- Email: [email protected]
Discovery of a 150 day period in the Venus condensational clouds
Accepted Manuscript
Discovery of a 150 day period in the Venus condensational clouds Kevin McGouldrick, Constantine C.C. Tsang PII: DOI: Reference:
S0019-1035(16)30652-2 10.1016/j.icarus.2016.10.005 YICAR 12221
To appear in:
Icarus
Received date: Revised date: Accepted date:
11 March 2016 15 September 2016 2 October 2016
Please cite this article as: Kevin McGouldrick, Constantine C.C. Tsang, Discovery of a 150 day period in the Venus condensational clouds, Icarus (2016), doi: 10.1016/j.icarus.2016.10.005
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Highlights • We find a 150 day periodic variation in the 1.74 µm and 2.30 µm radi-
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• The oscillation is most pronounced at mid-latitudes (30◦ − 60◦ ).
• The timescales are consistent with the cloud radiative-dynamical feedback.
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• Long-term increase in radiance at mid to low latitudes is also noted.
• Additional hypotheses to guide future modelling of this phenomenon
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Discovery of a 150 day period in the Venus condensational clouds
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Kevin McGouldricka,∗, Constantine C. C. Tsangb a
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Laboratory for Atmospheric and Space Physics, University of Colorado Boulder, 3665 Discovery Dr., Boulder, CO 80303 b Southwest Research Institute, Department of Space Studies, 1050 Walnut St., Suite 300, Boulder, CO 80302
Abstract
We have analyzed the long-term regional and global variation of emitted radiance in 1.74µm and 2.30µm near infrared spectral windows in the Venus atmosphere using the medium resolution, infrared channel of the Visible and
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Infrared Thermal Imaging Spectrometer (VIRTIS-M-IR) on the Venus Express spacecraft. We find a periodic variation in the 1.74µm radiance that
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is most pronounced at mid-latitudes (30◦ − 60◦ latitude). This oscillation has a period of approximately 150 days, and is shown to be unlikely to be
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driven by variations in viewing geometry, nor by variations in instrumental characteristics such as spectrometer temperature. The oscillation has an am-
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plitude at least as large as that of the typical day-to-day variations observed. The decay and recovery timescales are consistent with response of the cloud
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vertical structure to the radiative-dynamical feedback. It remains unclear why this variation would be seen only at mid-latitudes, but some hypotheses to guide future modelling testing are suggested. ∗
Corresponding author. Email address: [email protected] (Kevin McGouldrick)
Preprint submitted to Icarus
October 7, 2016
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Keywords: Venus, Atmosphere, Clouds, Meteorology, Dynamics 1. Introduction
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Spatial and temporal inhomogeneities in the near infrared emission spec-
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trum of Venus were first discovered by Allen and Crawford (1984). It was
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soon determined that these inhomogeneities were observed as a consequence
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of the existence of narrow spectral windows in the near infrared emission
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spectrum of Venus where absorption by (primarily) CO2 and H2 O was min-
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imal. Since then, these spectral windows have been used to elucidate the
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properties of the surface of Venus (for example, Mueller et al. (2008), Kappel
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et al. (2012), Haus et al. (2014), and Shalygin et al. (2015)), atmospheric
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composition and chemistry (for example, Marcq et al. (2005) and B´ezard
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et al. (2009)), and properties of the clouds of Venus (for example, Carlson
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et al. (1993) and Wilson et al. (2008)).
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Crisp et al. (1989) and Kamp et al. (1988) showed that the variability
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of night side near infrared emission from Venus in the spectral vicinity of
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the 1.74µm and 2.30µm windows was driven primarily by variations in the
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condensational clouds of Venus. The clouds of Venus cover a range of alti-
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tudes from about 50km above the surface to about 70km above the surface.
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When viewed in emitted near infrared radiation, spatial inhomogeneities are
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driven by variations in the lower regions of the clouds, between about 50-
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55km. The bulk of the cloud mass is located also in this region, but the origin
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of the volatiles that support the entire cloud system is the photochemically
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produced sulfuric acid around 63km.
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Grinspoon et al. (1993) used the 1.74µm and 2.30µm spectral windows
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observed by the Near Infrared Mapping Spectrometer (NIMS) during the
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Galileo flyby to constrain the total infrared optical depth of the photochem-
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ical and condensational clouds and the composition of the putative Mode 3
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particles first postulated by Knollenberg and Hunten (1980). Carlson et al.
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(1993) used the same data to characterize the spatial variability of the typical
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size of the particles that comprise the condensational cloud at the time of
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the Galileo encounter.
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More recently, the infrared mapping channel of the Visible and Infrared
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Thermal Mapping Spectrometer (VIRTIS-M-IR) on the Venus Express space-
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craft (Drossart et al., 2007) has been utilized to further characterize the
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short-term evolution of the clouds of Venus (McGouldrick et al., 2012) and
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to simultaneously retrieve additional properties of the Venus clouds region,
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including cloud base altitude, sulfuric acid weight percent, and sub-cloud and
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in-cloud water vapor concentrations (Barstow et al., 2012).
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Here, we build upon the work done in those two papers to character-
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ize the long-term evolution of the clouds of Venus, as can be determined
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through analysis of 921 orbits (about two and a half years) of VIRTIS-M-IR
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observations of the night side of Venus.
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2. Observational Data
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Venus Express launched in November 2005, was placed into orbit around
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Venus in April 2006, and continued to return valuable science data until
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it exhausted the fuel for its attitude control thrusters in November 2014.
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Its polar orbit exhibited a periapsis altitude generally between 150 km and 5
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250 km above the surface of Venus at about +80◦ latitude, and an apoapsis
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altitude of about 66,000 km. The VIRTIS-M infrared channel is a medium
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spatial resolution (0.25 mrad/pxl) infrared mapping spectrometer that cov-
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ers the range of wavelengths from 1µm to 5µm with a spectral resolution
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of roughly λ/∆λ ∼ 300, or about 0.01µm. Though, in practice, the effec-
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tive resolution has been shown to be about 0.017µm (B´ezard et al., 2009).
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This is sufficient spectral resolution to resolve many details of the spectral
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windows (Drossart et al., 2007). The spatial resolution is about 30 km when
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the spacecraft is at apoapse (d ∼ 66, 000 km), improving to about 5 km at
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a distance of about 10, 000 km. The near infrared detector was a mercury-
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cadmium-telluride (HgCdTe) semiconductor cooled to 70K. The instrument
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returned data over the course of nearly four sidereal Venus days until the
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cooling system failed during orbit 921 (UTC: 2008 October 27). The cooling
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system began to show signs of wear during the nominal mission (the first 500
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orbits), so the frequency of use of the VIRTIS-M-IR instrument was signif-
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icantly reduced between orbits 500 and 921, as compared with the nominal
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mission. Previous work by McGouldrick et al. (2012) exploring the long-term
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variability of the clouds relied on data only from the first 407 orbits of the
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mission. In the present work, we utilize the entire VIRTIS-M-IR data set.
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The entire volume of data produced by the instrument can be obtained
at the European Space Agency’s (ESA’s) Planetary Science Archive (PSA) website, and is mirrored by the National Astronautical and Space Adminis-
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tration’s (NASA’s) Planetary Data System (PDS), Atmospheres Node. The
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VIRTIS instrument produced about a terabyte of data over the course of the
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Venus Express mission. In order to efficiently analyze this large volume of
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data, it is necessary to filter it according to both instrumental and geometric
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constraints. Instrumentally, we consider only observations utilizing integra-
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tion times of at least 0.3 seconds. Acquired spectral cubes having integration
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times shorter than this are intended for the much higher radiance from day
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side observations, and have very low signal to noise ratios in emitted near
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infrared light. Geometrically, we constrain the data according to distance,
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viewing angle, and solar angle considerations. To generate spectral cubes,
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VIRTIS-M-IR scans its slit across the field of view to generate spectral im-
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age cubes. The time required to do this, combined with the motion of the
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spacecraft relative to the planet, means that mapping mode spectral cubes
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generally are not created when within 10,000 km of the planet. (Drossart
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et al., 2007). Thus, we consider only data acquired at distances greater than
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10, 000 km from the planet. In doing so, we are neglecting the pericenter
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observations – mostly of northern hemisphere targets. We choose to neglect
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these data for two reasons. First, these periapse observations are necessarily
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very parochial in nature, due to the small distance to Venus and the small
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field of view of VIRTIS-M-IR. While the inclusion of these nadir-viewing,
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near-periapse observations can improve the mission-long statistics, they also
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have the potential to introduce significant errors into the time series analysis
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performed in this work that are caused by the spatial inhomogeneity. Sec-
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ond, the present work is intended to be part of a larger project in which the
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information gathered here can inform the characterization of individual fea-
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tures, including morphology, in the Venus clouds over a variety of timescales.
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Since that effort will be necessarily limited to observations using the map-
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ping mode of VIRTIS-M-IR, we also constrain this preliminary work to that
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mode of observation. The pericenter observations obtained at distances less
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than 10,000 km will not be helpful in either of these contexts, so we disre-
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gard those observations for now in favor of concentrating on the southern
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hemisphere mapping data. We consider only those observations in which at
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least some of the night side is visible, discarding all data for which only the
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day side is seen. That is, we discard the data for the present analysis if the
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minimum hour angle of the Sun exceeds 5 a.m. and the maximum hour angle
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is less than 7 p.m. The 1 hour buffer from the dawn or dusk terminator is
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intended to minimize the effects of sunlight that is forward scattered from
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beyond the terminator. We also restrict the observations to those that are
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affected minimally (or not at all) by sunlight that is forward scattered from
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the day side of the planet by restricting the data in the nominal analysis to
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locations where the solar incidence angle exceeds 95◦ . In order to quantify
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the effects of this cutoff, we also compare results considering a range of inci-
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dence angle, among 100◦ , 105◦ , 110◦ , and 115◦ . Note that, due to our hour
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angle restriction, these incidence angle data filters will have their greatest ef-
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fect for observations near the pole. However, these cutoffs will have minimal
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effect on reducing the contribution by stray light sources in the data (Kappel
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et al., 2012). Finally, we restrict our analysis to the southern hemisphere.
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The highly eccentric polar orbit of Venus Express makes mapping type ob-
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servations by VIRTIS-M-IR of the southern hemisphere more favorable than
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the northern hemisphere. While portions of the northern hemisphere have
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been observed in mapping mode, the data are almost exclusively equatorial
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(|φ| < 30◦ ). If a north-south hemispheric dichotomy exists in the behavior
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of the clouds then this uneven distribution of north and south latitudinal
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observations could exacerbate the effect. Furthermore, even those north-
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ern hemisphere observations that do exist are very close to the limb, and
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hence are subject to significant foreshortening and limb darkening, resulting
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in larger uncertainties in the corrected upwelling radiance.
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Most of the time, at least some of the night side of Venus is visible to
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VIRTIS-M-IR. However, there are times when the change in the phase angle
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due to the revolution of Venus around the Sun, coupled with the telemetry
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requirements, makes it nearly impossible to observe the night side of the
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planet (which is necessary for the analysis of these near infrared emissions
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from Venus). Thus, even though VIRTIS-M-IR returned useful data over a
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window of 921 days (also 921 orbits, since the orbital period of Venus Express
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throughout this phase of the mission was 24 hours) before the failure of its
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cooling system, there are somewhat fewer than 921 orbits’ worth of data
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that will be useful for the present analysis. There are also several weeks-
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long breaks in the data during which times night side data that satisfy our
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declared criteria could not be obtained.
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Over the course of multiple orbits, significant latitudinal and longitudinal
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coverage of the clouds in the southern hemisphere was built up, which allows
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for the determination of possible latitudinal tendencies in the existence and
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optical thickness of the clouds. Furthermore, VIRTIS observations sometimes
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utilize a mosaic mode in which the entire visible hemisphere of the planet is
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observed over the course of up to nine separate cube acquisitions. Observing
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in this manner allowed a greater spatial coverage than is possible with a
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single cube, or a series of cubes over a particular location.
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Note that, due to the limited field of view of the VIRTIS-M-IR instru-
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ment, the brief lifetime of this instrument (fewer than four Venus sidereal
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days), and the existence of about a dozen unique science observation modes,
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the composite coverage of the planet is not homogeneous. In addition to
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the hemispherical observational imbalance driven by the polar and eccentric
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orbit, there may also be geographic locations that had been observed more
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frequently than others.
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The VIRTIS-M cubes demonstrate a significant amount of anomalous ra-
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diance that has been attributed to scattered sunlight, probably reflected from
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the baffle toward the detector (Mueller et al., 2008; Kappel et al., 2012). In
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order to correct for this scattered sunlight, we choose a series of wavelength
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bands in the Venus emitted near infrared spectrum for which we expect to
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see zero emitted radiance, due to the absorption of upwelling radiation by
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atmospheric constituents such as CO2 and H2 O. That is, we define a series
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of “muntins1 ” between the near infrared spectral windows with wavelengths:
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(1.05 ± 0.01 µm, 1.225 ± 0.015 µm, 1.38 ± 0.03 µm, 1.57 ± 0.03 µm). A VIR-
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TIS image cube is a three-dimensional data construct with dimensions termed
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band (wavelength), sample (pixels along the slit), and line (each new inte-
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gration by the detector). That is, a VIRTIS cube is a stack of band × sample
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images. For each band × sample image, we average over the sample (slit)
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dimension to find an average spectrum.
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Acting on the assumption that the stray light was likely scattered sun-
light, we had first attempted to fit the data in the muntins according to a
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1 A muntin is a bar or rigid supporting strip between adjacent panes of a glass window; formerly used to increase the structural integrity of a large window, today mostly used for decorative purposes.
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reflected solar Blackbody curve:
I(λ) = A
−1 2hc2 hc λkT − 1 e λ5
(1)
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where h is Planck’s Constant, c is the speed of light in vacuum, k is Boltz-
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mann’s constant, T is the temperature of the solar photosphere, and we
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choose A to be an arbitrary gray albedo that is a free parameter to be fit to
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the data along with λ. However, we found that such a spectrum could not
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match the measured muntins. If the gray albedo was chosen to fit the muntins
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near 1.5µm and 2.0µm, then the stray light radiance from the muntins at
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shorter wavelengths was underestimated. Similarly, if the curve was fitted to
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the muntins at wavelengths shorter than 1.3µm, then the stray light radiance
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from the longer wavelength muntins was overestimated. Similar to Kappel
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et al. (2012) and Longobardo et al. (2012), we found that the stray light
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radiance in the muntins closely matched a λ−4 curve. Likely interpretations
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of such a curve would mean that either the source of the stray light spectrum
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were a blackbody considerably hotter than the Sun or was produced by a
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non-gray albedo that increased strongly at shorter wavelengths. In the for-
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mer case, these near infrared wavelengths are too near the peak of the solar
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spectrum to be in the long-wavelength Rayleigh-Jeans regime of the solar
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spectrum that asymptotes to a λ−4 curve. In the latter case, Kappel et al.
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(2012) suggest that the stray light resembles λ−4 associated with scattering
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processes, but the Venus cloud particles are too large to be Rayleigh scat-
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terers at these wavelengths. Since neither of these explanations is likely, we
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chose to fit the data with an arbitrary power law or an arbitrary exponential: I(λ) = I0 λa
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I(λ) = I0 · eaλ
(2) (3)
We then fit the free parameters (I0 ) and (a) to the muntin data, finding their
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best fit values and standard deviations in each of these two cases. We found
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that the power law tended to identify best fit exponents of between λ−3 and
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λ−5 , somewhat consistent with previous suggestions by Kappel et al. (2012)
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and Longobardo et al. (2012). However, we found that the goodness of the fit
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was somewhat better when using the exponential curve in the vast majority
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of the analyzed data, so we chose to use the exponential curve as a best fit for
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the stray light correction. We then subtract this best fit stray light spectrum
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from each pixel in the slit (along the sample axis). All negative values in the
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scattered sunlight corrected spectra are treated as zeros. An example of the
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effect of this procedure for a given spectrum at one pixel (sample 100, line
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50) of one particular pure night side image cube (VIR0383 00) is shown in
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Fig. 1.
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Also shown in Fig. 1 is an example stray light spectrum obtained by av-
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eraging all valid data (i.e., pixels not exhibiting error flags) obtained from
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observations at least 200km above the limb of the planet for this same pure
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night side image cube. We see that the stray light present at 1.74µm and
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2.30µm is nearly negligible. So, even if our simple exponential stray light
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correction is invalid, it will introduce negligible error in the current analysis.
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Future analysis of the near surface windows will require us to apply a more
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Figure 1: In the left hand plot, the black curve is the uncorrected spectrum of sample 100 and line 50 of pure night side cube VIR0383 00. The red curve is the same data with the stray sunlight correction from Eq. 3 applied. In the right hand plot, an average spectrum collected from the empty space observations within the same image cube is compared with the same on-target uncorrected spectrum.
rigorous stray light correction, perhaps similar to that described by Kappel
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et al. (2012). Though the stray light has minimal effect at the wavelengths
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investigated in this paper, we include this description of our stray light cor-
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rection process in ourder to document this method and to allow reference to
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it from future work that we intend to carry out.
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Following the correction for the scattered light, in order to normalize
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the observations for long-term cross-comparisons, we apply a limb darkening
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correction to the data. In previous work, McGouldrick et al. (2008, 2012)
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utilized the corrections of Carlson et al. (1993). Here, we capitalize upon
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the efforts by Longobardo et al. (2012) to quantify the limb darkening seen
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in the VIRTIS-M-IR data in several of the near infrared spectral windows.
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Longobardo et al. (2012) found variations in the limb darkening behavior as a
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function of latitude. For the windows that Longobardo et al. (2012) analyzed
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and that we study here, we use the “average” limb darkening correction
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parameters to determine a nominal radiance at zero emission angle:
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3. Results
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3.1. Long-term global tendencies
(4)
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Iemitted = Iobserved · (αλ + βλ cos θe )−1 .
Bullock and Grinspoon (2001) and others have suggested that changes in
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SO2 in the upper atmosphere could lead to changes in overall cloud coverage,
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due to a greater availability of condensable materials. Orders of magnitude
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variations are seen in the SO2 concentrations above 70km (Esposito et al.,
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1988; Marcq et al., 2012). Although the concentrations at those altitudes
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are only at the tens to hundreds of ppbv (parts per billion by volume) level,
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the scale height of the SO2 at those altitudes has been measured to be about
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1 km, indicating that an orders of magnitude larger concentration at the
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tens to hundreds of ppmv (parts per million by volume) level exists deeper
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in the atmosphere in the cloud formation regions (near 62 km at equatorial
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latitudes). Thus, large changes in SO2 could to have significant effects on the
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total mass loading of the photochemical clouds, and potentially also effects
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on the total mass available to form the deeper condensational cloud.
