Role of stationary and transient waves in CO₂ supersaturation during northern winter in the Martian atmosphere revealed by MGS radio occultation measurements

Abstract

The Martian atmosphere, which mainly consists of carbon dioxide (CO₂), is characterized by extremely low temperatures that cause CO₂ gas to freeze and dry ice to form. To date, temperatures below the CO₂ saturation temperature, which can be attributed to the effects of atmospheric waves, have been observed in the polar winter and in the mesosphere. Using data from Mars Global Surveyor (MGS) radio occultation measurements, we investigated the role of large-scale atmospheric waves including stationary and transient waves at northern high latitudes in winter on CO₂ supersaturation. A distinct longitudinal dependence of CO₂ supersaturation was observed at altitudes higher than the pressure level of 200–400 Pa, where a stationary wave with a wave number of 2, whose temperature amplitude had minima at 30–100 Pa, lowered the background temperature to a level close to the CO₂ saturation temperature. However, the stationary wave alone was not sufficient to cause CO₂ supersaturation. Additional temperature disturbances caused by transient waves, namely, superposition of both waves, had a significant role in CO₂ supersaturation. The longitudinal dependence of the occurrence of CO₂ supersaturation revealed by our study might affect the longitudinal distribution of CO₂ snowfall and the formation of the seasonal polar ice cap.

Key Points

• Using data from MGS radio occultation measurements, we studied the role of stationary and transient waves on CO₂ supersaturation on Mars
• We found a longitudinal dependence of CO₂ supersaturation above 200–400 Pa, where stationary waves lowered the background temperature
• However, additional disturbances by transient waves, namely, superposition of both waves, had a significant role in CO₂ supersaturation

1 Introduction

The atmosphere of Mars consists of mainly carbon dioxide (CO₂) (∼95%), and supersaturation and condensation of the carbon dioxide occur due to its cold climate. It is well established that the supersaturation and condensation are caused in part by atmospheric waves. Previous studies have shown that CO₂ supersaturation and/or condensation is caused not only by small-scale waves like atmospheric gravity waves in the mesosphere [Schofield et al., 1997; Spiga et al., 2012] and mountain waves [Colaprete and Toon, 2002; Tobie et al., 2003] but also by large-scale waves like stationary and transient waves, which are the focus of this study.

Here we briefly describe previous studies of stationary and transient waves mainly in the northern hemisphere. A comprehensive study on stationary waves on Mars was conducted by Banfield et al. [2003], who used the temperature data obtained using the Thermal Emission Spectrometer (TES) [Christensen et al., 2001] on board the Mars Global Surveyor (MGS). The authors reported that stationary waves with wave numbers of 1 and 2 occurred in the polar jets in both the northern and southern hemispheres in winter. Hinson et al. [2001] focused on northern high latitudes and reported that stationary planetary waves were dominant at pressure levels above 200 Pa and thermal tidal waves were dominant at pressure levels below 200 Pa, although they studied only late spring. Hinson [2006] reported that stationary waves with wave numbers of 1 and 2 occurred at a pressure level of 610 Pa (∼2–3 km) at 55–80°N using MGS radio occultation data. Hinson and Wang [2010] used the MGS radio occultation data to study the influence of stationary waves on regional dust storms near the surface (610 Pa) in the northern hemisphere. The relationship between stationary waves and CO₂ supersaturation in the southern hemisphere was reported; Hinson and Wilson [2002] found that temperature minima in the stationary waves occurred at around 170°E and 330°E, where CO₂ supersaturation occurred. However, the effect of stationary waves on CO₂ supersaturation in the northern hemisphere has not yet been studied.

Transient waves on Mars were detected in surface measurements made by the Viking landers [Ryan et al., 1978]. The MGS TES observations found that the activity of transient waves with zonal wave number s = 1 is large around the winter solstice and s = 2 and s = 3 waves are strong in autumn and spring [Banfield et al., 2004; Lewis et al., 2016]. Using MGS radio occultation data, Hinson [2006] characterized periods and wave numbers of transient waves that were prominent at a pressure level of 610 Pa in the northern high latitudes. Hinson and Wang [2010] and Hinson et al. [2012] discussed the effect of transient waves on regional dust storms in the northern hemisphere. Barnes [2006] and Barnes et al. [2009] suggested that transient waves cause CO₂ condensation in the atmosphere. The results of a Martian General Circulation Model (MGCM) showed that baroclinic waves cause CO₂ supersaturation and condensation, which results in CO₂ clouds and even snowfall in the northern winter polar atmosphere [Kuroda et al., 2013].

