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Bimodal Distribution of Sulfuric Acid Aerosols in the Upper Atmosphere of Venus
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Peter Gao1*, Xi Zhang1, David Crisp2, Charles G. Bardeen3, and Yuk L. Yung1
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USA, 91125
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Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, CA,
Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USA, 91109
National Center for Atmospheric Research, Boulder, CO, USA, 80301
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*Corresponding author: pgao@caltech.edu
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Abstract
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Observations by the SPICAV/SOIR instruments aboard Venus Express have revealed that the upper
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haze (UH) of Venus is variable on the order of days, and that it is populated by two particle modes. In
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this work, we posit that one mode is made up of cloud particles that have diffused upwards from the
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cloud deck below, while the other mode is generated by the in situ nucleation on meteoric dust. We
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also posit that the variability is caused in part by transient winds. We test this hypothesis with the
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Community Aerosol and Radiation Model for Atmospheres. Using the meteoric dust production profile
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of Kalashnikova et al. (2000), the sulfur condensation nuclei and sulfuric acid vapor production profiles
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of Imamura and Hashimoto (2001), we numerically simulate a column of the Venus atmosphere from
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40 to 100 km above the surface. Our aerosol number density results are consistent with Pioneer Venus
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data from Knollenberg and Hunten (1980), while our gas distribution results match that of Kolodner
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and Steffes (1998) below 55 km. The size distribution of cloud particles shows two distinct modes,
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qualitatively matching the observations of Pioneer Venus. We also observe a third mode in our results
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with a radius of a few μm at 48 km altitude, supporting the existence of the controversial third mode in
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the Pioneer Venus data. This mode disappears if coagulation is not included in the simulation. The UH
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size distribution shows two lognormal distributions overlapping each other, possibly indicating the
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presence of the two modes, though they are not distinct. Simulating the atmospheric column with only
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meteoric dust input and with only sulfur nuclei input show that the combined UH size distribution is in
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essence the sum of the size distributions of these two cases. The results of the transient wind
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simulations yield a variability timescale that is consistent with Venus Express observations, as well as a
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clear bimodal size distribution in the UH.
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Keywords: Abundances, atmospheres; Atmospheres,
Atmospheres, dynamics; Venus; Venus, atmosphere
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composition;
Atmospheres,
structure;
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1. INTRODUCTION
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Sulfuric acid aerosols make up most of the global cloud deck and accompanying hazes that
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shroud the surface of Venus (Esposito et al. 1983). As a result, the radiation environment and energy
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budget at the surface and throughout the atmosphere is strongly affected by the vertical extent and size
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distribution, and thus the mean optical properties, of these particles. These aerosols also serve as
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storage for sulfur and oxygen, and so make up a major part of the global sulfur oxidation cycle due to
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transport by atmospheric circulation and sedimentation (Mills et al. 2007).
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Observations from the Pioneer Venus atmospheric probes (Knollenberg and Hunten 1980)
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helped constrain the number density and size distribution of the aerosols in the cloud deck, and
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revealed the possibility of two size modes, along with a third, controversial mode that may or may not
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exist (Toon et al. 1984). The clouds were also vertically resolved into three distinct regions: the upper
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cloud, from 58 to 70 km; the middle cloud, from 50 to 58 km; and the lower cloud, from 48 to 50 km
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(Knollenberg and Hunten 1980). The middle and lower clouds appear to be much more variable than
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the upper cloud. These observations have been interpreted using numerical models that take into
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account transport and/or aerosol microphysics. According to Krasnopolsky and Pollack (1994), for
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instance, the lower cloud is formed from the upwelling and subsequent condensation of sulfuric acid
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vapor due to the strong gradient in sulfuric acid mixing ratio below the clouds. James et al. (1997)
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showed that this process is very sensitive to the local eddy diffusion coefficient, and suggested that the
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variability of the lower and middle clouds was tied to the dynamical motions of the atmosphere in this
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region. This conclusion was also reached by McGouldrick and Toon (2007); they showed that
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organized downdrafts from convection and other dynamic processes could produce holes in the clouds.
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Indeed, observations from Pioneer Venus indicated that this region of the atmosphere has a lapse rate
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close to adiabatic, with parts of the middle cloud region being superadiabatic (Schubert et al. 1980).
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Imamura and Hashimoto (2001) modeled the entire cloud deck, and reached many of the same
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conclusions as James et al. (1997) and Krasnopolsky and Pollack (1994) regarding the lower and
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middle clouds. They also concluded that the upper cloud was a product of photochemically produced
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sulfuric acid vapor condensing on sulfur nuclei that are also photochemically produced, and that an
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upward wind may be necessary in order to reproduce the observations.
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The clouds lie below an upper haze (UH), which extends from 70 to 90 km (Mills et al. 2007).
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In Imamura and Hashimoto's model (2001), small particles are lofted by the aforementioned upward
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wind out of the top of the model domain, which would place them in this UH. This demonstrates that
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dynamical processes, regional and/or global, will lead to some mixing of the haze with the clouds and
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that variability will be high. This is reflected in data from the Pioneer Venus Orbiter Cloud
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Photopolarimeter (OCPP), which revealed latitudinal variations of an order of magnitude in haze
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optical thickness from the polar region (where it is more abundant) to the tropics, as well as temporal
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variations on the order of hundreds of days (Kawabata et al. 1980). More recently, Wilquet et al. (2009,
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2012) used Venus Express SPICAV/SOIR solar occultation observations to show the existence of
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bimodality in the size distribution of the UH, with a small mode of radius 0.1-0.3 μm, and a large mode
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of radius 0.4-1.0 μm. Interestingly, the mean size of the haze particles as reported by Kawabata et al.
