millimeter-wavelength remote sensing of the tropospheric structure of venus ... · 2018. 12....
TRANSCRIPT
![Page 1: Millimeter-Wavelength Remote Sensing of the Tropospheric Structure of Venus ... · 2018. 12. 29. · Remote Observations of Venus 11/7/2018 Millimeter-Wavelength Remote Sensing of](https://reader035.vdocument.in/reader035/viewer/2022071414/610f2b21d9d1b242ab292e55/html5/thumbnails/1.jpg)
Millimeter-Wavelength Remote Sensing of the Tropospheric Structure of Venus:
Exploratory SimulationsAlex B. Akins, Paul G. Steffes
November 7th, 201816th VEXAG Meeting
Correspondence: [email protected], [email protected]
![Page 2: Millimeter-Wavelength Remote Sensing of the Tropospheric Structure of Venus ... · 2018. 12. 29. · Remote Observations of Venus 11/7/2018 Millimeter-Wavelength Remote Sensing of](https://reader035.vdocument.in/reader035/viewer/2022071414/610f2b21d9d1b242ab292e55/html5/thumbnails/2.jpg)
Remote Observations of Venus
11/7/2018Millimeter-Wavelength Remote Sensing of the Tropospheric Structure of
Venus: Exploratory Simulations1
Peralta, et al. in Icarus (2017)
Cloud Base
Passive remote sensing of sub-cloud atmospheric structure limited to narrow IR bands, microwave/millimeter emission
8 GHz
20 GHz40 GHz
70 GHz
110 GHz
Microwave Emission Weighting Functions
(Microns)
![Page 3: Millimeter-Wavelength Remote Sensing of the Tropospheric Structure of Venus ... · 2018. 12. 29. · Remote Observations of Venus 11/7/2018 Millimeter-Wavelength Remote Sensing of](https://reader035.vdocument.in/reader035/viewer/2022071414/610f2b21d9d1b242ab292e55/html5/thumbnails/3.jpg)
Millimeter-Wavelength Continuum Images
11/7/2018 Millimeter-Wavelength Remote Sensing of the Tropospheric Structure of Venus: Exploratory Simulations 2
Encrenaz et al. (2015), 346 GHz, Phase: 0.902, Upper CloudSagawa (2008), 103 GHz,
Phase: 0.272, Cloud Basede Pater et al. (1991), 115 GHz,
Phase: 0.527, Cloud Base
• Longitudinal brightness temperature variations on the order of 30-80 K are observed in disk images
• 8-22% of the disk-average• Only observed on nightside • Uncorrelated with topographical features
• Is this a measurement artifact or the result of a physical process?
![Page 4: Millimeter-Wavelength Remote Sensing of the Tropospheric Structure of Venus ... · 2018. 12. 29. · Remote Observations of Venus 11/7/2018 Millimeter-Wavelength Remote Sensing of](https://reader035.vdocument.in/reader035/viewer/2022071414/610f2b21d9d1b242ab292e55/html5/thumbnails/4.jpg)
Microwave Radiative Transfer Model
• Temperature and pressure profiles from VIRA (Seiff 1985), PV entry probes
• CO2/N2 absorption• Ho, Kaufman, Thaddeus (1966)• Valid for 2-4 mm wavelengths
• SO2 and H2SO4 vapor absorption• Other contributing absorbers
• Abundances derived from remote sensing observations and inferred from chemical modeling• Krasnopolsky (2007)
• H2SO4 liquid aerosol – Absorption model of Fahd and Steffes (1991)• Scattering is negligible based on aerosol size distributions from Pioneer Venus LCPS results
• H2O – Modelled with modified opacity formalism of Karpowicz and Steffes (2011)• CO – Van Vleck-Weisskopf model, parameters from Bauer et al. (1989)• OCS - Van Vleck-Weisskopf model, parameters from Feeny et al. (1954)
11/7/2018 Millimeter-Wavelength Remote Sensing of the Tropospheric Structure of Venus: Exploratory Simulations 3
↵CO2/N2= 1.12 · 108
�q2CO2
+ 0.25qCO2qN2 + 0.0054q2N2
�f2p2T�5
<latexit sha1_base64="/ZQWpNugCQmMaF3G/NEa1yDoKqQ=">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</latexit><latexit sha1_base64="/ZQWpNugCQmMaF3G/NEa1yDoKqQ=">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</latexit><latexit sha1_base64="/ZQWpNugCQmMaF3G/NEa1yDoKqQ=">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</latexit>