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Our first goal is to determine whether a long-term global trend of Venusian
cloud cover is evident in the VIRTIS-M-IR data set by examining the long-
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term trends of the radiance in the 1.74µm and 2.30µm atmospheric windows.
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In Fig. 2, we show the hemispherically averaged radiance for each of these
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two windows as a function of orbit number. Also shown in the figure is a
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linear best fit to the data, with free parameters I0 (the radiance at orbit 14
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zero), and mI (the slope of the radiance per orbit). Finally, the five rows
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represent the five incidence angle cutoffs we considered in this analysis (95◦ ,
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100◦ , 105◦ , 110◦ , and 115◦ ).
Figure 2: Southern hemisphere radiance averaged across all cubes per orbit during the lifetime of VIRTIS-M-IR for both the 1.74µm and 2.30µm windows. From top to bottom, the rows represent data subject to differing minimum solar incidence angle restrictions of 95◦ , 100◦ , 105◦ , 110◦ , and 115◦ , respectively (0◦ is Sun at zenith).
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The linear fits to the data produce radiance at orbit 0, and the average 15
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slope of the radiance in units of W m−2 sr−1 µm−1 per orbit (or per day),
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as well as one sigma standard deviation uncertainties in those parameters.
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We overplot the best fit trend line (but not the uncertainty information) in
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Fig. 2. The unaveraged data for both windows and at most incidence angle
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restrictions shown in Fig. 2 shows a significant amount of scatter, and a
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best fit linear trend line that is essentially flat, indicating that there is no
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significant global change to the observed condensational cloud cover on Venus
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over the 2.5 year lifetime of the VIRTIS-M-IR instrument. Note also that
259
as the incidence angle cutoff is made more restrictive, a hint of a periodicity
260
begins to emerge from the data. However, since the larger emission angles
261
selectively remove observational data from the polar regions, it is unclear at
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this point whether the periodicity exists throughout the southern hemisphere
263
but has been masked by noise near the terminator, or whether is a more
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regional phenomenon.
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Because of the high level of scatter in the data, which is partly due to the
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small field of view of the instrument making it difficult to observe the same
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region of the atmosphere from orbit to orbit, as well as the intrinsic variability
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within the clouds, in Fig. 3 we have smoothed the data with a seven-day box
269
car mean window. A seven-day averaging of the data approximates extending
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the averaging over orbit done in Fig. 2 to a global average, since the period of
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rotation at the altitudes of these clouds is approximately seven days (Hueso
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et al., 2015).
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However, upon applying a seven day moving window average of the data,
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we notice in Fig. 3 the appearance of slight trends to the mean radiance in
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each window, and evidence of shorter-term (on the order of weeks to months)
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Figure 3: Southern hemisphere radiance averaged across all cubes per orbit during the lifetime of VIRTIS-M-IR for both the 1.74µm and 2.30µm windows, but further averaged with a seven day moving window to approximate a global average radiance. As in Fig. 2, from top to bottom, solar incidence angle restrictions of 95◦ , 100◦ , 105◦ , 110◦ , and 115◦ , are represented.
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variations in the cloud cover from radiance changes. The overall increase in
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radiance indicated by the mission-long linear best fit trend lines suggest that
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the overall cloud cover of Venus may have been thinning during the course of 17
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the mission. However, visual inspection of the plots indicates that for most
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incidence angle cutoffs this apparent trend is small compared to the overall
281
scatter in radiance that is observed on an observation-to-observation basis.
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If the decrease in the SO2 observed is driven by a conversion into H2 SO4 and
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thence into clouds, then the results presented here, though only of a 2.5 year
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duration, are inconsistent with that explanation, at least on the global scale.
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However, the highly spatially variable nature of the observed SO2 variations,
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and of the thickness of the condensational clouds, means that a regional scale
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relationship cannot yet be ruled out.
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The spectral registration of the VIRTIS-M-IR spectrometer varies with
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temperature (Moinelo et al., 2010), so that the mapping from band number
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to wavelength can vary with time. Thus, in generating the plots shown above,
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we use the radiance within the wavelength band that is closest to the defining
292
wavelength for each particular data cube. These changes in band number
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associated with a particular wavelength can produce small but detectable
294
variations in the measured flux. These variations are discussed at length by
295
Kappel et al. (2012), who concluded that they are the result of errors in
296
the ground calibration. Rather than reinvent the recalibration performed by
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Kappel et al. (2012), we attempt to rule out this so called Odd-Even effect
298
as a source of the variations we see by additionally performing our analysis
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using data that have been spectrally integrated across the entire range of
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each spectral window. This is similar to what is described by McGouldrick
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et al. (2012), for the 1.74µm window analyzed there. Here, we integrate
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the 1.74µm window from 1.67µm to 1.80µm; and the 2.30µm window from
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2.15µm to 2.60µm. In this analysis of spectrally integrated data, the Even-
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Odd effect should be reduced, as overestimations of measured flux in half the
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bands will be roughly balanced by underestimations of the flux in the other
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half of the bands.
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Fig. 4 shows the long term trends for the seven day averaging and spec-
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trally integrated windows. We see that both the long-term trend of increasing
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radiance, as well as the periodic shorter-term variations appear in the inte-
310
grated data. In fact, the relative magnitude of the day-to-day variations
311
compared with the average radiance measured is slightly smaller for the inte-
312
grated case, suggesting that the contribution to the measured radiance from
313
the Odd-Even effect has been minimized by this integration, and that that
314
effect is small for the present analysis. The data in Fig. 4 are best com-
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pared with the data in Fig. 3, since each has had the averaging extended
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across multiple orbits. Not shown, these similarities between the single band
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and integrated radiance for the unaveraged data are mirrored in the moving
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window averaged data.
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3.2. Mission-long latitudinal mean radiances
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One of our long-term goals in this project is to characterize the short-term
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behavior and variability of the condensational clouds of Venus. Previous work
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by McGouldrick et al. (2012) suggested that typical timescales of evolution
323
were around 30 hours, but that work only analyzed two orbits’ worth of
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observations. Part of the difficulty in establishing patterns of variability
325
among the condensational clouds is in quantifying what level of variability can
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be attributed to cloud variations. For example, Carlson et al. (1993) showed
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that variations in the clouds produce roughly 20 : 1 brightness contrast
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ratios at 2.30µm and roughly 5 : 1 brightness ratios at 1.74µm. However,
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Figure 4: Southern hemisphere radiance averaged across all cubes per orbit during the lifetime of VIRTIS-M-IR for both the 1.74µm and 2.30µm windows spectrally integrated across the entire spectral windows. The same incidence angle restrictions noted in Fig. 2 and Fig. 3 are represented.
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those contrast ratios do not account for the large magnitude of latitudinal
330
variance in the clouds as indicated by radiance variations observed by Crisp
331
et al. (1989) and Chanover et al. (1998). Within a given latitude region, the
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contrasts are about half of these global values. In previous analysis of short20
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term evolution of the clouds, McGouldrick et al. (2012) defined a cloud or hole
334
boundary according to closed radiance contours at a 0.02 W m−2 sr−1 µm−1
335
resolution. In order to reduce the arbitrariness of our cloud definition, we
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here develop a latitudinal profile of radiance for each of the windows, along
337
with their one-sigma standard deviations. In future analysis of short-term
338
cloud evolution, we plan to use these latitudinally resolved estimates of long-
339
term variability to define the presence or absence of a local cloud or hole
340
phenomenon.
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In Fig. 5, we show the latitudinal profiles for each of the spectral windows.
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These figures assimilate the entire VIRTIS-M-IR dataset that fit our criteria
343
detailed in Section 2 above. Note the local maximum in radiance evident
344
near 50◦ latitude in both the 2.30µm and 1.74µm data. This has been seen
345
since the NIR observations began in the 1980’s, and has been explained as
346
evidence of the interaction between the photochemical cloud production, the
347
condensational cloud production, and the near-global meridional Hadley-like
348
circulation by Imamura and Hashimoto (1998). The optically thick cloud
349
near the polar collar is also evident as the strong decrease in radiance pole-
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ward of that radiance maximum. The slight but sharp increase in radiance
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very near to the pole in the 1.74µm profile is possibly due to sunlight in the
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atmosphere scattered across the polar terminator, or is due to the deep emis-
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sion from the polar vortex. In the 1.74µm and 2.30µm profiles, we also see
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a significant but smaller increase in the variability of the clouds (evidenced
355
by an increase in the standard deviation about the mean) in the equatorial
356
region. However, since the orbit of Venus Express limited the number of
357
observations in this region that could match our criteria, and since these
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359
to potential errors or uncertainties in the limb darkening correction – the
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variation seen at equatorial latitudes should be taken cum grano salis. It is
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hoped that observations by JAXA’s Akatsuki spacecraft (Nakamura et al.,
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2007), having begun science operations from a more equatorial orbit in April
363
of 2016, will help to resolve the level of variability seen here by VIRTIS-M-IR
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on Venus Express in the equatorial clouds of Venus.
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0.15
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0 −10 −20 −30 −40 −50 −60 −70 −80 −90 90
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hr since midnight
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Radiance [W m −2 sr −1 µm −1 ] Surface Elevation from Magellan Altimetry
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latitude latitude
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observations tend also to be very close to the limb – hence more susceptible
latitude
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Figure 5: Zonally and temporally averaged mean radiance with their standard deviations as functions of latitude for the 1.74µm window, the 2.30µm window, and the Carlson et al. (1993) size parameter, in addition to geometrical data such as incidence and emission angles, surface elevation, and local solar time. The data here are subject to a minimum incidence angle of 95◦ .
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Also shown in Fig. 5 is the Carlson et al. (1993) size parameter: I1.74µm . (I2.30µm )0.53
(5)
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Carlson et al. (1993) showed that this weighted ratio of the 1.74µm and
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2.30µm emitted radiance can be used to estimate typical particle sizes in the
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Venus atmosphere, due to the relative Mie scattering properties of Mode 2
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and Mode 3 particles at these wavelengths. Wilson et al. (2008) applied
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this technique to a handful of early orbits of Venus Express, and found a
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significant increase in size parameter in the polar regions, when applying a
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zonal average, similar to what we have done here, but for individual orbits.
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Similarly, Barstow et al. (2012) found that the ratio of the Mode 3:Mode 20
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particle numbers increased toward the pole. This increase is likely the result
375
of the deeper altitude in which the condensational clouds exist at polar lat-
376
itudes. We reproduce this strong increase in size parameter (hence, particle
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size) poleward of about 50◦ . We also see a slight increase in size parame-
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ter seen with a local miximum near 20◦ was not reported by Barstow et al.
379
(2012). However, a reanalysis of the Barstow et al. (2012) work, presented
380
in the Barstow (2012) doctoral thesis, does report a similar phenomenon
381
with regard to the relative Mode 20 :Mode 3 particle number ratio. As can
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be seen in Fig. 5, the standard deviation about the mean is increasing at
383
these latitudes, due to the paucity of data and large emission angle of the
384
observations. Because we calculate the size parameter for a single band (we
385
do not use the spectrally integrated calculations), the size parameter calcu-
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lation is probably also still somewhat affected by the Odd-Even effect. If
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real, this increase could represent a slight increase in the relative population
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of Mode 3:Mode 20 particles at these latitudes, followed by a reversal of the
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trend (i.e., to an increase in Mode 20 relative to Mode 3) from about 20◦ to
390
about 50◦ latitude. Such a trend would be consistent with cloud formation
391
altered by the meridional circulation modelled by Imamura and Hashimoto
392
(1998). That is, the Mode 3 population would be driven by convection in the
393
condensational clouds maximized near the equator, while the Mode 2 popu-
394
lation would steadily increase as the parcels are carried from the equator to-
395
ward the poles. Since the gravitational sedimentation velocity of the Mode 2
396
particles is so slow, they simply accumulate in the observable cloud, slowly
397
skewing the population from larger to smaller particles, until the downwelling
398
branch takes over near 50◦ latitude. However, this slight increase in the size
399
parameter should also be taken with a grain of salt, since the large emission
400
angle, low observation frequency, and possible calibration artifacts may still
401
be playing significant roles in this calculation. Furthermore, the retrievals
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by Haus et al. (2014) did not find an increase in particles size at equatorial
403
latitudes. It is anticipated that JAXA’s Akatsuki spacecraft, observing from
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a more equatorial vantage point, will soon be able to resolve the veracity of
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this observation.
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The average surface elevation observed in the data that satisfy our cri-
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teria shows that lower elevations are slightly favored in the polar regions
408
compared with the elevations observed near the equatorial regions. How-
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ever, the total range of average surface elevations observed is less than one
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kilometer. The emission and incidence angle profiles are as expected from a
411
spacecraft imaging mostly the night side of a planet from a highly eccentric
412
and polar orbit. Namely, low emission angle near the pole, while the equator
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is imaged mostly near the limb; and near-terminator (low incidence angles)
414
near the poles, with gradually larger incidence angles at lower latitudes. The
415
effect of the incidence angle on the measured parameters is negligible. The
416
primary effect being a reduction in how far into the polar regions the analysis
417
can obtain data that fit the incidence angle criterion. Therefore, we do not
418
reproduce the latitudinal profiles for all incidence angle cutoffs.
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3.3. Regional Temporal Behavior
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Note again from Fig. 5 the significant changes in radiance as a func-
421
tion of latitude within all of the near infrared spectral windows. This large
422
amount of variability, and the differing frequency of observation as a func-
423
tion of latitude suggests that we ought to consider geographic sub-regions
424
when investigating possible existence of long term trends. Hence, we pro-
425
duce also zonally averaged radiance that have been averaged across 30◦ wide
426
latitude bands, in addition to the hemisphere-wide calculations we showed
427
in Section 3.1. We chose 30◦ wide regions for simplicity, and to ensure that
428
we do not subsample the data to a point where the signal begins to be lost
429
in the noise. We divide the southern hemisphere observations into polar
430
(60◦ − 90◦ ), mid-latitude (30◦ − 60◦ ) and equatorial (0◦ − 30◦ ) regions. Plots
431
of these regionally averaged data are shown in Fig. 6 for the 1.74µm and
432
2.30µm radiance, and the Carlson et al. (1993) size parameter. The best fit
433
linear trend parameters (I0 , mI ) and their uncertainties (δI0 , δmI ) for each
434
of these regions and spectral windows are shown in Table 1. In addition to
435
this, we calculate the total change in radiance expected from the beginning
436
to the end of the 921-orbit VIRTIS lifetime, if the best fit trends were to per-
437
sist throughout, and the total mission-long variability (standard deviation)
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of the radiance in each window and region. equ:w174
0.10
I [
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Figure 6: Regionally segregated time series data for (L−R) 1.74µm radiance, 2.30µm radiance, and Carlson et al. (1993) size parameter, with seven-day averaging applied. The regions are: hemispheric (‘hem’: 0◦ − 90◦ ), equatorial (‘equ’: 0◦ − 30◦ ), mid-latitude (‘mid’:30◦ − 60◦ ), and polar (‘pol’: 60◦ − 90◦ ). Also shown is the best fit trend line to the observed data.
Our strictest criterion for considering a best fit trend (slope) to be sig-
440
nificant requires that the total change in radiance predicted from the slope
441
of the fit (i.e., Norbit × mI ) exceeds the overall variability in (i.e., the stan-
442
dard deviation of) the measured emitted radiance (σI (φ)). That is, the trend
443
is significant only if the long term trend exceeds the per-observation varia-
444
tions. Note that, as expected from the hemispherical averages, the majority
445
of the windows and regions exhibit best fit trends that are consistent with
446
a null result; that is, no change in overall cloud coverage. In fact, only the
447
mid-latitude 1.74µm radiance indicates a significant long-term trend by this
448
criterion. However, the mid-latitude region at 1.74µm and 2.30µm, and the
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449
size parameter, all exhibit overall tendencies in that are suggestive of long-
450
term trends in cloud thickness or particle size population. But, even these
451
long-term variations require several years at their currently measured rates
452
to effect a significant difference in the overall emitted radiance, hence cloud 26
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Table 1: Parameters and their uncertainties to linear best fit to shown wavelength and region. Also included is the overall standard deviation. ‘hem’ represents the hemispheric average (0◦ − 90◦ ); ‘pol’, ‘mid’, ‘equ’ represent 60◦ − 90◦ , 30◦ − 60◦ , and 0◦ − 30◦ , respectively). region I0 δ I0 mI δmI Norb × mI σI p-value 1.74µm W m−2 sr−1 µm−1 W m−2 sr−1 µm−1 d−1 W m−2 sr−1 µm−1 hem 1.094e-01 1.886e-03 1.821e-06 4.569e-06 1.677e-03 6.182e-02 0.0017 pol 9.083e-02 6.720e-04 -3.584e-05 2.160e-06 -3.301e-02 4.052e-02 < 0.0001 mid 1.240e-01 3.896e-04 5.744e-05 8.338e-07 5.290e-02 5.212e-02 < 0.0001 equ 9.923e-02 7.656e-04 5.622e-05 3.114e-06 5.178e-02 6.793e-02 < 0.0001 2.30µm W m−2 sr−1 µm−1 W m−2 sr−1 µm−1 d−1 W m−2 sr−1 µm−1 hem 3.555e-02 5.508e-04 9.752e-06 1.157e-06 8.982e-03 4.055e-02 < 0.0001 pol 2.331e-02 2.925e-04 -1.256e-05 7.176e-07 -1.157e-02 1.720e-02 < 0.0001 mid 4.497e-02 3.554e-05 3.652e-05 7.472e-08 3.363e-02 3.741e-02 < 0.0001 equ 3.456e-02 1.203e-04 3.619e-05 8.334e-07 3.333e-02 5.063e-02 < 0.0001 Size < unitless > < unitless > d−1 < unitless > hem 7.115e-01 3.750e-03 1.270e-05 9.594e-06 1.170e-02 2.053e-01 0.3720 pol 7.479e-01 2.588e-03 1.662e-05 7.172e-06 1.530e-02 2.687e-01 0.3087 mid 6.588e-01 1.266e-03 7.154e-05 3.374e-06 6.589e-02 8.933e-02 < 0.0001 equ 6.448e-01 1.946e-03 5.195e-05 4.824e-06 4.784e-02 2.761e-01 < 0.0001 Elev km km d−1 km hem -1.799e-01 2.484e-02 9.167e-05 5.749e-05 8.443e-02 6.038e-01 0.0827 pol -2.170e-01 1.840e-02 2.911e-05 4.502e-05 2.681e-02 6.287e-01 0.2742 mid -2.342e-01 7.573e-03 1.260e-04 1.144e-05 1.160e-01 5.580e-01 0.2853 equ 2.358e-01 1.702e-02 -4.717e-06 4.029e-05 -4.345e-03 5.888e-01 0.5364 Emis < deg > < deg > d−1 < deg > hem 3.045e+01 7.891e-02 4.124e-03 2.425e-04 3.798e+00 1.692e+01 0.0585 pol 2.017e+01 1.628e-01 9.252e-04 5.886e-04 8.521e-01 9.383e+00 0.0139 mid 3.225e+01 5.829e-02 6.935e-03 1.004e-04 6.387e+00 1.289e+01 0.0394 equ 5.436e+01 7.993e-02 1.103e-02 1.597e-04 1.016e+01 1.181e+01 0.0024 Inc < deg > < deg > d−1 < deg > hem 1.147e+02 1.132e-02 -4.852e-03 1.465e-04 -4.469e+00 1.537e+01 0.1937 pol 1.059e+02 5.452e-02 -3.563e-03 1.294e-04 -3.281e+00 5.886e+00 < 0.0001 mid 1.173e+02 1.240e-02 -4.885e-03 6.183e-05 -4.499e+00 1.174e+01 0.0262 equ 1.272e+02 8.688e-02 -2.186e-03 1.595e-04 -2.013e+00 1.862e+01 0.0843 LST hr hr d−1 hr hem -8.239e-01 8.726e-05 1.467e-03 1.703e-07 1.351e+00 2.458e+00 0.0017 pol -5.108e-01 9.058e-05 5.384e-04 1.833e-07 4.959e-01 1.661e+00 0.2154 mid -7.590e-01 4.815e-05 1.492e-03 1.020e-07 1.374e+00 2.682e+00 0.0056 equ -1.506e+00 1.205e-04 3.028e-03 5.436e-07 2.789e+00 2.920e+00 < 0.0001
453
cover, based on this criterion. A longer time baseline as might be provided
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454
by the Akatsuki mission could elucidate the persistence or transience of these
455
long-term trends and their significance. Another method of testing the significance of the linear trend is to apply
457
a linear regression analysis to evaluate the correlation between the estimated
458
trend line and the data, compared with the null hypothesis. We calculate
459
the p-value, which is a measure of the probability that random variations
460
can explain the observed distribution as well as the modelled trend. Hence,
461
a p-value of 0.01 indicated that there is a 1% likelihood that the observed
462
data are better fit with random perturbations, and a 99% likelihood that the
463
best fit trend is a better predictor of the observed behavior. While a small
464
value of the p-value can be interpreted to mean the null hypothesis is highly
465
unlikely, it cannot confirm the existence of the posited trend. However, a
466
large p-value can be used to rule out a linear trend in the data. Here, we
467
will assume that a p-value of less than 0.0001 (a 99.99% likelihood that the
468
best fit trend line is a better predictor of the observed changes than random
469
variations) indicates that the trend based on the best fit parameters is likely
470
to be real. The rightmost column in Table 1 shows the calculated p-value
471
for each of the parameters and regions analyzed in this paper. We find that
472
the p-value for the 1.74µm and 2.30µm radiance data in all regions is less
473
than 0.002, and is less than 0.0001 in all but the 1.74µm hemispherical data.
