Modeling the effects of shear on the evolution of the holes in the condensational clouds of Venus

Icarus 196 (2008) 35–48 www.elsevier.com/locate/icarus

Modeling the effects of shear on the evolution of the holes in the condensational clouds of Venus Kevin McGouldrick a,∗ , Owen B. Toon b a Department of Astrophysical and Planetary Sciences, Laboratory for Atmospheric and Space Physics, University of Colorado, Boulder, CO 80309, USA b Department of Atmospheric and Oceanic Sciences, Laboratory for Atmospheric and Space Physics, University of Colorado, Boulder, CO 80309, USA

Received 9 July 2007; revised 21 February 2008 Available online 19 March 2008

Abstract Near-infrared brightness temperature contrasts observed on the night side of Venus indicate variations in the size and distribution of particles in the lower and middle cloud decks. McGouldrick and Toon [McGouldrick, K., Toon, O.B., 2007. Icarus 191, 1–24] have shown that these changes can be explained by large-scale dynamics; in particular, that downdrafts may produce optical depth “holes” in the clouds. The lifetimes of these holes are observed to be moderately short, on the order of ten days. Here, we explore a simple model to better understand this lifetime. We have coupled a microphysical model of the Venus clouds with a simple, two-dimensional (zonal, vertical) kinematical transport model to study the effects of the zonal flow on the lifetime of the holes in the clouds. We find that although wind shear may be negligible within the cloud itself, the shear that is present near the top and the bottom of the statically unstable cloud region can lead to changes in the radiative-dynamical feedback which ultimately lead to the dissipation of the holes. © 2008 Elsevier Inc. All rights reserved. Keywords: Venus, atmosphere; Meteorology; Atmospheres, dynamics

1. Introduction Variations in the brightness temperature of the night side of Venus at several near infrared wavelengths were discovered by Allen and Crawford (1984) and have been observed in detail by several observers, especially in co-ordination with the 1990 Galileo flyby (Crisp et al., 1991; Carlson et al., 1991, 1993; Grinspoon et al., 1993). These brightness temperature variations are observed only in very narrow spectral windows of the venusian atmosphere where there is very little gaseous absorption. The brightness temperature variations have been attributed to changes in the absorption and scattering properties of the middle and lower cloud decks (Crisp et al., 1989), that is, the brightness variations are holes in the clouds. We previously have investigated potential causes of the variations in the cloud properties with a one-dimensional microphysical model * Corresponding author. Present address: Department of Space Sciences, Denver Museum of Nature and Science, 2001 Colorado Blvd., Denver, CO 80205, USA. E-mail address: [email protected] (K. McGouldrick).

0019-1035/$ – see front matter © 2008 Elsevier Inc. All rights reserved. doi:10.1016/j.icarus.2008.02.020

of the Venus condensational cloud that included a radiativedynamical feedback (McGouldrick and Toon, 2007). We found that plausible thermodynamic variations, such as imposed temperature changes and variations in vertical mixing, are unlikely to cause opacity variations of the magnitude and timescale that are observed in the clouds. We concluded that only large-scale dynamical motions could bring about the opacity variations that have been observed. In this paper, we investigate the effects of global-scale dynamics on the middle and lower cloud deck of Venus using a two-dimensional (zonal and vertical) model of microphysics and kinematics. We seek answers to two questions: What processes are responsible for limiting the duration of the holes? What role does global-scale dynamics play in the evolution of the holes (and clouds) of Venus? McGouldrick and Toon (2007) suggested vertical shear of the zonal wind as a potential culprit in the filling of the holes. However, one-dimensional models such as the ones employed by McGouldrick and Toon (2007) are rather limited in their ability to describe dynamical effects. In one-dimensional models, simulation of vertical motion is restricted to non-divergent flow since convergent or

