First detection of wave interactions in the middle atmosphere of Mars

Transcription

1 GEOPHYSICAL RESEARCH LETTERS, VOL. 38,, doi: /2010gl045592, 2011 First detection of wave interactions in the middle atmosphere of Mars Y. Moudden 1 and J. M. Forbes 1 Received 22 September 2010; revised 16 November 2010; accepted 29 November 2010; published 22 February [1] Planetary wave tide interactions are known to exist in Earth s atmosphere and to account for some of its diurnal variability, or put another way, for variations in its diurnal cycle over time scales from days to weeks. In this study, using an elaborate arrangement of temperature profiles at a single local time from MRO/Mars Climate Sounder, we show that planetary wave tide interactions also occur in the middle atmosphere of Mars. These interactions excite secondary waves that amplify on average with altitude and appear to be an important source of tidal and longitudinal variability. Citation: Moudden, Y., and J. M. Forbes (2011), First detection of wave interactions in the middle atmosphere of Mars, Geophys. Res. Lett., 38,, doi: / 2010GL Introduction [2] In Earth s middle atmosphere, between about 20 and 100 km, considerable theoretical and observational evidence exists for the existence of secondary waves that arise from planetary wave tide and tide tide nonlinear interactions. The theoretical basis was first put forward by Teitelbaum and Vial [1991] who show that the secondary waves are characterized by the sum and differences of the primary waves frequencies and zonal wavenumbers. An equivalent view is that the secondary waves are the sideband waves resulting from the modulation of the tide by a longer period planetary wave. An early example that was discovered [Cevolani and Kingsley, 1992] is the modulation of the solar semidiurnal tide by the 2 day wave, which gives rise to a 9.6 h wave with zonal wavenumber s = 5 (westward propagating) and 16 h wave with s = 1 (eastward propagating). Using a numerical model Palo et al. [1999] demonstrated that these two waves, once generated, propagate as independent oscillations well into the thermosphere. Numerous other examples exist; for instance, Hagan and Roble [2001] and Angelats i Coll and Forbes [2002] demonstrated that the modulation of diurnal and semidiurnal tides, respectively, by stationary planetary waves lead to secondary diurnal and semidiurnal oscillations (with the sum and difference zonal wavenumbers) that propagate into the km region and are detectable there [e.g., Forbes et al., 2003; Forbes and Wu, 2006]. Furthermore, the modeling work of Hagan et al. [2009] predicts that the diurnal eastward propagating s = 3 and westward propagating s = 1 (sun synchronous) tides interact with each other to produce a stationary planetary wave with s = 4 and an eastward propagating semidiurnal 1 Department of Aerospace Engineering Science, University of Colorado at Boulder, Boulder, Colorado, USA. Copyright 2011 by the American Geophysical Union /11/2010GL tide with s = 2 in the lower thermosphere. And, planetary waves can interact with each other to produce secondary planetary waves [Pogoreltsev et al., 2002]. [3] The study of planetary wave tide interactions is of importance for two reasons. First, this represents one contribution to tidal variability over time scales of order days to weeks. Understanding this variability is relevant to the interpretation of observations and to atmospheric prediction. Second, planetary waves are generally not capable of propagating from the middle atmosphere into the thermosphere. However, if planetary waves modulate tides, then the tidal oscillations can propagate to higher altitudes and imprint the planetary wave periodicity at thermospheric heights. Terrestrial tides also modulate the dynamo generation of electric fields at the planetary wave period, and these electric fields map along magnetic field lines into the upper parts of the ionosphere where they are capable of redistributing plasma. In Mars atmosphere, we suspect that similar processes are occurring, and that this might be a mechanism for modulating densities in the km region at planetarywave periods. Presumably, this could be of practical interest for better operational predictions related to aerobraking or the initial stages of entry, descent and landing (EDL). It is the purpose of this paper to provide the first observational evidence of tide PW interactions in the middle atmosphere of Mars. A newly developed technique designed to circumvent the apparent limitation of sun synchronous observational sampling to explore tidal variability is employed for this purpose. [4] The following section describes the methodology and the observational data. Section 3 illustrates the spectral signatures that we interpret as arising from planetary wave tide interactions. Section 4 provides a summary of our results. 