dB/km<latexit sha1_base64="qIZwl3Jc4ynQLkNGz6S46LUxZ+Q=">AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBbBU02koMdSLx4rmLbQhrLZbNqlu5uwuxFK6G/w4kERr/4gb/4bt20O2vpg4PHeDDPzwpQzbVz32yltbG5t75R3K3v7B4dH1eOTjk4yRahPEp6oXog15UxS3zDDaS9VFIuQ0244uZv73SeqNEvko5mmNBB4JFnMCDZW8qPW1UQMqzW37i6A1olXkBoUaA+rX4MoIZmg0hCOte57bmqCHCvDCKezyiDTNMVkgke0b6nEguogXxw7QxdWiVCcKFvSoIX6eyLHQuupCG2nwGasV725+J/Xz0x8G+RMppmhkiwXxRlHJkHzz1HEFCWGTy3BRDF7KyJjrDAxNp+KDcFbfXmddK7rnlv3Hhq1ZquIowxncA6X4MENNOEe2uADAQbP8ApvjnRenHfnY9lacoqZU/gD5/MHUXWOWQ==</latexit><latexit sha1_base64="qIZwl3Jc4ynQLkNGz6S46LUxZ+Q=">AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBbBU02koMdSLx4rmLbQhrLZbNqlu5uwuxFK6G/w4kERr/4gb/4bt20O2vpg4PHeDDPzwpQzbVz32yltbG5t75R3K3v7B4dH1eOTjk4yRahPEp6oXog15UxS3zDDaS9VFIuQ0244uZv73SeqNEvko5mmNBB4JFnMCDZW8qPW1UQMqzW37i6A1olXkBoUaA+rX4MoIZmg0hCOte57bmqCHCvDCKezyiDTNMVkgke0b6nEguogXxw7QxdWiVCcKFvSoIX6eyLHQuupCG2nwGasV725+J/Xz0x8G+RMppmhkiwXxRlHJkHzz1HEFCWGTy3BRDF7KyJjrDAxNp+KDcFbfXmddK7rnlv3Hhq1ZquIowxncA6X4MENNOEe2uADAQbP8ApvjnRenHfnY9lacoqZU/gD5/MHUXWOWQ==</latexit><latexit sha1_base64="qIZwl3Jc4ynQLkNGz6S46LUxZ+Q=">AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBbBU02koMdSLx4rmLbQhrLZbNqlu5uwuxFK6G/w4kERr/4gb/4bt20O2vpg4PHeDDPzwpQzbVz32yltbG5t75R3K3v7B4dH1eOTjk4yRahPEp6oXog15UxS3zDDaS9VFIuQ0244uZv73SeqNEvko5mmNBB4JFnMCDZW8qPW1UQMqzW37i6A1olXkBoUaA+rX4MoIZmg0hCOte57bmqCHCvDCKezyiDTNMVkgke0b6nEguogXxw7QxdWiVCcKFvSoIX6eyLHQuupCG2nwGasV725+J/Xz0x8G+RMppmhkiwXxRlHJkHzz1HEFCWGTy3BRDF7KyJjrDAxNp+KDcFbfXmddK7rnlv3Hhq1ZquIowxncA6X4MENNOEe2uADAQbP8ApvjnRenHfnY9lacoqZU/gD5/MHUXWOWQ==</latexit><latexit sha1_base64="hP+6LrUf2d3tZaldqaQQvEKMXyw=">AAAB2XicbZDNSgMxFIXv1L86Vq1rN8EiuCozbnQpuHFZwbZCO5RM5k4bmskMyR2hDH0BF25EfC93vo3pz0JbDwQ+zknIvSculLQUBN9ebWd3b/+gfugfNfzjk9Nmo2fz0gjsilzl5jnmFpXU2CVJCp8LgzyLFfbj6f0i77+gsTLXTzQrMMr4WMtUCk7O6oyaraAdLMW2IVxDC9YaNb+GSS7KDDUJxa0dhEFBUcUNSaFw7g9LiwUXUz7GgUPNM7RRtRxzzi6dk7A0N+5oYkv394uKZ9bOstjdzDhN7Ga2MP/LBiWlt1EldVESarH6KC0Vo5wtdmaJNChIzRxwYaSblYkJN1yQa8Z3HYSbG29D77odBu3wMYA6nMMFXEEIN3AHD9CBLghI4BXevYn35n2suqp569LO4I+8zx84xIo4</latexit><latexit sha1_base64="oHw60sB1A05yPTfP1Fj38LUD3FU=">AAAB4XicbZDNSgMxFIXv1L9aq1a3boJFcFVn3OhSdOOyglML7VAymUwbmmSG5I5Qhj6DGxeK+FLufBvTn4W2Hgh8nJOQe0+cS2HR97+9ysbm1vZOdbe2V98/OGwc1Ts2KwzjIctkZroxtVwKzUMUKHk3N5yqWPKneHw3y5+eubEi0484yXmk6FCLVDCKzgqT24uxGjSafsufi6xDsIQmLNUeNL76ScYKxTUySa3tBX6OUUkNCib5tNYvLM8pG9Mh7znUVHEblfNhp+TMOQlJM+OORjJ3f78oqbJ2omJ3U1Ec2dVsZv6X9QpMr6NS6LxArtnio7SQBDMy25wkwnCGcuKAMiPcrISNqKEMXT81V0KwuvI6dC5bgd8KHnyowgmcwjkEcAU3cA9tCIGBgBd4g3dPe6/ex6Kuirfs7Rj+yPv8AS6IjQI=</latexit><latexit sha1_base64="oHw60sB1A05yPTfP1Fj38LUD3FU=">AAAB4XicbZDNSgMxFIXv1L9aq1a3boJFcFVn3OhSdOOyglML7VAymUwbmmSG5I5Qhj6DGxeK+FLufBvTn4W2Hgh8nJOQe0+cS2HR97+9ysbm1vZOdbe2V98/OGwc1Ts2KwzjIctkZroxtVwKzUMUKHk3N5yqWPKneHw3y5+eubEi0484yXmk6FCLVDCKzgqT24uxGjSafsufi6xDsIQmLNUeNL76ScYKxTUySa3tBX6OUUkNCib5tNYvLM8pG9Mh7znUVHEblfNhp+TMOQlJM+OORjJ3f78oqbJ2omJ3U1Ec2dVsZv6X9QpMr6NS6LxArtnio7SQBDMy25wkwnCGcuKAMiPcrISNqKEMXT81V0KwuvI6dC5bgd8KHnyowgmcwjkEcAU3cA9tCIGBgBd4g3dPe6/ex6Kuirfs7Rj+yPv8AS6IjQI=</latexit><latexit sha1_base64="8kZ/4D6HaS3u30my6UvxNLN/8EE=">AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBbBU0286LHUi8cKpi20oWw2m3bp7ibsboQS+hu8eFDEqz/Im//GTZuDtj4YeLw3w8y8MOVMG9f9diobm1vbO9Xd2t7+weFR/fikq5NMEeqThCeqH2JNOZPUN8xw2k8VxSLktBdO7wq/90SVZol8NLOUBgKPJYsZwcZKftS+mopRveE23QXQOvFK0oASnVH9axglJBNUGsKx1gPPTU2QY2UY4XReG2aapphM8ZgOLJVYUB3ki2Pn6MIqEYoTZUsatFB/T+RYaD0Toe0U2Ez0qleI/3mDzMS3Qc5kmhkqyXJRnHFkElR8jiKmKDF8ZgkmitlbEZlghYmx+dRsCN7qy+uke9303Kb34DZa7TKOKpzBOVyCBzfQgnvogA8EGDzDK7w50nlx3p2PZWvFKWdO4Q+czx9QNY5V</latexit><latexit sha1_base64="qIZwl3Jc4ynQLkNGz6S46LUxZ+Q=">AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBbBU02koMdSLx4rmLbQhrLZbNqlu5uwuxFK6G/w4kERr/4gb/4bt20O2vpg4PHeDDPzwpQzbVz32yltbG5t75R3K3v7B4dH1eOTjk4yRahPEp6oXog15UxS3zDDaS9VFIuQ0244uZv73SeqNEvko5mmNBB4JFnMCDZW8qPW1UQMqzW37i6A1olXkBoUaA+rX4MoIZmg0hCOte57bmqCHCvDCKezyiDTNMVkgke0b6nEguogXxw7QxdWiVCcKFvSoIX6eyLHQuupCG2nwGasV725+J/Xz0x8G+RMppmhkiwXxRlHJkHzz1HEFCWGTy3BRDF7KyJjrDAxNp+KDcFbfXmddK7rnlv3Hhq1ZquIowxncA6X4MENNOEe2uADAQbP8ApvjnRenHfnY9lacoqZU/gD5/MHUXWOWQ==</latexit><latexit