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K. McGouldrick, O.B. Toon / Icarus 196 (2008) 35–48

divergent flow in a one-dimensional model results in a flux of mass into or out of the column; and horizontal motion cannot be examined at all. Elsewhere (McGouldrick and Toon, 2008), we investigate the effects of two-dimensional gravity waves and convective cells on the clouds, taking into account the effects of convergence on relatively small spatial scales. Here, we investigate the effects of large-scale horizontal motion and shear on the clouds with a two-dimensional model. While this current model can treat divergent flow, the vertical motions that are generated by large scale flow are likely to be weak. Hence, the primary source of vertical motion is convection, which we treat with a parameterized eddy diffusion model. We first review observations of the Venus clouds pertinent to understanding their dynamical evolution. Then, we describe the changes made in the course of extending our model to two dimensions. Next, we present the results of tests that demonstrate the effects that the newly introduced physics and numerics have on the model, by themselves. Finally, we present the results of a series of simulations of the evolution of a typical large hole in the Venus middle and lower cloud deck under the influence of various profiles of the vertical shear of the zonal wind. 1.1. Description of clouds and holes Sulfuric acid clouds enshroud the planet Venus between the altitudes of about 50 and about 70 km. The upper cloud (between about 57 and about 70 km) is formed by photochemical production of sulfuric acid from sulfur dioxide and water vapor (Young, 1973). The middle and lower clouds (between about 48 and about 57 km) are supported by condensation of sulfuric acid vapor, transported into the clouds from a large subcloud reservoir (Krasnopolsky and Pollack, 1994; James et al., 1997). One-dimensional simulations by Imamura and Hashimoto (2001) that included vertical winds suggest that variations in the lower cloud observed by the Pioneer Venus descent probes can be explained by variations in the vertical winds active near the cloud base. Previous analyses by Grinspoon et al. (1993) and Carlson et al. (1993) suggest that such lower cloud variability is responsible for much of the variation seen to cause the holes in the clouds. Finally, McGouldrick and Toon (2007) showed that the middle and lower clouds of Venus are supported by a radiative-dynamical feedback whereby absorption of upwelling infrared radiation by the cloud base sustains an unstable lapse rate within the cloud layer. Crisp et al. (1991), as part of a coordinated effort to support the Galileo Venus flyby with extensive Earth-based observations, performed repeated observations of the night side of Venus in the near infrared in the weeks leading up to and including the flyby. They observed a large (∼2000 km) bright spot (i.e., diminished cloud optical thickness) at about 16◦ latitude that was present at the very outset of their observing program. This bright spot was seen twice to pass over to the day side of the planet and return to the night side; but it was not observed to return a third time. Thus, it persisted for at least two weeks. However, since its initial formation was not observed, it could have persisted for a longer period of time. They noted that this feature (one of the optical “holes” in the clouds) traveled around

the planet with a mean zonal velocity of about 83 ± 2 m/s. They could not detect any meridional motion which, they reported, constrains the meridional velocity of the feature to be no greater than 0.5 m/s. Bell et al. (1991), also part of the ground-based observations supporting the Galileo flyby, reported that the brightness contrasts associated with the 2000 km feature observed by Crisp et al. (1991) could be explained by the removal of about 60% of the Mode 2 and Mode 3 particles below an altitude of 57 km, where the middle and lower cloud decks are located. Carlson et al. (1991), analyzing the Galileo Near Infrared Mapping Spectrometer (NIMS) data, determined that the intensity contrasts between the bright and the dark regions were about 5:1 at 1.74 µm, and about 20:1 at 2.30 µm. Nearly a year and a half before the Galileo flyby, Crisp et al. (1989) observed the night side of Venus in the near infrared close to the time of inferior conjunction. They found that the brightness temperature at 1.74 µm of the brightest (least cloudy) features was around 480 K, while that of the darkest (most cloudy) features was only about 425 K. They found that the brightest one-quarter of the night side exhibited 1.74 µm brightness temperatures in excess of 455 K; and the darkest one-quarter of the night side exhibited brightness temperatures inferior to 440 K. 1.2. Description of Venus cloud-level dynamics The atmospheric dynamics of Venus is dominated by the global super-rotation. At all altitudes above at least 10 km, the flow of the atmosphere is from east-to-west (the same direction as the planet’s retrograde rotation), and increases in magnitude from just a few m/s near the surface up to approximately 100 m/s at the altitude of the cloud tops. The zonal winds are fast enough at the altitude of the clouds (about 45 to 70 km) that the clouds travel around the planet with periods of less than a week. The large change in zonal wind speed with altitude suggests that vertical shear of the zonal wind could possibly play a role in the dynamical evolution of the clouds. The Pioneer Venus descent probes detected alternating regions of high and low wind shear, which were correlated with alternating regions of high and low static stability, respectively (Schubert et al., 1980). On average, the magnitude of the shear between 40 and 60 km (the extent of our model domain) is about 2.5 m/s km−1 . All of the Pioneer Venus probes—except the north probe—experienced roughly 2.5 m/s km−1 shear below 48 km, relatively constant zonal velocity with negligible shear between 48 and 55 km, and about 4 m/s km−1 shear above 55 km. The north probe, however, which descended at a latitude of 60◦ , observed only a very narrow region of minimal shear from about 50 to 53 km. Otherwise, the north probe measured levels of wind shear that steadily and gradually increased with altitude. 2. Model details This work extends the one-dimensional microphysical model described in McGouldrick and Toon (2007) to a two-dimen-