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from OCPP measurements 30 years earlier (0.23 ± 0.04 μm) lies well within the small mode size range,
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suggesting that the large mode may be a transient population. In addition, the extinction of the haze
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was observed to vary by as much as an order of magnitude in a matter of days. The degree of
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variability also changed, as observations a few months later showed time variability in the haze
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extinction of only a factor of two. Time variability of the haze was also reported by Markiewicz et al.
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(2007), who showed infrared images of the Venus southern hemisphere where the appearance of the
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haze changed dramatically across tens of degrees of latitude, also in the span of a few days. Both of the
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above studies showed that the haze optical depth could exceed unity, making it an active participant in
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the regulation of solar radiation reaching lower altitudes, and its variability a property that requires
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better understanding. However, numerical models with adequate microphysics that include the UH are
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rare. Yamamoto and Tanaka (1998) and Yamamoto and Takahashi (2006) included the UH in their
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simulations of aerosol transport via global atmospheric dynamics and reproduced much of the
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observations satisfactorily. However, the aerosol microphysics in both studies is inadequate due to the
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lack of a detailed treatment of nucleation.
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In this study, we investigate the formation and evolution of the UH by constructing a one-
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dimensional (1D) microphysical and vertical transport model that couples the clouds to the haze with a
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more detailed treatment of the microphysics involved. We propose that the haze's bimodality is
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representative of two processes at work, each producing its own haze particle population. One process
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involves the lofting of cloud particles into the haze via winds and eddy diffusion, while the other
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process involves the in situ condensation of sulfuric acid vapor onto meteoric dust, a possibility
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discussed by Turco et al. (1983) for terrestrial atmospheres. This latter process depends on the injection
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of sulfuric acid vapor into the UH, which can be done by the same processes that lofts particles into this
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region. If the injection is indeed done mainly by diffusive or advective processes, then the variability of
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the haze would be easily understandable, as transport is highly variable; the haze would grow in extent
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after a “random” injection of sulfuric acid vapor, and then dissipate as the larger particles fall out.
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Behavior such as this may be more frequent near the poles due to the dynamic nature of the polar
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vortices (Luz et al. 2011), creating the spatial variability between the poles and the tropics observed by
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Kawabata et al. (1980).
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We describe our basic model in section 2, with emphasis on the model attributes unique to our
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case of aerosols in the Venus atmosphere, such as the addition of meteoric dust as condensation nuclei
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and the effect of winds. In section 3 we present our model results, along with comparisons with data
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from Pioneer Venus and Venus Express. We also discuss our results in the context of physical processes
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involved in our model, focusing on the effects of cloud processes on the properties of the UH, as well
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as the sensitivity of the steady state to different initial conditions. We summarize our work and state our
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conclusions in section 4.
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2. MODEL
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We use version 3.0 of the Community Aerosol and Radiation Model for Atmospheres
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(CARMA) as our base microphysical and vertical transport code. The model is an upgrade from the
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original CARMA (Turco et al. 1979, Toon et al. 1988) by Bardeen et al. (2008). We will describe our
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model setup and departures from the base model below, and we refer the reader to Turco et al. (1979),
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Toon et al. (1988, 1989), and Jacobson et al. (1994) for detailed descriptions of the microphysics and
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vertical transport in CARMA. Our departures from the model include the conversion from a simulation
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of Earth's atmosphere to Venus' atmosphere, the addition of gas transport and eddy diffusion, the use of
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meteoric dust as condensation nuclei, and the addition of transient winds.
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2.1. Model Setup
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The basic processes we model are the nucleation of liquid sulfuric acid droplets on soluble
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condensation nuclei, the condensational growth, evaporation, and coagulation of these particles, and
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their transport by wind and diffusion.
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Table 1 compares several quantities that were changed for this model in order to convert it from
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an Earth simulation to a Venus simulation. In addition, the temperature and pressure profiles are
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significantly different between the two planets. Figure 1 shows the profiles used (Seiff et al. 1985),
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which were fixed in the model.
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The model atmosphere extends from 40 to 100 km, covering the altitudes of the cloud deck and
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UH. This vertical range in the nominal case is split into 300 levels of 200 m thickness each. Cases
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where the vertical resolution was doubled (i.e. the setup of Imamura and Hashimoto's model (2001))
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showed no significant changes and therefore were discarded to save computing resources.
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In order to cover the range from meteoric dust to large droplets and represent both volatile and
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nonvolatile particles, we use two groups of particle bins each covering the radius range from 1.3 nm to
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~30 μm. The lower radius limit is set to correspond to the size of meteoric dust as described in
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Kalashnikova et al. (2000), while the upper radius limit is set to the upper limit of Imamura and
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Hashimoto's model (2001). We tested both volume doubling and volume tripling between successive
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bins, resulting in 45 and 29 total bins, respectively. The latter case was used for the transient wind
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simulations (described in section 2.5) in order to save on computation time. Comparison of the 45 and
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29 bin cases showed that, although the size resolution decreased, the basic shape and dispersion of the
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size distribution remained consistent. Both cases are considered here, however, as the 45 bins case
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shows details in the size distribution not found in the 29 bins case. It should be noted that the inclusion
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of multiple bins for nonvolatile particles differs from the approach by Imamura and Hashimoto (2001),
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and allows for a more realistic treatment of the consequences of coagulation. For instance, the
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nonvolatile particle produced from the evaporation of a droplet originally formed from the coagulation
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of smaller droplets would be larger than the condensation nuclei that went into forming the original
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droplets, assuming they have not gone through coagulation themselves. This would have the effect of
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producing fewer, larger nonvolatile particles compared to Imamura and Hashimoto's model (2001).