474
We find p-values for the size parameter to be less than 0.0001 in the mid-
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latitude and equatorial data; but larger than 0.3 for the hemispherical and
476
polar data, suggesting that the trends a lower latitudes are more reliable
477
than those at high latitude or planet-wide. However, the calculated trend
478
in the hemispheric and polar size parameter data is very shallow, so there
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is very little difference between the linear best fit and the null hypothesis,
480
once the overall average has been corrected for. Finally, among the geometric
481
parameters analyzed (emission angle, incidence angle, surface elevation, and
482
local solar time), all but a few of the quantities demonstrate relatively large
483
p-values, indicating at least that the linear best fit trends to these quantities
484
are less statistically significant than those discussed above. Furthermore, the
485
absence of significant linear trends found in these parameters suggests that
486
it is unlikely that variations in these geometric parameters are responsible
487
for the long-term trends observed in the radiance data.
488
3.4. 150 day oscillation in the mid-latitudes
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In addition to these long-term trends, a months-long periodic variation
490
can be seen in the mid-latitude region for the 1.74µm and 2.30µm data. Such
491
a periodicity is most noticeable for larger incidence angle restrictions and at
492
mid-latitudes, and was previously suggested by McGouldrick et al. (2012)
493
using a somewhat smaller subset of this data; it is reinforced here with the
494
full dataset. This periodicity is not seen at the shorter wavelengths that
495
are less cloud dominated and more surface dominated. However, this may
496
be a function of our stray light removal technique. Further analysis of the
497
variability of these surface dominated windows is underway. McGouldrick
498
et al. (2012) qualitatively estimated a period of about 140 days. Here, in
499
order to quantitatively determine the periodicity, we applied a least squares
500
sinusoidal fit analysis (LSSA) (Lomb, 1976; Scargle, 1982) to produce a fre-
501
quency spectrum of the 1.74µm radiance, shown in Fig. 7. We perform the
502
LSSA calculation by starting with the time series data shown in Fig. 3, and
503
subtracting the linear trend for the 1.74µm mid-latitude data shown in Ta-
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ble 1, in order to achieve a data set with a mean of zero. We then apply the
505
LSSA calculation to this adjusted radiance data. Fig. 7 shows the LSSA frequency analysis for the mid-latitude (30◦ − 60◦ )
507
data at 1.74µm, 2.30µm, the Carlson et al. (1993) size parameter, and several
508
geometric parameters, with the seven-day averaging applied (i.e., the data
509
shown in Fig. 3). As discussed previously, the seven-day moving average is
510
designed to minimize the regionalism that results from the limited field of
511
view of the VIRTIS-M instrument. By thus averaging the data, we arrive
512
more closely at a measure of the zonally averaged behavior. However, as we
513
will show later, this averaging to ensure a zonally averaged radiance does not
514
appear to affect the values of the measured periods significantly. One period
515
stands clear above all others in each of the 1.74µm and the 2.30µm radiance
516
data periodograms. At 1.74µm, this period is found to be 150.3 days, while
517
at 2.30µm it is found to be 150.5 days. This peak is rather broad, with
518
a half-width of about 20 days, indicating either that this is a quasi-period,
519
whose frequency varies with time, or we have too short a baseline of data
520
for a more precise measurement of the frequency spectrum. It is possible
521
that wavelet analysis (Bravo et al., 2014) of this dataset may resolve this
522
discrepancy; but it is subject to the same difficulties of the sporadic nature
523
and somewhat brief temporal duration of the observations.
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Also shown in Fig. 7 is the periodogram for the Carlson et al. (1993)
size parameter. There are no dominant peaks with significant power in the
526
frequency spectrum. Since our calculation of the size parameter involves a
527
comparison of radiance at two separate bands, it is likely that the odd-even
528
effect discussed by Kappel et al. (2012) may have more of an effect here. Not
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w174:mid
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0.45 0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00
Normalized power
Normalized power
0.45 0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00
PT
Figure 7: Frequency spectrum for the mid-latitude 1.74µm and 2.30µm radiance, Carlson et al. (1993) size parameter, emission and incidence angles, surface elevation, local solar time, and spectrometer temperature.
only might the radiance in one of the bands fall into an enhanced or a reduced
530
sensitivity pixel of the detector, but since the wavelength registration is non-
531
linear, it is possible that the odd versus even location of each band might
532
not occur in parallel. That is, one band might be enhanced while the other
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533
is reduced. This is possibly also the reason for the larger and more variable
534
standard deviation found in the latitudinal profile of the size parameter data
535
compared with the radiances themselves, as seen in Fig. 5. The lack of a
536
significant peak in the size parameter periodogram around 150 days indicates 31
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that changes in the relative populations of Mode 20 and Mode 3 particles in
538
the clouds of Venus are not likely to be driving the observed periodicity at
539
1.74µm and 2.30µm.
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537
We compare also the periodograms of various geometrical parameters of
541
the observations, including incidence angle, emission angle, surface elevation,
542
and local solar time. None of these show a significant peak near 150 days,
543
suggesting that changes in the viewing geometry are not responsible for the
544
periodicity seen at 1.74µm and 2.30µm. Notably, the LSSA periodogram
545
does find strong evidence for periodicity in several of the geometric parame-
546
ters, For example, the emission angle and the local solar time show a strong
547
period at about 220 days and 216 days, very close to the 225 day sidereal
548
orbital period of Venus. This is not surprising, since these are both tied to
549
the the viewed phase of Venus by VIRTIS-M-IR, which evolves in parallel
550
with the orbit of Venus around the Sun. In addition, the solar incidence
551
angle and the surface elevation shows a significant peak at 115 days and
552
116 days, almost exactly the Venusian synodic (or solar) day of 116.75 days,
553
as expected. Since the observations in the present analysis are restricted to
554
the night side, and the view of the surface of Venus from VIRTIS will vary
555
along with the orbit of Venus around the Sun, then the surface data that fit
556
our criteria should be seen on a periodicity very closely tied to the synodic
557
period of Venus, or the solar day. That the LSSA finds these periodicities
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in the geometry data that match what would be expected a priori, from the
559
known orbital and observational parameters and criteria, lends further cre-
560
dence to the veracity of the periods measured in the analysis of the radiance
561
data and their absence in the size parameter data.
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Finally, we also compare the periodogram of the spectrometer tempera-
563
ture to the observed radiance variations. Since the wavelength registration
564
of the spectrometer is temperature dependent, and there is evidence for re-
565
maining imperfections in the calibration of the detector (Moinelo et al., 2010;
566
Kappel et al., 2012), changes in the spectrometer temperature might produce
567
spurious changes in measured radiance. However, Fig. 7 shows that the LSSA
568
found no dominant period in the spectrometer temperature. Other relevant
569
instrumental temperatures are measured and reported by the VIRTIS house-
570
keeping, including the focal plane temperature, telescope temperature, and
571
cooling point temperature. We do not reproduce those analyses here because
572
each shows nearly identical periodogram spectra, even as the magnitudes of
573
the temperatures are significantly different.
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562
We have run the LSSA analysis for a number of different averaging win-
575
dow sizes, incidence angle cutoffs, and frequency space resolutions. Although
576
the specific values of the periods change slightly in response to changes in the
577
incidence angle criterion and the size of the averaging window, the salient
578
points mentioned in the discussion of Fig. 7 remain unchanged through each
579
of these. That is, an oscillation is found in the 1.74µm and 2.30µm radiance
580
with a period of about 150 days. None of the other measured or calculated
581
quantities exhibit a dominant periodicity with a similar frequency. The emis-
582
sion angle and local solar time show periodicities of approximately the Venus
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sidereal orbital period. And the surface elevation and solar incidence angles
584
show periodicities of approximately the Venus synodic period, or solar day.
585
The results of these calculations are summarized in Table 2.
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In order to further quantify and characterize the observed variability, in 33
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Table 2: Summary of most prominant period found for each parameter for each tested incidence angle restriction, and each size of the moving window averaging. All units of periods are in days. window min(θinc ) I1.74 I2.30 size θemi θinc elevation LST 95◦ 147.4 146.9 109.2 216.7 116.8 116.8 215.9 100◦ 147.3 146.8 109.6 215.8 117.0 116.6 215.5 1 105◦ 146.7 146.4 41.7 212.7 118.8 116.8 215.5 110◦ 146.6 146.2 253.5 213.8 119.6 116.7 212.1 115◦ 144.6 145.3 247.9 211.4 145.2 119.6 232.1 95◦ 150.3 150.5 245.9 219.0 114.9 116.3 215.2 100◦ 149.9 150.3 108.9 218.5 115.7 116.0 215.1 7 105◦ 149.7 150.0 108.8 218.0 147.4 116.0 214.7 110◦ 149.7 149.9 109.0 217.6 148.7 116.0 214.4 115◦ 146.6 148.8 258.4 217.4 76.8 117.2 227.1 95◦ 150.7 151.0 254.0 218.8 113.6 116.2 215.9 100◦ 150.4 150.8 262.1 219.2 145.4 116.2 215.8 14 105◦ 150.3 150.8 109.1 219.6 146.1 116.0 215.6 110◦ 150.3 150.7 259.3 219.2 147.1 115.9 215.3 115◦ 145.8 148.8 265.9 218.8 76.7 117.1 226.5
Fig. 8, we produce period-folded plots of the parameters analyzed in Fig. 7.
588
Here, we see that the amplitude of the periodic behavior is approximately
589
as large as the the magnitude of the per-observation variability seen in the
590
data. By phase-shifting the period-folded 1.74µm radiance by about 45 days,
591
we can see that the variation can be well matched with a sinusoid with
592
an amplitude that is half of the maximum radiance measured. The phase
593
folded data suggest that the sinusoids describing the near infrared radiance
594
variations may not be quite symmetric. That is, the comparison suggests
595
that the decrease in radiance might occur slightly more quickly than the
596
corresponding increase. In Section 4, we consider potential drivers of the
597
observed variations, and a difference in the rate of increase or decrease in
598
radiance can help to discriminate among the possibilities. However, since the
599
difference between a standard and a skewed sinusoid is so slight, compared
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with the data, we do not make any conclusions based on the shape of the
601
curve at this time.
602
4. Discussion
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600
Here we explore some various drivers of the observed variations and con-
604
sider their likelihood, based on the analyzed data set and other constraints.
605
We report a possible long-term increase in 1.74µm and 2.30µm radiance
606
at mid-latitudes, that would indicate an overall reduction in total cloud opac-
607
ity in this region. This increase in mid-latitude radiances is accompanied by
608
a decrease in polar radiances. On a hemisphere-wide averaging, there is little
609
change seen in these radiances over the course of the VIRTIS-M-IR instru-
610
mental lifetime. These trends are not consistent with a scenario in which the
611
observed decrease in SO2 at higher altitudes reported by Marcq et al. (2012)
612
is coupled with a conversion of SO2 into H2 SO4 and thence into clouds. Hence
613
some other sink for the SO2 loss observed must be found. However, as the
614
observed trends are barely larger than the overall variance in the data, more
615
detailed analysis of this and future data (including the Akatsuki mission) will
616
be required for more definitive conclusions.
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Previous investigations have reported increases in wind speeds in the
618
Venus atmosphere over time (Khatuntsev et al., 2013; Kouyama et al., 2013).
619
These investigations interpret motions of high contrast features in the re-
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620
flected sunlight at ultraviolet wavelengths as indicators of local wind speeds
621
at an altitude of the cloud tops, around 70km above the surface of the planet.
622
There remains some ambiguity as to whether these measured winds are in-
623
dicative of the true wind speeds of the features themselves, or of the large 35
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Figure 8: Phase-folded data for the mid-latitude data, for each of the parameters shown in the previous figures, with seven-day averaging applied, assuming the period found by LSSA having the greatest spectral power for each parameter. The radiance curves are phase shifted by 45 days to align with the baseline sinusoid. Phase shifts of −75 days, 25 days, 30 days, −50 days, and 45 days have been added to the plots of size parameter, emission angle, incidence, angle, surface elevation, local solar time, and spectrometer temperature, respectively.
36
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scale dynamics (similar to the “steering winds” at 500mb on Earth that
625
transport tropical and extratropical cyclones), or of morphological or com-
626
positional changes. However, if we accept that the measured wind speeds
627
are representative of the overall dynamics of the Venus atmosphere, then the
628
increase in the mean zonal wind speeds reported by both Khatuntsev et al.
629
(2013) and Kouyama et al. (2013) would imply that some mechanism is act-
630
ing that either adds momentum to the atmosphere as a whole, or transports
631
momentum from another atmospheric region to the level of the cloud tops
632
seen in ultraviolet wavelengths. If momentum is being transported to this
633
region of the atmosphere, then so too must energy be transported. Such a
634
transport of energy could manifest itself as an increase in local temperature
635
at regions where the clouds have been accelerated by the deposition of mo-
636
mentum. Another possibility is that the energy could be trasnported in the
637
form of latent heat, but the very small mass of the Venus clouds tends to pre-
638
clude latent heat as an efficient means of energy transport. Because the vapor
639
pressure of the sulfuric acid cloud particles is so small, small changes in tem-
640
perature tend to have rapid and significant effects on the mass and opacity
641
of the Venus clouds (McGouldrick and Toon, 2007). This increase in radi-
642
ance emitted from the cloud-dominated spectral windows at equatorial and
643
mid-latitudes, coupled with the decrease in radiance at polar latitudes could
644
indicate a net transport of energy from high to low latitude over the course
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624
of these observations. Such an energy transport would be consistent with
646
the increase in momentum seen by Khatuntsev et al. (2013) and Kouyama
647
et al. (2013). It is beyond the scope of this paper to thoroughly compare
648
the variation in the previously measured wind speeds at the cloud tops using
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VMC ultraviolet data with the emitted radiance through the condensational
650
(and photochemical) clouds of Venus using VIRTIS infrared data, but we
651
note that the apprearance of a correlation suggests fertile ground for future
652
comparison.
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We might consider that this 150-day oscillation is a manifestation of a
654
Hadley-like meridional circulation in the clouds. If we consider a meridional
655
circulation cell that runs from the equator to about 50◦ latitude, consistent
656
with previous models by Imamura and Hashimoto (1998), then we calculate
657
an average meridional wind speed of only 0.9 m/s. Hueso et al. (2012, 2015),
658
using VIRTIS-M-Vis ultraviolet observations, and Khatuntsev et al. (2013),
659
using VMC ultraviolet observations, report meridional wind speeds peaking
660
at about 10 m/s in the poleward direction at a latitude of around 50◦ -55◦ ,
661
and decreasing to 0 m/s at the pole and equator. They each interpret this as
662
a manifestation of a hemispherical-scale Hadley-like meridional circulation
663
cell. If we assume a sinusoidal shape to the meridional wind speed as a func-
664
tion of latitude, then we can estimate the average flow speed over the entire
665
cell to be about 6 m/s. Hence, the timescale for the Hadley-like meridional
666
circulation would then be about 35 days, much shorter than the periodicity
667
measured here. Note that Hueso et al. (2015) report measured meridional
668
wind speeds of a few m/s in infrared wavelengths (corresponding to similar
669
altitudes to those inhabited by the clouds that drive the radiance variations
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anlayzed here). However, they also point out that their measured wind speed
671
is significantly smaller than their measured standard deviations, indicating
672
that the meridional circulation likely has its return branch at a deeper alti-
673
tude than that occupied by the clouds. Hence, for the meridional circulation
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to directly affect the properties of the condensational clouds between about
675
50 km and 57 km that are analyzed here, there would need to be a verti-
676
cal wander of the mean circulation. Similar wanderings of the meridional
677
circulation were found in VenusCAM General Circulation Model simulations
678
by Parish et al. (2011). However, subsequent analysis showed that a later
679
version of VenusCAM that addressed a number of angular momentum errors
680
did not show as significant a variation (Lebonnois et al., 2012).
