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Measurement of Martian atmospheric winds by the O2 1.27 μm airglow observations using Doppler Michelson Interferometry: A concept study

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Abstract

China’s Mars exploration mission has stimulated tremendous interest in planetary science exploration recently. To propose potential scientific research projects, this study presents a concept simulation for the measurement of Martian atmospheric winds using the Doppler Michelson interferometry technique. The simulation is based on the satellite instrument initially designed for the Dynamic Atmosphere Mars Observer (DYNAMO) project to measure vertical profiles of winds from the 1.27 μm airglow observations in the Martian atmosphere. A comprehensive DYNAMO measurement simulation forward model based on an orbit submodel, an atmospheric background field submodel, and an instrument submodel is developed using the Michelson equation. The simulated interferogram signal over the field of view (FOV) calculated by the forward model is associated with the filter transmittance function, column emission rate of airglow, wind velocity, temperature, and the Michelson phase. The agreement between the derived atmospheric signals from the simulated interferogram without altitude inversion and the input parameters used to initiate the forward model confirms the validity of the forward model.

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References

  • Baird D T, Tolson R, Bougher S, Steers B. 2007. Zonal wind calculations from Mars global surveyor accelerometer and rate data. J Spacecr Rocket, 44: 1180–1187

    Article  Google Scholar 

  • Banfield D, Conrath B, Pearl J C, Smith M D, Christensen P. 2000. Thermal tides and stationary waves on Mars as revealed by Mars Global Surveyor thermal emission spectrometer. J Geophys Res, 105: 9521–9537

    Article  Google Scholar 

  • Banfield D, Rodriguez-Manfredi J A, Russell C T, Rowe K M, Leneman D, Lai H R, Cruce P R, Means J D, Johnson C L, Mittelholz A, Joy S P, Chi P J, Mikellides I G, Carpenter S, Navarro S, Sebastian E, Gomez-Elvira J, Torres J, Mora L, Peinado V, Lepinette A, Hurst K, Lognonné P, Smrekar S E, Banerdt W B. 2019. InSight auxiliary payload sensor suite (APSS). Space Sci Rev, 215: 4

    Article  Google Scholar 

  • Barth C A, Hord C W. 1971. Mariner ultraviolet spectrometer: Topography and polar cap. Science, 173: 197–201

    Article  Google Scholar 

  • Barth C A, Hord C W, Stewart A I, Lane A L, Dick M L, Anderson G P. 1973. Mariner 9 ultraviolet spectrometer experiment: Seasonal variation of ozone on Mars. Science, 179: 795–796

    Article  Google Scholar 

  • Bertaux J L, Gondet B, Lefèvre F, Bibring J P, Montmessin F. 2012. First detection of O2 1.27 μm nightglow emission at Mars with OMEGA/MEX and comparison with general circulation model predictions. J Geophys Res, 117: E00J04

    Google Scholar 

  • Benna M, Bougher S W, Lee Y, Roeten K J, Yiğit E, Mahaffy P R, Jakosky B M. 2019. Global circulation of Mars’ upper atmosphere. Science, 366: 1363–1366

    Article  Google Scholar 

  • Bougher S W, Pawlowski D, Bell J M, Nelli S, McDunn T, Murphy J R, Chizek M, Ridley A. 2015. Mars Global Ionosphere-Thermosphere Model: Solar cycle, seasonal, and diurnal variations of the Mars upper atmosphere. J Geophys Res-Planets, 120: 311–342

    Article  Google Scholar 

  • Chiang C Y, Tam W Y, Chang T F. 2018. Variations of the 630.0 nm airglow emission with meridional neutral wind and neutral temperature around midnight. Ann Geophys, 36: 1471–1481

    Article  Google Scholar 

  • Cho Y M, Shepherd G. 2015. Resolving daily wave 4 nonmigrating tidal winds at equatorial and midlatitudes with WINDII: DE3 and SE2. J Geophys Res-Space Phys, 120: 10053–10068