Hu et al. [2012] is a comprehensive study of CO₂ condensation on Mars. The authors used the multi-instrument data from MGS radio occultation, the Mars Orbiter Laser Altimeter (MOLA) [Zuber et al., 1992; Smith et al., 2001] on board MGS, and the Mars Climate Sounder (MCS) [McCleese et al., 2007] on board the Mars Reconnaissance Orbiter (MRO) [Zurek and Smrekar, 2007] to show that MOLA nonground echoes were associated with CO₂ clouds, obtaining the total atmospheric CO₂ condensation mass and the average size of condensate particles in each hemisphere. They also identified several key aspects of CO₂ supersaturation appearing in the MGS radio occultation temperature profiles. For example, they conducted statistical analyses of the degree of supersaturation. They also investigated distinct inversion layers below and above the layer of CO₂ supersaturation, suggesting the relationship with CO₂ sublimation in spring from the surface and atmospheric circulation in the upper atmosphere, respectively. Moreover, the authors studied the seasonal variation in the area and vertical ranges of atmospheric CO₂ condensation. They found that the occurrence of condensation was very variable, even at the same latitudes in the northern hemisphere, attributing the northern seasonal variation in CO₂ condensation to multiple meteorological events, including the development of baroclinic waves. More detailed analyses for the relationship between transient waves and CO₂ supersaturation using observational data are needed to confirm the results suggested in Hu et al. [2012] and Kuroda et al. [2013].

Building on the above mentioned studies, we analyzed the temperature and pressure profiles obtained from the MGS radio occultation measurements to investigate the relationship between stationary and transient waves and CO₂ supersaturation in the northern hemisphere high latitudes on Mars. We examined the seasonal changes in temperature to identify the events with temperatures below the CO₂ saturation temperature. Then, we investigated the effects of stationary and transient waves on CO₂ supersaturation. We also compared the observational results with outputs from numerical models to elucidate the longitudinal, latitudinal, and vertical dependence of CO₂ condensation.

2 Data and Method

2.1 MGS Radio Occultation Data

The MGS radio occultation data set [Tyler et al., 2001], which can be obtained from the NASA Planetary Data System (PDS), includes more than 20,000 profiles during four Martian years from Mars Years (MYs) 24 to 27. The MGS radio occultation measurements sampled the data fairly uniformly along longitude but nonuniformly along latitude and Martian local time (local true solar time: LTST). Therefore, we examined the sampling inhomogeneity to determine its effects on our analysis.

Figure 1 shows the dependence of the data sampling on latitude along Ls in the northern high latitudes. It can be seen that the latitudes from 60°N to 70°N are well covered throughout the range of Ls in Figure 1. The latitudes from 70°N to 80°N are also covered by the observations, but the range of Ls is very limited. Therefore, we investigated the latitudes from 60°N to 80°N, especially focusing on 60°N to 70°N.

Figure 1

Locations of the MGS radio occultation measurements in the northern high latitudes. Diamonds in red indicate MY 24 data, crosses in green MY 25, triangles in blue MY 26, and squares in pink MY 27. The black curve indicates the boundary of polar night.

Figure 2 shows the dependence of the data sampling on LTST along Ls. Data sampling for LTST in early winter (Ls = 180–210°) and late winter/spring equinox (Ls = 330–360°) was concentrated in the afternoon and early morning, respectively. In contrast, the data sampling for midwinter (210–330°) was distributed more widely during daytime (LTST 06–15). Thus, the data analyzed in the present study included diurnal changes in temperature during the daytime for the midwinter period. However, it is reasonable to assume that variation with local time is not important for the types of waves considered in this study. Therefore, we will neglect the local time change in temperature.

Figure 2

Same as Figure 1 but for local true solar time (LTST).

It was also important to examine the effect of changes in the atmospheric composition due to CO₂ condensation on the derivation of radio occultation measurements. Noguchi et al. [2014] reported that changes in the atmospheric composition of Mars caused by CO₂ condensation during polar nighttime affected the derivation of temperature in radio occultation measurements, in which the value of the atmospheric composition ratio was assumed. The authors showed that the magnitude of the effect was less than 1 K in the northern hemisphere, which is not significant in the present study. Therefore, we used the original MGS radio occultation data, ignoring the effect of changes in atmospheric composition.