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674
The 150 day oscillation is closer in magnitude to the time scale for the
682
meridional circulation assumed in the models of Imamura and Hashimoto
683
(1998). Imamura and Hashimoto (1998) prescribed a meridional Hadley-like
684
circulation with a cycle timescale of 90 days. This would correspond to a
685
maximum mid-latitude merdional cloud top wind speed of a few m/s, or a
686
factor of three or so smaller than the wind speed reported from the Venus
687
Express observations described above. Based on the results of Imamura and
688
Hashimoto (1998), who considered the effect of a variation in the magnitude
689
of the meridional circulation, a meridional Hadley-like circulation with a
690
150 day timescale would produce smaller latitudinal contrasts in cloud opac-
691
ity than those that are observed. This occurs because for slower circulations,
692
particle sedimentation timescales become moree important to the cloud par-
693
ticle lifetimes than the meridional transportation timescales. Note that the
694
Imamura and Hashimoto (1998) models did not consider effects of the zonal
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681
circulation, having treated a 2D (latitude-altitude) model. The 2D cloud
696
structure found by Imamura and Hashimoto (1998) was consistent with lat-
697
itudinal opacity variations derived from the observations of Venus by Crisp
698
et al. (1989) and Chanover et al. (1998), indicating that the magnitude of
AC 695
39
ACCEPTED MANUSCRIPT
the meridional circulation that Imamura and Hashimoto (1998) proposed is
700
consistent with observations. Our long-term average latitudinal profiles also
701
are consistent with the previous work by Crisp et al. (1989) and Chanover
702
et al. (1998), suggesting that the meridional circulation remains similar to
703
that postulated by Imamura and Hashimoto (1998). However, our analysis
704
does not investigate potential temporal variations in the latitudinal profile,
705
which might indicate variations in the magnitude of the meridional circu-
706
lation. It is difficult to achieve a high level of confidence in the temporal
707
variations in latitudinal profiles using VIRTIS-M-IR data, because the spa-
708
tial coverage is so limited. Perhaps the Akatsuki mission (Nakamura et al.,
709
2016), with its more equatorially-inclined orbit, and frequent high spatial
710
resolution full-disk imaging capability, might address this issue.
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In addition to the long-term trend in the measured wind speeds, previous
712
investigators such as Khatuntsev et al. (2013) and Kouyama et al. (2013)
713
have indicated periodic variations in the wind speeds. Kouyama et al. (2013)
714
reported a 255 day period in their measured wind speeds; but this does not
715
seem to be related to the 150 day period found here. Furthermore, their
716
analysis does not find a comparable periodicity near 150 days. Khatuntsev
717
et al. (2013) reports on a number of short-period (4 − 5 days) oscillations
718
in their measured wind speeds, and also some weaker 238 day and 117 day
719
periods; but these are probably related to Venus orbital characteristics, and
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711
in any case, are not very close to the 150 day period presented in this paper.
721
We note that the 150 day period is approximately 2/3 of the Venus sidereal
722
orbital period. Perhaps the periodic variations seen in the clouds are an
723
indication of a 3:2 resonance between the meridional Hadley-like circulation
AC 720
40
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724
and solar influences (such as solar tides). Looking toward microphysical phenomena, we compare the observed pe-
726
riodicity to the sedimentation and eddy diffusion (or, effectively, convective)
727
timescales in the clouds. We noted previously that the Carlson et al. (1993)
728
size parameter does not indicate an oscillation at the period exhibited by
729
the 1.74µm and 2.30µm radiances, consistent with the findings of Barstow
730
(2012). This behavior suggests that large scale changes in the ratio of the
731
number of Mode 3 particles to the number of Mode 20 particles are not re-
732
sponsible for the radiance variations observed. Now, there is sufficient vari-
733
ation in the calculated size parameter over the course of the observations
734
reported here that we cannot say with certainty that the size parameter does
735
not change at all during the course of the oscillation in the radiances. But
736
we can say that if changes in the size parameter were driving the radiance
737
changes seen, then a 150 day period should have appeared in the size param-
738
eter periodogram.
ED
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725
That it does not can only mean that either 1) only Mode 3 particles
740
are growing larger (and smaller) to drive the oscillation, or 2) both Mode 20
741
and Mode 3 are increasing (and decreasing) in total number concentration
742
at similar rates. For the remainder of the discussion in this paragraph, we
743
invite the reader to please consult Figure 1a of Grinspoon et al. (1993).
744
That figure shows the extinction coefficients of the four traditional modes
CE
PT
739
of cloud particles generally used in radiative transfer analysis of the Venus
746
atmosphere. Note that the extinction coefficient of the Mode 3 particles is
747
essentially flat between 1.74µm and 2.30µm, while the extinction coefficient
748
for each of the Mode 2 and Mode 20 particle modes exhibits a strong gradient
AC 745
41
ACCEPTED MANUSCRIPT
with increasing wavelength between these two spectral windows. Hence, the
750
size parameter is most strongly affected by changes in the size of the Mode 2
751
(or Mode 20 ) particles, or by changes in the relative numbers of the Mode 3
752
and Mode 2 (or Mode 20 ) particles. But, it is less strongly affected by changes
753
in the size of the Mode 3 particles. In the 2.30µm radiance (cloud opacity)
754
and the 1.74µm radiance (cloud opacity), we observe parallel variations, while
755
noting an absence of a parallel variation in the size parameter. A change in
756
Mode 3 particle size alone will increase the opacity of the clouds, but will have
757
minimal effect on the size parameter, since the effect of the change in opacity
758
will be comparable at the two wavelengths. Thus, an increase in Mode 3
759
particle size, while the number remains constant, and while the Mode 20
760
number and size remain constant would be consistent with the observations
761
reported here. Similarly, if the numbers of Mode 20 and Mode 3 particles
762
increase in a comparable manner (the more traditional interpretation of the
763
size parameter), then we would expect an increase in opacity with a relatively
764
unchanged size parameter.
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749
If both modes of particles are considered to be sulfuric acid, then simple
766
growth and evaporation mechanisms would suffice to explain changes in total
767
particle number (option 2). But for one mode to increase in size while the
768
other mode does not (option 1) would require either that the two modes have
769
distinct compositions or that they are a single modal size distribution with a
CE
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765
consistent composition that has been mistaken for two distinct populations,
771
as Toon et al. (1984) have suggested. Furthermore, this would rule out
772
coagulation processes as driving the observed variations, since this would
773
preferentially increase the number of larger particles at the expense of the
AC 770
42
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smaller particles. Of course, since coalescence time scales are so slow for
775
the conditions in the condensational cloud (McGouldrick, 2007), it would be
776
difficult to imagine them driving such variations.
777
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774
Since the clouds that are the primary drivers of opacity differences at
1.74µm are located between about 50 km and 57 km, we consider the timescales
779
for particles to fall through such a 7 km distance. Furthermore, since the
780
sedimentation can only remove particles from the clouds, we need another
781
mechanism to re-supply the cloud mass. So, we consider half the period to
782
be the relevant timescale to compare to sedimentation processes. Thus, for
783
a particle falling through the Venus atmosphere from an altitude of about
784
57 km to an altitude of about 50 km in a time of about 75 days, requires
785
a sedimentation velocity of 0.11 cm/s. The gravitational sedimentation ve-
786
locity of a droplet falling through a medium is given by Seinfeld and Pandis
787
(1998) as:
M
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778
ED
vsed =
2 rp2 ρp gCc 9 µ
(6)
where rp is the radius of the particle, ρp is its mass density (about 1.75 g/cm3 ),
789
g µ is the viscosity of the medium (about 2 × 10−4 cm·s for this region of the
790
Venus atmopshere), and Cc is the unitless “Cunningham slip-correction fac-
791
tor,” which for a 0.1µm particles is about 3, is about 1.2 for a 1µm radius
792
particle, and asymptotes to 1.0 for particles with radius larger than ∼ 3µm.
793
The sedimentation velocity for a typical Mode 3 particle (3.65µm) under
AC
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PT
788
794
these consitions is 0.23 cm/s, while that of a Mode 20 particle having a
795
1.4µm radius is 0.041 cm/s, and of a Mode 2 particle with a 1.0µmradius
796
is 0.021 cm/s. For a gravitational sedimentation velocity of 0.11 cm/s, and
797
expecting a particle radius near 1µm, consistent with previous in situ and 43
ACCEPTED MANUSCRIPT
remote measurements of the Venus clouds (Knollenberg and Hunten, 1980;
799
Grinspoon et al., 1993), Eq. 6 can be solved to find a particle size, rp = 2.2µm.
800
If instead, we allow for very large particles (typical of Mode 3 and larger)
801
by using a slip correction factor of 1.0, then we find a typical particle size
802
of rp = 2.4µm. This is located between the sizes of the Mode 20 and the
803
Mode 3 particles generally considered to exist in the Venus condensational
804
clouds. Hence, it is plausible that the clearing of the clouds (the increase in
805
radiance) is consistent with rainout of the typically 1 − 3 µm-sized droplets
806
in the Venus condensational clouds. If we consider instead a 10 km thick
807
layer through which the particles must fall – which is plausible since a 47 km
808
cloud base is not unreasonable, based on other analyses (Barstow et al.,
809
2012) – then we find a typical particle size of 2.6 − 2.8µm, which is even
810
closer to the Mode 3 population. However, if the Mode 3 particles are sim-
811
ply a large-radius tail of the Knollenberg and Hunten (1980) Mode 2, as
812
suggested by Toon et al. (1984), then the typical modal radius of Mode 20
813
would be pulled to larger values, possibly consistent with these calculations.
814
In fact, these calculated modal radii would equate to effective radii (i.e.,
815
area-averaged radii) of between 2.8µm and 3.7µm, a range that includes
816
the effective radii found in microphysics simulations of the condensational
817
cloud driven by radiative-dynamical feedback (McGouldrick and Toon, 2007;
818
McGouldrick, 2016). Note also that changes in the typical radius of cloud
CE
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798
particles in the range from 2.2µm to 2.8µm will have minimal effect on the
820
Carlson et al. (1993) size parameter in most cases, since the Mie scattering
821
spectrum would more closely resemble Mode 3 than Mode 20 at these radii,
822
and hence would lie in a relatively flat part of the Mie scattering spectrum,
AC 819
44
ACCEPTED MANUSCRIPT
823
according to previous work by Grinspoon et al. (1993), cf. their Figure 1a. If we next consider the particle lifetime being driven by the eddy diffusion
825
time scale, (∆z)2 /κdif f , then we find that a typical eddy diffusion coefficient
826
of κdif f = 8 m2 /s is required to fully mix a 10 km thick region within the
827
75 day observed timescale, while an eddy diffusion coefficient of 15 m2 /s is
828
required to fully mix a 7 km layer. Each of these also are consistent with
829
the time-averaged eddy diffusion coefficients that were obtained from the
830
radiative-dynamical simulations by McGouldrick and Toon (2007).
832
AN US
831
CR IP T
824
Finally, the radiative time constant for cooling from the altitude of the condensational clouds of Venus can be calculated as
F
,
(7)
M
τrad =
cp Pg Tmean
where P/g is the total atmospheric column mass above the altitude in ques-
834
tion (in this case, the condensational cloud tops at about 50 kPa), cp ∼
835
800 J/kg/K is the specific heat capacity of the Venus atmosphere averaged
836
across that layer, Tmean ∼ 230 K is the mean temperature above the cloud
ED
833
tops, and F = 157 W/m2 is the emitted flux. The values of the atmospheric
838
values listed above are calculated from the standard Venus International
839
Reference Atmosphere (Seiff et al., 1985). The emitted flux is calculated by
840
assuming that Venus has a Bond albedo of 0.76 (Moroz et al., 1985) and that
841
the globally averaged emitted flux exactly balances the globally averaged
842
incident solar flux. Performing this calculation, we find a radiative cooling
843
time scale of about 76 days, almost exactly half the observed periodicity.
844
Combining this with the eddy diffusional time scale above (which was driven
845
by radiative heating of cloud base and cooling from the condensational cloud
AC
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837
45
ACCEPTED MANUSCRIPT
tops), we suggest that the 150 day period we see in the 1.74µm mid-latitude
847
radiance measured by VIRTIS-M on Venus Express is sustained by an inter-
848
action between radiative cooling and microphysical cloud processes, similar
849
to those demonstrated by McGouldrick and Toon (2007).
CR IP T
846
Please note that, since the tendencies plotted here are averaged over large
851
areas and times, and since the known spatial and temporal variability in the
852
Venus condensational clouds is very large, it will be necessary to explore
853
these relationships on shorter timescales; work that we are preparing for a
854
future paper.
855
5. Conclusions
AN US
850
We have presented analysis of the complete Venus Express VIRTIS-M-IR
857
data set for night side thermal emission in the near infrared spectral win-
858
dows for all southern hemisphere observations made before the failure of the
859
instrument’s cooling system after orbit 921 (2008 October 27). We find no
860
clear evidence of global long-term increase or decrease in the overall radiance
861
(hence overall cloud coverage and thickness) from analysis of just the 1.74µm
862
and 2.30µm spectral windows that are most sensitive to the cloud variations.
863
However, at mid-latitudes, the radiance steadily increases through the dura-
864
tion of the VIRTIS-M-IR lifetime, while steadily decreasing with time near
865
the poles. This may be an indication of a transfer of cloud mass poleward,
AC
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PT
ED
M
856
866
an inhibiting of heat transfer by the meridional circulation, or subtle vertical
867
or meridional wanderings of the meridional circualtion cell. This long-term
868
radiance trend might represent a manifestation of heat energy transport in
869
parallel with the momentum transport indicated by the variations in zonal 46
ACCEPTED MANUSCRIPT
870
wind speeds previously inferred from cloud tracking studies. Our global analysis of the Carlson et al. (1993) size parameter demon-
872
strates an overall increase in size parameter, hence particle size, from equator
873
to pole, consistent with previous particular analysis by Wilson et al. (2008).
874
We also note a subtle increase in the size parameter peaking at about −20◦
875
latitude; but it is difficult to state its existence with certainty, due to the
876
increasing magnitude of the standard deviation of the calculated size param-
877
eter in the equatorial latitudes observed by VIRTIS-M-IR, possibly amplified
878
by instrumental artifacts.
AN US
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871
We observe in the VIRTIS-M-IR data that the 1.74µm and 2.30µm win-
880
dows demonstrate local maxima in radiance peaking around 50◦ latitude,
881
consistent with previous observations of these spectral windows, dating to
882
the time of their discovery in the 1980’s. We also measure a large amount of
883
variability to the typical cloud coverage as at latitudes between 0◦ and 60◦ ,
884
as evidenced by the very large standard deviations about the mean in the
885
cloud-dominated windows at those latitudes.
ED
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879
Finally, we report the existence of a roughly 150-day periodic variation
887
in the cloud coverage, seen most prominently at mid-latitudes in the 1.74µm
888
radiance data. A least squares frequency analysis quantifies this period that
889
was suggested in earlier work by McGouldrick et al. (2012). The timescale
890
is consistent with a cloud formation and evolution cycle that is driven by
CE
PT
886
the radiative dynamical feedback and gravitational settling of particles with
892
sizes typical of the condensational clouds. Further modeling investigations
893
will be necessary to elucidate the drivers of this periodicity in the clouds.
AC 891
47
ACCEPTED MANUSCRIPT
894
6. Acknowledgments This work was supported through NASA Planetary Mission Data Analysis
896
Program Grant Number NNX14AP94G, and greatly benefitted from discus-
897
sions sponsored by the International Space Sciences Institute (ISSI). This
898
manuscript was much improved thanks to thoughtful and helpful reviews by
899
Nils Mueller and Jo Barstow.
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Discovery of a 150 day period in the Venus condensational clouds Kevin McGouldrick, Constantine C.C. Tsang PII: DOI: Reference:
S0019-1035(16)30652-2 10.1016/j.icarus.2016.10.005 YICAR 12221
To appear in:
Icarus
Received date: Revised date: Accepted date:
11 March 2016 15 September 2016 2 October 2016
Please cite this article as: Kevin McGouldrick, Constantine C.C. Tsang, Discovery of a 150 day period in the Venus condensational clouds, Icarus (2016), doi: 10.1016/j.icarus.2016.10.005
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Highlights • We find a 150 day periodic variation in the 1.74 µm and 2.30 µm radi-
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• The oscillation is most pronounced at mid-latitudes (30◦ − 60◦ ).
• The timescales are consistent with the cloud radiative-dynamical feedback.
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• Long-term increase in radiance at mid to low latitudes is also noted.
• Additional hypotheses to guide future modelling of this phenomenon
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Discovery of a 150 day period in the Venus condensational clouds
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Kevin McGouldricka,∗, Constantine C. C. Tsangb a
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Laboratory for Atmospheric and Space Physics, University of Colorado Boulder, 3665 Discovery Dr., Boulder, CO 80303 b Southwest Research Institute, Department of Space Studies, 1050 Walnut St., Suite 300, Boulder, CO 80302
Abstract
We have analyzed the long-term regional and global variation of emitted radiance in 1.74µm and 2.30µm near infrared spectral windows in the Venus atmosphere using the medium resolution, infrared channel of the Visible and
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Infrared Thermal Imaging Spectrometer (VIRTIS-M-IR) on the Venus Express spacecraft. We find a periodic variation in the 1.74µm radiance that
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is most pronounced at mid-latitudes (30◦ − 60◦ latitude). This oscillation has a period of approximately 150 days, and is shown to be unlikely to be
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driven by variations in viewing geometry, nor by variations in instrumental characteristics such as spectrometer temperature. The oscillation has an am-
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plitude at least as large as that of the typical day-to-day variations observed. The decay and recovery timescales are consistent with response of the cloud
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vertical structure to the radiative-dynamical feedback. It remains unclear why this variation would be seen only at mid-latitudes, but some hypotheses to guide future modelling testing are suggested. ∗
Corresponding author. Email address: [email protected] (Kevin McGouldrick)
Preprint submitted to Icarus
October 7, 2016
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Keywords: Venus, Atmosphere, Clouds, Meteorology, Dynamics 1. Introduction
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Spatial and temporal inhomogeneities in the near infrared emission spec-
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trum of Venus were first discovered by Allen and Crawford (1984). It was
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soon determined that these inhomogeneities were observed as a consequence
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of the existence of narrow spectral windows in the near infrared emission
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spectrum of Venus where absorption by (primarily) CO2 and H2 O was min-
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imal. Since then, these spectral windows have been used to elucidate the
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properties of the surface of Venus (for example, Mueller et al. (2008), Kappel
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et al. (2012), Haus et al. (2014), and Shalygin et al. (2015)), atmospheric
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composition and chemistry (for example, Marcq et al. (2005) and B´ezard
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et al. (2009)), and properties of the clouds of Venus (for example, Carlson
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et al. (1993) and Wilson et al. (2008)).