    Article  Google Scholar 

  • Christensen P R, Anderson D L, Chase S C, Clark R N, Kieffer H H, Malin M C, Pearl J C, Carpenter J, Bandiera N, Brown F G, Silverman S. 1992. Thermal emission spectrometer experiment: Mars Observer mission. J Geophys Res, 97: 7719–7734

    Article  Google Scholar 

  • Clancy R T, Wolff M J, Lefèvre F, Cantor B A, Malin M C, Smith M D. 2016. Daily global mapping of Mars ozone column abundances with MARCI UV band imaging. Icarus, 266: 112–133

    Article  Google Scholar 

  • Conrath B, Curran R, Hanel R, Kunde V, Maguire W, Pearl J, Pirraglia J, Welker J, Burke T. 1973. Atmospheric and surface properties of Mars obtained by infrared spectroscopy on Mariner 9. J Geophys Res, 78: 4267-4278

    Article  Google Scholar 

  • Crowley G, Tolson R H. 2007. Mars thermospheric winds from mars global surveyor and mars odyssey accelerometers. J Spacecr Rocket, 44: 1188–1194

    Article  Google Scholar 

  • Encrenaz T, Greathouse T K, Lefèvre F, Atreya S K. 2012. Hydrogen peroxide on Mars: Observations, interpretation and future plans. Planet Space Sci, 68: 3–17

    Article  Google Scholar 

  • Encrenaz T, Greathouse T K, Lefèvre F, Montmessin F, Forget F, Fouchet T, DeWitt C, Richter M J, Lacy J H, Bézard B, Atreya S K. 2015. Seasonal variations of hydrogen peroxide and water vapor on Mars: Further indications of heterogeneous chemistry. Astron Astrophys, 578: A127

    Article  Google Scholar 

  • Ern M, Trinh Q T, Preusse P, Gille J C, Mlynczak M G, Russell James M. I, Riese M. 2018. GRACILE: A comprehensive climatology of atmospheric gravity wave parameters based on satellite limb soundings. Earth Syst Sci Data, 10: 857–892

    Article  Google Scholar 

  • Fedorova A, Korablev O, Perrier S, Bertaux J L, Lefèvre F, Rodin A. 2006. Observation of O2 1.27 μm dayglow by SPICAM IR: Seasonal distribution for the first Martian year of Mars Express. J Geophys Res, 111: E09S07

    Google Scholar 

  • Forget F, Hourdin F, Fournier R, Hourdin C, Talagrand O, Collins M, Lewis S R, Read P L, Huot J P. 1999. Improved general circulation models of the Martian atmosphere from the surface to above 80 km. J Geophys Res, 104: 24155–24175

    Article  Google Scholar 

  • Forget F, Beaudin G, Encrenaz A D P, Gheudin M, Thomas B, Capderou M, Dassas K, Ricaud P, Urban J, Frerking M, Gulkis S, Janssen M, Riley L, Encrenaz T, Lellouch E, Hartogh P, Clancy T. 2002. Microwave sounding of the Martian atmosphere with mambo. EGS XXVII General Assembly, 27

    Google Scholar 

  • Gault W A, Brown S, Moise A, Liang D, Sellar G, Shepherd G G, Wimperis J. 1996. ERWIN: An E-region wind interferometer. Appl Opt, 35: 2913–2922

    Article  Google Scholar 

  • Gérard J C, Aoki S, Willame Y, Gkouvelis L, Depiesse C, Thomas I R, Ristic B, Vandaele A C, Daerden F, Hubert B, Mason J, Patel M R, López-Moreno J J, Bellucci G, López-Valverde M A, Beeckman B. 2020. Detection of green line emission in the dayside atmosphere of Mars from NOMAD-TGO observations. Nat Astron, 4: 1049–1052

    Article  Google Scholar 

  • Gierasch P, Sagan C. 1971. A preliminary assessment of Martian wind regimes. Icarus, 14: 312–318

    Article  Google Scholar 

  • Haberle R M, Leovy C B, Pollack J B. 1979. A numerical model of the Martian polar cap winds. Icarus, 39: 151–183