Modeling the effects of shear on the evolution of the holes in the condensational clouds of Venus

37

Fig. 1. Comparison of the solar (dashed) and infrared (solid) heating rates in the model domain.

sional model with simple kinematical transport. A more detailed description of the microphysical model, which is based on Toon et al. (1988); the radiative transfer model, which is based on Toon et al. (1989) and Bullock and Grinspoon (1996); and the radiative-dynamical feedback turbulent transport model, which is based on Mellor and Yamada (1974, 1982), can be found in McGouldrick and Toon (2007). The grid structure and the mechanics of the transport scheme used are described by Toon et al. (1988). Here, we shall describe only the changes we made to the dynamical transport portions of the model, and the changes we made in extending the model to two dimensions. 2.1. Model domain As in McGouldrick and Toon (2007), we utilize a model with 1 km vertical resolution over the range 40 to 60 km altitude. We have extended the model to two dimensions by defining 100 columns in the zonal direction. Each column has a width of ∼368 km, so that our two-dimensional model represents a ring around the planet situated at about 16◦ latitude. The choice of this latitude is somewhat arbitrary, though it is based on observations. As discussed in Section 1.1, Crisp et al. (1991) observed a conspicuous bright spot on the night side of Venus at about 16◦ latitude. Although Galileo was unable to observe this particular bright spot (it had rotated around to the daylight side of the planet at the time of the flyby), Crisp et al. (1991) were able to study it extensively from the ground over a span of several weeks. Since we have so much temporal information about this particular hole, we compare our simulations to the observations of this hole. In our previous one-dimensional simulations, we assumed a globally-averaged value of the solar flux (McGouldrick and Toon, 2007). Despite the fact that the two-dimensional simulations we perform in the present work cover the full range of longitudes, we retain this globally-averaged value for the solar flux. We are able to do this because the solar heating rate in this region of the atmosphere is significantly smaller than the infrared heating rate. Fig. 1 shows the heating rates that are at

Fig. 2. Adapted from Fig. 8A in Carlson et al. (1991). The solid curve represents the spectrum of the 1.74 µm band, as observed by Galileo NIMS, where the diamonds indicate the observed wavelengths. The dashed curve indicates the appearance of this spectral feature at the resolution of our radiative transfer model.