2.2 Model Data

For comparison with observations, we used the results from two numerical simulations based on MGCMs: the Mars Climate Database (MCD) [Millour et al., 2012], and Dynamics, RAdiation, MAterial Transport and their mutual InteraCtions (DRAMATIC) developed by Kuroda et al. [2005].

The MCD is a database of atmospheric physical variables, including temperature, pressure, wind velocity, dust, and ice clouds, compiled from the simulation results of the MGCM developed by the Laboratoire de Météorologie Dynamique in France. The horizontal grid size of the MGCM simulation is 5.625° longitude and 3.75° latitude, and the vertical domain ranges from the surface to ∼300 km.

The DRAMATIC model is based on a terrestrial GCM developed at the Center for Climate System Research (University of Tokyo), the National Institute of Environmental Studies, and the Frontier Research Center for Global Change (CCSR/NIES/FRCGC) in Japan [K-1 Model Developers, 2004]. The calculations were performed using a horizontal resolution of T21 (∼5.6° in longitude and latitude) and vertical 49 or 99 sigma levels from the surface to ∼80 km. DRAMATIC allows a CO₂ supersaturation of 35% [Kuroda et al., 2013] based on the results of laboratory experiments [Glandorf et al., 2002].

2.3 Detection of CO₂ Supersaturation

To detect the occurrence of CO₂ supersaturation at each observation point in the MGS radio occultation profiles, we calculated the CO₂ saturation temperature T_s for a given pressure. We considered the 1σ measurement uncertainty of temperature by using the upper limit value of temperature [Hu et al., 2012] for each sample where the measured temperature is colder than saturation. The formulae for calculating CO₂ saturation pressure P_s for a given temperature T were taken from Kasting [1991]:

(1)

for T>216.56 K and

(2)

for T < 216.56 K. We used the Newton-Raphson method to solve the formulae with respect to T_s using the observed pressure. Then, we compared the observed temperature with T_s to identify CO₂ supersaturation.

The degree of CO₂ supersaturation (S) was calculated as follows:

(3)

where X is the mixing ratio of CO₂ and P is the observed total pressure.

3 Results and Discussion

3.1 Seasonal Change in Temperature

Figures 3 and 4 show the seasonal change in temperature of MGS radio occultation measurements for latitudes 60–70°N and 70–80°N, respectively, together with the two model results. The results for 60–70°N showed clearly defined seasonal trend, with a summer maximum and winter minimum, except at the higher altitudes at 60–70°N, where very large variability in both the observed and modeled temperatures occurred from autumn to winter. The magnitude of the temperature variability in winter was several tens of kelvins. Above the 100 Pa pressure level, the winter maximum temperature was comparable to or higher than the temperature of the summer maximum (Figures 3a and 3b). Below 100 Pa, the average temperature in winter was close to the CO₂ saturation temperature, which suggests that CO₂ gas frequently supersaturates and possibly condenses at these altitudes.

Figure 3

Seasonal changes in temperature at 60–70°N at (a) 30 Pa, (b) 60 Pa, (c) 100 Pa, (d) 300 Pa, and (e) 600 Pa. The colored dots represent the zonal average of the MGS radio occultation data (MYs 24–27), and the error bars denote the standard deviation about the mean within each Ls bin (10°). Color legends are the same as in Figure 1. The results from numerical models (MCD and DRAMATIC) are shown in gray, with error bars indicating variability with LTST and longitude. The straight line in black shows the saturation temperature of CO₂ at the given pressure level.

Figure 4

Same as Figure 3 but for 70–80°N.

At the lowest altitudes (600 Pa) at latitudes 60–70°N, the magnitude of the temperature variability was greater at the autumn and spring equinoxes than at the winter solstice. Those seasonal changes include the effects of both stationary and transient waves. Hinson [2006] found stationary wave activity peaks near the equinoxes at the 610 Pa pressure level, whereas transient wave activity peaks in early to middle autumn and middle to late winter, with a pause at the winter solstice. These findings were confirmed by Hinson and Wang [2010] through analysis of subsequent MGS radio occultation measurements and are consistent with results derived from MGS TES measurements [Banfield et al., 2004; Lewis et al., 2016].