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Crisp et al. (1989) and Kamp et al. (1988) showed that the variability
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of night side near infrared emission from Venus in the spectral vicinity of
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the 1.74µm and 2.30µm windows was driven primarily by variations in the
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condensational clouds of Venus. The clouds of Venus cover a range of alti-
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tudes from about 50km above the surface to about 70km above the surface.
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When viewed in emitted near infrared radiation, spatial inhomogeneities are
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driven by variations in the lower regions of the clouds, between about 50-
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55km. The bulk of the cloud mass is located also in this region, but the origin
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of the volatiles that support the entire cloud system is the photochemically
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produced sulfuric acid around 63km.
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Grinspoon et al. (1993) used the 1.74µm and 2.30µm spectral windows
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observed by the Near Infrared Mapping Spectrometer (NIMS) during the
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Galileo flyby to constrain the total infrared optical depth of the photochem-
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ical and condensational clouds and the composition of the putative Mode 3
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particles first postulated by Knollenberg and Hunten (1980). Carlson et al.
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(1993) used the same data to characterize the spatial variability of the typical
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size of the particles that comprise the condensational cloud at the time of
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the Galileo encounter.
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More recently, the infrared mapping channel of the Visible and Infrared
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Thermal Mapping Spectrometer (VIRTIS-M-IR) on the Venus Express space-
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craft (Drossart et al., 2007) has been utilized to further characterize the
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short-term evolution of the clouds of Venus (McGouldrick et al., 2012) and
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to simultaneously retrieve additional properties of the Venus clouds region,
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including cloud base altitude, sulfuric acid weight percent, and sub-cloud and
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in-cloud water vapor concentrations (Barstow et al., 2012).
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Here, we build upon the work done in those two papers to character-
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ize the long-term evolution of the clouds of Venus, as can be determined
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through analysis of 921 orbits (about two and a half years) of VIRTIS-M-IR
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observations of the night side of Venus.
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2. Observational Data
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Venus Express launched in November 2005, was placed into orbit around
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Venus in April 2006, and continued to return valuable science data until
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it exhausted the fuel for its attitude control thrusters in November 2014.
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Its polar orbit exhibited a periapsis altitude generally between 150 km and 5
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250 km above the surface of Venus at about +80◦ latitude, and an apoapsis
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altitude of about 66,000 km. The VIRTIS-M infrared channel is a medium
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spatial resolution (0.25 mrad/pxl) infrared mapping spectrometer that cov-
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ers the range of wavelengths from 1µm to 5µm with a spectral resolution
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of roughly λ/∆λ ∼ 300, or about 0.01µm. Though, in practice, the effec-
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tive resolution has been shown to be about 0.017µm (B´ezard et al., 2009).
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This is sufficient spectral resolution to resolve many details of the spectral
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windows (Drossart et al., 2007). The spatial resolution is about 30 km when
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the spacecraft is at apoapse (d ∼ 66, 000 km), improving to about 5 km at
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a distance of about 10, 000 km. The near infrared detector was a mercury-
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cadmium-telluride (HgCdTe) semiconductor cooled to 70K. The instrument
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returned data over the course of nearly four sidereal Venus days until the
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cooling system failed during orbit 921 (UTC: 2008 October 27). The cooling
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system began to show signs of wear during the nominal mission (the first 500
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orbits), so the frequency of use of the VIRTIS-M-IR instrument was signif-
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icantly reduced between orbits 500 and 921, as compared with the nominal
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mission. Previous work by McGouldrick et al. (2012) exploring the long-term
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variability of the clouds relied on data only from the first 407 orbits of the
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mission. In the present work, we utilize the entire VIRTIS-M-IR data set.
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The entire volume of data produced by the instrument can be obtained
at the European Space Agency’s (ESA’s) Planetary Science Archive (PSA) website, and is mirrored by the National Astronautical and Space Adminis-
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tration’s (NASA’s) Planetary Data System (PDS), Atmospheres Node. The
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VIRTIS instrument produced about a terabyte of data over the course of the
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Venus Express mission. In order to efficiently analyze this large volume of
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data, it is necessary to filter it according to both instrumental and geometric
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constraints. Instrumentally, we consider only observations utilizing integra-
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tion times of at least 0.3 seconds. Acquired spectral cubes having integration
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times shorter than this are intended for the much higher radiance from day
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side observations, and have very low signal to noise ratios in emitted near
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infrared light. Geometrically, we constrain the data according to distance,
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viewing angle, and solar angle considerations. To generate spectral cubes,
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VIRTIS-M-IR scans its slit across the field of view to generate spectral im-
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age cubes. The time required to do this, combined with the motion of the
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spacecraft relative to the planet, means that mapping mode spectral cubes
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generally are not created when within 10,000 km of the planet. (Drossart
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et al., 2007). Thus, we consider only data acquired at distances greater than
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10, 000 km from the planet. In doing so, we are neglecting the pericenter
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observations – mostly of northern hemisphere targets. We choose to neglect
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these data for two reasons. First, these periapse observations are necessarily
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very parochial in nature, due to the small distance to Venus and the small
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field of view of VIRTIS-M-IR. While the inclusion of these nadir-viewing,
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near-periapse observations can improve the mission-long statistics, they also
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have the potential to introduce significant errors into the time series analysis
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performed in this work that are caused by the spatial inhomogeneity. Sec-
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ond, the present work is intended to be part of a larger project in which the
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information gathered here can inform the characterization of individual fea-
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tures, including morphology, in the Venus clouds over a variety of timescales.
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Since that effort will be necessarily limited to observations using the map-
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ping mode of VIRTIS-M-IR, we also constrain this preliminary work to that
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mode of observation. The pericenter observations obtained at distances less
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than 10,000 km will not be helpful in either of these contexts, so we disre-
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gard those observations for now in favor of concentrating on the southern
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hemisphere mapping data. We consider only those observations in which at
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least some of the night side is visible, discarding all data for which only the
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day side is seen. That is, we discard the data for the present analysis if the
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minimum hour angle of the Sun exceeds 5 a.m. and the maximum hour angle
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is less than 7 p.m. The 1 hour buffer from the dawn or dusk terminator is
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intended to minimize the effects of sunlight that is forward scattered from
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beyond the terminator. We also restrict the observations to those that are
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affected minimally (or not at all) by sunlight that is forward scattered from
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the day side of the planet by restricting the data in the nominal analysis to
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locations where the solar incidence angle exceeds 95◦ . In order to quantify
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the effects of this cutoff, we also compare results considering a range of inci-
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dence angle, among 100◦ , 105◦ , 110◦ , and 115◦ . Note that, due to our hour
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angle restriction, these incidence angle data filters will have their greatest ef-
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fect for observations near the pole. However, these cutoffs will have minimal
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effect on reducing the contribution by stray light sources in the data (Kappel
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et al., 2012). Finally, we restrict our analysis to the southern hemisphere.
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The highly eccentric polar orbit of Venus Express makes mapping type ob-
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servations by VIRTIS-M-IR of the southern hemisphere more favorable than
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the northern hemisphere. While portions of the northern hemisphere have
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been observed in mapping mode, the data are almost exclusively equatorial
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(|φ| < 30◦ ). If a north-south hemispheric dichotomy exists in the behavior
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of the clouds then this uneven distribution of north and south latitudinal
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observations could exacerbate the effect. Furthermore, even those north-
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ern hemisphere observations that do exist are very close to the limb, and
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hence are subject to significant foreshortening and limb darkening, resulting
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in larger uncertainties in the corrected upwelling radiance.
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Most of the time, at least some of the night side of Venus is visible to
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VIRTIS-M-IR. However, there are times when the change in the phase angle
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due to the revolution of Venus around the Sun, coupled with the telemetry
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requirements, makes it nearly impossible to observe the night side of the
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planet (which is necessary for the analysis of these near infrared emissions
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from Venus). Thus, even though VIRTIS-M-IR returned useful data over a
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window of 921 days (also 921 orbits, since the orbital period of Venus Express
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throughout this phase of the mission was 24 hours) before the failure of its
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cooling system, there are somewhat fewer than 921 orbits’ worth of data
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that will be useful for the present analysis. There are also several weeks-
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long breaks in the data during which times night side data that satisfy our
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declared criteria could not be obtained.
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Over the course of multiple orbits, significant latitudinal and longitudinal
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coverage of the clouds in the southern hemisphere was built up, which allows
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for the determination of possible latitudinal tendencies in the existence and
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optical thickness of the clouds. Furthermore, VIRTIS observations sometimes
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utilize a mosaic mode in which the entire visible hemisphere of the planet is
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observed over the course of up to nine separate cube acquisitions. Observing
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in this manner allowed a greater spatial coverage than is possible with a
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single cube, or a series of cubes over a particular location.
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Note that, due to the limited field of view of the VIRTIS-M-IR instru-
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ment, the brief lifetime of this instrument (fewer than four Venus sidereal
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days), and the existence of about a dozen unique science observation modes,
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the composite coverage of the planet is not homogeneous. In addition to
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the hemispherical observational imbalance driven by the polar and eccentric
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orbit, there may also be geographic locations that had been observed more
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frequently than others.
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The VIRTIS-M cubes demonstrate a significant amount of anomalous ra-
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diance that has been attributed to scattered sunlight, probably reflected from
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the baffle toward the detector (Mueller et al., 2008; Kappel et al., 2012). In
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order to correct for this scattered sunlight, we choose a series of wavelength
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bands in the Venus emitted near infrared spectrum for which we expect to
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see zero emitted radiance, due to the absorption of upwelling radiation by
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atmospheric constituents such as CO2 and H2 O. That is, we define a series
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of “muntins1 ” between the near infrared spectral windows with wavelengths:
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(1.05 ± 0.01 µm, 1.225 ± 0.015 µm, 1.38 ± 0.03 µm, 1.57 ± 0.03 µm). A VIR-
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TIS image cube is a three-dimensional data construct with dimensions termed
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band (wavelength), sample (pixels along the slit), and line (each new inte-
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gration by the detector). That is, a VIRTIS cube is a stack of band × sample
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images. For each band × sample image, we average over the sample (slit)
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dimension to find an average spectrum.
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Acting on the assumption that the stray light was likely scattered sun-
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1 A muntin is a bar or rigid supporting strip between adjacent panes of a glass window; formerly used to increase the structural integrity of a large window, today mostly used for decorative purposes.
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reflected solar Blackbody curve:
I(λ) = A
−1 2hc2 hc λkT − 1 e λ5
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where h is Planck’s Constant, c is the speed of light in vacuum, k is Boltz-
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mann’s constant, T is the temperature of the solar photosphere, and we
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choose A to be an arbitrary gray albedo that is a free parameter to be fit to
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the data along with λ. However, we found that such a spectrum could not
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match the measured muntins. If the gray albedo was chosen to fit the muntins
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near 1.5µm and 2.0µm, then the stray light radiance from the muntins at
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shorter wavelengths was underestimated. Similarly, if the curve was fitted to
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the muntins at wavelengths shorter than 1.3µm, then the stray light radiance
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from the longer wavelength muntins was overestimated. Similar to Kappel
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et al. (2012) and Longobardo et al. (2012), we found that the stray light
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radiance in the muntins closely matched a λ−4 curve. Likely interpretations
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of such a curve would mean that either the source of the stray light spectrum
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were a blackbody considerably hotter than the Sun or was produced by a
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non-gray albedo that increased strongly at shorter wavelengths. In the for-
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mer case, these near infrared wavelengths are too near the peak of the solar
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spectrum to be in the long-wavelength Rayleigh-Jeans regime of the solar
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spectrum that asymptotes to a λ−4 curve. In the latter case, Kappel et al.
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(2012) suggest that the stray light resembles λ−4 associated with scattering
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processes, but the Venus cloud particles are too large to be Rayleigh scat-
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terers at these wavelengths. Since neither of these explanations is likely, we
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chose to fit the data with an arbitrary power law or an arbitrary exponential: I(λ) = I0 λa
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I(λ) = I0 · eaλ
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We then fit the free parameters (I0 ) and (a) to the muntin data, finding their
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best fit values and standard deviations in each of these two cases. We found
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that the power law tended to identify best fit exponents of between λ−3 and
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λ−5 , somewhat consistent with previous suggestions by Kappel et al. (2012)
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and Longobardo et al. (2012). However, we found that the goodness of the fit
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was somewhat better when using the exponential curve in the vast majority
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of the analyzed data, so we chose to use the exponential curve as a best fit for
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the stray light correction. We then subtract this best fit stray light spectrum
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from each pixel in the slit (along the sample axis). All negative values in the
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scattered sunlight corrected spectra are treated as zeros. An example of the
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effect of this procedure for a given spectrum at one pixel (sample 100, line
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50) of one particular pure night side image cube (VIR0383 00) is shown in
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Fig. 1.
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Also shown in Fig. 1 is an example stray light spectrum obtained by av-
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eraging all valid data (i.e., pixels not exhibiting error flags) obtained from
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observations at least 200km above the limb of the planet for this same pure
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night side image cube. We see that the stray light present at 1.74µm and
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2.30µm is nearly negligible. So, even if our simple exponential stray light
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correction is invalid, it will introduce negligible error in the current analysis.
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Future analysis of the near surface windows will require us to apply a more
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Figure 1: In the left hand plot, the black curve is the uncorrected spectrum of sample 100 and line 50 of pure night side cube VIR0383 00. The red curve is the same data with the stray sunlight correction from Eq. 3 applied. In the right hand plot, an average spectrum collected from the empty space observations within the same image cube is compared with the same on-target uncorrected spectrum.
rigorous stray light correction, perhaps similar to that described by Kappel
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et al. (2012). Though the stray light has minimal effect at the wavelengths
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investigated in this paper, we include this description of our stray light cor-
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rection process in ourder to document this method and to allow reference to
215
it from future work that we intend to carry out.
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Following the correction for the scattered light, in order to normalize
217
the observations for long-term cross-comparisons, we apply a limb darkening
218
correction to the data. In previous work, McGouldrick et al. (2008, 2012)
219
utilized the corrections of Carlson et al. (1993). Here, we capitalize upon
220
the efforts by Longobardo et al. (2012) to quantify the limb darkening seen
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216
221
in the VIRTIS-M-IR data in several of the near infrared spectral windows.
222
Longobardo et al. (2012) found variations in the limb darkening behavior as a
223
function of latitude. For the windows that Longobardo et al. (2012) analyzed
224
and that we study here, we use the “average” limb darkening correction
13
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225
parameters to determine a nominal radiance at zero emission angle:
226
3. Results
227
3.1. Long-term global tendencies
(4)
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Iemitted = Iobserved · (αλ + βλ cos θe )−1 .
Bullock and Grinspoon (2001) and others have suggested that changes in
229
SO2 in the upper atmosphere could lead to changes in overall cloud coverage,
230
due to a greater availability of condensable materials. Orders of magnitude
231
variations are seen in the SO2 concentrations above 70km (Esposito et al.,
232
1988; Marcq et al., 2012). Although the concentrations at those altitudes
233
are only at the tens to hundreds of ppbv (parts per billion by volume) level,
234
the scale height of the SO2 at those altitudes has been measured to be about
235
1 km, indicating that an orders of magnitude larger concentration at the
236
tens to hundreds of ppmv (parts per million by volume) level exists deeper
237
in the atmosphere in the cloud formation regions (near 62 km at equatorial
238
latitudes). Thus, large changes in SO2 could to have significant effects on the
239
total mass loading of the photochemical clouds, and potentially also effects
240
on the total mass available to form the deeper condensational cloud.
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Our first goal is to determine whether a long-term global trend of Venusian
cloud cover is evident in the VIRTIS-M-IR data set by examining the long-
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243
term trends of the radiance in the 1.74µm and 2.30µm atmospheric windows.
244
In Fig. 2, we show the hemispherically averaged radiance for each of these
245
two windows as a function of orbit number. Also shown in the figure is a
246
linear best fit to the data, with free parameters I0 (the radiance at orbit 14
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247
zero), and mI (the slope of the radiance per orbit). Finally, the five rows
248
represent the five incidence angle cutoffs we considered in this analysis (95◦ ,
0.16 0.12
2
0.10 0.08 0.06
I [
0.04 0.02
0.10 0.08 0.06 0.04 0.02 0.00 0
]
1
W m − sr − µm −
200
0.14 0.12
Radiance
400
600
800
2
1
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0.10
I [
0.08 0.06 0.04 0.02 0.00
800
]
1
W m − sr − µm − 1
0
200
400
600
800
0
200
400
600
800
0
200
400
600
800
0
200
400
600
800
0.12 0.10 0.08 0.06
0.30
0.22 0.20 0.18 0.16
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0.14
600
1 2
I [
0.12 0.10
I [
0.08 0.06
200
400
0.16 0.14 0.12 0.10 0.08 0.06 0.04 0.02 0.00
0.12 0.10 0.08 0.06
600
800
orbit
0.04 0.02 0.00
orbit
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0
0.00
800 ]
400
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0.24
200
1
0.00
1
0.05
0.02
2
0.10
W m − sr − µm −
0.15
0.04
800
0.25 0.20
I [
2
600
]
400
1
200
M
0.00
W m − sr − µm −
1
I [ ]
1 1 2
W m − sr − µm − I [ ]
1
I [ ]
1
600
0.05
0
1
400
0.20
2
1
200
0.25
0
2
0.12
800
0.00
0.10
W m − sr − µm −
600
0.05
0.15
I [
400
0.20
0
W m − sr − µm −
200
0.25
2
W m − sr − µm −
1
]
0
0.10
0.14
1
0.14
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1
W m − sr − µm −
0.18
0.15
. µm
2 30
Radiance ]
. µm
1 74
0.20
ED
I [
2
1
W m − sr − µm −
1
]
100◦ , 105◦ , 110◦ , and 115◦ ).
Figure 2: Southern hemisphere radiance averaged across all cubes per orbit during the lifetime of VIRTIS-M-IR for both the 1.74µm and 2.30µm windows. From top to bottom, the rows represent data subject to differing minimum solar incidence angle restrictions of 95◦ , 100◦ , 105◦ , 110◦ , and 115◦ , respectively (0◦ is Sun at zenith).
249 250
The linear fits to the data produce radiance at orbit 0, and the average 15
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slope of the radiance in units of W m−2 sr−1 µm−1 per orbit (or per day),
252
as well as one sigma standard deviation uncertainties in those parameters.