sha1_base64="qIZwl3Jc4ynQLkNGz6S46LUxZ+Q=">AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBbBU02koMdSLx4rmLbQhrLZbNqlu5uwuxFK6G/w4kERr/4gb/4bt20O2vpg4PHeDDPzwpQzbVz32yltbG5t75R3K3v7B4dH1eOTjk4yRahPEp6oXog15UxS3zDDaS9VFIuQ0244uZv73SeqNEvko5mmNBB4JFnMCDZW8qPW1UQMqzW37i6A1olXkBoUaA+rX4MoIZmg0hCOte57bmqCHCvDCKezyiDTNMVkgke0b6nEguogXxw7QxdWiVCcKFvSoIX6eyLHQuupCG2nwGasV725+J/Xz0x8G+RMppmhkiwXxRlHJkHzz1HEFCWGTy3BRDF7KyJjrDAxNp+KDcFbfXmddK7rnlv3Hhq1ZquIowxncA6X4MENNOEe2uADAQbP8ApvjnRenHfnY9lacoqZU/gD5/MHUXWOWQ==</latexit><latexit sha1_base64="qIZwl3Jc4ynQLkNGz6S46LUxZ+Q=">AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBbBU02koMdSLx4rmLbQhrLZbNqlu5uwuxFK6G/w4kERr/4gb/4bt20O2vpg4PHeDDPzwpQzbVz32yltbG5t75R3K3v7B4dH1eOTjk4yRahPEp6oXog15UxS3zDDaS9VFIuQ0244uZv73SeqNEvko5mmNBB4JFnMCDZW8qPW1UQMqzW37i6A1olXkBoUaA+rX4MoIZmg0hCOte57bmqCHCvDCKezyiDTNMVkgke0b6nEguogXxw7QxdWiVCcKFvSoIX6eyLHQuupCG2nwGasV725+J/Xz0x8G+RMppmhkiwXxRlHJkHzz1HEFCWGTy3BRDF7KyJjrDAxNp+KDcFbfXmddK7rnlv3Hhq1ZquIowxncA6X4MENNOEe2uADAQbP8ApvjnRenHfnY9lacoqZU/gD5/MHUXWOWQ==</latexit><latexit sha1_base64="qIZwl3Jc4ynQLkNGz6S46LUxZ+Q=">AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBbBU02koMdSLx4rmLbQhrLZbNqlu5uwuxFK6G/w4kERr/4gb/4bt20O2vpg4PHeDDPzwpQzbVz32yltbG5t75R3K3v7B4dH1eOTjk4yRahPEp6oXog15UxS3zDDaS9VFIuQ0244uZv73SeqNEvko5mmNBB4JFnMCDZW8qPW1UQMqzW37i6A1olXkBoUaA+rX4MoIZmg0hCOte57bmqCHCvDCKezyiDTNMVkgke0b6nEguogXxw7QxdWiVCcKFvSoIX6eyLHQuupCG2nwGasV725+J/Xz0x8G+RMppmhkiwXxRlHJkHzz1HEFCWGTy3BRDF7KyJjrDAxNp+KDcFbfXmddK7rnlv3Hhq1ZquIowxncA6X4MENNOEe2uADAQbP8ApvjnRenHfnY9lacoqZU/gD5/MHUXWOWQ==</latexit><latexit sha1_base64="qIZwl3Jc4ynQLkNGz6S46LUxZ+Q=">AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBbBU02koMdSLx4rmLbQhrLZbNqlu5uwuxFK6G/w4kERr/4gb/4bt20O2vpg4PHeDDPzwpQzbVz32yltbG5t75R3K3v7B4dH1eOTjk4yRahPEp6oXog15UxS3zDDaS9VFIuQ0244uZv73SeqNEvko5mmNBB4JFnMCDZW8qPW1UQMqzW37i6A1olXkBoUaA+rX4MoIZmg0hCOte57bmqCHCvDCKezyiDTNMVkgke0b6nEguogXxw7QxdWiVCcKFvSoIX6eyLHQuupCG2nwGasV725+J/Xz0x8G+RMppmhkiwXxRlHJkHzz1HEFCWGTy3BRDF7KyJjrDAxNp+KDcFbfXmddK7rnlv3Hhq1ZquIowxncA6X4MENNOEe2uADAQbP8ApvjnRenHfnY9lacoqZU/gD5/MHUXWOWQ==</latexit><latexit sha1_base64="hP+6LrUf2d3tZaldqaQQvEKMXyw=">AAAB2XicbZDNSgMxFIXv1L86Vq1rN8EiuCozbnQpuHFZwbZCO5RM5k4bmskMyR2hDH0BF25EfC93vo3pz0JbDwQ+zknIvSculLQUBN9ebWd3b/+gfugfNfzjk9Nmo2fz0gjsilzl5jnmFpXU2CVJCp8LgzyLFfbj6f0i77+gsTLXTzQrMMr4WMtUCk7O6oyaraAdLMW2IVxDC9YaNb+GSS7KDDUJxa0dhEFBUcUNSaFw7g9LiwUXUz7GgUPNM7RRtRxzzi6dk7A0N+5oYkv394uKZ9bOstjdzDhN7Ga2MP/LBiWlt1EldVESarH6KC0Vo5wtdmaJNChIzRxwYaSblYkJN1yQa8Z3HYSbG29D77odBu3wMYA6nMMFXEEIN3AHD9CBLghI4BXevYn35n2suqp569LO4I+8zx84xIo4</latexit><latexit sha1_base64="oHw60sB1A05yPTfP1Fj38LUD3FU=">AAAB4XicbZDNSgMxFIXv1L9aq1a3boJFcFVn3OhSdOOyglML7VAymUwbmmSG5I5Qhj6DGxeK+FLufBvTn4W2Hgh8nJOQe0+cS2HR97+9ysbm1vZOdbe2V98/OGwc1Ts2KwzjIctkZroxtVwKzUMUKHk3N5yqWPKneHw3y5+eubEi0484yXmk6FCLVDCKzgqT24uxGjSafsufi6xDsIQmLNUeNL76ScYKxTUySa3tBX6OUUkNCib5tNYvLM8pG9Mh7znUVHEblfNhp+TMOQlJM+OORjJ3f78oqbJ2omJ3U1Ec2dVsZv6X9QpMr6NS6LxArtnio7SQBDMy25wkwnCGcuKAMiPcrISNqKEMXT81V0KwuvI6dC5bgd8KHnyowgmcwjkEcAU3cA9tCIGBgBd4g3dPe6/ex6Kuirfs7Rj+yPv8AS6IjQI=</latexit><latexit sha1_base64="oHw60sB1A05yPTfP1Fj38LUD3FU=">AAAB4XicbZDNSgMxFIXv1L9aq1a3boJFcFVn3OhSdOOyglML7VAymUwbmmSG5I5Qhj6DGxeK+FLufBvTn4W2Hgh8nJOQe0+cS2HR97+9ysbm1vZOdbe2V98/OGwc1Ts2KwzjIctkZroxtVwKzUMUKHk3N5yqWPKneHw3y5+eubEi0484yXmk6FCLVDCKzgqT24uxGjSafsufi6xDsIQmLNUeNL76ScYKxTUySa3tBX6OUUkNCib5tNYvLM8pG9Mh7znUVHEblfNhp+TMOQlJM+OORjJ3f78oqbJ2omJ3U1Ec2dVsZv6X9QpMr6NS6LxArtnio7SQBDMy25wkwnCGcuKAMiPcrISNqKEMXT81V0KwuvI6dC5bgd8KHnyowgmcwjkEcAU3cA9tCIGBgBd4g3dPe6/ex6Kuirfs7Rj+yPv8AS6IjQI=</latexit><latexit