The autumn and winter increases in temperature variability were also observed at latitudes 70–80°N, but the magnitudes of the variability were significantly smaller than those at 60–70°N. This suggests that there was a marked decline in the temperature variability in autumn and winter at around 70°N.

The observed seasonal changes in temperature were well reproduced by the two numerical models. The significant variability in temperature observed from autumn to winter was also reproduced by the models and was repeated each MY. Therefore, we will neglect interannual changes in seasonal variations in temperature in the following sections.

3.2 Longitudinal and Latitudinal Dependence of Temperature

Figures 5 and 6 show the dependence of temperature on longitude and latitude, respectively, at the pressure level of 100 Pa. The longitude and latitude distributions of temperature were also well reproduced by the two numerical models. As shown in Figures 3 and 4, there was no significant difference among MY. The longitude distribution in Figure 5 shows that there was significant increase in temperature at 60°E and 240°E, which suggests the occurrence of a wave with a wave number of 2. Temperatures close to CO₂ saturation occurred at longitudes where the temperature was low. The variance about the mean of the MGS radio occultation data shown in Figure 5 includes the effects of atmospheric disturbances except stationary waves, namely, mainly the effects of transient waves, and the dependence of temperature on other parameters (LTST, Ls, and latitude within 60–70°N).The latitude distribution in Figure 6 shows that the variability in temperature decreased at higher latitudes, as shown in Figures 3 and 4.

Figure 5

Longitudinal distribution of temperature in winter (Ls = 300–360°) at 60–70°N at 100 Pa. The red dots represent the zonal average of the MGS radio occultation data (MYs 24–27), and the error bars denote the standard deviation about the mean within each longitude bin (10°). The results from numerical models (MCD and DRAMATIC) are shown in gray, with error bars indicating variability with LTST and Ls. The straight line in black shows the saturation temperature of CO₂.

Figure 6

Latitudinal distribution of temperature in winter (Ls = 210–360°) at 60–70°N at 100 Pa. The red dots represent the zonal average of the MGS radio occultation data (MYs 24–27), and the error bars denote the standard deviation about the mean within each latitude bin (2°). The results from numerical models (MCD and DRAMATIC) at 60°E (temperature maximum) and 330°E (temperature minimum) are shown in gray, with error bars indicating variability with LTST and Ls. The straight line in black shows the saturation temperature of CO₂.

3.3 Longitudinal and Vertical Distribution of CO₂ Supersaturation and Its Relationship to Zonal Deviation in Temperature

We investigated the longitudinal and vertical distributions of CO₂ supersaturation at latitudes 60–70°N (Figure 7). The zonal deviation in temperature was also plotted to investigate the relationship of the occurrence of CO₂ supersaturation with the temperature deviation, which was fixed to longitude. We neglected the interannual difference and used the data from all MYs because the differences among MYs were small.

Figure 7

Longitude-pressure cross sections of deviation in temperature from zonal averages (positive deviation in red and negative in blue) for latitudes 60–70°N at (a) Ls = 180–210°, (b) Ls = 210–240°, (c) Ls = 240–270°, (d) Ls = 270–300°, (e) Ls = 300–330°, and (f) Ls = 330–360°. Circles in black indicate the locations where the temperature was below CO₂ saturation (i.e., supersaturation). The size of the circles indicates the degree of supersaturation. Data were taken from the MGS radio occultation measurements for MYs 24–27.

Figure 7 shows that the longitudinal distributions of CO₂ supersaturation in the upper and lower layers are different. The border is located at a pressure level of 200–400 Pa. At higher altitudes, CO₂ supersaturation occurred at the zonal temperature minima at longitudes 150°E and 330°E. This suggests that the occurrence of CO₂ supersaturation is associated with the temperature minima of the stationary wave with s = 2 shown in Figure 5.

At lower altitudes, CO₂ supersaturation occurred not only at the temperature minima but also at the temperature maxima, although supersaturation occurred less frequently at the maxima than at the minima. The degree of supersaturation was greater at the temperature minima than at the temperature maxima. This also suggests that the stationary wave affected the occurrence and degree of CO₂ supersaturation even at lower altitudes. Based on those results, we first focus on the nature of stationary waves that are associated with the occurrence of CO₂ supersaturation and then we analyze the influence of both stationary and transient waves on CO₂ supersaturation.