253
We overplot the best fit trend line (but not the uncertainty information) in
254
Fig. 2. The unaveraged data for both windows and at most incidence angle
255
restrictions shown in Fig. 2 shows a significant amount of scatter, and a
256
best fit linear trend line that is essentially flat, indicating that there is no
257
significant global change to the observed condensational cloud cover on Venus
258
over the 2.5 year lifetime of the VIRTIS-M-IR instrument. Note also that
259
as the incidence angle cutoff is made more restrictive, a hint of a periodicity
260
begins to emerge from the data. However, since the larger emission angles
261
selectively remove observational data from the polar regions, it is unclear at
262
this point whether the periodicity exists throughout the southern hemisphere
263
but has been masked by noise near the terminator, or whether is a more
264
regional phenomenon.
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Because of the high level of scatter in the data, which is partly due to the
266
small field of view of the instrument making it difficult to observe the same
267
region of the atmosphere from orbit to orbit, as well as the intrinsic variability
268
within the clouds, in Fig. 3 we have smoothed the data with a seven-day box
269
car mean window. A seven-day averaging of the data approximates extending
270
the averaging over orbit done in Fig. 2 to a global average, since the period of
271
rotation at the altitudes of these clouds is approximately seven days (Hueso
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et al., 2015).
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However, upon applying a seven day moving window average of the data,
274
we notice in Fig. 3 the appearance of slight trends to the mean radiance in
275
each window, and evidence of shorter-term (on the order of weeks to months)
16
1
W m − sr − µm −
0.16
1
0.14 0.12
0.06
I [
0.04 0.02 600
0.08 0.06 0.04 0.02 0.00
800 ]
1
W m − sr − µm −
0.16
0
200
0
200
0.14 0.12 0.10
1
0.14 0.12
2
0.10 0.08 0.06
I [
0.04 0.02 200
400
600
W m − sr − µm −
1
]
0.20
0.04 0.02 0.00
0.10 0.08
0.12 0.10 0.08 0.06
0.06 0.04
I [
0.04
1
0.14
2
0.16
0.02 400
0.06
400
600
800
400
600
800
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0.18
200
0.08
800
600
0.02 0.00
800
W m − sr − µm −
1
]
0.20 0.18 0.16
1
0.14 0.12
0
200
400
600
800
0
200
400
600
800
0
200
400
600
800
0.12 0.10 0.08 0.06
2
0.10 0.06 0.04 0.02 200
400
600
1
0.16 0.14 0.12
0.08 0
PT
0.10 200
400
600
0.00
0.12 0.10
1
1
0.18
0.02
0.08
2
W m − sr − µm −
ED
0.20
0.04
800
]
0.22
I [
0.08
0.06
I [
]
1 2
1
W m − sr − µm − I [ ]
1 2
1
W m − sr − µm − I [ ]
1 2
1
W m − sr − µm − I [ ]
400
0.18
0
1
200
0.20
0
2
Radiance
0.10
CR IP T
0.08
0
W m − sr − µm −
0.12
2
0.10
0
I [
. µm
2 30
Radiance ]
. µm
1 74
0.18
M
I [
2
1
W m − sr − µm −
1
]
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800
orbit
0.04 0.02
orbit
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Figure 3: Southern hemisphere radiance averaged across all cubes per orbit during the lifetime of VIRTIS-M-IR for both the 1.74µm and 2.30µm windows, but further averaged with a seven day moving window to approximate a global average radiance. As in Fig. 2, from top to bottom, solar incidence angle restrictions of 95◦ , 100◦ , 105◦ , 110◦ , and 115◦ , are represented.
276
variations in the cloud cover from radiance changes. The overall increase in
277
radiance indicated by the mission-long linear best fit trend lines suggest that
278
the overall cloud cover of Venus may have been thinning during the course of 17
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the mission. However, visual inspection of the plots indicates that for most
280
incidence angle cutoffs this apparent trend is small compared to the overall
281
scatter in radiance that is observed on an observation-to-observation basis.
282
If the decrease in the SO2 observed is driven by a conversion into H2 SO4 and
283
thence into clouds, then the results presented here, though only of a 2.5 year
284
duration, are inconsistent with that explanation, at least on the global scale.
285
However, the highly spatially variable nature of the observed SO2 variations,
286
and of the thickness of the condensational clouds, means that a regional scale
287
relationship cannot yet be ruled out.
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The spectral registration of the VIRTIS-M-IR spectrometer varies with
289
temperature (Moinelo et al., 2010), so that the mapping from band number
290
to wavelength can vary with time. Thus, in generating the plots shown above,
291
we use the radiance within the wavelength band that is closest to the defining
292
wavelength for each particular data cube. These changes in band number
293
associated with a particular wavelength can produce small but detectable
294
variations in the measured flux. These variations are discussed at length by
295
Kappel et al. (2012), who concluded that they are the result of errors in
296
the ground calibration. Rather than reinvent the recalibration performed by
297
Kappel et al. (2012), we attempt to rule out this so called Odd-Even effect
298
as a source of the variations we see by additionally performing our analysis
299
using data that have been spectrally integrated across the entire range of
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each spectral window. This is similar to what is described by McGouldrick
301
et al. (2012), for the 1.74µm window analyzed there. Here, we integrate
302
the 1.74µm window from 1.67µm to 1.80µm; and the 2.30µm window from
303
2.15µm to 2.60µm. In this analysis of spectrally integrated data, the Even-
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Odd effect should be reduced, as overestimations of measured flux in half the
305
bands will be roughly balanced by underestimations of the flux in the other
306
half of the bands.
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304
Fig. 4 shows the long term trends for the seven day averaging and spec-
308
trally integrated windows. We see that both the long-term trend of increasing
309
radiance, as well as the periodic shorter-term variations appear in the inte-
310
grated data. In fact, the relative magnitude of the day-to-day variations
311
compared with the average radiance measured is slightly smaller for the inte-
312
grated case, suggesting that the contribution to the measured radiance from
313
the Odd-Even effect has been minimized by this integration, and that that
314
effect is small for the present analysis. The data in Fig. 4 are best com-
315
pared with the data in Fig. 3, since each has had the averaging extended
316
across multiple orbits. Not shown, these similarities between the single band
317
and integrated radiance for the unaveraged data are mirrored in the moving
318
window averaged data.
319
3.2. Mission-long latitudinal mean radiances
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One of our long-term goals in this project is to characterize the short-term
321
behavior and variability of the condensational clouds of Venus. Previous work
322
by McGouldrick et al. (2012) suggested that typical timescales of evolution
323
were around 30 hours, but that work only analyzed two orbits’ worth of
324
observations. Part of the difficulty in establishing patterns of variability
325
among the condensational clouds is in quantifying what level of variability can
326
be attributed to cloud variations. For example, Carlson et al. (1993) showed
327
that variations in the clouds produce roughly 20 : 1 brightness contrast
328
ratios at 2.30µm and roughly 5 : 1 brightness ratios at 1.74µm. However,
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1
200
400
600
600
800
]
1
W m − sr − µm − 1 2
]
1 2
1
W m − sr − µm −
I [
I [
0.02 0.01
]
1
W m − sr − µm − 1
0.05 0.03 0.02
I [
0.01 0.00 200
400
600
0
200
0.035 0.030 0.025 0.020 0.015 0.010 0.005 0.000
0.030 0.025 0.020 0.015
W m − sr − µm −
1
]
0.050 0.045
0.005 0.000
0
200
400
600
800
0
200
400
600
800
0
200
400
600
800
0.035 0.030 0.025
1
0.040
0.010
800
0.035
2
0.030 0.025
0.015 0.010 200
400
1
W m − sr − µm −
0.040 0.035 0.030
0.020 0
PT
0.025 200
400
600
2
1
0.045
0.015 0.010 0.005 0.000
0.040 0.035 0.030
1
ED
0.050
0.020
800
]
0.055
600
I [
0.020
M
]
1 2
1
W m − sr − µm − I [ ]
200
2
0.04
I [
]
1 2
1
W m − sr − µm − I [
0.08
0 0.040
800
0.09
0.06
0.000
400
0.03
0.07
0.005
800
0.04
600
0.010
600
0.05
400
0.015
400
0.06
200
0.020
800
0.07
0
1
0.025
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0.00
0
2
Radiance
0.030
CR IP T
0.01
I [
I [
0.02
0
W m − sr − µm −
0.035
1
0.03
2
]
1
W m − sr − µm −
0.04
2
1
W m − sr − µm −
0.05
0
I [
. µm
2 30
Radiance ]
. µm
1 74
0.06
800
orbit
0.025 0.020 0.015 0.010 0.005
orbit
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Figure 4: Southern hemisphere radiance averaged across all cubes per orbit during the lifetime of VIRTIS-M-IR for both the 1.74µm and 2.30µm windows spectrally integrated across the entire spectral windows. The same incidence angle restrictions noted in Fig. 2 and Fig. 3 are represented.
329
those contrast ratios do not account for the large magnitude of latitudinal
330
variance in the clouds as indicated by radiance variations observed by Crisp
331
et al. (1989) and Chanover et al. (1998). Within a given latitude region, the
332
contrasts are about half of these global values. In previous analysis of short20
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term evolution of the clouds, McGouldrick et al. (2012) defined a cloud or hole
334
boundary according to closed radiance contours at a 0.02 W m−2 sr−1 µm−1
335
resolution. In order to reduce the arbitrariness of our cloud definition, we
336
here develop a latitudinal profile of radiance for each of the windows, along
337
with their one-sigma standard deviations. In future analysis of short-term
338
cloud evolution, we plan to use these latitudinally resolved estimates of long-
339
term variability to define the presence or absence of a local cloud or hole
340
phenomenon.
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In Fig. 5, we show the latitudinal profiles for each of the spectral windows.
342
These figures assimilate the entire VIRTIS-M-IR dataset that fit our criteria
343
detailed in Section 2 above. Note the local maximum in radiance evident
344
near 50◦ latitude in both the 2.30µm and 1.74µm data. This has been seen
345
since the NIR observations began in the 1980’s, and has been explained as
346
evidence of the interaction between the photochemical cloud production, the
347
condensational cloud production, and the near-global meridional Hadley-like
348
circulation by Imamura and Hashimoto (1998). The optically thick cloud
349
near the polar collar is also evident as the strong decrease in radiance pole-
350
ward of that radiance maximum. The slight but sharp increase in radiance
351
very near to the pole in the 1.74µm profile is possibly due to sunlight in the
352
atmosphere scattered across the polar terminator, or is due to the deep emis-
353
sion from the polar vortex. In the 1.74µm and 2.30µm profiles, we also see
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341
a significant but smaller increase in the variability of the clouds (evidenced
355
by an increase in the standard deviation about the mean) in the equatorial
356
region. However, since the orbit of Venus Express limited the number of
357
observations in this region that could match our criteria, and since these
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359
to potential errors or uncertainties in the limb darkening correction – the
360
variation seen at equatorial latitudes should be taken cum grano salis. It is
361
hoped that observations by JAXA’s Akatsuki spacecraft (Nakamura et al.,
362
2007), having begun science operations from a more equatorial orbit in April
363
of 2016, will help to resolve the level of variability seen here by VIRTIS-M-IR
364
on Venus Express in the equatorial clouds of Venus.
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0.15
0.20
0.25
0.6
0.8
1.0
1.2
80
0 −10 −20 −30 −40 −50 −60 −70 −80 −90 90
Emission Angle
0
10
20
30
40
0 −10 −20 −30 −40 −50 −60 −70 −80 −90 −6
60
−2
0
2
hr since midnight
70
4
90
2.30µm
0.02
0.04
0.06
0.08
0.10
0.12
0.14
Radiance [W m −2 sr −1 µm −1 ] Surface Elevation from Magellan Altimetry
−1.5
−1.0
−0.5
0.0
0.5
1.0
km above mean radius
1.5
2.0
170
180
Incidence Angle
100
110
120
130
140
degrees
150
160
6
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−4
50
degrees Local Solar Time
0 −10 −20 −30 −40 −50 −60 −70 −80 −90 0.00
0 −10 −20 −30 −40 −50 −60 −70 −80 −90 −2.0
M
0.4
ED
0 −10 −20 −30 −40 −50 −60 −70 −80 −90
0.10
Radiance [W m −2 sr −1 µm −1 ] size parameter
PT
latitude latitude
0 −10 −20 −30 −40 −50 −60 −70 −80 −90
0.05
CE
latitude
1.74µm
0 −10 −20 −30 −40 −50 −60 −70 −80 −90 0.00
CR IP T
observations tend also to be very close to the limb – hence more susceptible
latitude
358
Figure 5: Zonally and temporally averaged mean radiance with their standard deviations as functions of latitude for the 1.74µm window, the 2.30µm window, and the Carlson et al. (1993) size parameter, in addition to geometrical data such as incidence and emission angles, surface elevation, and local solar time. The data here are subject to a minimum incidence angle of 95◦ .
22
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365
Also shown in Fig. 5 is the Carlson et al. (1993) size parameter: I1.74µm . (I2.30µm )0.53
(5)
CR IP T
m=
Carlson et al. (1993) showed that this weighted ratio of the 1.74µm and
367
2.30µm emitted radiance can be used to estimate typical particle sizes in the
368
Venus atmosphere, due to the relative Mie scattering properties of Mode 2
369
and Mode 3 particles at these wavelengths. Wilson et al. (2008) applied
370
this technique to a handful of early orbits of Venus Express, and found a
371
significant increase in size parameter in the polar regions, when applying a
372
zonal average, similar to what we have done here, but for individual orbits.
373
Similarly, Barstow et al. (2012) found that the ratio of the Mode 3:Mode 20
374
particle numbers increased toward the pole. This increase is likely the result
375
of the deeper altitude in which the condensational clouds exist at polar lat-
376
itudes. We reproduce this strong increase in size parameter (hence, particle
377
size) poleward of about 50◦ . We also see a slight increase in size parame-
378
ter seen with a local miximum near 20◦ was not reported by Barstow et al.
379
(2012). However, a reanalysis of the Barstow et al. (2012) work, presented
380
in the Barstow (2012) doctoral thesis, does report a similar phenomenon
381
with regard to the relative Mode 20 :Mode 3 particle number ratio. As can
382
be seen in Fig. 5, the standard deviation about the mean is increasing at
383
these latitudes, due to the paucity of data and large emission angle of the
384
observations. Because we calculate the size parameter for a single band (we
385
do not use the spectrally integrated calculations), the size parameter calcu-
386
lation is probably also still somewhat affected by the Odd-Even effect. If
387
real, this increase could represent a slight increase in the relative population
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of Mode 3:Mode 20 particles at these latitudes, followed by a reversal of the
389
trend (i.e., to an increase in Mode 20 relative to Mode 3) from about 20◦ to
390
about 50◦ latitude. Such a trend would be consistent with cloud formation
391
altered by the meridional circulation modelled by Imamura and Hashimoto
392
(1998). That is, the Mode 3 population would be driven by convection in the
393
condensational clouds maximized near the equator, while the Mode 2 popu-
394
lation would steadily increase as the parcels are carried from the equator to-
395
ward the poles. Since the gravitational sedimentation velocity of the Mode 2
396
particles is so slow, they simply accumulate in the observable cloud, slowly
397
skewing the population from larger to smaller particles, until the downwelling
398
branch takes over near 50◦ latitude. However, this slight increase in the size
399
parameter should also be taken with a grain of salt, since the large emission
400
angle, low observation frequency, and possible calibration artifacts may still
401
be playing significant roles in this calculation. Furthermore, the retrievals
402
by Haus et al. (2014) did not find an increase in particles size at equatorial
403
latitudes. It is anticipated that JAXA’s Akatsuki spacecraft, observing from
404
a more equatorial vantage point, will soon be able to resolve the veracity of
405
this observation.
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The average surface elevation observed in the data that satisfy our cri-
407
teria shows that lower elevations are slightly favored in the polar regions
408
compared with the elevations observed near the equatorial regions. How-
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406
ever, the total range of average surface elevations observed is less than one
410
kilometer. The emission and incidence angle profiles are as expected from a
411
spacecraft imaging mostly the night side of a planet from a highly eccentric
412
and polar orbit. Namely, low emission angle near the pole, while the equator
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is imaged mostly near the limb; and near-terminator (low incidence angles)
414
near the poles, with gradually larger incidence angles at lower latitudes. The
415
effect of the incidence angle on the measured parameters is negligible. The
416
primary effect being a reduction in how far into the polar regions the analysis
417
can obtain data that fit the incidence angle criterion. Therefore, we do not
418
reproduce the latitudinal profiles for all incidence angle cutoffs.
419
3.3. Regional Temporal Behavior
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413
Note again from Fig. 5 the significant changes in radiance as a func-
421
tion of latitude within all of the near infrared spectral windows. This large
422
amount of variability, and the differing frequency of observation as a func-
423
tion of latitude suggests that we ought to consider geographic sub-regions
424
when investigating possible existence of long term trends. Hence, we pro-
425
duce also zonally averaged radiance that have been averaged across 30◦ wide
426
latitude bands, in addition to the hemisphere-wide calculations we showed
427
in Section 3.1. We chose 30◦ wide regions for simplicity, and to ensure that
428
we do not subsample the data to a point where the signal begins to be lost
429
in the noise. We divide the southern hemisphere observations into polar
430
(60◦ − 90◦ ), mid-latitude (30◦ − 60◦ ) and equatorial (0◦ − 30◦ ) regions. Plots
431
of these regionally averaged data are shown in Fig. 6 for the 1.74µm and
432
2.30µm radiance, and the Carlson et al. (1993) size parameter. The best fit
433
linear trend parameters (I0 , mI ) and their uncertainties (δI0 , δmI ) for each
434
of these regions and spectral windows are shown in Table 1. In addition to
435
this, we calculate the total change in radiance expected from the beginning
436
to the end of the 921-orbit VIRTIS lifetime, if the best fit trends were to per-
437
sist throughout, and the total mission-long variability (standard deviation)
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Figure 6: Regionally segregated time series data for (L−R) 1.74µm radiance, 2.30µm radiance, and Carlson et al. (1993) size parameter, with seven-day averaging applied. The regions are: hemispheric (‘hem’: 0◦ − 90◦ ), equatorial (‘equ’: 0◦ − 30◦ ), mid-latitude (‘mid’:30◦ − 60◦ ), and polar (‘pol’: 60◦ − 90◦ ). Also shown is the best fit trend line to the observed data.
