2. Background and motivation
This section provides a brief summary of the basic characteristics of baroclinic waves in the northern hemisphere. We limit the discussion to results derived from observations, including those obtained through data assimilation. See Barnes et al. (2017) for a comprehensive review of both observations and numerical simulations of baroclinic waves. This section also illustrates the limitations of MCS limb profiles for research in this area.
The Viking Landers monitored the atmosphere of Mars at two locations in the northern hemisphere, providing a multi-year record of pressure and temperature along with more limited measurements of winds. This led to numerous advances in our understanding of Martian weather and climate (Zurek et al., 1992). In particular, eastward-traveling baroclinic waves were observed for the first time (Ryan et al., 1978; Barnes, 1980, 1981; Ryan and Sharman, 1981; Leovy et al., 1985), confirming predictions by numerical models (Leovy and Mintz, 1969). The waves appear in autumn and winter with typical periods of 2–8 sols and an amplitude in surface pressure of a few percent. Amplitudes are much larger at 48°N (Lander 2) than at 22°N (Lander 1). Subsequent missions have shown that the waves have a discernible effect on surface pressure at 4.5°S in Gale Crater (Haberle et al., 2018) and at 4.5°N in Elysium Planitia (Banfield et al., 2020b).
The MGS TES sounded the atmosphere of Mars from summer of MY24 through spring of MY27 (Smith et al., 2001; Smith, 2004). Temperature profiles retrieved from nadir observations have a vertical resolution of about 10 km and provide complete global coverage at two local times. This space-time coverage is favorable for investigations of transient eddies, and much of what is known about this subject derives from the TES data. After Wilson et al. (2002) reported initial results from northern autumn and winter of MY24, Banfield et al. (2004) methodically analyzed TES data from MY24 and 25, solving for the amplitude, period, and zonal wavenumber of the transient eddies and mapping their three-dimensional spatial structure and seasonal evolution in both the northern and southern hemispheres. Subsequent analyses of TES profiles extended the survey of eddy activity in the northern hemisphere through MY26 (Wang, 2007; Wang et al., 2013). Rather than attempting to synthesize the results from these studies, we summarize basic properties of the transient eddies in the context of subsequent work by Lewis et al. (2016), especially as it applies to low-altitude baroclinic waves.
Lewis et al. (2016) investigated the 'winter weather' on Mars through data assimilation, using TES retrievals of temperature and dust opacity to guide a General Circulation Model (GCM). The reanalysis relies on the simulated general circulation and the model physics to determine the vertical structure of the baroclinic waves, which is not fully resolved by TES. We consider only the results in the northern hemisphere. The baroclinic waves have zonal wavenumbers of 1–3. The temperature field of both the wave-1 and wave-2 modes has a large amplitude at the surface, a minimum at a pressure of about 200 Pa, and a local maximum at about 20 Pa; the temperature field of wave-3 mode is largely confined to pressures exceeding 200 Pa. The amplitude is largest in early-to-mid autumn (Ls = 180–240°) and mid-to-late winter (Ls = 300–360°) near the edge of the seasonal CO2 ice cap. In all 3 MYs observed by TES, the baroclinic waves subside near the winter solstice. This "solstitial pause" is apparent only at pressures greater than about 300 Pa, owing to the presence of a different type of transient eddy at higher altitudes in late autumn and early winter. The solstitial pause has a significant impact on the seasonal dust cycle: frontal and flushing dust storms, which are initiated by baroclinic waves, cease at about Ls = 240° and do not resume until after about Ls = 300° (Wang et al., 2005; Wang, 2007; Wang and Richardson, 2015).
Greybush et al. (2019) used a different type of data assimilation in a similar investigation of baroclinic waves at low altitudes. In this approach, the output from the reanalysis is a 16-member ensemble, which provides information about the reliability of the results: confidence increases as the ensemble spread decreases. When applied to TES temperature profiles, there is little difference among the members of the ensemble, and the ensemble mean closely resembles the results obtained by Lewis et al. (2016). However, similar reanalysis of MCS temperature profiles yielded mixed results. The ensemble does not converge consistently, owing to the scarcity of successful retrievals at pressures exceeding 350 Pa, as discussed below. This implies that the information contained in the MCS profiles (version 5) is not sufficient to support a comprehensive investigation of wave activity near the surface.
MGS radio occultation (RO) profiles of temperature and geopotential height provide additional information about baroclinic waves (Hinson and Wilson, 2002; Hinson, 2006; Hinson and Wang, 2010; Hinson et al., 2012). In particular, the vertical structure of the waves can be determined with sub-kilometer resolution. Fig. 1 shows three examples. In each case, the amplitude in temperature is largest at about 600 Pa and it decreases rapidly at lower pressures. This type of wave structure is largely inaccessible to MCS limb sounding. Among the 100,000 profiles available at mid-to-high northern latitudes during Ls = 180–360° of MY30, fewer than 20% reach pressures greater than 350 Pa, as shown in Fig. 1.
The scarcity of MCS profiles at low altitudes is a serious impediment to studies of baroclinic waves. We illustrate this point in Appendix A by extracting samples of temperature at 610 Pa from 1 MY of MCS profiles and using the procedure described in Section 4 to search for waves. (Initial results from a similar effort were reported recently by Banfield et al. (2020a).) This yielded some tantalizing results, but there is a major gap in coverage throughout polar night and extending well into the surrounding baroclinic zone. The results from limb sounding are not sufficient to meet our objectives, which led us to consider another type of MCS observation.