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Our nominal time step is 10 seconds. To test the robustness of the model, we both increased and
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decreased this by an order of magnitude. In the case where the time step was 100 seconds, numerical
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instabilities appeared in the results; therefore, this case was not considered. In the case where the time
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step was 1 second, the results were similar to those at 10 seconds and were therefore not needed. We
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found that a simulation time on the order of 107 seconds, or about 100 Earth days, was necessary for
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the model to reach steady state. This is similar to the advective exchange time and the characteristic
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vertical diffusion time of the Venus mesosphere calculated by Imamura (1997).
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The sensitivity of the results after 107 seconds to the initial conditions is tested by using two
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different initial conditions. In case 1, we begin each run with no model-relevant species in the model
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box, e.g. no sulfuric acid vapor or condensation nuclei of any kind. This case would be consistent with
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the photochemical model of Yung and DeMore (1982) and Krasnopolsky and Parshev (1983), where
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both the sulfuric acid vapor and the sulfur that is assumed to make up the condensation nuclei are
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produced at the same time:
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3SO2  2H 2O  S  2H 2 SO4
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Therefore, either both species are present, or none are. However, in the case where both are present, it
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is likely that nucleation would occur before a large amount of condensation nuclei is built up, e.g. the
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initial conditions of Imamura and Hashimoto (2001); therefore, we conclude that the empty-box initial
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condition that we use here is more realistic. Case 2 allows for an initial mixing ratio of H2SO4 vapor of
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4 ppm across all altitudes, again similar to those of Imamura and Hashimoto (2001). This would
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correspond to the case where the condensation nuclei are not produced via reaction 1 above and which
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in fact would have an unknown origin and make-up. This is similar to the simulations by James et al.
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(1997), where the only property of the condensation nuclei of the best-fit model was that it was soluble.
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Thus, the sulfuric acid vapor can persist in large quantities (e.g. 4 ppm) until condensation nuclei
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appear by some unknown mechanism.
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During each model run, mass is injected into the model atmosphere in the form of sulfuric acid
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vapor and condensation nuclei. The latter is split into two populations, one corresponding to
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photochemical products, and one corresponding to meteoric dust. As a result, the density of the
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condensation nuclei is chosen to be 1.9 g cm-3, as an average between the density of sulfur (1.8 g cm-3,
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Imamura and Hashimoto 2001) and meteoric dust (2.0 g cm-3, Hunten et al. 1980). Both populations are
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treated the same – as soluble nuclei that are “activated” upon condensation of sulfuric acid vapor on
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their surfaces, similar to James et al. (1997). We again emulate Imamura and Hashimoto (2001) by
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assigning the photochemical products to be mode 1 particles, with radius 0.152 μm in the 29 bins case,
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and 0.166 μm in the 45 bins case. The difference comes from starting the bin sizes at the same quantity
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(1.3 nm), and increasing the bin sizes at different rates (volume-doubling vs. volume-tripling).
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We initially used the same production profiles of sulfuric acid vapor and photochemical
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condensation nuclei as Imamura and Hashimoto (2001) for the production rates PH2SO4 and PCN,
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respectively:
PH 2SO4   p g ( z) cm 2 s 1
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PCN
 4 3
1
  p g ( z ) CN rCN
2
 Ms 3



1
cm 2 s 1
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Where σp is the column-integrated production rate of sulfuric acid vapor, 1012 cm-2 s-1; the function g(z)
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is a gaussian with a peak at 61 km altitude and full-width-half-max of 2 km; ρCN is the density of the
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condensation nuclei, 1.9 g cm-3; rCN is the radius of the condensation nuclei, 0.152 and 0.166 μm; and
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Ms is the molecular mass of sulfur. However, our results showed that agreement between model and
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data was best if the above rates were both halved, which are still within the bounds given by Yung and
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DeMore (1982) and Krasnopolsky and Parshev (1983), 2x1011 to 1013 cm-3s-1. Thus, our nominal values
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for the above quantities are half that of Imamura and Hashimoto (2001), and our nominal production
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profiles are plotted in Figure 2. For simplicity, the production rate of the condensation nuclei at 61 km
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is identical whether we assume they are made of sulfur (case 1) or an unknown compound (case 2).
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We adopt a similar lower boundary condition as those of Imamura and Hashimoto (2001),
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where mode 1, nonvolatile particles of size ~0.17 μm are fixed to have a number density of 40 cm-3 in
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accordance with LCPS data (Knollenberg and Hunten 1980). We set the mixing ratio of H2SO4 to be 3
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ppm at the lower boundary, within the 0-4 ppm estimates from analysis of Magellan radio occultation
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observations by Koloder and Steffes (1998), in order to maximize agreement between model and data.
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We adopt a zero flux boundary condition for the top boundary, as we assume that no particles or H2SO4
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vapor escape the mesosphere above 100 km.