Our strictest criterion for considering a best fit trend (slope) to be sig-
440
nificant requires that the total change in radiance predicted from the slope
441
of the fit (i.e., Norbit × mI ) exceeds the overall variability in (i.e., the stan-
442
dard deviation of) the measured emitted radiance (σI (φ)). That is, the trend
443
is significant only if the long term trend exceeds the per-observation varia-
444
tions. Note that, as expected from the hemispherical averages, the majority
445
of the windows and regions exhibit best fit trends that are consistent with
446
a null result; that is, no change in overall cloud coverage. In fact, only the
447
mid-latitude 1.74µm radiance indicates a significant long-term trend by this
448
criterion. However, the mid-latitude region at 1.74µm and 2.30µm, and the
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size parameter, all exhibit overall tendencies in that are suggestive of long-
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term trends in cloud thickness or particle size population. But, even these
451
long-term variations require several years at their currently measured rates
452
to effect a significant difference in the overall emitted radiance, hence cloud 26
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Table 1: Parameters and their uncertainties to linear best fit to shown wavelength and region. Also included is the overall standard deviation. ‘hem’ represents the hemispheric average (0◦ − 90◦ ); ‘pol’, ‘mid’, ‘equ’ represent 60◦ − 90◦ , 30◦ − 60◦ , and 0◦ − 30◦ , respectively). region I0 δ I0 mI δmI Norb × mI σI p-value 1.74µm W m−2 sr−1 µm−1 W m−2 sr−1 µm−1 d−1 W m−2 sr−1 µm−1 hem 1.094e-01 1.886e-03 1.821e-06 4.569e-06 1.677e-03 6.182e-02 0.0017 pol 9.083e-02 6.720e-04 -3.584e-05 2.160e-06 -3.301e-02 4.052e-02 < 0.0001 mid 1.240e-01 3.896e-04 5.744e-05 8.338e-07 5.290e-02 5.212e-02 < 0.0001 equ 9.923e-02 7.656e-04 5.622e-05 3.114e-06 5.178e-02 6.793e-02 < 0.0001 2.30µm W m−2 sr−1 µm−1 W m−2 sr−1 µm−1 d−1 W m−2 sr−1 µm−1 hem 3.555e-02 5.508e-04 9.752e-06 1.157e-06 8.982e-03 4.055e-02 < 0.0001 pol 2.331e-02 2.925e-04 -1.256e-05 7.176e-07 -1.157e-02 1.720e-02 < 0.0001 mid 4.497e-02 3.554e-05 3.652e-05 7.472e-08 3.363e-02 3.741e-02 < 0.0001 equ 3.456e-02 1.203e-04 3.619e-05 8.334e-07 3.333e-02 5.063e-02 < 0.0001 Size < unitless > < unitless > d−1 < unitless > hem 7.115e-01 3.750e-03 1.270e-05 9.594e-06 1.170e-02 2.053e-01 0.3720 pol 7.479e-01 2.588e-03 1.662e-05 7.172e-06 1.530e-02 2.687e-01 0.3087 mid 6.588e-01 1.266e-03 7.154e-05 3.374e-06 6.589e-02 8.933e-02 < 0.0001 equ 6.448e-01 1.946e-03 5.195e-05 4.824e-06 4.784e-02 2.761e-01 < 0.0001 Elev km km d−1 km hem -1.799e-01 2.484e-02 9.167e-05 5.749e-05 8.443e-02 6.038e-01 0.0827 pol -2.170e-01 1.840e-02 2.911e-05 4.502e-05 2.681e-02 6.287e-01 0.2742 mid -2.342e-01 7.573e-03 1.260e-04 1.144e-05 1.160e-01 5.580e-01 0.2853 equ 2.358e-01 1.702e-02 -4.717e-06 4.029e-05 -4.345e-03 5.888e-01 0.5364 Emis < deg > < deg > d−1 < deg > hem 3.045e+01 7.891e-02 4.124e-03 2.425e-04 3.798e+00 1.692e+01 0.0585 pol 2.017e+01 1.628e-01 9.252e-04 5.886e-04 8.521e-01 9.383e+00 0.0139 mid 3.225e+01 5.829e-02 6.935e-03 1.004e-04 6.387e+00 1.289e+01 0.0394 equ 5.436e+01 7.993e-02 1.103e-02 1.597e-04 1.016e+01 1.181e+01 0.0024 Inc < deg > < deg > d−1 < deg > hem 1.147e+02 1.132e-02 -4.852e-03 1.465e-04 -4.469e+00 1.537e+01 0.1937 pol 1.059e+02 5.452e-02 -3.563e-03 1.294e-04 -3.281e+00 5.886e+00 < 0.0001 mid 1.173e+02 1.240e-02 -4.885e-03 6.183e-05 -4.499e+00 1.174e+01 0.0262 equ 1.272e+02 8.688e-02 -2.186e-03 1.595e-04 -2.013e+00 1.862e+01 0.0843 LST hr hr d−1 hr hem -8.239e-01 8.726e-05 1.467e-03 1.703e-07 1.351e+00 2.458e+00 0.0017 pol -5.108e-01 9.058e-05 5.384e-04 1.833e-07 4.959e-01 1.661e+00 0.2154 mid -7.590e-01 4.815e-05 1.492e-03 1.020e-07 1.374e+00 2.682e+00 0.0056 equ -1.506e+00 1.205e-04 3.028e-03 5.436e-07 2.789e+00 2.920e+00 < 0.0001
453
cover, based on this criterion. A longer time baseline as might be provided
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by the Akatsuki mission could elucidate the persistence or transience of these
455
long-term trends and their significance. Another method of testing the significance of the linear trend is to apply
457
a linear regression analysis to evaluate the correlation between the estimated
458
trend line and the data, compared with the null hypothesis. We calculate
459
the p-value, which is a measure of the probability that random variations
460
can explain the observed distribution as well as the modelled trend. Hence,
461
a p-value of 0.01 indicated that there is a 1% likelihood that the observed
462
data are better fit with random perturbations, and a 99% likelihood that the
463
best fit trend is a better predictor of the observed behavior. While a small
464
value of the p-value can be interpreted to mean the null hypothesis is highly
465
unlikely, it cannot confirm the existence of the posited trend. However, a
466
large p-value can be used to rule out a linear trend in the data. Here, we
467
will assume that a p-value of less than 0.0001 (a 99.99% likelihood that the
468
best fit trend line is a better predictor of the observed changes than random
469
variations) indicates that the trend based on the best fit parameters is likely
470
to be real. The rightmost column in Table 1 shows the calculated p-value
471
for each of the parameters and regions analyzed in this paper. We find that
472
the p-value for the 1.74µm and 2.30µm radiance data in all regions is less
473
than 0.002, and is less than 0.0001 in all but the 1.74µm hemispherical data.
474
We find p-values for the size parameter to be less than 0.0001 in the mid-
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latitude and equatorial data; but larger than 0.3 for the hemispherical and
476
polar data, suggesting that the trends a lower latitudes are more reliable
477
than those at high latitude or planet-wide. However, the calculated trend
478
in the hemispheric and polar size parameter data is very shallow, so there
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is very little difference between the linear best fit and the null hypothesis,
480
once the overall average has been corrected for. Finally, among the geometric
481
parameters analyzed (emission angle, incidence angle, surface elevation, and
482
local solar time), all but a few of the quantities demonstrate relatively large
483
p-values, indicating at least that the linear best fit trends to these quantities
484
are less statistically significant than those discussed above. Furthermore, the
485
absence of significant linear trends found in these parameters suggests that
486
it is unlikely that variations in these geometric parameters are responsible
487
for the long-term trends observed in the radiance data.
488
3.4. 150 day oscillation in the mid-latitudes
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In addition to these long-term trends, a months-long periodic variation
490
can be seen in the mid-latitude region for the 1.74µm and 2.30µm data. Such
491
a periodicity is most noticeable for larger incidence angle restrictions and at
492
mid-latitudes, and was previously suggested by McGouldrick et al. (2012)
493
using a somewhat smaller subset of this data; it is reinforced here with the
494
full dataset. This periodicity is not seen at the shorter wavelengths that
495
are less cloud dominated and more surface dominated. However, this may
496
be a function of our stray light removal technique. Further analysis of the
497
variability of these surface dominated windows is underway. McGouldrick
498
et al. (2012) qualitatively estimated a period of about 140 days. Here, in
499
order to quantitatively determine the periodicity, we applied a least squares
500
sinusoidal fit analysis (LSSA) (Lomb, 1976; Scargle, 1982) to produce a fre-
501
quency spectrum of the 1.74µm radiance, shown in Fig. 7. We perform the
502
LSSA calculation by starting with the time series data shown in Fig. 3, and
503
subtracting the linear trend for the 1.74µm mid-latitude data shown in Ta-
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ble 1, in order to achieve a data set with a mean of zero. We then apply the
505
LSSA calculation to this adjusted radiance data. Fig. 7 shows the LSSA frequency analysis for the mid-latitude (30◦ − 60◦ )
507
data at 1.74µm, 2.30µm, the Carlson et al. (1993) size parameter, and several
508
geometric parameters, with the seven-day averaging applied (i.e., the data
509
shown in Fig. 3). As discussed previously, the seven-day moving average is
510
designed to minimize the regionalism that results from the limited field of
511
view of the VIRTIS-M instrument. By thus averaging the data, we arrive
512
more closely at a measure of the zonally averaged behavior. However, as we
513
will show later, this averaging to ensure a zonally averaged radiance does not
514
appear to affect the values of the measured periods significantly. One period
515
stands clear above all others in each of the 1.74µm and the 2.30µm radiance
516
data periodograms. At 1.74µm, this period is found to be 150.3 days, while
517
at 2.30µm it is found to be 150.5 days. This peak is rather broad, with
518
a half-width of about 20 days, indicating either that this is a quasi-period,
519
whose frequency varies with time, or we have too short a baseline of data
520
for a more precise measurement of the frequency spectrum. It is possible
521
that wavelet analysis (Bravo et al., 2014) of this dataset may resolve this
522
discrepancy; but it is subject to the same difficulties of the sporadic nature
523
and somewhat brief temporal duration of the observations.
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Also shown in Fig. 7 is the periodogram for the Carlson et al. (1993)
size parameter. There are no dominant peaks with significant power in the
526
frequency spectrum. Since our calculation of the size parameter involves a
527
comparison of radiance at two separate bands, it is likely that the odd-even
528
effect discussed by Kappel et al. (2012) may have more of an effect here. Not
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Figure 7: Frequency spectrum for the mid-latitude 1.74µm and 2.30µm radiance, Carlson et al. (1993) size parameter, emission and incidence angles, surface elevation, local solar time, and spectrometer temperature.
only might the radiance in one of the bands fall into an enhanced or a reduced
530
sensitivity pixel of the detector, but since the wavelength registration is non-
531
linear, it is possible that the odd versus even location of each band might
532
not occur in parallel. That is, one band might be enhanced while the other
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533
is reduced. This is possibly also the reason for the larger and more variable
534
standard deviation found in the latitudinal profile of the size parameter data
535
compared with the radiances themselves, as seen in Fig. 5. The lack of a
536
significant peak in the size parameter periodogram around 150 days indicates 31
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that changes in the relative populations of Mode 20 and Mode 3 particles in
538
the clouds of Venus are not likely to be driving the observed periodicity at
539
1.74µm and 2.30µm.
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We compare also the periodograms of various geometrical parameters of
541
the observations, including incidence angle, emission angle, surface elevation,
542
and local solar time. None of these show a significant peak near 150 days,
543
suggesting that changes in the viewing geometry are not responsible for the
544
periodicity seen at 1.74µm and 2.30µm. Notably, the LSSA periodogram
545
does find strong evidence for periodicity in several of the geometric parame-
546
ters, For example, the emission angle and the local solar time show a strong
547
period at about 220 days and 216 days, very close to the 225 day sidereal
548
orbital period of Venus. This is not surprising, since these are both tied to
549
the the viewed phase of Venus by VIRTIS-M-IR, which evolves in parallel
550
with the orbit of Venus around the Sun. In addition, the solar incidence
551
angle and the surface elevation shows a significant peak at 115 days and
552
116 days, almost exactly the Venusian synodic (or solar) day of 116.75 days,
553
as expected. Since the observations in the present analysis are restricted to
554
the night side, and the view of the surface of Venus from VIRTIS will vary
555
along with the orbit of Venus around the Sun, then the surface data that fit
556
our criteria should be seen on a periodicity very closely tied to the synodic
557
period of Venus, or the solar day. That the LSSA finds these periodicities
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in the geometry data that match what would be expected a priori, from the
559
known orbital and observational parameters and criteria, lends further cre-
560
dence to the veracity of the periods measured in the analysis of the radiance
561
data and their absence in the size parameter data.
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Finally, we also compare the periodogram of the spectrometer tempera-
563
ture to the observed radiance variations. Since the wavelength registration
564
of the spectrometer is temperature dependent, and there is evidence for re-
565
maining imperfections in the calibration of the detector (Moinelo et al., 2010;
566
Kappel et al., 2012), changes in the spectrometer temperature might produce
567
spurious changes in measured radiance. However, Fig. 7 shows that the LSSA
568
found no dominant period in the spectrometer temperature. Other relevant
569
instrumental temperatures are measured and reported by the VIRTIS house-
570
keeping, including the focal plane temperature, telescope temperature, and
571
cooling point temperature. We do not reproduce those analyses here because
572
each shows nearly identical periodogram spectra, even as the magnitudes of
573
the temperatures are significantly different.
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562
We have run the LSSA analysis for a number of different averaging win-
575
dow sizes, incidence angle cutoffs, and frequency space resolutions. Although
576
the specific values of the periods change slightly in response to changes in the
577
incidence angle criterion and the size of the averaging window, the salient
578
points mentioned in the discussion of Fig. 7 remain unchanged through each
579
of these. That is, an oscillation is found in the 1.74µm and 2.30µm radiance
580
with a period of about 150 days. None of the other measured or calculated
581
quantities exhibit a dominant periodicity with a similar frequency. The emis-
582
sion angle and local solar time show periodicities of approximately the Venus
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sidereal orbital period. And the surface elevation and solar incidence angles
584
show periodicities of approximately the Venus synodic period, or solar day.
585
The results of these calculations are summarized in Table 2.
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In order to further quantify and characterize the observed variability, in 33
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Table 2: Summary of most prominant period found for each parameter for each tested incidence angle restriction, and each size of the moving window averaging. All units of periods are in days. window min(θinc ) I1.74 I2.30 size θemi θinc elevation LST 95◦ 147.4 146.9 109.2 216.7 116.8 116.8 215.9 100◦ 147.3 146.8 109.6 215.8 117.0 116.6 215.5 1 105◦ 146.7 146.4 41.7 212.7 118.8 116.8 215.5 110◦ 146.6 146.2 253.5 213.8 119.6 116.7 212.1 115◦ 144.6 145.3 247.9 211.4 145.2 119.6 232.1 95◦ 150.3 150.5 245.9 219.0 114.9 116.3 215.2 100◦ 149.9 150.3 108.9 218.5 115.7 116.0 215.1 7 105◦ 149.7 150.0 108.8 218.0 147.4 116.0 214.7 110◦ 149.7 149.9 109.0 217.6 148.7 116.0 214.4 115◦ 146.6 148.8 258.4 217.4 76.8 117.2 227.1 95◦ 150.7 151.0 254.0 218.8 113.6 116.2 215.9 100◦ 150.4 150.8 262.1 219.2 145.4 116.2 215.8 14 105◦ 150.3 150.8 109.1 219.6 146.1 116.0 215.6 110◦ 150.3 150.7 259.3 219.2 147.1 115.9 215.3 115◦ 145.8 148.8 265.9 218.8 76.7 117.1 226.5
Fig. 8, we produce period-folded plots of the parameters analyzed in Fig. 7.
588
Here, we see that the amplitude of the periodic behavior is approximately
589
as large as the the magnitude of the per-observation variability seen in the
590
data. By phase-shifting the period-folded 1.74µm radiance by about 45 days,
591
we can see that the variation can be well matched with a sinusoid with
592
an amplitude that is half of the maximum radiance measured. The phase
593
folded data suggest that the sinusoids describing the near infrared radiance
594
variations may not be quite symmetric. That is, the comparison suggests
595
that the decrease in radiance might occur slightly more quickly than the
596
corresponding increase. In Section 4, we consider potential drivers of the
597
observed variations, and a difference in the rate of increase or decrease in
598
radiance can help to discriminate among the possibilities. However, since the
599
difference between a standard and a skewed sinusoid is so slight, compared
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with the data, we do not make any conclusions based on the shape of the
601
curve at this time.
602
4. Discussion
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600
Here we explore some various drivers of the observed variations and con-
604
sider their likelihood, based on the analyzed data set and other constraints.
605
We report a possible long-term increase in 1.74µm and 2.30µm radiance
606
at mid-latitudes, that would indicate an overall reduction in total cloud opac-
607
ity in this region. This increase in mid-latitude radiances is accompanied by
608
a decrease in polar radiances. On a hemisphere-wide averaging, there is little
609
change seen in these radiances over the course of the VIRTIS-M-IR instru-
610
mental lifetime. These trends are not consistent with a scenario in which the
611
observed decrease in SO2 at higher altitudes reported by Marcq et al. (2012)
612
is coupled with a conversion of SO2 into H2 SO4 and thence into clouds. Hence
613
some other sink for the SO2 loss observed must be found. However, as the
614
observed trends are barely larger than the overall variance in the data, more
615
detailed analysis of this and future data (including the Akatsuki mission) will
616
be required for more definitive conclusions.
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Previous investigations have reported increases in wind speeds in the
618
Venus atmosphere over time (Khatuntsev et al., 2013; Kouyama et al., 2013).
619
These investigations interpret motions of high contrast features in the re-
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flected sunlight at ultraviolet wavelengths as indicators of local wind speeds
621
at an altitude of the cloud tops, around 70km above the surface of the planet.
622
There remains some ambiguity as to whether these measured winds are in-
623
dicative of the true wind speeds of the features themselves, or of the large 35
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Figure 8: Phase-folded data for the mid-latitude data, for each of the parameters shown in the previous figures, with seven-day averaging applied, assuming the period found by LSSA having the greatest spectral power for each parameter. The radiance curves are phase shifted by 45 days to align with the baseline sinusoid. Phase shifts of −75 days, 25 days, 30 days, −50 days, and 45 days have been added to the plots of size parameter, emission angle, incidence, angle, surface elevation, local solar time, and spectrometer temperature, respectively.
36
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scale dynamics (similar to the “steering winds” at 500mb on Earth that
625
transport tropical and extratropical cyclones), or of morphological or com-
626
positional changes. However, if we accept that the measured wind speeds
627
are representative of the overall dynamics of the Venus atmosphere, then the
628
increase in the mean zonal wind speeds reported by both Khatuntsev et al.