work in our model simulations. The solar heating rate is calculated from the solar flux profiles that were derived by Tomasko et al. (1980). The infrared heating rate is calculated by our two-stream, correlated-K radiative transfer code. This infrared heating of the lower cloud drives convection in the clouds, as discussed by McGouldrick and Toon (2007). 2.2. Calculation of thermal emission In order to compare our model results with observations, we analyze the spectrally-resolved upwelling infrared radiative flux at the top of the model atmosphere. The observations are typically made at a high spectral resolution. However, our correlated-K treatment of the radiative transfer is at a comparably lower resolution. Fig. 2 is based on Fig. 8A from Carlson et al. (1991), which indicates the spectral shape of the 1.74 µm window at Galileo NIMS resolution. The Galileo NIMS observations of the hole are reported at 1.74 µm, the peak of the emission in the spectral window. Our correlatedK scheme considers a relatively narrow band (as compared with other bands in our correlated-K spectrum), centered at 1.735 µm and covering the wavelengths 1.717 to 1.755 µm. Comparing the integrated average intensity in this wavelength range to the intensity at 1.74 µm in Fig. 2, we estimate that our correlated-K intensities will underestimate the emitted flux by about 25%. We use the emitted thermal energy only as a means of visualizing our results. Hence, we did not attempt a higher resolution calculation. Because of our lower spectral resolution, the values we report do not correspond to the observed thermal emission. However, the ratio we calculate between the modeled maximum and minimum flux ought to (and does) correspond to the flux ratio calculated by Carlson et al. (1991).

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2.3. Model numerics In addition to extending the model to two dimensions, we have also changed the manner in which we take time steps. In McGouldrick and Toon (2007), we employed a variable timestep in which changes to all of the concentrations present in the model were checked at every time step to decide whether the current size of the time step was adequate to produce an accurate answer. Since growth and evaporation are such rapid processes, the timestep usually was limited to a small value. The shortest timestep in any grid cell was then employed as the time step at all grid cells. To enhance the computation speed, we decided in our twodimensional model to employ a constant dynamical (and radiative) time step for all grid cells, but to divide that time step into smaller substeps in each grid cell in which we calculate the effects of the faster microphysical processes. The benefit of this is that we no longer waste time performing repeated microphysical calculations when they would be unnecessary (e.g., several kilometers below cloud base where there is a dearth of cloud particles and the atmosphere is severely subsaturated). It is important to choose the size of the substep wisely. We calculate a candidate maximum timestep that considers the rate of growth of the particles themselves (dtpc ); a candidate maximum timestep that considers the rate of change in gas concentration that will result from growth or evaporation of the particles (dtgc ); and a candidate maximum timestep that considers the change in the concentrations that results from the advective phase of the calculations (dtdgc ). The Courant number for growth in each size bin is |dm/dt| · dtpc , dm where |dm/dt| is the growth rate in the bin, and dm is the size of the bin. We require a dtpc such that the Courant number for growth does not exceed 0.5. To do this, we visit each bin in which there exist a significant number of particles, and estimate the growth rate in that bin. We then calculate dtpc such that the largest Courant number for growth does not exceed 0.5. Changes in gas concentration that can cause trouble for the model include those that result in a large change to the supersaturation ratio and those that cause the gas concentration to become negative (since the gas concentration is not calculated implicitly, as are the particle concentrations, a rapid growth rate for a few particles or a moderate growth rate of a very large number of particles can lead to negative gas concentration). We compare the gas concentration at the beginning of the dynamical time step with zero, and with the saturation gas concentration (that is, the gas concentration that occurs at the equilibrium vapor pressure). We first determine dtdgc to be one-tenth of the time required for advection to cause our gas concentrations to reach either of those unseemly limits. Finally, we estimate the total rate of mass transfer between the condensed phase and the vapor phase. This value is an estimate of the growth rate as seen by the vapor, rather than by the particles. We compare this “vapor growth rate” to zero gas concentration and saturation gas concentration, and calculate dtgc to be half the time required