sha1_base64="8kZ/4D6HaS3u30my6UvxNLN/8EE=">AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBbBU0286LHUi8cKpi20oWw2m3bp7ibsboQS+hu8eFDEqz/Im//GTZuDtj4YeLw3w8y8MOVMG9f9diobm1vbO9Xd2t7+weFR/fikq5NMEeqThCeqH2JNOZPUN8xw2k8VxSLktBdO7wq/90SVZol8NLOUBgKPJYsZwcZKftS+mopRveE23QXQOvFK0oASnVH9axglJBNUGsKx1gPPTU2QY2UY4XReG2aapphM8ZgOLJVYUB3ki2Pn6MIqEYoTZUsatFB/T+RYaD0Toe0U2Ez0qleI/3mDzMS3Qc5kmhkqyXJRnHFkElR8jiKmKDF8ZgkmitlbEZlghYmx+dRsCN7qy+uke9303Kb34DZa7TKOKpzBOVyCBzfQgnvogA8EGDzDK7w50nlx3p2PZWvFKWdO4Q+czx9QNY5V</latexit><latexit sha1_base64="qIZwl3Jc4ynQLkNGz6S46LUxZ+Q=">AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBbBU02koMdSLx4rmLbQhrLZbNqlu5uwuxFK6G/w4kERr/4gb/4bt20O2vpg4PHeDDPzwpQzbVz32yltbG5t75R3K3v7B4dH1eOTjk4yRahPEp6oXog15UxS3zDDaS9VFIuQ0244uZv73SeqNEvko5mmNBB4JFnMCDZW8qPW1UQMqzW37i6A1olXkBoUaA+rX4MoIZmg0hCOte57bmqCHCvDCKezyiDTNMVkgke0b6nEguogXxw7QxdWiVCcKFvSoIX6eyLHQuupCG2nwGasV725+J/Xz0x8G+RMppmhkiwXxRlHJkHzz1HEFCWGTy3BRDF7KyJjrDAxNp+KDcFbfXmddK7rnlv3Hhq1ZquIowxncA6X4MENNOEe2uADAQbP8ApvjnRenHfnY9lacoqZU/gD5/MHUXWOWQ==</latexit><latexit sha1_base64="qIZwl3Jc4ynQLkNGz6S46LUxZ+Q=">AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBbBU02koMdSLx4rmLbQhrLZbNqlu5uwuxFK6G/w4kERr/4gb/4bt20O2vpg4PHeDDPzwpQzbVz32yltbG5t75R3K3v7B4dH1eOTjk4yRahPEp6oXog15UxS3zDDaS9VFIuQ0244uZv73SeqNEvko5mmNBB4JFnMCDZW8qPW1UQMqzW37i6A1olXkBoUaA+rX4MoIZmg0hCOte57bmqCHCvDCKezyiDTNMVkgke0b6nEguogXxw7QxdWiVCcKFvSoIX6eyLHQuupCG2nwGasV725+J/Xz0x8G+RMppmhkiwXxRlHJkHzz1HEFCWGTy3BRDF7KyJjrDAxNp+KDcFbfXmddK7rnlv3Hhq1ZquIowxncA6X4MENNOEe2uADAQbP8ApvjnRenHfnY9lacoqZU/gD5/MHUXWOWQ==</latexit><latexit sha1_base64="qIZwl3Jc4ynQLkNGz6S46LUxZ+Q=">AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBbBU02koMdSLx4rmLbQhrLZbNqlu5uwuxFK6G/w4kERr/4gb/4bt20O2vpg4PHeDDPzwpQzbVz32yltbG5t75R3K3v7B4dH1eOTjk4yRahPEp6oXog15UxS3zDDaS9VFIuQ0244uZv73SeqNEvko5mmNBB4JFnMCDZW8qPW1UQMqzW37i6A1olXkBoUaA+rX4MoIZmg0hCOte57bmqCHCvDCKezyiDTNMVkgke0b6nEguogXxw7QxdWiVCcKFvSoIX6eyLHQuupCG2nwGasV725+J/Xz0x8G+RMppmhkiwXxRlHJkHzz1HEFCWGTy3BRDF7KyJjrDAxNp+KDcFbfXmddK7rnlv3Hhq1ZquIowxncA6X4MENNOEe2uADAQbP8ApvjnRenHfnY9lacoqZU/gD5/MHUXWOWQ==</latexit><latexit sha1_base64="qIZwl3Jc4ynQLkNGz6S46LUxZ+Q=">AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBbBU02koMdSLx4rmLbQhrLZbNqlu5uwuxFK6G/w4kERr/4gb/4bt20O2vpg4PHeDDPzwpQzbVz32yltbG5t75R3K3v7B4dH1eOTjk4yRahPEp6oXog15UxS3zDDaS9VFIuQ0244uZv73SeqNEvko5mmNBB4JFnMCDZW8qPW1UQMqzW37i6A1olXkBoUaA+rX4MoIZmg0hCOte57bmqCHCvDCKezyiDTNMVkgke0b6nEguogXxw7QxdWiVCcKFvSoIX6eyLHQuupCG2nwGasV725+J/Xz0x8G+RMppmhkiwXxRlHJkHzz1HEFCWGTy3BRDF7KyJjrDAxNp+KDcFbfXmddK7rnlv3Hhq1ZquIowxncA6X4MENNOEe2uADAQbP8ApvjnRenHfnY9lacoqZU/gD5/MHUXWOWQ==</latexit><latexit sha1_base64="qIZwl3Jc4ynQLkNGz6S46LUxZ+Q=">AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBbBU02koMdSLx4rmLbQhrLZbNqlu5uwuxFK6G/w4kERr/4gb/4bt20O2vpg4PHeDDPzwpQzbVz32yltbG5t75R3K3v7B4dH1eOTjk4yRahPEp6oXog15UxS3zDDaS9VFIuQ0244uZv73SeqNEvko5mmNBB4JFnMCDZW8qPW1UQMqzW37i6A1olXkBoUaA+rX4MoIZmg0hCOte57bmqCHCvDCKezyiDTNMVkgke0b6nEguogXxw7QxdWiVCcKFvSoIX6eyLHQuupCG2nwGasV725+J/Xz0x8G+RMppmhkiwXxRlHJkHzz1HEFCWGTy3BRDF7KyJjrDAxNp+KDcFbfXmddK7rnlv3Hhq1ZquIowxncA6X4MENNOEe2uADAQbP8ApvjnRenHfnY9lacoqZU/gD5/MHUXWOWQ==</latexit><latexit sha1_base64="hP+6LrUf2d3tZaldqaQQvEKMXyw=">AAAB2XicbZDNSgMxFIXv1L86Vq1rN8EiuCozbnQpuHFZwbZCO5RM5k4bmskMyR2hDH0BF25EfC93vo3pz0JbDwQ+zknIvSculLQUBN9ebWd3b/+gfugfNfzjk9Nmo2fz0gjsilzl5jnmFpXU2CVJCp8LgzyLFfbj6f0i77+gsTLXTzQrMMr4WMtUCk7O6oyaraAdLMW2IVxDC9YaNb+GSS7KDDUJxa0dhEFBUcUNSaFw7g9LiwUXUz7GgUPNM7RRtRxzzi6dk7A0N+5oYkv394uKZ9bOstjdzDhN7Ga2MP/LBiWlt1EldVESarH6KC0Vo5wtdmaJNChIzRxwYaSblYkJN1yQa8Z3HYSbG29D77odBu3wMYA6nMMFXEEIN3AHD9CBLghI4BXevYn35n2suqp569LO4I+8zx84xIo4</latexit><latexit sha1_base64="oHw60sB1A05yPTfP1Fj38LUD3FU=">AAAB4XicbZDNSgMxFIXv1L9aq1a3boJFcFVn3OhSdOOyglML7VAymUwbmmSG5I5Qhj6DGxeK+FLufBvTn4W2Hgh8nJOQe0+cS2HR97+9ysbm1vZOdbe2V98/OGwc1Ts2KwzjIctkZroxtVwKzUMUKHk3N5yqWPKneHw3y5+eubEi0484yXmk6FCLVDCKzgqT24uxGjSafsufi6xDsIQmLNUeNL76ScYKxTUySa3tBX6OUUkNCib5tNYvLM8pG9Mh7znUVHEblfNhp+TMOQlJM+OORjJ3f78oqbJ2omJ3U1Ec2dVsZv6X9QpMr6NS6LxArtnio7SQBDMy25wkwnCGcuKAMiPcrISNqKEMXT81V0KwuvI6dC5bgd8KHnyowgmcwjkEcAU3cA9tCIGBgBd4g3dPe6/ex6Kuirfs7Rj+yPv8AS6IjQI=</latexit><latexit