629
(2013) and Kouyama et al. (2013) would imply that some mechanism is act-
630
ing that either adds momentum to the atmosphere as a whole, or transports
631
momentum from another atmospheric region to the level of the cloud tops
632
seen in ultraviolet wavelengths. If momentum is being transported to this
633
region of the atmosphere, then so too must energy be transported. Such a
634
transport of energy could manifest itself as an increase in local temperature
635
at regions where the clouds have been accelerated by the deposition of mo-
636
mentum. Another possibility is that the energy could be trasnported in the
637
form of latent heat, but the very small mass of the Venus clouds tends to pre-
638
clude latent heat as an efficient means of energy transport. Because the vapor
639
pressure of the sulfuric acid cloud particles is so small, small changes in tem-
640
perature tend to have rapid and significant effects on the mass and opacity
641
of the Venus clouds (McGouldrick and Toon, 2007). This increase in radi-
642
ance emitted from the cloud-dominated spectral windows at equatorial and
643
mid-latitudes, coupled with the decrease in radiance at polar latitudes could
644
indicate a net transport of energy from high to low latitude over the course
CE
PT
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624
of these observations. Such an energy transport would be consistent with
646
the increase in momentum seen by Khatuntsev et al. (2013) and Kouyama
647
et al. (2013). It is beyond the scope of this paper to thoroughly compare
648
the variation in the previously measured wind speeds at the cloud tops using
AC 645
37
ACCEPTED MANUSCRIPT
VMC ultraviolet data with the emitted radiance through the condensational
650
(and photochemical) clouds of Venus using VIRTIS infrared data, but we
651
note that the apprearance of a correlation suggests fertile ground for future
652
comparison.
CR IP T
649
We might consider that this 150-day oscillation is a manifestation of a
654
Hadley-like meridional circulation in the clouds. If we consider a meridional
655
circulation cell that runs from the equator to about 50◦ latitude, consistent
656
with previous models by Imamura and Hashimoto (1998), then we calculate
657
an average meridional wind speed of only 0.9 m/s. Hueso et al. (2012, 2015),
658
using VIRTIS-M-Vis ultraviolet observations, and Khatuntsev et al. (2013),
659
using VMC ultraviolet observations, report meridional wind speeds peaking
660
at about 10 m/s in the poleward direction at a latitude of around 50◦ -55◦ ,
661
and decreasing to 0 m/s at the pole and equator. They each interpret this as
662
a manifestation of a hemispherical-scale Hadley-like meridional circulation
663
cell. If we assume a sinusoidal shape to the meridional wind speed as a func-
664
tion of latitude, then we can estimate the average flow speed over the entire
665
cell to be about 6 m/s. Hence, the timescale for the Hadley-like meridional
666
circulation would then be about 35 days, much shorter than the periodicity
667
measured here. Note that Hueso et al. (2015) report measured meridional
668
wind speeds of a few m/s in infrared wavelengths (corresponding to similar
669
altitudes to those inhabited by the clouds that drive the radiance variations
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653
anlayzed here). However, they also point out that their measured wind speed
671
is significantly smaller than their measured standard deviations, indicating
672
that the meridional circulation likely has its return branch at a deeper alti-
673
tude than that occupied by the clouds. Hence, for the meridional circulation
AC 670
38
ACCEPTED MANUSCRIPT
to directly affect the properties of the condensational clouds between about
675
50 km and 57 km that are analyzed here, there would need to be a verti-
676
cal wander of the mean circulation. Similar wanderings of the meridional
677
circulation were found in VenusCAM General Circulation Model simulations
678
by Parish et al. (2011). However, subsequent analysis showed that a later
679
version of VenusCAM that addressed a number of angular momentum errors
680
did not show as significant a variation (Lebonnois et al., 2012).
CR IP T
674
The 150 day oscillation is closer in magnitude to the time scale for the
682
meridional circulation assumed in the models of Imamura and Hashimoto
683
(1998). Imamura and Hashimoto (1998) prescribed a meridional Hadley-like
684
circulation with a cycle timescale of 90 days. This would correspond to a
685
maximum mid-latitude merdional cloud top wind speed of a few m/s, or a
686
factor of three or so smaller than the wind speed reported from the Venus
687
Express observations described above. Based on the results of Imamura and
688
Hashimoto (1998), who considered the effect of a variation in the magnitude
689
of the meridional circulation, a meridional Hadley-like circulation with a
690
150 day timescale would produce smaller latitudinal contrasts in cloud opac-
691
ity than those that are observed. This occurs because for slower circulations,
692
particle sedimentation timescales become moree important to the cloud par-
693
ticle lifetimes than the meridional transportation timescales. Note that the
694
Imamura and Hashimoto (1998) models did not consider effects of the zonal
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681
circulation, having treated a 2D (latitude-altitude) model. The 2D cloud
696
structure found by Imamura and Hashimoto (1998) was consistent with lat-
697
itudinal opacity variations derived from the observations of Venus by Crisp
698
et al. (1989) and Chanover et al. (1998), indicating that the magnitude of
AC 695
39
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the meridional circulation that Imamura and Hashimoto (1998) proposed is
700
consistent with observations. Our long-term average latitudinal profiles also
701
are consistent with the previous work by Crisp et al. (1989) and Chanover
702
et al. (1998), suggesting that the meridional circulation remains similar to
703
that postulated by Imamura and Hashimoto (1998). However, our analysis
704
does not investigate potential temporal variations in the latitudinal profile,
705
which might indicate variations in the magnitude of the meridional circu-
706
lation. It is difficult to achieve a high level of confidence in the temporal
707
variations in latitudinal profiles using VIRTIS-M-IR data, because the spa-
708
tial coverage is so limited. Perhaps the Akatsuki mission (Nakamura et al.,
709
2016), with its more equatorially-inclined orbit, and frequent high spatial
710
resolution full-disk imaging capability, might address this issue.
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699
In addition to the long-term trend in the measured wind speeds, previous
712
investigators such as Khatuntsev et al. (2013) and Kouyama et al. (2013)
713
have indicated periodic variations in the wind speeds. Kouyama et al. (2013)
714
reported a 255 day period in their measured wind speeds; but this does not
715
seem to be related to the 150 day period found here. Furthermore, their
716
analysis does not find a comparable periodicity near 150 days. Khatuntsev
717
et al. (2013) reports on a number of short-period (4 − 5 days) oscillations
718
in their measured wind speeds, and also some weaker 238 day and 117 day
719
periods; but these are probably related to Venus orbital characteristics, and
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711
in any case, are not very close to the 150 day period presented in this paper.
721
We note that the 150 day period is approximately 2/3 of the Venus sidereal
722
orbital period. Perhaps the periodic variations seen in the clouds are an
723
indication of a 3:2 resonance between the meridional Hadley-like circulation
AC 720
40
ACCEPTED MANUSCRIPT
724
and solar influences (such as solar tides). Looking toward microphysical phenomena, we compare the observed pe-
726
riodicity to the sedimentation and eddy diffusion (or, effectively, convective)
727
timescales in the clouds. We noted previously that the Carlson et al. (1993)
728
size parameter does not indicate an oscillation at the period exhibited by
729
the 1.74µm and 2.30µm radiances, consistent with the findings of Barstow
730
(2012). This behavior suggests that large scale changes in the ratio of the
731
number of Mode 3 particles to the number of Mode 20 particles are not re-
732
sponsible for the radiance variations observed. Now, there is sufficient vari-
733
ation in the calculated size parameter over the course of the observations
734
reported here that we cannot say with certainty that the size parameter does
735
not change at all during the course of the oscillation in the radiances. But
736
we can say that if changes in the size parameter were driving the radiance
737
changes seen, then a 150 day period should have appeared in the size param-
738
eter periodogram.
ED
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725
That it does not can only mean that either 1) only Mode 3 particles
740
are growing larger (and smaller) to drive the oscillation, or 2) both Mode 20
741
and Mode 3 are increasing (and decreasing) in total number concentration
742
at similar rates. For the remainder of the discussion in this paragraph, we
743
invite the reader to please consult Figure 1a of Grinspoon et al. (1993).
744
That figure shows the extinction coefficients of the four traditional modes
CE
PT
739
of cloud particles generally used in radiative transfer analysis of the Venus
746
atmosphere. Note that the extinction coefficient of the Mode 3 particles is
747
essentially flat between 1.74µm and 2.30µm, while the extinction coefficient
748
for each of the Mode 2 and Mode 20 particle modes exhibits a strong gradient
AC 745
41
ACCEPTED MANUSCRIPT
with increasing wavelength between these two spectral windows. Hence, the
750
size parameter is most strongly affected by changes in the size of the Mode 2
751
(or Mode 20 ) particles, or by changes in the relative numbers of the Mode 3
752
and Mode 2 (or Mode 20 ) particles. But, it is less strongly affected by changes
753
in the size of the Mode 3 particles. In the 2.30µm radiance (cloud opacity)
754
and the 1.74µm radiance (cloud opacity), we observe parallel variations, while
755
noting an absence of a parallel variation in the size parameter. A change in
756
Mode 3 particle size alone will increase the opacity of the clouds, but will have
757
minimal effect on the size parameter, since the effect of the change in opacity
758
will be comparable at the two wavelengths. Thus, an increase in Mode 3
759
particle size, while the number remains constant, and while the Mode 20
760
number and size remain constant would be consistent with the observations
761
reported here. Similarly, if the numbers of Mode 20 and Mode 3 particles
762
increase in a comparable manner (the more traditional interpretation of the
763
size parameter), then we would expect an increase in opacity with a relatively
764
unchanged size parameter.
ED
M
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749
If both modes of particles are considered to be sulfuric acid, then simple
766
growth and evaporation mechanisms would suffice to explain changes in total
767
particle number (option 2). But for one mode to increase in size while the
768
other mode does not (option 1) would require either that the two modes have
769
distinct compositions or that they are a single modal size distribution with a
CE
PT
765
consistent composition that has been mistaken for two distinct populations,
771
as Toon et al. (1984) have suggested. Furthermore, this would rule out
772
coagulation processes as driving the observed variations, since this would
773
preferentially increase the number of larger particles at the expense of the
AC 770
42
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smaller particles. Of course, since coalescence time scales are so slow for
775
the conditions in the condensational cloud (McGouldrick, 2007), it would be
776
difficult to imagine them driving such variations.
777
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774
Since the clouds that are the primary drivers of opacity differences at
1.74µm are located between about 50 km and 57 km, we consider the timescales
779
for particles to fall through such a 7 km distance. Furthermore, since the
780
sedimentation can only remove particles from the clouds, we need another
781
mechanism to re-supply the cloud mass. So, we consider half the period to
782
be the relevant timescale to compare to sedimentation processes. Thus, for
783
a particle falling through the Venus atmosphere from an altitude of about
784
57 km to an altitude of about 50 km in a time of about 75 days, requires
785
a sedimentation velocity of 0.11 cm/s. The gravitational sedimentation ve-
786
locity of a droplet falling through a medium is given by Seinfeld and Pandis
787
(1998) as:
M
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778
ED
vsed =
2 rp2 ρp gCc 9 µ
(6)
where rp is the radius of the particle, ρp is its mass density (about 1.75 g/cm3 ),
789
g µ is the viscosity of the medium (about 2 × 10−4 cm·s for this region of the
790
Venus atmopshere), and Cc is the unitless “Cunningham slip-correction fac-
791
tor,” which for a 0.1µm particles is about 3, is about 1.2 for a 1µm radius
792
particle, and asymptotes to 1.0 for particles with radius larger than ∼ 3µm.
793
The sedimentation velocity for a typical Mode 3 particle (3.65µm) under
AC
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PT
788
794
these consitions is 0.23 cm/s, while that of a Mode 20 particle having a
795
1.4µm radius is 0.041 cm/s, and of a Mode 2 particle with a 1.0µmradius
796
is 0.021 cm/s. For a gravitational sedimentation velocity of 0.11 cm/s, and
797
expecting a particle radius near 1µm, consistent with previous in situ and 43
ACCEPTED MANUSCRIPT
remote measurements of the Venus clouds (Knollenberg and Hunten, 1980;
799
Grinspoon et al., 1993), Eq. 6 can be solved to find a particle size, rp = 2.2µm.
800
If instead, we allow for very large particles (typical of Mode 3 and larger)
801
by using a slip correction factor of 1.0, then we find a typical particle size
802
of rp = 2.4µm. This is located between the sizes of the Mode 20 and the
803
Mode 3 particles generally considered to exist in the Venus condensational
804
clouds. Hence, it is plausible that the clearing of the clouds (the increase in
805
radiance) is consistent with rainout of the typically 1 − 3 µm-sized droplets
806
in the Venus condensational clouds. If we consider instead a 10 km thick
807
layer through which the particles must fall – which is plausible since a 47 km
808
cloud base is not unreasonable, based on other analyses (Barstow et al.,
809
2012) – then we find a typical particle size of 2.6 − 2.8µm, which is even
810
closer to the Mode 3 population. However, if the Mode 3 particles are sim-
811
ply a large-radius tail of the Knollenberg and Hunten (1980) Mode 2, as
812
suggested by Toon et al. (1984), then the typical modal radius of Mode 20
813
would be pulled to larger values, possibly consistent with these calculations.
814
In fact, these calculated modal radii would equate to effective radii (i.e.,
815
area-averaged radii) of between 2.8µm and 3.7µm, a range that includes
816
the effective radii found in microphysics simulations of the condensational
817
cloud driven by radiative-dynamical feedback (McGouldrick and Toon, 2007;
818
McGouldrick, 2016). Note also that changes in the typical radius of cloud
CE
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M
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798
particles in the range from 2.2µm to 2.8µm will have minimal effect on the
820
Carlson et al. (1993) size parameter in most cases, since the Mie scattering
821
spectrum would more closely resemble Mode 3 than Mode 20 at these radii,
822
and hence would lie in a relatively flat part of the Mie scattering spectrum,
AC 819
44
ACCEPTED MANUSCRIPT
823
according to previous work by Grinspoon et al. (1993), cf. their Figure 1a. If we next consider the particle lifetime being driven by the eddy diffusion
825
time scale, (∆z)2 /κdif f , then we find that a typical eddy diffusion coefficient
826
of κdif f = 8 m2 /s is required to fully mix a 10 km thick region within the
827
75 day observed timescale, while an eddy diffusion coefficient of 15 m2 /s is
828
required to fully mix a 7 km layer. Each of these also are consistent with
829
the time-averaged eddy diffusion coefficients that were obtained from the
830
radiative-dynamical simulations by McGouldrick and Toon (2007).
832
AN US
831
CR IP T
824
Finally, the radiative time constant for cooling from the altitude of the condensational clouds of Venus can be calculated as
F
,
(7)
M
τrad =
cp Pg Tmean
where P/g is the total atmospheric column mass above the altitude in ques-
834
tion (in this case, the condensational cloud tops at about 50 kPa), cp ∼
835
800 J/kg/K is the specific heat capacity of the Venus atmosphere averaged
836
across that layer, Tmean ∼ 230 K is the mean temperature above the cloud
ED
833
tops, and F = 157 W/m2 is the emitted flux. The values of the atmospheric
838
values listed above are calculated from the standard Venus International
839
Reference Atmosphere (Seiff et al., 1985). The emitted flux is calculated by
840
assuming that Venus has a Bond albedo of 0.76 (Moroz et al., 1985) and that
841
the globally averaged emitted flux exactly balances the globally averaged
842
incident solar flux. Performing this calculation, we find a radiative cooling
843
time scale of about 76 days, almost exactly half the observed periodicity.
844
Combining this with the eddy diffusional time scale above (which was driven
845
by radiative heating of cloud base and cooling from the condensational cloud
AC
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PT
837
45
ACCEPTED MANUSCRIPT
tops), we suggest that the 150 day period we see in the 1.74µm mid-latitude
847
radiance measured by VIRTIS-M on Venus Express is sustained by an inter-
848
action between radiative cooling and microphysical cloud processes, similar
849
to those demonstrated by McGouldrick and Toon (2007).
CR IP T
846
Please note that, since the tendencies plotted here are averaged over large
851
areas and times, and since the known spatial and temporal variability in the
852
Venus condensational clouds is very large, it will be necessary to explore
853
these relationships on shorter timescales; work that we are preparing for a
854
future paper.
855
5. Conclusions
AN US
850
We have presented analysis of the complete Venus Express VIRTIS-M-IR
857
data set for night side thermal emission in the near infrared spectral win-
858
dows for all southern hemisphere observations made before the failure of the
859
instrument’s cooling system after orbit 921 (2008 October 27). We find no
860
clear evidence of global long-term increase or decrease in the overall radiance
861
(hence overall cloud coverage and thickness) from analysis of just the 1.74µm
862
and 2.30µm spectral windows that are most sensitive to the cloud variations.
863
However, at mid-latitudes, the radiance steadily increases through the dura-
864
tion of the VIRTIS-M-IR lifetime, while steadily decreasing with time near
865
the poles. This may be an indication of a transfer of cloud mass poleward,
AC
CE
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M
856
866
an inhibiting of heat transfer by the meridional circulation, or subtle vertical
867
or meridional wanderings of the meridional circualtion cell. This long-term
868
radiance trend might represent a manifestation of heat energy transport in
869
parallel with the momentum transport indicated by the variations in zonal 46
ACCEPTED MANUSCRIPT
870
wind speeds previously inferred from cloud tracking studies. Our global analysis of the Carlson et al. (1993) size parameter demon-
872
strates an overall increase in size parameter, hence particle size, from equator
873
to pole, consistent with previous particular analysis by Wilson et al. (2008).
874
We also note a subtle increase in the size parameter peaking at about −20◦
875
latitude; but it is difficult to state its existence with certainty, due to the
876
increasing magnitude of the standard deviation of the calculated size param-
877
eter in the equatorial latitudes observed by VIRTIS-M-IR, possibly amplified
878
by instrumental artifacts.
AN US
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871
We observe in the VIRTIS-M-IR data that the 1.74µm and 2.30µm win-
880
dows demonstrate local maxima in radiance peaking around 50◦ latitude,
881
consistent with previous observations of these spectral windows, dating to
882
the time of their discovery in the 1980’s. We also measure a large amount of
883
variability to the typical cloud coverage as at latitudes between 0◦ and 60◦ ,
884
as evidenced by the very large standard deviations about the mean in the
885
cloud-dominated windows at those latitudes.
ED
M
879
Finally, we report the existence of a roughly 150-day periodic variation
887
in the cloud coverage, seen most prominently at mid-latitudes in the 1.74µm
888
radiance data. A least squares frequency analysis quantifies this period that
889
was suggested in earlier work by McGouldrick et al. (2012). The timescale
890
is consistent with a cloud formation and evolution cycle that is driven by
CE
PT
886
the radiative dynamical feedback and gravitational settling of particles with
892
sizes typical of the condensational clouds. Further modeling investigations
893
will be necessary to elucidate the drivers of this periodicity in the clouds.
AC 891
47
ACCEPTED MANUSCRIPT
894
6. Acknowledgments This work was supported through NASA Planetary Mission Data Analysis
896
Program Grant Number NNX14AP94G, and greatly benefitted from discus-
897
sions sponsored by the International Space Sciences Institute (ISSI). This
898
manuscript was much improved thanks to thoughtful and helpful reviews by
899
Nils Mueller and Jo Barstow.
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