    Article  Google Scholar 

  • Haberle R M, Pollack J B, Barnes J R, Zurek R W, Leovy C B, Murphy J R, Lee H, Schaeffer J. 1993. Mars atmospheric dynamics as simulated by the NASA Ames General Circulation Model: 1. The zonal-mean circulation. J Geophys Res, 98: 3093–3123

    Article  Google Scholar 

  • Hanel R, Conrath B, Hovis W, Kunde V, Lowman P, Maguire W, Pearl J, Pirraglia J, Prabhakara C, Schlachman B, Levin G, Straat P, Burke T. 1972. Investigation of the Martian environment by infrared spectroscopy on Mariner 9. Icarus, 17: 423–442

    Article  Google Scholar 

  • Hartogh P. 1998. Solar system research with microwaves. In: Attema E, Schwehm G, Wilson A, eds. Proceedings of the 32nd ESLAB Symposium: Remote Sensing Methodology for Earth Observation and Planetary Exploration. Noordwijk: ESA Publ. Div. 23–32

    Google Scholar 

  • Hartogh P, Medvedev A S, Kuroda T, Saito R, Villanueva G, Feofilov A G, Kutepov A A, Berger U. 2005. Description and climatology of a new general circulation model of the Martian atmosphere. J Geophys Res, 110: E11008

    Article  Google Scholar 

  • Hartogh P, Jarchow C, Lellouch E, de Val-Borro M, Rengel M, Moreno R, Medvedev A S, Sagawa H, Swinyard B M, Cavalié T, Lis D C, Błęcka M I, Banaszkiewicz M, Bockeleé-Morvan D, Crovisier J, Encrenaz T, Kuppers M, Lara L M, Szutowicz S, Vandenbussche B, Bensch F, Bergin E A, Billebaud F, Biver N, Blake G A, Blommaert J A D L, Cernicharo J, Decin L, Encrenaz P, Feuchtgruber H, Fulton T, de Graauw T, Jehin E, Kidger M, Lorente R, Naylor D A, Portyankina G, Sanchez-Portal M, Schieder R, Sidher S, Thomas N, Verdugo E, Waelkens C, Whyborn N, Teyssier D, Helmich F, Roelfsema P, Stutzki J, LeDuc H G, Stern J A. 2010. Herschel/HIFI observations of Mars: First detection of O2 at submillimetre wavelengths and upper limits on HCl and H2 O2. Astron Astrophys, 521: L49

    Article  Google Scholar 

  • He W, Wu K, Feng Y, Fu D, Chen Z, Li F. 2019. The near-space wind and temperature sensing interferometer: Forward model and measurement simulation. Remote Sens, 11: 914

    Article  Google Scholar 

  • Holstein-Rathlou C, Gunnlaugsson H P, Merrison J P, Bean K M, Cantor B A, Davis J A, Davy R, Drake N B, Ellehoj M D, Goetz W, Hviid S F, Lange C F, Larsen S E, Lemmon M T, Madsen M B, Malin M, Moores J E, Nornberg P, Smith P, Tamppari L K, Taylor P A. 2010. Winds at the Phoenix landing site. J Geophys Res, 115: E00E18

    Google Scholar 

  • Indebetouw G. 1980. Tunable spatial filtering with a Fabry-Perot etalon. Appl Opt, 19: 761–764

    Article  Google Scholar 

  • Kahn R. 1983. Some observational constraints on the global-scale wind systems of Mars. J Geophys Res, 88: 10189–10209

    Article  Google Scholar 

  • Kahn R. 1984. The spatial and seasonal distribution of Martian clouds and some meteorological implications. J Geophys Res, 89: 6671–6688

    Article  Google Scholar 

  • Kasai Y, Sagawa H, Kuroda T, Manabe T, Ochiai S, Kikuchi K, Nishibori T, Baron P, Mendrok J, Hartogh P, Murtagh D, Urban J, von Scheele F, Frisk U. 2012. Overview of the Martian atmospheric submillimetre sounder FIRE. Planet Space Sci, 63-64: 62–82