3.4 Wave Number Analysis of Stationary Waves and CO₂ Supersaturation

To investigate the nature of the stationary waves that might affect the occurrence of CO₂ supersaturation, we extracted the wave components of temperature that were fixed to longitude using zonal harmonics. Referring to Hinson et al. [2001], we assumed that the observed temperature could be modeled as the sum of constant components and zonal harmonics, which were stationary for longitude through a wave number of 4:

(4)

(5)

Here T(λ,p) is the observed temperature at east longitude λ and pressure p, is the zonal mean temperature, is the wave component of temperature, s is the zonal wave number, and C_s and γ_s are the amplitude and phase for s, respectively.

Figure 8 shows the time series of the pressure, longitude, and magnitude of the temperature maxima of the stationary waves with s = 1 and 2 using the MGS radio occultation temperatures for the latitudes of 60–70°N during MYs 24–27. The vertical cross section of the amplitudes of temperature of the stationary waves with s = 1 and 2 immediately after winter solstice (Ls = 270–285°) is shown in Figure 9. The s = 1 wave had local maxima of temperature amplitude at the pressure level of 20–30 Pa at 220–270°E. The s = 2 wave had local maxima of temperature amplitude at the pressure level of 30–100 Pa at ∼60°E and ∼240°E. Banfield et al. [2003] reported similar features using MGS TES; Figure 9 of Banfield et al. [2003] shows that the temperature maximum of the s = 1 wave occurred in the polar jet core (60–70°N) at the pressure level of 30–60 Pa with an amplitude of ∼8 K, and its phase maximum was located at 220–230°E at Ls = 255–285°. Figure 10 of Banfield et al. [2003] shows that the temperature maximum of the s = 2 wave also occurred in the polar jet core (60–70°N) at the pressure level of 80 Pa with an amplitude of ∼8 K and that its phase maximum was located at 45–90°E (and 225–270°E) at Ls = 255–285°. These features are consistent with the features shown in Figures 8 and 9. Therefore, the features shown in Figures 8 and 9, which are derived from the MGS radio occultation measurements, are consistent with the results of Banfield et al. [2003], which were based on MGS TES measurements. Thus, the nature of the s = 1 and s = 2 stationary waves has been confirmed from independent measurements.

Figure 8

Ls changes in (a) pressure levels, (b) longitudes, and (c) amplitudes of the local temperature maximum of stationary waves with s = 1 (circles in red) and s = 2 (crosses in blue). The pressure levels of Figures 8b and 8c are shown in Figure 8a. Data were taken from the MGS radio occultation measurements for MYs 24–27.

Figure 9

Longitude-pressure cross sections of temperature amplitudes of (a) s = 1 and (b) s = 2. Positive and negative components are colored in red and blue, respectively. Contour lines in black are drawn every 2 K. Data were taken from the MGS radio occultation measurements during Ls = 270–285° for MYs 24–27.

Figures 8 and 9 also suggest an insignificant contribution of the temperature minima of the s = 1 stationary wave, which occurred at the pressure level of 20–30 Pa at 40–70°E, to CO₂ supersaturation, and a much larger contribution of the temperature minima of the s = 2 stationary wave, which occurred at the pressure level of 30–100 Pa at 150°E and 330°E. To investigate the difference in the contribution of the two waves to CO₂ supersaturation, we examined the amplitudes of the temperature of the s = 1 and s = 2 waves and the average temperature, focusing on the longitude of the temperature minimum and maximum (Figure 10). The absolute values of the temperature of the s = 2 wave approached the CO₂ saturation temperature at the longitude of its temperature minimum (150–160°E). However, the amplitude of the s = 1 wave was ∼10 K, which was comparable to that of the s = 2 wave, but the absolute values of temperature at the longitude of the temperature minimum (50–60°E) did not reach the CO₂ saturation temperature. Therefore, the contribution of the s = 1 wave to CO₂ supersaturation seems to be insignificant, despite the fact that it had a similar amplitude to that of the s = 2 wave.

