geometry is 400-500km400-500 \mathrm{~km} horizontally, depending on the height. This constrains the upper limit for unresolved wavelengths. In our calculations, we assumed a representative horizontal wavelength lambda_(h)=2pi//k_(h)=300km\lambda_{h}=2 \pi / k_{h}=300 \mathrm{~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 FF 是各个谐波贡献的总和 F=sum_(m)F_(k,m)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 FF 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 400-500km400-500 \mathrm{~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 lambda_(h)=2pi//k_(h)=300km\lambda_{h}=2 \pi / k_{h}=300 \mathrm{~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//rho_(0)F / \rho_{0} and GW momentum deposition, that is, wave drag aa 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 ∼110km\sim 110 \mathrm{~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 ∼110km\sim 110 \mathrm{~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)N^{2}(z) (Figure 5c, black). N^(2)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)N^{2} from the original profiles (see Figure 5c, red-dashed) shows large swings associated with temperature disturbances. Near 110km,N^(2)110 \mathrm{~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 2,000ms^(-1)sol^(-1)2,000 \mathrm{~m} \mathrm{~s}^{-1} \mathrm{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^(@)L_{s}=164^{\circ} to 354^(@)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^(@)L_{s}=164^{\circ} 到 354^(@)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^(@)L_{s}=185^{\circ} and 190^(@)190^{\circ}, attained its maximum around L_(s)=220^(@)L_{s}=220^{\circ}, and gradually decreased until L_(s)~~290^(@)L_{s} \approx 290^{\circ}. A regional storm occurred at the end of MY34 between approximately L_(s)=325^(@)L_{s}=325^{\circ} and 345^(@)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^(@)L_{s}=185^{\circ} 和 190^(@)190^{\circ} 之间进行的，达到最大值是在 L_(s)=220^(@)L_{s}=220^{\circ} ，并逐渐减少直到 L_(s)~~290^(@)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^(@)L_{s}=325^{\circ} 和 345^(@)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^(')|\left|T^{\prime}\right|, Figure 7a) grows with height reaching up to ∼10K\sim 10 \mathrm{~K} near the top of the domain. At higher altitudes ( 170-220km170-220 \mathrm{~km}