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2.2. Thermodynamics of H2SO4
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Of particular importance in this model is the treatment of certain thermodynamic quantities of
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H2SO4, such as the saturation vapor pressure and surface tension. Both of these quantities control
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whether a sulfuric acid droplet is growing by condensation or evaporating.
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The saturation vapor pressure pH2SO4 is calculated via the equation of Ayers et al. (1980),
modified by Kulmala and Laaksonen (1990):
 1 1
0.38 
 T  T  H
Lnp H 2 SO4  Lnp H0 2 SO4  10156  
1  Ln o   o   

 T  T   RT
 T To Tc  To 
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Where T is temperature, R is the universal gas constant, To = 340 K is a reference temperature, Tc =
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905 K is the critical temperature, p0 H2SO4 is a reference pressure given by:
Lnp H0 2 SO4 
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 10156
 16.259
To
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and H is the enthalpy associated with the mixing of water and sulfuric acid, given by the
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parameterization of Giauque (1959):
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

1.14208  108
H  4.18423624.8 
 J mol 1
2
4798.69  WH 2 SO4  105.318 



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where WH2SO4 is the weight percentage of H2SO4 in the aerosol droplet calculated from Tabazadeh et al.
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(1997) as a parameterization to temperature and water vapor concentration.
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The surface tension is derived from data collected by Sabinina and Turpugow (1935)
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parameterized linearly with respect to temperature by Mills (1996), and linearly interpolated between
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the H2SO4 data points.
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2.3. Eddy Diffusion and Gas Transport
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The eddy diffusion coefficient profile is shown in Figure 3. The values between 40 and 70 km
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altitude are parameterized from Imamura and Hashimoto (2001) by the sum of an exponential and a
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gaussian function. The large increase in eddy diffusion coefficient at ~53 km simulates the convective
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overturning present in the middle cloud as inferred from Schubert et al. (1980). The eddy diffusion
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coefficient above 70 km is parameterized as a gaussian from Fig. 11 of Krasnopolsky (1983), which
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itself is generated from continuity arguments with respect to the aerosol distribution observed in this
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region at the time. We note that observations since then (Wilquet et al. 2009, 2012) have shown this
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region to be highly variable, and thus it is not certain if this method will give the mean eddy diffusion
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coefficient, especially when the sedimentation time scale is much greater than the ~24 h variability
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time scale the observations seem to suggest. The empirical formula of the eddy diffusion coefficient Kzz
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as a function of altitude z in kilometers above 40 km is then:
K zz  10
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z
38.55
2
2

   z  12.5   z  60   

2
1
 250exp  
 
  m s

   1.201   12.01   

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To implement eddy diffusion in CARMA 3.0, we adopt similar numerical methods used by the
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code to implement Brownian diffusion, except we replace the density of the species by its mixing ratio.
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The upward and downward velocities of eddy diffusion of species j, vju and vjd, respectively, are then
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given by:
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 f j K
f j
vuj  Ln i j  zz j i 1 j
 f i 1  dz f i  f i 1
cm s 1
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 f j K
f j
vdj  Ln i j  zz j i j
 f i 1  dz f i  f i 1
cm s 1
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where dz is the thickness of an atmospheric layer (200 m in our model) and fji is the mixing ratio of
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species j in the ith layer. The natural log prevents numerical instabilities in the event the denominator
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becomes too small. We see that, if the ith level has a much greater j mixing ratio than the level below,
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or fji >> fji-1, then there would be a large diffusive flow downwards, or vjd >> vju, which is exactly what
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results from the above equations.
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Gas transport is handled in the same way as the transport of particles, except we do not consider
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sedimentation.
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2.4. Meteoric Dust
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Turco et al. (1983) discussed the possible properties of meteoric dust in the Venus atmosphere,
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concluding that it is similar to meteoric dust in the atmosphere of Earth and could act as condensation
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nuclei to water vapor, forming thin ice hazes. We propose that meteoric dust could also serve as
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condensation nuclei to sulfuric acid vapor, as its saturation vapor pressure is extremely low at the
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altitude of the UH, on the order of 10-19 mbars for pure sulfuric acid, and 10-31 mbars for a water-
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sulfuric acid mixture with 75 wt% sulfuric acid (Kulmala and Laaksonen 1990), typical of the UH
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(Hansen and Hovenier, 1974). Thus, any sulfuric acid vapor that is lofted into the UH by diffusion or
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winds could potentially condense on the meteoric dust present in this region.
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One argument against meteoric dust being condensation nuclei is its small size and whether the
Kelvin effect will play a large role. The Kelvin effect on the pressure is given by:
Ln
p
2M

p 0 rRT
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where p0 is the original pressure; p is the augmented pressure after the Kelvin effect is taken into
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account; γ is the surface tension; M and ρ are the molar mass and density of the substance, respectively;
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r is the radius of the droplet; R is the gas constant; and T is the temperature. If we use the appropriate
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values for sulfuric acid in the UH, a typical condensation nuclei size of 1.3 nm (Kalashnikova et al.
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2000), and the parameterization of Mills (1996) for the surface tension, then we get an approximate
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increase of 7 orders of magnitude in the saturation vapor pressure. This is indeed a large effect, but the
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resulting saturation vapor pressure is still only 10-24 mbars, which is far less than recent upper limits on
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the abundance of H2SO4 in the UH, e.g. 3 ppb, or about 3x10-11 mbar, from Sandor et al. (2012).