sha1_base64="oHw60sB1A05yPTfP1Fj38LUD3FU=">AAAB4XicbZDNSgMxFIXv1L9aq1a3boJFcFVn3OhSdOOyglML7VAymUwbmmSG5I5Qhj6DGxeK+FLufBvTn4W2Hgh8nJOQe0+cS2HR97+9ysbm1vZOdbe2V98/OGwc1Ts2KwzjIctkZroxtVwKzUMUKHk3N5yqWPKneHw3y5+eubEi0484yXmk6FCLVDCKzgqT24uxGjSafsufi6xDsIQmLNUeNL76ScYKxTUySa3tBX6OUUkNCib5tNYvLM8pG9Mh7znUVHEblfNhp+TMOQlJM+OORjJ3f78oqbJ2omJ3U1Ec2dVsZv6X9QpMr6NS6LxArtnio7SQBDMy25wkwnCGcuKAMiPcrISNqKEMXT81V0KwuvI6dC5bgd8KHnyowgmcwjkEcAU3cA9tCIGBgBd4g3dPe6/ex6Kuirfs7Rj+yPv8AS6IjQI=</latexit><latexit sha1_base64="8kZ/4D6HaS3u30my6UvxNLN/8EE=">AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBbBU0286LHUi8cKpi20oWw2m3bp7ibsboQS+hu8eFDEqz/Im//GTZuDtj4YeLw3w8y8MOVMG9f9diobm1vbO9Xd2t7+weFR/fikq5NMEeqThCeqH2JNOZPUN8xw2k8VxSLktBdO7wq/90SVZol8NLOUBgKPJYsZwcZKftS+mopRveE23QXQOvFK0oASnVH9axglJBNUGsKx1gPPTU2QY2UY4XReG2aapphM8ZgOLJVYUB3ki2Pn6MIqEYoTZUsatFB/T+RYaD0Toe0U2Ez0qleI/3mDzMS3Qc5kmhkqyXJRnHFkElR8jiKmKDF8ZgkmitlbEZlghYmx+dRsCN7qy+uke9303Kb34DZa7TKOKpzBOVyCBzfQgnvogA8EGDzDK7w50nlx3p2PZWvFKWdO4Q+czx9QNY5V</latexit><latexit sha1_base64="qIZwl3Jc4ynQLkNGz6S46LUxZ+Q=">AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBbBU02koMdSLx4rmLbQhrLZbNqlu5uwuxFK6G/w4kERr/4gb/4bt20O2vpg4PHeDDPzwpQzbVz32yltbG5t75R3K3v7B4dH1eOTjk4yRahPEp6oXog15UxS3zDDaS9VFIuQ0244uZv73SeqNEvko5mmNBB4JFnMCDZW8qPW1UQMqzW37i6A1olXkBoUaA+rX4MoIZmg0hCOte57bmqCHCvDCKezyiDTNMVkgke0b6nEguogXxw7QxdWiVCcKFvSoIX6eyLHQuupCG2nwGasV725+J/Xz0x8G+RMppmhkiwXxRlHJkHzz1HEFCWGTy3BRDF7KyJjrDAxNp+KDcFbfXmddK7rnlv3Hhq1ZquIowxncA6X4MENNOEe2uADAQbP8ApvjnRenHfnY9lacoqZU/gD5/MHUXWOWQ==</latexit><latexit sha1_base64="qIZwl3Jc4ynQLkNGz6S46LUxZ+Q=">AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBbBU02koMdSLx4rmLbQhrLZbNqlu5uwuxFK6G/w4kERr/4gb/4bt20O2vpg4PHeDDPzwpQzbVz32yltbG5t75R3K3v7B4dH1eOTjk4yRahPEp6oXog15UxS3zDDaS9VFIuQ0244uZv73SeqNEvko5mmNBB4JFnMCDZW8qPW1UQMqzW37i6A1olXkBoUaA+rX4MoIZmg0hCOte57bmqCHCvDCKezyiDTNMVkgke0b6nEguogXxw7QxdWiVCcKFvSoIX6eyLHQuupCG2nwGasV725+J/Xz0x8G+RMppmhkiwXxRlHJkHzz1HEFCWGTy3BRDF7KyJjrDAxNp+KDcFbfXmddK7rnlv3Hhq1ZquIowxncA6X4MENNOEe2uADAQbP8ApvjnRenHfnY9lacoqZU/gD5/MHUXWOWQ==</latexit><latexit sha1_base64="qIZwl3Jc4ynQLkNGz6S46LUxZ+Q=">AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBbBU02koMdSLx4rmLbQhrLZbNqlu5uwuxFK6G/w4kERr/4gb/4bt20O2vpg4PHeDDPzwpQzbVz32yltbG5t75R3K3v7B4dH1eOTjk4yRahPEp6oXog15UxS3zDDaS9VFIuQ0244uZv73SeqNEvko5mmNBB4JFnMCDZW8qPW1UQMqzW37i6A1olXkBoUaA+rX4MoIZmg0hCOte57bmqCHCvDCKezyiDTNMVkgke0b6nEguogXxw7QxdWiVCcKFvSoIX6eyLHQuupCG2nwGasV725+J/Xz0x8G+RMppmhkiwXxRlHJkHzz1HEFCWGTy3BRDF7KyJjrDAxNp+KDcFbfXmddK7rnlv3Hhq1ZquIowxncA6X4MENNOEe2uADAQbP8ApvjnRenHfnY9lacoqZU/gD5/MHUXWOWQ==</latexit><latexit sha1_base64="qIZwl3Jc4ynQLkNGz6S46LUxZ+Q=">AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBbBU02koMdSLx4rmLbQhrLZbNqlu5uwuxFK6G/w4kERr/4gb/4bt20O2vpg4PHeDDPzwpQzbVz32yltbG5t75R3K3v7B4dH1eOTjk4yRahPEp6oXog15UxS3zDDaS9VFIuQ0244uZv73SeqNEvko5mmNBB4JFnMCDZW8qPW1UQMqzW37i6A1olXkBoUaA+rX4MoIZmg0hCOte57bmqCHCvDCKezyiDTNMVkgke0b6nEguogXxw7QxdWiVCcKFvSoIX6eyLHQuupCG2nwGasV725+J/Xz0x8G+RMppmhkiwXxRlHJkHzz1HEFCWGTy3BRDF7KyJjrDAxNp+KDcFbfXmddK7rnlv3Hhq1ZquIowxncA6X4MENNOEe2uADAQbP8ApvjnRenHfnY9lacoqZU/gD5/MHUXWOWQ==</latexit><latexit sha1_base64="qIZwl3Jc4ynQLkNGz6S46LUxZ+Q=">AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBbBU02koMdSLx4rmLbQhrLZbNqlu5uwuxFK6G/w4kERr/4gb/4bt20O2vpg4PHeDDPzwpQzbVz32yltbG5t75R3K3v7B4dH1eOTjk4yRahPEp6oXog15UxS3zDDaS9VFIuQ0244uZv73SeqNEvko5mmNBB4JFnMCDZW8qPW1UQMqzW37i6A1olXkBoUaA+rX4MoIZmg0hCOte57bmqCHCvDCKezyiDTNMVkgke0b6nEguogXxw7QxdWiVCcKFvSoIX6eyLHQuupCG2nwGasV725+J/Xz0x8G+RMppmhkiwXxRlHJkHzz1HEFCWGTy3BRDF7KyJjrDAxNp+KDcFbfXmddK7rnlv3Hhq1ZquIowxncA6X4MENNOEe2uADAQbP8ApvjnRenHfnY9lacoqZU/gD5/MHUXWOWQ==</latexit><latexit