Figure 10

Amplitudes of temperature (upper panels) and averaged temperature (lower panels) at the pressure level of (a) 30 Pa (s = 1) and (b) 100 Pa (s = 2) at the longitudes of the local maximum and minimum of each wave. Data were taken from the MGS radio occultation measurements for MYs 24–27. The black line indicates the saturation temperature of CO₂ for each pressure. Error bars in the lower panels are the standard deviation for each average.

The smaller contribution of the s = 1 wave can be attributed in part to the fact that the CO₂ saturation temperature decreases when pressure decreases with increasing altitude. The s = 1 wave, which was located at slightly higher altitudes than the s = 2 wave, requires a greater decrease in temperature to cause CO₂ supersaturation.

It is interesting to know how much of the temperature variance shown in Figure 3 was captured by the stationary wave model shown in equation 5. We found that the temperature variances of 10–30% at 30 Pa and 20–60% at 100 Pa during the northern winter shown in Figure 3 were captured by the stationary waves with s = 1 and s = 2, respectively. The remaining temperature variance should be explained by other atmospheric disturbances, including transient waves. In the next section, we investigate the effect of not only stationary waves but also transient waves on CO₂ supersaturation.

3.5 Effect of Stationary and Transient Waves on CO₂ Supersaturation

To consider the effects of both stationary and transient waves on CO₂ supersaturation, we assumed that the observed temperature could be modeled as the sum of a gradual seasonal trend and zonal harmonics, which represented the dynamic oscillations caused by stationary and transient waves and were dependent on longitude and universal time t_U through a wave number of 3 [Hinson, 2006]:

(6)

(7)

Here T(λ,Ls,t_U,p) is the observed temperature, is the seasonal trend depending only on Ls, is the wave component of temperature, σ is the wave frequency in sol⁻¹, and B_s and α_s are the amplitude and phase of s, respectively.

Least squares fitting of the observed temperature to the above equations was conducted within an Ls window with width D_Ls of 8° (D_sol=12–18 sol, depending on Ls) to make periodograms for the waves with −0.25 sol⁻¹<σ≤ +0.75 sol⁻¹ [Hinson, 2006] by the frequency step of 0.1 sol⁻¹. We calculated one periodogram using an Ls step of 0.1°. We looked for local maxima in the periodograms to determine the frequencies of the waves, which were detected using the least squares. We finally reconstructed the detected atmospheric waves by using the frequencies and other wave parameters obtained using the least squares. The estimated frequency resolution δ_sol in the least squares analysis is approximately 1/D_sol [Hinson, 2006]. Therefore, we regarded the waves with a frequency of |σ|≤δ_sol/2 as stationary waves and determined that transient waves were all waves other than the stationary waves.

The amplitude of the finally reconstructed waves, which include all of the waves detected in the least squares, namely, the result of superposition of stationary and transient waves, is expressed as

(8)

Here and are the amplitudes of stationary and transient waves reconstructed in the least squares analysis, respectively. To check whether the reconstructed waves caused CO₂ supersaturation at a given point of pressure, Ls, and longitude, we subtracted the saturation temperature T_s from , , and , where T₀ is the average temperature ( ). If the value of for a given reconstructed stationary wave was negative, for example, we judged that the reconstructed stationary wave caused CO₂ supersaturation. To check whether the phases of the reconstructed waves were positive or negative, we focused on the signs of , , and .

In Figure 11, we show an example of reconstructed waves at a pressure level of 610 Pa during Ls = 325–335° (605.2–623.0 sol) in MY 24. During the period, a stationary wave with s = 1 and transient waves with s = 1–3 and with a period of 2–3 sol were dominant. Figure 11a shows the difference in temperature of the reconstructed waves from the CO₂ saturation temperature ( ), showing that the least squares analysis during this period could reproduce only about half of the supersaturation events found in the MGS radio occultation data. However, the values of depend not only on the quality of the least squares but also on the quality of the estimation of the absolute value in T₀. To avoid this problem, we investigated , which is the relationship between the phase of the reconstructed waves and the CO₂ supersaturation events (Figure 11b). Almost all of the CO₂ supersaturation events observed were included in the negative phase of the reconstructed waves. This suggests that the supersaturation events were affected by temperature minima caused by the superposition of stationary and transient waves. Figures 11c and 11d show the stationary wave component ( ) and the transient wave component ( ). While many supersaturation events observed were included in the negative phase of the stationary waves (mainly a s = 1 wave), some of the supersaturation events (e.g., the sample at Ls = 328° and 270°E) were found in the positive phase of the stationary waves. The temperature disturbance caused by the stationary waves for this sample is about +4 K, as shown in Figure 11c, while the temperature disturbance caused by transient waves is about −9 K (Figure 11d). Supersaturation of this sample is thought to have occurred because the magnitude of the negative disturbance caused by the transient waves was larger than that of the positive disturbance caused by the stationary waves.