2. Data Description and Analysis Method [5] The data used in this study are temperature profiles from the Mars Climate Sounder (MCS) instrument onboard the Mars Reconnaissance Orbiter (MRO) spacecraft. MRO s orbit is nearly polar and Sun synchronous with an inclination of At any given time the spacecraft s local solar time (LST) is near 3 p.m. or 3 a.m. during the northward or southward nodes respectively, except poleward of 75 latitude where the spacecraft shifts from 3 p.m. to 3 a.m and vice versa in the opposite polar region. The orbit s period is 112 min which translates to nearly 13 passages per sol [Zurek and Smrekar, 2007]. Each orbit is shifted by about 27 in longitude from the earlier one in either the dayside or nightside node. In other words: while the spacecraft has performed one orbit the planet has rotated by 27. This value takes the form of a longitude resolution in the way we arrange the data. The retrieved profiles extend from the 1of5

2 Figure 1. Equatorial temperature profiles from MCS arranged using pseudo longitudes. Pseudo longitudes shown on the upper row of the x axis legend are the traditional longitudes incremented by 360 every time the planet completes one revolution in one sol. The observations included here span 66 sol between L s = 70 and 100. The y axis represents the altitude in km. surface to about km altitude covering the entire troposphere and mesosphere of Mars [McCleese et al., 2008]. The analysis here is restricted to nighttime observations; the daytime observations suffer from large latitude gaps but are nevertheless consistent with nighttime observations presented here. Figure 1 provides an example of how the data is arranged. Each passage of the satellite from north to south provides a track of observations across different latitudes and altitudes. The next passage provides a similar track only shifted by about 27 from the previous one. These tracks are laid down on a latitude longitude map with only one difference from the traditional latitude longitude maps: once the planet has completed a revolution during 1 sol period the longitudes of the new tracks are incremented by 2p to form a continuous time series. Each cycle resulting from observations collected during a single planet s revolution or 1 sol is counted using integers from 1 to 66 in Figure 1. We thus define a pseudo longitude l p from the traditional longitude l as: l p = l + c 2p where c denotes the number of completed cycles. c is also the number of sols elapsed since the start of the data series. This equivalency between time and pseudo longitude is a direct result of the Sunsynchronous nature of the orbit since in a Sun synchronous configuration: t = t + l p sol/2p where t and t are the absolute and local times respectively. This same data arrangement is used and explained with further details by Moudden and Forbes [2010]. The first orbit in Figure 1 is orbit number 8348 which corresponds to an Earth date of May 08, 2008 and a martian solar longitude of Figure 1 is a plot of equatorial temperature profiles measured by MCS during a 66 sol period from this first orbit. [6] This arrangement allows the detection of slow moving waves. Theoretically the smallest frequency that can be detected from a 66 sol time series is 1/(2 66 sol) which is equivalent to a period of 33 sol. In a Sun synchronous configuration a tide appears with a zonal wavenumber of s n where s is the actual zonal wavenumber (in a universal time configuration) and n is the solar harmonic (number of local oscillations per sol) [see Moudden and Forbes, 2008]. Similarly a planetary wave with a zonal wavenumber m and a solar harmonic d appears to have a zonal wavenumber equal to m d from a Sun synchronous orbit. A (n, s) tide modulated by a slowly moving (d, m) PW produces in principle two secondary waves whose time and longitudes wavenumbers are (n + d, s + m) and (n d, s m) respectively [Teitelbaum et al., 1989; Teitelbaum and Vial, 1991]. In an analogous fashion to tides and PWs, secondary waves appear in a fixed local time with a zonal wavenumber equal to s + m n d or s m n + d. 3. Signature of PW Tide Interactions [7] It is expected that a spectral analysis of MCS data arranged as