    Article  Google Scholar 

  • Krasnopolsky V A. 1997. Photochemical mapping of Mars. J Geophys Res, 102: 13313–13320

    Article  Google Scholar 

  • Kristoffersen S K, Ward W E, Brown S, Drummond J R. 2013. Calibration and validation of the advanced E-Region Wind Interferometer. Atmos Meas Tech, 6: 1761–1776

    Article  Google Scholar 

  • Lefèvre F, Montmessin F, Baggio L, Lacombe G, Bertaux J, Korablev O, Schneider N, Deighan J, Jain S K, Stewart A, Chaffin M, Crismani M, McClintock W, Holsclaw G, Jakosky B. 2018. The Martian ozone layer as seen by Mars Express and by MAVEN. Scientific Workshop F“rom Mars Express to ExoMars”

    Google Scholar 

  • Lissberger P H. 1968. Effective refractive index as a criterion of performance of interference filters. J Opt Soc Am, 58: 1586–1590

    Article  Google Scholar 

  • Martínez G M, Newman C N, De Vicente-Retortillo A, Fischer E, Renno N O, Richardson M I, Fairén A G, Genzer M, Guzewich S D, Haberle R M, Harri A M, Kemppinen O, Lemmon M T, Smith M D, de la Torre-Juárez M, Vasavada A R. 2017. The modern near-surface martian climate: A review of in-situ meteorological data from Viking to curiosity. Space Sci Rev, 212: 295–338

    Article  Google Scholar 

  • Medvedev A S, Yiğit E, Hartogh P. 2011a. Estimates of gravity wave drag on Mars: Indication of a possible lower thermospheric wind reversal. Icarus, 211: 909–912

    Article  Google Scholar 

  • Medvedev A S, Yiğit E, Hartogh P, Becker E. 2011b. Influence of gravity waves on the Martian atmosphere: General circulation modeling. J Geophys Res, 116: E10004

    Article  Google Scholar 

  • Mischna M A, Bell James F. I, James P B, Crisp D. 1998. Synoptic measurements of Martian winds using the Hubble space telescope. Geophys Res Lett, 25: 611–614

    Article  Google Scholar 

  • Montmessin F, Korablev O, Lefèvre F, Bertaux J L, Fedorova A, Trokhimovskiy A, Chaufray J Y, Lacombe G, Reberac A, Maltagliati L, Willame Y, Guslyakova S, Gérard J C, Stiepen A, Fussen D, Mateshvili N, Määttänen A, Forget F, Witasse O, Leblanc F, Vandaele A C, Marcq E, Sandel B, Gondet B, Schneider N, Chaffin M, Chapron N. 2017. SPICAM on Mars Express: A 10 year in-depth survey of the Martian atmosphere. Icarus, 297: 195–216

    Article  Google Scholar 

  • Montenbruck O, Gill E, Lutze F H. 2002. Satellite orbits: Models, methods, and applications. Appl Mech Rev, 55: B27

    Article  Google Scholar 

  • Moudden Y, McConnell J C. 2005. A new model for multiscale modeling of the Martian atmosphere, GM3. J Geophys Res, 110: E04001

    Google Scholar 

  • Muhleman D O, Clancy R T. 1995. Microwave spectroscopy of the Mars atmosphere. Appl Opt, 34: 6067–6080

    Article  Google Scholar 

  • Murphy J R, Leovy C B, Tillman J E. 1990. Observations of Martian surface winds at the Viking Lander 1 site. J Geophys Res, 95: 14555–14576

    Article  Google Scholar 

  • Noxon J F, Traub W A, Carleton N P, Connes P. 1976. Detection of O2 dayglow emission from Mars and the Martian ozone abundance. Astrophys J, 207: 1025–1035

    Article  Google Scholar 

  • Rahnama P, Rochon Y J, McDade I C, Shepherd G G, Gault W A, Scott A. 2006. Satellite measurement of stratospheric winds and ozone using doppler michelson interferometry. part I: Instrument model and measurement simulation. J Atmos Ocean Tech, 23: 753–769