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We also note that, in our model, meteoric dust is treated in the same way as the condensation
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nuclei formed from photochemistry. However, it is clear that meteoric dust, which is typically made of
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silicates (Hunten et al. 1980), may react differently to sulfuric acid than typical photochemical
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products. However, Saunders et al. (2012) showed that silicates do dissolve in sulfuric acid, even for
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concentrations of up to 75 wt%. Therefore, we conclude that our assumption of nucleation by
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activation of soluble condensation nuclei is valid, at least to first order, for meteoric dust.
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The production profile of meteoric dust we use in our model is shown in Figure 4 as an
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empirical approximation of the profile calculated by Kalashnikova et al. (2000). All meteoric dust
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particles are assumed to have a radius of 1.3 nm. We have shifted the profile maximum from 87 km to
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83 km in order to match the maximum in the small mode curve in Fig. 9 of Wilquet et al. (2009). The
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parameterization of the profile is given by:
 z 83 



3
5  10 e  21.201 

2
 z 83 



3
 71.201 
5  10 e
2
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Pmd
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where z has units of kilometers.
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2.5. Winds
z  83
cm 3 s 1
z  83
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Figure 5 shows the wind profile we use to test the effects of transient upward winds on the
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number density and size distribution of the cloud and haze aerosols. The wind beneath 70 km is a
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constant flux wind, identical to that of Imamura and Hashimoto (2001) but increased in strength by two
283
orders of magnitude, similar to the eddy experiments of Imamura and Hashimoto (2001):
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w
8.0  10 3

cm s 1
where w is upward wind speed and ρ is atmospheric density, both in cgs units. In order to adhere to our
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top boundary condition and simulate turning over of the wind currents, we allow the upward wind to
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fall off linearly above 70 km so that it vanishes at 75 km.
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3. RESULTS AND DISCUSSION
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3.1 Equilibrium Results
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Figure 6 shows the number density results of our model for the two initial conditions. We see
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that both cases are consistent with LCPS upper cloud data (Knollenberg and Hunten 1980). However,
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case 1 overestimates the number density of the middle cloud while both cases underestimate the
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number density of the lower cloud, though case 1 gives a better fit to the data. The difference between
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the two cases in the middle and lower clouds is caused by the initial reservoir of gas present in one case
296
but not the other; such a reservoir of gas would result in vigorous nucleation and condensational growth
297
of the first condensation nuclei and meteoric dust that are produced in the model, giving rise to an
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initial population of large particles of radius ~1 μm both in the upper haze and the upper cloud. These
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particles would then sediment and coagulate with smaller particles, reducing the number density of the
300
latter. This depletion in smaller droplets leads to the smaller number densities of the middle and lower
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clouds in case 2. In contrast, no initial large population existed in case 1, and thus the number density is
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increased by the presence of smaller particles. This conclusion is supported by Figures 7 and 8, which
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show the size distributions of the cloud and haze particles at various altitudes, and reproduces
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qualitatively the bimodality of the middle and lower clouds as seen by Pioneer Venus (Knollenberg and
305
Hunten 1980). We see that the amount of ~0.2 μm (mode 1) particles at 48, 51, and 54 km (e.g. in the
306
middle and lower clouds) are all greater in case 1 results than case 2 results, while case 2 results at 58
307
and 63 km exhibit many more ~1-2 μm (mode 2) particles than case 1 results.
308
The difference between the two cases extends to the upper haze as well. Case 1 size
309
distributions above 70 km show a simple mono-modal curve, while case 2 size distributions show an
14
310
increase in both the abundance of larger particles and smaller particles. The former feature is caused by
311
the initial burst of growth due to the presence of 4 ppm of sulfuric acid vapor. Figure 9 reveals the
312
origin of the latter feature as the tail of a haze population originally created from the aforementioned
313
initial rapid growth of large particles. The two orders of magnitude difference between the haze-only
314
curve and the nominal curve is caused by the coagulation of haze particles and upwelled cloud particles
315
in the latter case, leading to the loss of the smaller haze particles. Despite the two different sources of
316
particles, the overall size distributions in the UH are still mono-modal (although many particles do exist
317
in the mode 2 size range), especially at the higher altitudes, and thus cannot explain the bimodality
318
detected by Wilquet et al. (2009). However, the average cloud top haze particle radius (excluding
319
meteoric dust), ~0.26 μm at 70 km, is fairly close to the average haze particle radius originally detected
320
by Kawabata et al. (1980), indicating that this is likely the small mode detected by Wilquet et al.
321
(2009), and that a steady state model may not yield a large mode. The small mode number density data
322
is plotted in Figure 6 alongside the model number density of all particles with r > 1.3 nm. Though the
323
model follows the trend of the data above 80 km, it underestimates it by about a factor of 2; below 80
324
km, it overestimates it by about the same amount.