explained above will yield signatures of tides, PWs and secondary waves. The unknowns are (n, s) values for the tides, (d, m) for PWs, (n + d, s + m) and (n d, s m) values for the secondary waves. Spectral analysis of MCS temperature profiles would yield the values of s n, m d and s ± m n d of the dominating waves. Figure 2 shows the spectral analysis of temperatures in Figure 1 at three altitudes: 15, 55 and 82 km. The x axis represents the frequency in number of cycles per 2p in pseudo longitude and the y axis the amplitude in K. The major peaks at all altitudes correspond to integer values which directly points to tides: among all possible values of s n, m d and s ± m n d only s n are integers. These integer peaks are marked by blue lines. The abbreviated name of the diurnal and semidiurnal tides potentially involved in the observed integer peaks are indicated in Figure 2 (top). D stands for diurnal, S for semidiurnal, E and W for eastward and westward propagating tides respectively. Each abbreviated name ends with the zonal wavenumber. Based on modeling work [Moudden and Forbes, 2008] most westward propagating and terdiurnal tides are assumed to be of lesser amplitude although they do contribute to each peak. The migrating tides are not distinguishable from the average since s n = 0. It is apparent from Figure 2 that tidal amplitudes increase with altitude on average, and that the diurnal standing (D0), eastward propagating with s = 1 (DE1) and s = 2 (DE2) are among the strongest tides in the atmosphere of Mars which confirms simulation results of Moudden and Forbes [2008]. [8] Since planetary waves are slower than any tides (d <1), any PW s signature will be shifted from integer values (tidal peaks) by d. Secondary waves resulting from PWtide interactions will also be shifted from integer values by d since their apparent zonal wavenumber from a Sunsynchronous orbit is s ± m n d. In Figure 2 there is a 2of5

3 Figure 2. Spectral analysis using Fast Fourier Transform of the data in Figure 1 at three different altitudes: 15, 55 and 82 km. The x axis is wavenumber in pseudo longitude and the y axis is the amplitude in K. Tidal peaks at integer values are marked by blue lines. Secondary peaks corresponding to a shift in frequency equal to 1/5.4 are marked by red lines. The amplitudes of some peaks which are not accommodated in the graphs are indicated numerically. recurring shift that points to a value of d = 1/5.4 (2p) 1 or d = 1/5.4 sol 1 (see Appendix for the equivalency between 1 sol and 2p). This points to the presence, at the time these observations were recorded, of a dominating PW with a period of 5.4 sol; indeed a spectral peak at 1/5.4 sol 1 is seen at the lowest two heights. These secondary peaks, marked by red lines, exist in the vicinity of different integer values and can only be interpreted by a 5.4 sol PW interacting with various tides (see Moudden and Forbes [2010] on how to interpret the side peaks). Since the actual zonal wavenumber of the PW is unknown it is not possible to determine which secondary peaks are a direct signature of the PW as opposed to an indirect signature through interaction with tides. [9] These secondary waves have frequencies close to but not equal to the solar harmonics of tides. Their amplitudes appear to be generally on the order of 1/4th to 1/3rd of the largest tides at the same altitude. [10] The amplitudes of the secondary waves in K are shown in Figure 3. Since MCS offers 3D spatial coverage this kind of spectral analysis allows one to discover the latitude altitude structure of the secondary waves and the parent tides. Figure 3 shows the amplitudes of the first three wavenumbers (1, 2 and 3 in pseudo longitude frequency) and their six sidebands. The top row shows the integrated amplitudes of the tidal broadened lines. Tides potentially responsible for the observed amplitudes are indicated in Figure 3 (top). The amplitudes of the left and right sidebands are shown in Figures 3 (middle) and 3 (bottom). The strongest tides appear to be D0 and DE1 which can reach 10 K below 80 km altitude. The secondary waves have maximum amplitudes that are about one quarter to one third of the strongest tides. This confirms that secondary waves are second to tides in defining the diurnal variability in the atmosphere of Mars. Although this analysis does not cover any aerobraking altitudes, it appears that these amplitudes grow with altitude and are expected to amplify in strength into the thermosphere, affecting the variability at aerobraking altitudes. [11] It is important to note that tides responsible for a peak in Figure 2 are not necessarily responsible for the associated sidebands. This is only true if the PW is standing or m =0. 3of5