    Article  Google Scholar 

  • Read W G, Tamppari L K, Livesey N J, Clancy R T, Forget F, Hartogh P, Rafkin S C R, Chattopadhyay G. 2018. Retrieval of wind, temperature, water vapor and other trace constituents in the Martian Atmosphere. Planet Space Sci, 161: 26–40

    Article  Google Scholar 

  • Roeten K J, Bougher S W, Benna M, Mahaffy P R, Lee Y, Pawlowski D, González-Galindo F, López-Valverde M Á. 2019. MAVEN/NGIMS thermospheric neutral wind observations: Interpretation using the MGITM general circulation model. J Geophys Res-Planets, 124: 3283–3303

    Article  Google Scholar 

  • Rochon Y J, Rahnama P, McDade I C. 2006. Satellite measurement of stratospheric winds and ozone using doppler michelson interferometry. part II: Retrieval method and expected performance. J Atmos Ocean Tech, 23: 770–784

    Article  Google Scholar 

  • Santee M L, Crisp D. 1995. Diagnostic calculations of the circulation in the Martian atmosphere. J Geophys Res, 100: 5465–5484

    Article  Google Scholar 

  • Shepherd G G, Thuillier G, Gault W A, Solheim B H, Hersom C, Alunni J M, Brun J F, Brune S, Charlot P, Cogger L L, Desaulniers D L, Evans W F J, Gattinger R L, Girod F, Harvie D, Hum R H, Kendall D J W, Llewellyn E J, Lowe R P, Ohrt J, Pasternak F, Peillet O, Powell I, Rochon Y, Ward W E, Wiens R H, Wimperis J. 1993. WINDII, the wind imaging interferometer on the upper atmosphere research satellite. J Geophys Res, 98: 10725–10750

    Article  Google Scholar 

  • Shepherd G G. 2002. Spectral Imaging of the Atmosphere. Academic Press

    Google Scholar 

  • Smith M D, Pearl J C, Conrath B J, Christensen P R. 2001. Thermal emission spectrometer results: Mars atmospheric thermal structure and aerosol distribution. J Geophys Res, 106: 23929–23945

    Article  Google Scholar 

  • Smith M D. 2008. Spacecraft observations of the Martian atmosphere. Annu Rev Earth Planet Sci, 36: 191–219

    Article  Google Scholar 

  • Takahashi Y O, Fujiwara H, Fukunishi H, Odaka M, Hayashi Y Y, Watanabe S. 2003. Topographically induced north-south asymmetry of the meridional circulation in the Martian atmosphere. J Geophys Res, 108: 5018

    Article  Google Scholar 

  • Urban J, Dassas K, Forget F, Ricaud P. 2005. Retrieval of vertical constituents and temperature profiles from passive submillimeter wave limb observations of the Martian atmosphere: A feasibility study. Appl Opt, 44: 2438–2455

    Article  Google Scholar 

  • Viúdez-Moreiras D, Gómez-Elvira J, Newman C E, Navarro S, Marin M, Torres J, de la Torre-Júarez M. 2019. Gale surface wind characterization based on the Mars Science Laboratory REMS dataset. Part I: Wind retrieval and Gale’ s wind speeds and directions. Icarus, 319: 909–925

    Article  Google Scholar 

  • Ward W E, Gault W A, Shepherd G G, Rowlands N. 2001. Waves Michelson Interferometer: A visible/near-IR interferometer for observing middle atmosphere dynamics and constituents. Toulouse: Proceedings of SPIE-The International Society for Optical Engineering, 4540

    Google Scholar 

  • Ward W E, Gault W A, Rowlands N, Wang S, Shepherd G G, Mcdade I C, Mcconnell J C, Michelangeli D, Caldwell J. 2003. An imaging interferometer for satellite observations of wind and temperature on Mars, the Dynamic Atmosphere Mars Observer (DYNAMO). Quebec City: Proceedings of SPIE-The International Society for Optical Engineering. 4833: 226–236