sha1_base64="hP+6LrUf2d3tZaldqaQQvEKMXyw=">AAAB2XicbZDNSgMxFIXv1L86Vq1rN8EiuCozbnQpuHFZwbZCO5RM5k4bmskMyR2hDH0BF25EfC93vo3pz0JbDwQ+zknIvSculLQUBN9ebWd3b/+gfugfNfzjk9Nmo2fz0gjsilzl5jnmFpXU2CVJCp8LgzyLFfbj6f0i77+gsTLXTzQrMMr4WMtUCk7O6oyaraAdLMW2IVxDC9YaNb+GSS7KDDUJxa0dhEFBUcUNSaFw7g9LiwUXUz7GgUPNM7RRtRxzzi6dk7A0N+5oYkv394uKZ9bOstjdzDhN7Ga2MP/LBiWlt1EldVESarH6KC0Vo5wtdmaJNChIzRxwYaSblYkJN1yQa8Z3HYSbG29D77odBu3wMYA6nMMFXEEIN3AHD9CBLghI4BXevYn35n2suqp569LO4I+8zx84xIo4</latexit><latexit sha1_base64="oHw60sB1A05yPTfP1Fj38LUD3FU=">AAAB4XicbZDNSgMxFIXv1L9aq1a3boJFcFVn3OhSdOOyglML7VAymUwbmmSG5I5Qhj6DGxeK+FLufBvTn4W2Hgh8nJOQe0+cS2HR97+9ysbm1vZOdbe2V98/OGwc1Ts2KwzjIctkZroxtVwKzUMUKHk3N5yqWPKneHw3y5+eubEi0484yXmk6FCLVDCKzgqT24uxGjSafsufi6xDsIQmLNUeNL76ScYKxTUySa3tBX6OUUkNCib5tNYvLM8pG9Mh7znUVHEblfNhp+TMOQlJM+OORjJ3f78oqbJ2omJ3U1Ec2dVsZv6X9QpMr6NS6LxArtnio7SQBDMy25wkwnCGcuKAMiPcrISNqKEMXT81V0KwuvI6dC5bgd8KHnyowgmcwjkEcAU3cA9tCIGBgBd4g3dPe6/ex6Kuirfs7Rj+yPv8AS6IjQI=</latexit><latexit sha1_base64="oHw60sB1A05yPTfP1Fj38LUD3FU=">AAAB4XicbZDNSgMxFIXv1L9aq1a3boJFcFVn3OhSdOOyglML7VAymUwbmmSG5I5Qhj6DGxeK+FLufBvTn4W2Hgh8nJOQe0+cS2HR97+9ysbm1vZOdbe2V98/OGwc1Ts2KwzjIctkZroxtVwKzUMUKHk3N5yqWPKneHw3y5+eubEi0484yXmk6FCLVDCKzgqT24uxGjSafsufi6xDsIQmLNUeNL76ScYKxTUySa3tBX6OUUkNCib5tNYvLM8pG9Mh7znUVHEblfNhp+TMOQlJM+OORjJ3f78oqbJ2omJ3U1Ec2dVsZv6X9QpMr6NS6LxArtnio7SQBDMy25wkwnCGcuKAMiPcrISNqKEMXT81V0KwuvI6dC5bgd8KHnyowgmcwjkEcAU3cA9tCIGBgBd4g3dPe6/ex6Kuirfs7Rj+yPv8AS6IjQI=</latexit><latexit sha1_base64="8kZ/4D6HaS3u30my6UvxNLN/8EE=">AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBbBU0286LHUi8cKpi20oWw2m3bp7ibsboQS+hu8eFDEqz/Im//GTZuDtj4YeLw3w8y8MOVMG9f9diobm1vbO9Xd2t7+weFR/fikq5NMEeqThCeqH2JNOZPUN8xw2k8VxSLktBdO7wq/90SVZol8NLOUBgKPJYsZwcZKftS+mopRveE23QXQOvFK0oASnVH9axglJBNUGsKx1gPPTU2QY2UY4XReG2aapphM8ZgOLJVYUB3ki2Pn6MIqEYoTZUsatFB/T+RYaD0Toe0U2Ez0qleI/3mDzMS3Qc5kmhkqyXJRnHFkElR8jiKmKDF8ZgkmitlbEZlghYmx+dRsCN7qy+uke9303Kb34DZa7TKOKpzBOVyCBzfQgnvogA8EGDzDK7w50nlx3p2PZWvFKWdO4Q+czx9QNY5V</latexit><latexit sha1_base64="qIZwl3Jc4ynQLkNGz6S46LUxZ+Q=">AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBbBU02koMdSLx4rmLbQhrLZbNqlu5uwuxFK6G/w4kERr/4gb/4bt20O2vpg4PHeDDPzwpQzbVz32yltbG5t75R3K3v7B4dH1eOTjk4yRahPEp6oXog15UxS3zDDaS9VFIuQ0244uZv73SeqNEvko5mmNBB4JFnMCDZW8qPW1UQMqzW37i6A1olXkBoUaA+rX4MoIZmg0hCOte57bmqCHCvDCKezyiDTNMVkgke0b6nEguogXxw7QxdWiVCcKFvSoIX6eyLHQuupCG2nwGasV725+J/Xz0x8G+RMppmhkiwXxRlHJkHzz1HEFCWGTy3BRDF7KyJjrDAxNp+KDcFbfXmddK7rnlv3Hhq1ZquIowxncA6X4MENNOEe2uADAQbP8ApvjnRenHfnY9lacoqZU/gD5/MHUXWOWQ==</latexit><latexit sha1_base64="qIZwl3Jc4ynQLkNGz6S46LUxZ+Q=">AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBbBU02koMdSLx4rmLbQhrLZbNqlu5uwuxFK6G/w4kERr/4gb/4bt20O2vpg4PHeDDPzwpQzbVz32yltbG5t75R3K3v7B4dH1eOTjk4yRahPEp6oXog15UxS3zDDaS9VFIuQ0244uZv73SeqNEvko5mmNBB4JFnMCDZW8qPW1UQMqzW37i6A1olXkBoUaA+rX4MoIZmg0hCOte57bmqCHCvDCKezyiDTNMVkgke0b6nEguogXxw7QxdWiVCcKFvSoIX6eyLHQuupCG2nwGasV725+J/Xz0x8G+RMppmhkiwXxRlHJkHzz1HEFCWGTy3BRDF7KyJjrDAxNp+KDcFbfXmddK7rnlv3Hhq1ZquIowxncA6X4MENNOEe2uADAQbP8ApvjnRenHfnY9lacoqZU/gD5/MHUXWOWQ==</latexit><latexit sha1_base64="qIZwl3Jc4ynQLkNGz6S46LUxZ+Q=">AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBbBU02koMdSLx4rmLbQhrLZbNqlu5uwuxFK6G/w4kERr/4gb/4bt20O2vpg4PHeDDPzwpQzbVz32yltbG5t75R3K3v7B4dH1eOTjk4yRahPEp6oXog15UxS3zDDaS9VFIuQ0244uZv73SeqNEvko5mmNBB4JFnMCDZW8qPW1UQMqzW37i6A1olXkBoUaA+rX4MoIZmg0hCOte57bmqCHCvDCKezyiDTNMVkgke0b6nEguogXxw7QxdWiVCcKFvSoIX6eyLHQuupCG2nwGasV725+J/Xz0x8G+RMppmhkiwXxRlHJkHzz1HEFCWGTy3BRDF7KyJjrDAxNp+KDcFbfXmddK7rnlv3Hhq1ZquIowxncA6X4MENNOEe2uADAQbP8ApvjnRenHfnY9lacoqZU/gD5/MHUXWOWQ==</latexit><latexit sha1_base64="qIZwl3Jc4ynQLkNGz6S46LUxZ+Q=">AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBbBU02koMdSLx4rmLbQhrLZbNqlu5uwuxFK6G/w4kERr/4gb/4bt20O2vpg4PHeDDPzwpQzbVz32yltbG5t75R3K3v7B4dH1eOTjk4yRahPEp6oXog15UxS3zDDaS9VFIuQ0244uZv73SeqNEvko5mmNBB4JFnMCDZW8qPW1UQMqzW37i6A1olXkBoUaA+rX4MoIZmg0hCOte57bmqCHCvDCKezyiDTNMVkgke0b6nEguogXxw7QxdWiVCcKFvSoIX6eyLHQuupCG2nwGasV725+J/Xz0x8G+RMppmhkiwXxRlHJkHzz1HEFCWGTy3BRDF7KyJjrDAxNp+KDcFbfXmddK7rnlv3Hhq1ZquIowxncA6X4MENNOEe2uADAQbP8ApvjnRenHfnY9lacoqZU/gD5/MHUXWOWQ==</latexit><latexit