3. Observations
This investigation relies on data from two infrared sounders, the MRO MCS and the MGS TES. The data sets have similar coverage in longitude, latitude, and local time. There is no overlap in atmospheric measurements by the two instruments.
3.1. The MRO Mars Climate Sounder
We examined MCS data acquired when the instrument was pointed at the surface and found that the B1 channel is the best source of information about baroclinic waves in the northern hemisphere. However, other channels may be needed when we extend the analysis to the southern hemisphere, where the surface pressure is generally smaller than in the north.
The observations used here come from Reduced Data Records (RDRs) stored at the Atmospheres Node of the NASA Planetary Data System (PDS). We consider only data acquired in a uniform viewing geometry with MCS pointed in the forward direction (178° < azimuth < 182°) and viewing the surface at an emission angle of about 60° (118° < elevation < 123°). In addition, we exclude any observation performed under abnormal conditions, such as when the spacecraft was rolling or when MCS was safing, safed, freezing, frozen, dumping, or moving (as defined in the PDS documentation for the RDRs).
The information extracted from the RDRs includes the calibrated B1 radiance, the time of observation (UTC), and the longitude, latitude, and local time at the observation point on the surface of Mars (based on reconstructions of spacecraft position and MCS pointing direction). We computed Ls for each data sample using classical orbital elements for Mars. Observations that meet all criteria mentioned above are obtained routinely as part of the standard MCS observing sequence (McCleese et al., 2007), providing regular coverage of both the dayside and the nightside as shown in Fig. 2.
We used radiances from detectors B1–10, B1–11 (the middle detector), and B1–12; the other 18 detectors of the B1 channel are ignored. The brightness temperature is computed from the average radiance in these three detectors using the inverse Planck function for the central wavenumber of detector B-11 (317.788 cm−1). For example, Fig. 3 shows the variations of brightness temperature with latitude for the observations in Fig. 2. Atmospheric gases are transparent at 32 microns, so the emission comes primarily from the surface with a smaller contribution from atmospheric dust. Fig. 3 has several notable features. First, there is a large day-night temperature difference (about 80 K) at low latitudes. Second, spatial variations in surface thermal inertial cause substantial zonal variations in nightside temperature at latitudes south of 50°N. Third, there is a strong meridional gradient of brightness temperature at high latitudes, particularly on the dayside, where the temperature decreases from about 225 K at 60°N to less than 170 K at 70°N. Finally, the bimodal temperature distribution at latitudes north of about 70°N is a consequence of zonal variations in the distribution of CO2 ice (Calvin et al., 2015). As we show in Section 5.4 (Fig. 11), a baroclinic wave is present at the time of these observations, with a zonal wavenumber of 2 and an amplitude of 2–3 K at 60–75°N.
We computed the zonal-mean surface temperature at a local time of 15 h from B1 measurements such as those in Fig. 3. The results provide context for interpreting some aspects of the wave measurements. In particular, the 150-K contour gives the approximate location of the edge of the CO2 ice cap. (See Figs. 6–8, below.)
Although it is not obvious from Fig. 3, the B1 channel also contains valuable information about baroclinic waves at pressures greater than 300 Pa. Two aspects of the results support the conclusions about the identity of the wave and its vertical location: (1) the presence of a deep solstitial pause, as discussed in Sections 5.1 and 6.2; and (2) the strong resemblance to baroclinic waves observed by TES at 610 Pa, as discussed in Sections 5.3, 5.4, and 6.2. Results derived through analysis of MCS temperature profiles also support this conclusion, as discussed in Appendix A.
The MCS measurements considered here extend from Ls = 329° of MY28 through Ls = 90° of MY34. There were no planet-enshrouding dust storms (PEDS) during this period.
3.2. The MGS Thermal Emission Spectrometer
As part of this investigation we also analyzed temperatures retrieved from TES nadir measurements (Conrath et al., 2000; Smith, 2004). Like MCS, TES provided daily global coverage at two local times, but the TES coverage differs in several respects from that shown in Fig. 2. First, profiles were obtained more frequently by TES, which reduces the separation in latitude between successive measurements. Second, MGS completed 12.6 orbits per sol, as compared with 13.2 for MRO. Finally, TES sampled local times of about 2 and 14 h, 1 h earlier than MCS. None of these differences is important in the context of this investigation.
TES nadir profiles extend from the surface to the 10-Pa pressure level; the vertical resolution is about 10 km. For present purposes it is sufficient to consider only temperature measurements at the 610-Pa pressure level, which is well aligned with the near-surface peak in wave amplitude (see Fig. 1). In the autumn and winter seasons, the surface pressure in the northern hemisphere generally exceeds 610 Pa at mid-to-high latitudes, where the wave amplitude is largest.
The TES measurements used in this investigation extend from Ls = 141° of MY24 through Ls = 72° of MY27. One PEDS occurred within this period, in autumn of MY25.
4. Method of analysis
Several methods of analysis have been used in previous investigations of baroclinic waves, as reviewed by Barnes et al. (2017). We chose a least-squares method for several reasons. First, it can be applied directly to data with irregular sample spacing in longitude and time of observation, which makes it easy to combine data from the dayside and the nightside. In addition, each data sample can be weighted according to its accuracy; equal weights are used here, but we may assign different weights to data from the dayside and the nightside in future work. Finally, the method can be applied directly to data sets with occasional missing samples; no special treatment, such as interpolation, is required.