    Google Scholar 

  • Wang H, Ingersoll A P. 2003. Cloud-tracked winds for the first Mars Global Surveyor mapping year. J Geophys Res, 108: 5110

    Article  Google Scholar 

  • Wang D Y, Ward W E, Rochon Y J, Shepherd G G. 2001a. Airglow intensity variations induced by gravity waves. Part 1: Generalization of the Hines-Tarasick’ s theory. J Atmos Sol-Terr Phys, 63: 35–46

    Article  Google Scholar 

  • Wang D Y, Rochon Y J, Zhang S P, Ward W E, Wiens R H, Liang D Y, Gault W A, Solheim B H, Shepherd G G. 2001b. Airglow intensity variations induced by gravity waves. Part 2: Comparisons with observations. J Atmos Sol-Terr Phys, 63: 47–60

    Article  Google Scholar 

  • Withers P, Catling D C. 2010. Observations of atmospheric tides on Mars at the season and latitude of the Phoenix atmospheric entry. Geophys Res Lett, 37: L24204

    Article  Google Scholar 

  • Wu K, Fu D, Feng Y, Li J, Hao X, Li F. 2018. Simulation and application of the emission line O19 P18 of O2(a1Δg) dayglow near 127 μm for wind observations from limb-viewing satellites. Opt Express, 26: 16984

    Article  Google Scholar 

  • Zhang R, Ward W E, Zhang C. 2017. O2 nightglow snapshots of the 1.27 μm emission at low latitudes on Mars with a static field-widened Michelson interferometer. J Quant Spectrosc Ra, 203: 565–571

    Article  Google Scholar 

  • Zurek R W. 1976. Diurnal tide in the Martian atmosphere. J Atmos Sci, 33: 321–337

    Article  Google Scholar 

  • Zurek R W, Barnes J R, Haberle R M, Pollack J B, Tillman J E, Leovy C. 1992. Dynamics of the atmosphere of Mars. In: Kieffer H H, Jakosky B M, Snyder C W, Mathews M S, eds. Mars. Tuscon: University of Arizona Press. 835–933

    Google Scholar 

Download references

Acknowledgements

This work was supported by the Pre-Research Project on Civil Aerospace Technologies Funded by China’s National Space Administration (Grant No. D020105), the National Natural Science Foundation of China (Grant Nos. 41904142, 41774164, 42030202, 41822403, 41774165, 41774161), the B-type Strategic Priority Program of the Chinese Academy of Sciences (Grant No. XDB41000000) and Youth Innovation Promotion Association CAS. W. Ward acknowledges support from the Canadian Space Agency and the National Science and Engineering Council (NSERC) of Canada.

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  1. Hubei Subsurface Multi-scale Imaging Key Laboratory, Institute of Geophysics and Geomatics, China University of Geosciences, Wuhan, 430074, China

    Na Yang, Chunliang Xia, Tao Yu, Xiaomin Zuo, Yangyi Sun, Xiangxiang Yan, Jian Zhang & Jin Wang

  2. Key Laboratory of Earth and Planetary Physics, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, 100029, China

    Huijun Le & Libo Liu

  3. Institutions of Earth Science, Chinese Academy of Sciences, Beijing, 100029, China

    Huijun Le & Libo Liu

  4. Mohe Observatory of Geophysics, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, 100029, China

    Huijun Le & Libo Liu

  5. University of the Chinese Academy of Sciences, Beijing, 100049, China

    Huijun Le & Libo Liu

  6. Department of Physics, University of New Brunswick, New Brunswick, Fredericton, E3B 5A3, Canada

    William Edmund Ward

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  1. Na Yang
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Yang, N., Xia, C., Yu, T. et al. Measurement of Martian atmospheric winds by the O2 1.27 μm airglow observations using Doppler Michelson Interferometry: A concept study. Sci. China Earth Sci. 64, 2027–2042 (2021). https://doi.org/10.1007/s11430-020-9814-7

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