Figure 11

Hovmöller diagrams of temperature components of (a) , (b) , (c) , and (d) (see text), which were reconstructed from the least squares analysis (color shaded) and CO₂ supersaturation events observed by the MGS radio occultation (crosses) at 60–70°N and 610 Pa during Ls = 325–335° in MY 24.

We conducted a statistical analysis to investigate the contribution of the reconstructed stationary and transient waves to CO₂ supersaturation events observed by the MGS radio occultation (Table 1). At a lower altitude (610 Pa), the reconstructed stationary waves alone reproduced only ∼5% of the supersaturation events observed, while the reconstructed transient waves alone reproduced slightly less than half of the events. The superposition of the reconstructed stationary and transient waves, however, reproduced more than half the supersaturation events. The great majority of supersaturation events were included in the negative phase of the superimposed waves. Table 1 indicates that superposition of stationary and transient waves results in more frequent CO₂ supersaturation. The importance of superposition on supersaturation was also shown at a higher altitude (100 Pa), although very few samples were available.

Table 1. Proportion of Reconstructed MGS Radio Occultation Temperature Samples Which Satisfies the Condition Shown in the First Line (in a Percentage)

Pressure	Sample
(Pa)	Number	−Ts≤0	−Ts≤0	−Ts≤0	≤0	≤0	≤0
610	471	55.0	4.9	46.3	90.0	13.2	27.4
100	10	90.0	0.0	40.0	100.0	0.0	10.0

The results of the least squares analysis in this section clearly show that the superposition of stationary and transient waves plays a significant role in CO₂ supersaturation, but the results do not refute the fact that stationary s = 2 waves lower the background temperature at a pressure level of 100 Pa, as shown in section 3.4. We confirmed that the intense seasonal variation in the atmospheric condensation in the northern polar regions reported by Hu et al. [2012] could be attributed not only to transient waves including baroclinic waves, which Hu et al. [2012] suggested as one candidate, but also to stationary waves, which also play a role in lowering the background temperature.

Although we found that large-scale waves played a significant role in CO₂ supersaturation, the auxiliary roles of other small-scale waves and atmospheric disturbances should not be excluded. Spiga et al. [2012] concluded that CO₂ supersaturation in the Martian mesosphere occurred in “cold pockets” caused by atmospheric gravity waves in the background temperature, which is not cold enough to cause CO₂ supersaturation by itself. Similar situations can occur in the altitude ranges of the present study; the superposition of other waves and atmospheric disturbances on the large-scale waves, the focus of this study, can also facilitate CO₂ supersaturation.

3.6 Comparison With Numerical Model

We calculated the average of the degree of CO₂ supersaturation derived from DRAMATIC (Figure 12) for comparison with the MGS radio occultation results shown in Figure 7. The averaged values were weighted by the occurrence of CO₂ supersaturation. The longitudinal structure of CO₂ supersaturation was well reproduced by the model; increases in the degree of CO₂ supersaturation occurred at 150–160°E and 310–320°E at higher altitudes, and there was almost no longitudinal dependence at lower altitudes.

Figure 12

Longitude-pressure cross sections of averaged degree of CO₂ supersaturation derived from DRAMATIC output for latitude 69.2°N at (a) Ls = 180–210°, (b) Ls = 210–240°, (c) Ls = 240–270°, (d) Ls = 270–300°, (e) Ls = 300–330°, and (f) Ls = 330–360°.

The vertical distribution of CO₂ supersaturation calculated by the model, however, extended to higher altitudes; no CO₂ supersaturation occurred above 100 Pa (above 30 Pa if we do not consider the 1σ measurement uncertainty of temperature) in the observations but was still present at these altitudes in the model outputs. In addition to the problem the model has with calculations in those altitude regions, a possible explanation for this difference is that the initial temperature at the uppermost level used for the radio occultation retrievals must be assumed when starting temperature retrieval from the top of the profile. Therefore, the temperature values at levels close to the uppermost level of the profile could have been affected by the initial value of temperature. The original MGS radio occultation data from PDS utilized two fixed values (160 K and 170 K) for the initial values of temperature. Rederivation with more realistic initial values might confirm the degree of CO₂ supersaturation at higher altitudes, which is beyond the scope of the present study.