sha1_base64="qIZwl3Jc4ynQLkNGz6S46LUxZ+Q=">AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBbBU02koMdSLx4rmLbQhrLZbNqlu5uwuxFK6G/w4kERr/4gb/4bt20O2vpg4PHeDDPzwpQzbVz32yltbG5t75R3K3v7B4dH1eOTjk4yRahPEp6oXog15UxS3zDDaS9VFIuQ0244uZv73SeqNEvko5mmNBB4JFnMCDZW8qPW1UQMqzW37i6A1olXkBoUaA+rX4MoIZmg0hCOte57bmqCHCvDCKezyiDTNMVkgke0b6nEguogXxw7QxdWiVCcKFvSoIX6eyLHQuupCG2nwGasV725+J/Xz0x8G+RMppmhkiwXxRlHJkHzz1HEFCWGTy3BRDF7KyJjrDAxNp+KDcFbfXmddK7rnlv3Hhq1ZquIowxncA6X4MENNOEe2uADAQbP8ApvjnRenHfnY9lacoqZU/gD5/MHUXWOWQ==</latexit><latexit sha1_base64="qIZwl3Jc4ynQLkNGz6S46LUxZ+Q=">AAAB7HicbVBNS8NAEJ3Ur1q/qh69LBbBU02koMdSLx4rmLbQhrLZbNqlu5uwuxFK6G/w4kERr/4gb/4bt20O2vpg4PHeDDPzwpQzbVz32yltbG5t75R3K3v7B4dH1eOTjk4yRahPEp6oXog15UxS3zDDaS9VFIuQ0244uZv73SeqNEvko5mmNBB4JFnMCDZW8qPW1UQMqzW37i6A1olXkBoUaA+rX4MoIZmg0hCOte57bmqCHCvDCKezyiDTNMVkgke0b6nEguogXxw7QxdWiVCcKFvSoIX6eyLHQuupCG2nwGasV725+J/Xz0x8G+RMppmhkiwXxRlHJkHzz1HEFCWGTy3BRDF7KyJjrDAxNp+KDcFbfXmddK7rnlv3Hhq1ZquIowxncA6X4MENNOEe2uADAQbP8ApvjnRenHfnY9lacoqZU/gD5/MHUXWOWQ==</latexit>
![Page 5: Millimeter-Wavelength Remote Sensing of the Tropospheric Structure of Venus ... · 2018. 12. 29. · Remote Observations of Venus 11/7/2018 Millimeter-Wavelength Remote Sensing of](https://reader035.vdocument.in/reader035/viewer/2022071414/610f2b21d9d1b242ab292e55/html5/thumbnails/5.jpg)
SO2 Millimeter–Wavelength Absorption
• Measured from 2-4 mm under simulated Venus conditions
• Bellotti and Steffes (2015)• 0 – 2 bar CO2, 308-343 K
• Matches Van-Vleck Weisskopf absorption model• Fahd (1992)• This model is valid from microwave to millimeter
wavelengths under cloud-base to surface conditions (Steffes et al. 2015)
11/7/2018Millimeter-Wavelength Remote Sensing of the Tropospheric Structure of
Venus: Exploratory Simulations 4
2–3 mm absorp,on of 76 mbar SO2 broadened with 833 mbar CO2 at 345 K
![Page 6: Millimeter-Wavelength Remote Sensing of the Tropospheric Structure of Venus ... · 2018. 12. 29. · Remote Observations of Venus 11/7/2018 Millimeter-Wavelength Remote Sensing of](https://reader035.vdocument.in/reader035/viewer/2022071414/610f2b21d9d1b242ab292e55/html5/thumbnails/6.jpg)
H2SO4 Vapor Millimeter-Wavelength Absorption
• Measured with a semi-confocal corrosion-resistant open resonator from 2–4 mm
• 0 – 3 bar CO2, 533-550K• Measurements at lower temperatures are prohibitive
• Microwave measurements of Kolodner and Steffes(1998) overstates absorption at millimeter-wavelengths
• Closer fit to lineshape model• Using JPL catalog (Cohen and Drouin 2013)• Δ"#$%&' = 97.17 -.//1233, Δ"4&$ = 4.86 -.//1233
11/7/2018 Millimeter-Wavelength Remote Sensing of the Tropospheric Structure of Venus: Exploratory Simulations 5
Absorp'on spectra of 2̴0 mbar H2SO4broadened with 2.975 bar CO2 at 550 K
![Page 7: Millimeter-Wavelength Remote Sensing of the Tropospheric Structure of Venus ... · 2018. 12. 29. · Remote Observations of Venus 11/7/2018 Millimeter-Wavelength Remote Sensing of](https://reader035.vdocument.in/reader035/viewer/2022071414/610f2b21d9d1b242ab292e55/html5/thumbnails/7.jpg)
What is Causing Continuum Emission Longitudinal Variability?
• ~8 K decrease from disk center to near-limb emission
• Physical processes in the 40-55 km range
• Changes in temperature and pressure conditions due to dynamic processes• However, minimal evidence for significant longitudinal variations in this range (Limaye et al. 2018)
• Some unknown spatially-variable absorber• Unlikely
Considered here
• Variations in H2SO4 vapor or SO2 vertical abundance structure with longitude
• Variations in cloud bulk density• Larger aerosol
• Sizes are unlikely to be large enough (McGouldrick et al. 2011) to result in significant 2-4 mm scattering
Disclaimer: Thermal structure, cloud cover, and constituent abundances are all linked!