4 Figure 3. Amplitudes in K of the most prominent tides and sidebands in a latitude altitude format. (top) Amplitudes of the tides corresponding to wavenumbers 1, 2 and 3 in Figure 2 and (middle and bottom) their corresponding sidebands. This also applies in Figure 3: the tides whose amplitudes are shown Figure 3 (top) are not necessarily exciting the secondary waves Figure 3 (bottom). 4. Summary [12] In this study we show that PW tide interactions do occur in the middle atmosphere of Mars. This modulation of tides by PWs exists throughout the troposphere and mesosphere and is likely to exist in the thermosphere. Interactiongenerated waves appear to hold non negligible importance in explaining the diurnal variability since their amplitudes are about 1/4 1/3 of the largest tidal amplitudes. This is particularly important for characterizing the variability at aerobraking altitudes. Further analysis is necessary to extract detailed information about the tides and planetary waves involved and how the interactions occur. Appendix [13] Time and longitude are equivalent in a constant local time format. By definition: t = t + l sol/2p. Local time (t ) takes values between 0 and 1 sol (or 0 to 24 hours). The relationship therefore only holds when the absolute time t is restricted to the same interval (0 1 sol) since the geographical longitude l does not exceed 2p. Ift represents for example the internal clock of the spacecraft which counts time elapsed in seconds from the start of the operations a new definition of longitudes is in order. Pseudo longitude 4of5

5 l p can be defined by the relationship above as l p =(t t ) 2p/sol. [14] Acknowledgments. This work was supported under grant NNX09AL24G from the NASA Mars Fundamental Research Program to the University of Colorado. References Angelats i Coll, M., and J. M. Forbes (2002), Nonlinear interactions in the upper atmosphere: The s = 1 and s = 3 nonmigrating semidiurnal tides, J. Geophys. Res., 107(A8), 1157, doi: /2001ja Cevolani, G., and S. Kingsley (1992), Non linear effects on tidal and planetary waves in the lower thermosphere, Adv. Space Res., 12, Forbes, J. M., and D. Wu (2006), Solar tides as revealed by measurements of mesosphere temperature by the MLS experiment on UARS, J. Atmos. Sci., 63, Forbes, J. M., X. Zhang, E. R. Talaat, and W. Ward (2003), Nonmigrating diurnal tides in the thermosphere, J. Geophys. Res., 108(A1), 1033, doi: /2002ja Hagan, M. E., and R. G. Roble (2001), Modeling diurnal tidal variability with the NCAR TIME GCM, J. Geophys. Res., 106, 24,869 24,882. Hagan, M. E., A. Maute, and R. G. Roble (2009), Tropospheric tidal effects on the middle and upper atmosphere, J. Geophys. Res., 114, A01302, doi: /2008ja McCleese, D. J., et al. (2008), Intense polar temperature inversion in the middle atmosphere of mars, Nat. Geosci., 1, , doi: / ngeo332. Moudden, Y., and J. M. Forbes (2008), Topographic connections with density waves in Mars aerobraking regime, J. Geophys. Res., 113, E11009, doi: /2008je Moudden, Y., and J. M. Forbes (2010), A new interpretation of Mars aerobraking variability: Planetary wave tide interactions, J. Geophys. Res., 115, E09005, doi: /2009je Palo, S. E., R. G. Roble, and M. E. Hagan (1999), Middle atmosphere effects of the quasi two day wave determined from a general circulation model, Earth Planets Space, 51, Pogoreltsev, A. I., I. N. Fedulina, N. J. Mitchell, H. G. Muller, Y. Luo, C. E. Meek, and A. H. Manson (2002), Global free oscillations of the atmosphere and secondary planetary waves in the mesosphere and lower thermosphere region during August/September time conditions, J. Geophys. Res., 107(D24), 4799, doi: /2001jd Teitelbaum, H., and F. Vial (1991), On tidal variability induced by nonlinear interaction with planetary waves, J. Geophys. Res., 96, 14,169 14,178. Teitelbaum, H., F. Vial, A. H. Manson, R. Giraldez, and M. Massbeuf (1989), Non linear interaction between the diurnal and semidiurnal tides: Terdiurnal and diurnal secondary waves, J. Atmos. Terr. Phys., 51, Zurek, R. W., and S. E. Smrekar (2007), An overview of the Mars Reconnaissance Orbiter (MRO) science mission, J. Geophys. Res., 112, E05S01, doi: /2006je J. M. Forbes and Y. Moudden, Department of Aerospace Engineering Science, University of Colorado at Boulder, UCB 429, Boulder, CO 80309, USA. (moudden@colorado.edu) 5of5