325
The underestimation of the lower cloud in both models may further speak to the necessity of
326
including transient events in our model. We see from Figure 6 that the number density curve becomes
327
jagged at the same altitude as the lower cloud, indicating sensitivity to the model state. This is the
328
altitude at which the sulfuric acid vapor mixing ratio intersects its saturation vapor pressure curve, as
329
shown in Figure 10, and thus any rapid addition of extra sulfuric acid vapor would lead to growth. The
330
phenomenon of transient mixing leading to growth was observed in the model of Imamura and
331
Hashimoto (2001). This may also be supported by the size distributions of the middle and lower clouds
332
underestimating both the abundance of mode 1 and mode 3 particles when compared to LCPS data at
333
54 km, while adequately fitting the mode 2 particles. For instance, any injection of sulfuric acid vapor
15
334
would cause both the growth of particles, producing the large mode 3 particles, and the generation of
335
mode 1 particles due to the evaporation of sedimenting mode 3 particles. However, this depends on the
336
assumption that mode 3 particles are sulfuric acid droplets like mode 2, which it may not be, given the
337
original observations and conclusions of Knollenberg and Hunten (1980) discussed below.
338
In our model, where all particles are assumed to be either nonvolatile spheres of density ~1.9 g
339
cm-3, or spherical sulfuric acid droplets, a distinct third peak in the size distribution is seen at 48 km for
340
case 2 centered on 4.23 μm. A smaller, less distinct peak is seen at 51 km for case 1 centered on 2.66
341
μm. Both peaks are close to the mean radius of mode 3 particles detected by Pioneer Venus, ~3.6 μm
342
(Knollenberg and Hunten 1980). The origins of these particles in our model results appear to be related
343
to coagulation, as indicated in Figure 11 where a case without coagulation resulted in very few particles
344
with radius greater than 2 μm. The difference in the behavior of our mode 3 between cases 1 and 2 also
345
point to coagulation as a means of generating it, as the large particles formed from the initial growth
346
phase of the latter case would have coagulated with each other and smaller particles to form larger
347
particles in the mode 3 size regime, while in case 1 the effect of coagulation would’ve been smaller due
348
to the lack of the initial large particle population, leading to a more diminutive mode 3. However, it
349
should be noted that the nominal observations point to mode 3 as solid, crystalline particles, rather than
350
liquid, spherical droplets (Knollenberg and Hunten 1980). On the other hand, Toon et al. (1984)
351
discussed the possibility that mode 3 is merely the tail of the mode 2 size distribution. This is supported
352
by our results, where mode 3 blends into mode 2 at higher altitudes.
353
Figure 11 shows the mixing ratio of sulfuric acid vapor for both cases plotted with the sulfuric
354
acid saturation vapor pressure curve and Magellan radio occultation data as analyzed by Kolodner and
355
Steffes (1998). We see immediately that the dispersion of the data from 0-6 ppm allows for both cases
356
to fit it. However, only case 2 exhibits the local sulfuric acid maximum that fits the nonzero data points.
357
This difference between the results of the two cases arise naturally from the initial 4 ppm of H 2SO4
16
358
vapor in case 2 but not in case 1. In both cases, vapor is deposited at the base of the clouds by
359
evaporating, sedimenting particles. In case 1, this vapor is added to essentially no vapor, while in case
360
2, this vapor is added to the 4 ppm already present. Another source of vapor below the clouds is the
361
upward diffusion from below 40 km due to the assumed vapor mixing ratio of 3 ppm at the base of the
362
model atmosphere. In case 1, this source leads to the negative gradient in sulfuric acid vapor mixing
363
ratio, causing a persistent upward vapor flux. In case 2, this results in a downward flux, as the mixing
364
ratio below the clouds exceeds 3 ppm. The two cases are consistent with each other above 52 km, and
365
only deviate from the saturation vapor pressure at 61 km, where sulfuric acid vapor is photochemically
366
produced, and above 80 km. This latter deviation may be caused by numerical instabilities caused by
367
the low saturation vapor pressure (~10-31 mbars), the effects of possible condensation of water vapor
368
into ice clouds (Toon et al. 1984), or the phase properties of sulfuric acid in this region (McGouldrick
369
et al. 2011).
370
Figures 12 and 13 give a summary of the processes occurring in the clouds and UH of Venus.
371
The production of nonvolatile photochemical condensation nuclei causes the nucleation and
372
condensational growth of liquid sulfuric acid droplets at 61 km. These droplets then diffuse upwards
373
and sediment downwards, leading to the positive (upward) particle flux above 61 km and the negative
374
(downward) particle flux below 61 km. The vigorous convection in the middle cloud then drives the
375
upward flux of sulfuric acid vapor, resulting in enhanced production of mode 2 particles, which are
376
transported downwards by sedimentation and diffusion.
377
The particles begin to evaporate as they sediment past the altitude at which the sulfuric acid
378
saturation vapor pressure becomes greater than its partial pressure, causing the regeneration of mode 1
379
and the deposition of sulfuric acid vapor beneath the clouds. This creates a local maximum in sulfuric
380
acid vapor mixing ratio around 44 km, creating both an upward and downward flux that diverges at that
381
altitude; the upward vapor flux leads to the growth of particles in the lower cloud, which then promotes
17
382
a greater downward flux of particles due to faster sedimentation.
383
Again we see clear differences between cases 1 and 2. The upper haze of case 2 contains the
384
background haze particles formed from the initial growth phase, which is absent in case 1. The
385
existence of these first, large particles also leads to a larger mean size for mode 2 and the regenerated
386
mode 1, as well as a tail of large particles that eventually forms a distinct third mode upon evaporation
387
due to the faster evaporation rate of the smaller mode 2 particles caused by the Kelvin effect.
388
It is worth noting that the fluxes in case 1 above 55 km are more positive than those of case 2,
389
most likely due to the smaller particles being easier to transport upwards. Similarly, below 55 km the
390
absolute value of case 1 particle fluxes are slightly smaller than those of case 2 due to the lower mass
391
loading caused by the abundance of small particles rather than a smaller number of large particles.