11/7/2018Millimeter-Wavelength Remote Sensing of the Tropospheric Structure of
Venus: Exploratory Simulations6
(Assuming it is physical)
![Page 8: Millimeter-Wavelength Remote Sensing of the Tropospheric Structure of Venus ... · 2018. 12. 29. · Remote Observations of Venus 11/7/2018 Millimeter-Wavelength Remote Sensing of](https://reader035.vdocument.in/reader035/viewer/2022071414/610f2b21d9d1b242ab292e55/html5/thumbnails/8.jpg)
Abundances of SO2
and H2SO
4 Below the Clouds
• H2SO
4profiles retrieved from radio occultation profiles
• Mariner 10, Pioneer Venus, Magellan, Venus Express,
Akatsuki
• Possible supersaturation suggested by VeRa results
• Previously, SO2 vertical abundance profile assumed
uniform below clouds
• Latitudinally dependent, ranges from 50-150 ppm (Marcq et
al. 2008, Jenkins et al. 2002)
• Results from ISAV-1 and ISAV-2 experiments call this into
question (Bertraux et al. 1996)
• Upper troposphere dynamics may result in radical variations
11/7/2018Millimeter-Wavelength Remote Sensing of the Tropospheric Structure of Venus:
Exploratory Simulations7
Mariner 10 low latitude occultation
![Page 9: Millimeter-Wavelength Remote Sensing of the Tropospheric Structure of Venus ... · 2018. 12. 29. · Remote Observations of Venus 11/7/2018 Millimeter-Wavelength Remote Sensing of](https://reader035.vdocument.in/reader035/viewer/2022071414/610f2b21d9d1b242ab292e55/html5/thumbnails/9.jpg)
Abundances of H2SO4 Below the Clouds
• Abundance scaling representative of possible H2SO4 supersaturation
• Lower SO2 abundance should lead to enhanced effect of H2SO4 abundance variation
• Physical conditions are prohibitive to high vapor abundance above 52 km
• H2SO4 abundance variations would not (directly) result in substantial brightness temperature variations
11/7/2018Millimeter-Wavelength Remote Sensing of the Tropospheric Structure of Venus:
Exploratory Simulations 8
Thermal dissocia.on to
SO3, H2O
Decreasing SVP and
condensationShift
Shift
Scale
Variation of equatorial nadir brightness (103 GHz) with 5x scaled and shifting H2SO4
abundance profile (50 ppm SO2)
![Page 10: Millimeter-Wavelength Remote Sensing of the Tropospheric Structure of Venus ... · 2018. 12. 29. · Remote Observations of Venus 11/7/2018 Millimeter-Wavelength Remote Sensing of](https://reader035.vdocument.in/reader035/viewer/2022071414/610f2b21d9d1b242ab292e55/html5/thumbnails/10.jpg)
Abundances of SO2 Below the Clouds
11/7/2018 Millimeter-Wavelength Remote Sensing of the Tropospheric Structure of Venus: Exploratory Simulations 9
• Scaling SO2 abundance features seen in the ISAV UV results from Vega 1 and Vega 2 landers
• Nightside measurements• Potential issue with cloud condensation on
mirrors
• Spatial variations in the SO2 mixing ratio below 40 kilometers would not be observable from 2-4 mm
• Opaque due to CO2/N2 absorption
• Substantial SO2 abundance variations in the clouds could explain variations in millimeter-wavelength continuum images
ISAV 1
ISAV 2
High Peak
Low Peak
![Page 11: Millimeter-Wavelength Remote Sensing of the Tropospheric Structure of Venus ... · 2018. 12. 29. · Remote Observations of Venus 11/7/2018 Millimeter-Wavelength Remote Sensing of](https://reader035.vdocument.in/reader035/viewer/2022071414/610f2b21d9d1b242ab292e55/html5/thumbnails/11.jpg)
Variations in Cloud Structure
• Scaled from PV Large Probe• Knollenberg and Hunten (1980)
• Substantial variations in the bulk density of the lower cloud would result in 30-40K brightness temperature variations
• Cloud scattering is not significant for previously observed particle sizes
• Larger particle sizes are unlikely (McGouldrick et al. 2011)
11/7/2018Millimeter-Wavelength Remote Sensing of the Tropospheric Structure of Venus:
Exploratory Simulations 10
300 micron
![Page 12: Millimeter-Wavelength Remote Sensing of the Tropospheric Structure of Venus ... · 2018. 12. 29. · Remote Observations of Venus 11/7/2018 Millimeter-Wavelength Remote Sensing of](https://reader035.vdocument.in/reader035/viewer/2022071414/610f2b21d9d1b242ab292e55/html5/thumbnails/12.jpg)
Conclusions
• Variations in H2SO4 vapor are not likely responsible for millimeter wavelength features
• ALMA observations with long baselines can provide precise constraints on brightness temperature variations
• Multi-band coordinated microwave and millimeter-wavelength observations can retrieve regional constituent abundance and temperature profiles
• Future microwave/millimeter radiometer on Venera-D?• Further measurements of pressure broadened H2SO4 absorption
could be key to interpret future Ka band radio occultations
11/7/2018 Millimeter-Wavelength Remote Sensing of the Tropospheric Structure of Venus: Exploratory Simulations 11
![Page 13: Millimeter-Wavelength Remote Sensing of the Tropospheric Structure of Venus ... · 2018. 12. 29. · Remote Observations of Venus 11/7/2018 Millimeter-Wavelength Remote Sensing of](https://reader035.vdocument.in/reader035/viewer/2022071414/610f2b21d9d1b242ab292e55/html5/thumbnails/13.jpg)
Backup Slides
![Page 14: Millimeter-Wavelength Remote Sensing of the Tropospheric Structure of Venus ... · 2018. 12. 29. · Remote Observations of Venus 11/7/2018 Millimeter-Wavelength Remote Sensing of](https://reader035.vdocument.in/reader035/viewer/2022071414/610f2b21d9d1b242ab292e55/html5/thumbnails/14.jpg)
Distinguishing between SO2 and cloud variations
9/14/18Millimeter-Wavelength Remote Sensing of the Tropospheric Structure of
Venus: Exploratory Simulations13
Frequency dependence of lower cloud bulk density variations
Frequency dependence of 52 km SO2
mole frac<on varia<ons
Multi-wavelength observations would help tell the sources apart, particularly between 130 and 140 GHz
![Page 15: Millimeter-Wavelength Remote Sensing of the Tropospheric Structure of Venus ... · 2018. 12. 29. · Remote Observations of Venus 11/7/2018 Millimeter-Wavelength Remote Sensing of](https://reader035.vdocument.in/reader035/viewer/2022071414/610f2b21d9d1b242ab292e55/html5/thumbnails/15.jpg)
Vertical Wave Propagation
9/14/18 Millimeter-Wavelength Remote Sensing of the Tropospheric Structure of Venus: Exploratory Simulations 14
Imamura et al. 2014
![Page 16: Millimeter-Wavelength Remote Sensing of the Tropospheric Structure of Venus ... · 2018. 12. 29. · Remote Observations of Venus 11/7/2018 Millimeter-Wavelength Remote Sensing of](https://reader035.vdocument.in/reader035/viewer/2022071414/610f2b21d9d1b242ab292e55/html5/thumbnails/16.jpg)
2013 CARMA Images (Preliminary)
9/14/18 Millimeter-Wavelength Remote Sensing of the Tropospheric Structure of Venus: Exploratory Simulations 15
99.2 GHz 114.8 GHz
• Concurrently imaged at elongation• Disclaimer: Heterogeneous array
makes imaging particularly difficult
Devaraj, CookNCSA CARMA Data Archive