Using a similar method as used for the analysis of the MGS radio occultation data shown in section 3.5, we conducted least squares fitting and a statistical analysis to investigate the contribution of stationary and transient waves to CO₂ supersaturation events found in the DRAMATIC outputs (Table 2). We considered the same ranges of wave number and frequency as in the MGS radio occultation analysis. The result showed that it is difficult for stationary or transient waves to cause CO₂ supersaturation independently, without superposition of both waves, which is consistent with the result of the MGS radio occultation data. We can also see that the proportion of the samples satisfying ( ) increases (decreases) at higher levels, suggesting that the contribution of stationary waves increases in the higher altitude regions.

We also examined the latitudinal dependence of CO₂ supersaturation in the model. CO₂ supersaturation was insignificant at lower latitudes (63.7°N) and had less longitudinal dependence at higher latitudes (74.7°N and 80.3°N). Hence, the longitudinal dependence of CO₂ supersaturation was localized around 70°N, which is consistent with the fact that a strong s = 2 stationary wave was found only around the polar jet, which was located at ∼70°N [Banfield et al., 2003], and the fact that baroclinic waves are also confined to the polar jet [Banfield et al., 2004; Lewis et al., 2016], suggesting that both stationary and transient waves are equally viable as a source of CO₂ supersaturation around 70°N.

Table 2. Proportion of Reconstructed DRAMATIC Temperature Samples Which Satisfies the Condition Shown in the First Line (in a Percentage)

Pressure	Sample
(Pa)	Number	−Ts≤0	−Ts≤0	−Ts≤0	≤0	≤0	≤0
631	10222	19.5	0.0	12.3	98.4	1.3	23.2
100	1171	0.0	0.0	0.0	98.8	8.5	16.1

4 Concluding Remarks

We investigated seasonal changes in temperature retrieved by MGS radio occultation measurements and determined the relationship between large-scale atmospheric waves including stationary and transient waves and the occurrence of CO₂ supersaturation in the northern hemisphere winter on Mars. The s = 1 stationary wave had a maximum of temperature amplitude at a longitude of ∼220–270°E at a pressure level of 20–30 Pa, and the s = 2 stationary wave had two maxima of temperature amplitude at ∼60°E and ∼240°E at 30–100 Pa. These results are consistent with previous studies of stationary waves in the Martian atmosphere. The s = 2 stationary wave played a significant role in lowering the background temperature, and it was close to the CO₂ saturation temperature at around 100 Pa, where strong longitudinal dependence of CO₂ supersaturation was observed, but the stationary wave alone was not sufficient to cause CO₂ supersaturation. In addition to stationary waves, transient waves were also important and the superposition of both waves had a significant role in causing CO₂ supersaturation. We observed no well-defined interannual dependence of these features during the study period (MYs 24–27), which suggests that these phenomena occur every Martian year.

The observations of CO₂ removal from the atmosphere due to condensation and deposition onto the polar ground are important for the quantitative estimation of the development and decay of the seasonal ice cap [Hayne et al., 2014]. Because CO₂ supersaturation can lead to the generation of CO₂ (dry ice) clouds and snowfall, the longitudinal dependence of CO₂ supersaturation observed in the present study provides information about the nature of CO₂ condensation and deposition in the polar regions on Mars. It has been shown that the mechanism of polar ice cap formation has longitudinal dependence at the south pole [Giuranna et al., 2008]. Future studies on the effects of snowfall due to CO₂ supersaturation at specific longitudes in the northern polar region will elucidate the role of such CO₂ snowfall in forming the northern seasonal ice cap.

Acknowledgments

The authors are grateful to David P. Hinson and the MGS radio occultation team for providing pressure-temperature data from the radio occultation measurements. The MGS radio occultation data are available at the Atmospheres Node of the NASA Planetary Data System (http://atmos.pds.nasa.gov/MGS/tp.html). Atmospheric data of the DRAMATIC MGCM are available from T.K. ([email protected]). This work was supported by JSPS KAKENHI grant 15K05289.