392
Also, the sulfuric acid vapor flux in case 1 is slightly positive for all altitudes below 49 km, while the
393
particle flux is close to zero, leading to net generation of sulfuric acid in this region. This is
394
unsurprisingly, as the negative gradient will deliver gas to this region from below the model domain,
395
while sedimenting particles will deliver gas from above. It is likely then, that given enough time, the
396
vapor curve in case 1 will look similar to the curve in case 2. This indicates that case 1 has not reached
397
a steady state even after 107 s of simulation time, calling into question its validity in this region.
398
3.1 Transient Wind Results
399
Figure 14 gives the number density results before, immediately after, and about an Earth week
400
after a transient updraft event lasting ~1 Earth day, using the wind speed profile given in Figure 5, and
401
case 2 initial conditions. We see that a detached haze layer forms at 75 km. The location of the haze is
402
likely artificial given our wind profile, but the increase in number density at the altitude of the turn-
403
over should be profile-dependent, though the magnitude of the increase in number density (a factor of a
404
few 10’s in our results) should not be as high as we have not taken into account horizontal transport. In
405
the few Earth days that follow, the detached haze layer diffuses away so that the peak number density is
18
406
an order of magnitude lower than its maximum immediately following the wind event. This shows that
407
such a wind event produces the right time scales for haze variability, on the order of days. A wind
408
forcing particles into a thin haze layer also increases the rate of coagulation at that location due to the
409
increased number density. Figure 15 shows the size distributions at altitudes close to the detached haze
410
layer at the same times as Figure 14. For all plotted altitudes we observe an increase in large particles,
411
and a decrease in smaller particles, as would be the result of coagulation. The size distributions also
412
exhibit clear bimodality after the wind event, and even “trimodality” at 70 km after the relaxation
413
period. In these cases, the small mode is caused by the upwelling of mode 1 particles, while the large
414
mode is caused by the condensational growth and coagulation of mode 1 particles, as well as the
415
upwelling of some mode 2 particles. The middle mode in the trimodal case, as it is very similar to the
416
peak of the distribution immediately after the wind at 75 km, is caused by the sedimentation of mode 1
417
particles that have grown due to condensational growth only, essentially filling the gap between the
418
mode 1 particles and the mode 2 particles. In summary, the effect of such a transient wind is the
419
generation and depletion of a haze layer on the time scale of days, and the perturbation of the mono-
420
modal size distribution of the region into bimodal, or even trimodal distributions. This qualitatively
421
reproduces the variability and size spectrum of the UH as observed by Venus Express (Wilquet et al.
422
2009, 2012).
423
424
4. SUMMARY AND CONCLUSIONS
425
In this study we simulated the clouds and upper haze of Venus using version 3.0 of the
426
microphysical and vertical transport model CARMA. We showed that appropriate choices of initial,
427
boundary, and model atmospheric conditions can reproduce the number density and size distributions
428
of the Venus clouds as seen in Pioneer Venus data, including the bimodal and possible trimodal particle
429
size spectrum and the three separate cloud layers. The two initial conditions we used, one representing
19
430
the simultaneous photochemical production of sulfuric acid vapor and sulfur condensation nuclei (case
431
1), and another representing the injection of condensation nuclei of unknown make up into a reservoir
432
of sulfuric acid (case 2), both reproduce the upper cloud satisfactorily. However, case 1 overestimates
433
the middle cloud while case 2 underestimates the lower cloud. We deduced that these discrepancies are
434
caused by an initial population of large particles forming in case 2 but not in case 1, and the lack of
435
transient events simulated in these nominal runs, which may be necessary to reproduce the highly
436
variable lower cloud (James et al. 1997, Imamura and Hashimoto 2001).
437
We observed a mode 3 in our model at the altitudes of the lower cloud. It appears to originate as
438
the large particle tail of mode 2, thereby supporting one of the current hypotheses regarding this
439
controversial issue (Toon et al. 1984). The evaporation of the cloud particles at the base of the clouds
440
then causes a split between mode 2 particles and these larger particles due to the latter`s lower
441
evaporation rate, resulting in a distinct mode 3. The mode 2 large particle tail itself is formed by
442
coagulation in our model.
443
We also simulated the upper haze as a mixture of droplets formed from in situ nucleation of
444
sulfuric acid vapor on meteoric dust and droplets upwelled from the cloud decks below. We showed
445
that the latter population dominates the haze and is likely the particles originally observed by the
446
Pioneer Venus OCPP (Kawabata et al. 1980), and the mode 1 particles observed by Venus Express
447
SPICAV/SOIR (Wilquet et al. 2009). A distinct mode 2 was not observed in our results, though the size
448
distribution does cover the appropriate size range.
449
We appealed to the effects of transient winds for the generation of mode 2 haze particles. A
450
constant flux upward wind capped by a rapid fall-off to zero wind speed to represent turnover was
451
used. The application of this wind for 105 s on a steady state cloud and haze distribution resulted in the
452
formation of a detached haze at the altitude of the turnover with a peak number density ~20 times the
453
original steady state number density at the same altitude. Relaxation of the detached haze over an Earth
20
454
week resulted in the decrease of number density by a factor of 10. We conclude that a transient wind
455
can reproduce the time scales of haze variability observed by Venus Express (Luz et al. 2011,
456
Markiewicz et al. 2007). The resulting size distribution showed a clear bimodal structure below the
457
detached haze at the end of the wind event, with a trimodal structure appearing at 70 km after the
458
relaxation period. A less distinct bimodal structure also appeared above the detached haze. We note
459
that, while the location and specific number density of the detached haze are dependent on the wind
460
profile, the qualitative effects of such a wind, namely the formation of a detached haze and the
461
increased coagulation and growth of particles, are general.
462
Clouds and hazes are major constituents of the atmosphere of Venus, affecting both its
463
chemistry and its climate. Understanding the observed variability in number density and size
464
distribution of these features are therefore important in characterizing the atmospheric state. In this
465
work we showed that models such as CARMA are invaluable in revealing the physical processes that
466
control it, such as the effects of different condensable production methods, meteoric dust nucleation,
467
and transient winds events.
468
469
Acknowledgements
470
We thank S. Garimella and R. L. Shia for assistance with the setting up and running of the CARMA
471
code. This research was supported in part by the Venus Express program via NASA NNX10AP80G
472
grant to the California Institute of Technology, and in part by an NAI Virtual Planetary Laboratory
473
grant from the University of Washington to the Jet Propulsion Laboratory and California Institute of
474
Technology.
475
21
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477
478
479
480
481
482
TABLES
Earth
Venus
Surface gravity (cm s-2) 980.6
887.0
Major atmospheric
component(s)
N2, O2 (avg. wt. = 29.97 g/mol)
CO2 (wt. = 43.45 g/mol)
Main condensable
H2O (wt. = 18.02 g/mol)
H2SO4 (wt. = 98.08 g/mol)
Atmospheric viscosity
(10-4 g cm-1 s-1)*
1.851 (at 300K)
1.496 (at 300 K)
* - The viscosity dependence on temperature is calculated using Sutherland's equation and parameters
from the Smithsonian Meteorological Tables (for H2O) and White (1974) (for H2SO4).
Table 1. Comparison of relevant planetary parameters between Earth and Venus.
22
483
484
485
486
487
488
489
FIGURES
Figure 1. Model temperature and pressure profile taken from the Venus International Reference
Atmosphere (Seiff et al. 1985).
23
490
491
492
493
Figure 2. Production rate profile for sulfuric acid vapor and photochemical condensation nuclei, taken
from Imamura and Hashimoto (2001), with the peak rate halved for the best fit to LCPS data.
24
494
495
496
497
498
Figure 3. Model eddy diffusion coefficient profile, with the 40-70 km section based on Imamura and
Hashimoto (2001), and the 70-100 km section based on Krasnopolsky (1983).
25
499
500
501
502
503
504
505
Figure 4. Model meteoric dust production rate profile, based on Kalashnikova et al. (2000), normalized
to 1.3 nm particles, and shifted down from the original distribution by 4 km in order for the maximum
of this profile to match that of the number density profile of the small mode particles in the UH, as
retrieved from solar occultation data by Wilquet et al. (2009)
26
506
507
508
509
510
Figure 5. Model wind speed profile, with the portion below 70 km taken from Imamura and Hashimoto
(2001), and the cut-off above 70 km to represent the turning over of the upwelling.
27
511
512
513
514
515
516
Figure 6. Number density profile of cloud and haze particles for case 1 (red) and case 2 (blue) for
particles with radius r > 1.3 nm. These curves are compared to data from LCPS (points) (Knollenberg
and Hunten et al. 1980) and Venus Express (pluses) (Wilquet et al. 2009).
28
517
518
519
520
521
522
523
524
525
526
Figure 7. Particle size distributions for case 1, plotted at various altitudes. LCPS size data at 54.2 km
(Knollenberg and Hunten 1980) is plotted for comparison.
29
527
528
529
530
531
532
533
534
535
Figure 8. Same as Figure 7, for case 2.
30
536
537
538
539
540
541
542
Figure 9. Particle size distribution at 78 km for the nominal, no meteoric dust (MD) production, and no
photochemical condensation nuclei (CN) production cases. All curves are results of case 2 initial
conditions.
31
543
544
545
546
547
548
549
Figure 10. Sulfuric acid vapor mixing ratios for the two initial condition cases plotted against the
sulfuric acid saturation vapor pressure (see text for source) and Magellan radio occultation data
analyzed by Kolodner and Steffes (1998).
32
550
551
552
553
554
Figure 11. Particle size distribution at 48 km for both the nominal and the no coagulation cases. All
curves are results of case 2 initial conditions.
33
555
556
557
558
559
560
561
562
563
Figure 12. Contour plots of number density as a function of particle size and altitude for case 1 (top)
and case 2 (bottom). The sharp feature near 0.1 μm is caused by assigning a single size bin to represent
the input photochemical condensation nuclei.
34
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566
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568
569
Figure 13. The sulfuric acid flux for cases 1 and 2 after 107 seconds.
35
570
571
572
573
574
575
Figure 14. Number density profiles of the upper cloud and haze before (black), immediately after
(purple), and 5x105 s after (green) a 1x105 s transient wind event, using case 2 initial conditions. The
wind speed profile is shown in Fig. 5.
36
576
577
578
579
Figure 15. Particle size distribution before (black), immediately after (purple), and 1x105 s after (green)
a 1x105 s transient wind event, plotted for various altitudes. Initial condition case 2 is used.
37
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