to reach either of these limits. Finally, the substep we use is whichever of these three (dtpc , dtdgc , dtgc ) is the smallest. This choice of timestep ensures that we: • Do not exceed a growth Courant number of 0.5 (dtpc ). • Do not allow advection to drive gas concentrations negative (dtdgc ). • Do not allow advection to change the sign of the supersaturation ratio in a single substep (dtdgc ). • Do not allow growth to drive gas concentrations negative (dtgc ). • Do not allow growth or evaporation to change the sign of the supersaturation ratio (dtgc ). While a combination of advection and growth might permit one of the above restrictions on dtgc or dtdgc to occur—especially after several substeps have elapsed—these choices of substep length tend to limit the step-to-step changes sufficiently to prevent the instabilities in vapor concentration that can lead to instability of the model. Also, while it might appear as though these restrictions require that the supersaturation ratio can never change sign from its value at the beginning of the initial substep, the changes to gas concentration and temperature that result from the incremental application of the advective changes and growth processes are indeed sufficient to effect a change in the sign of the supersaturation ratio. These restrictions help to prevent numerical instability associated with overshooting the equilibrium solution by large amounts. 2.4. Model kinematics and initialization We define a longitudinally-independent non-divergent background zonal wind flow (Fig. 3a) that approximates the vertical profile of the mean Venus super-rotation at 16◦ latitude. In each of our simulations, we assume that the zonal wind at 48 km is equal to −83 m/s, consistent with the observations made by Crisp et al. (1991). This zonal velocity equates to a planetcircling period of about 5.14 days. We consider two different shear profiles which are demonstrated in Fig. 3a. The first shear profile we consider is a “typical” shear profile in which the shear is based on the dynamical model of Baker et al. (2000), and observations by three of the four Pioneer Venus descent probes (Counselman et al., 1980). In our typical shear case, we consider the shear to have a constant value of 2.5 m/s km−1 below 48.5 km, a constant value of 6.0 m/s km−1 above 54.5 km, and zero between 48.5 and 54.5 km. In later simulations, we use a profile in which the shear attains a constant value of 2.5 m/s km−1 throughout the model domain. This “constant” shear profile is identical to the typical shear profile at all altitudes below 48.5 km. Finally, we consider a “variable” shear profile which is based on the evolution of the static stability. In this case, we use the typical shear profile in a column if there is static instability anywhere in the column. That is, if the column at any altitude is susceptible to convective overturning, we assume that the convective overturning suppresses the vertical shear of the zonal wind. If the entire column exhibits positive static stability, we assume the constant shear profile in that col-

Modeling the effects of shear on the evolution of the holes in the condensational clouds of Venus

(a)

(b) Fig. 3. (a) Vertical profile of the zonal winds used in this model. The dashed line indicates the “typical” shear profile based on Baker et al. (2000) that we use in simulations 3 and 4; the solid line represents the “constant shear” profile we use in simulations 5 and 6. The magnitude of the winds in the middle cloud deck are based on the observations of Crisp et al. (1991). The two profiles are identical below 48.5 km. Also plotted, for comparison, are the Pioneer Venus descent probes’ measurements of the zonal velocity, estimated from Fig. 1 of Counselman et al. (1980). The observed winds have been shifted so that they have a mean zonal velocity of −83 m/s at 50 km; the north probe is denoted by (P), the night probe by (+), the day probe by (∗), and the large probe by (E). (b) The “raised cosine” curve by which we determine the horizontal profile of the particle concentrations in our simulations.

umn. The use of this variable shear profile is intended to address the point that significant vertical motions are incompatible with significant vertical shear of horizontal winds. In the variable shear case, a vertical wind is calculated to account for the convergence that results from the zonal variability of the zonal wind. This correction is unnecessary in the con∂u = 0, hence stant shear and typical shear simulations, since ∂x ∂w = 0. However, since the zonal wind in the variable shear ∂z simulation depends upon the spatially variable static stability in ∂u = 0. Hence, a vertical velocity must be generthe column, ∂x ated in order to satisfy mass continuity. In the variable shear simulation, this correction is very small, relative to the convective motions (on the order of 1–3 cm s−1 , compared with 100–300 cm s−1 ). We arbitrarily assume that the vertical winds at the x-domain model boundaries are zero. Clearly these winds are highly idealized. Our goal is to understand the interactions between microphysics, radiation, and dynamics. We assume here that only small scale dynamics (i.e., convection) is tightly coupled to radiation and microphysics. In later work, we will explore whether the large scale dynamics is coupled to microphysics and short term changes in the radiation budget. The horizontal transport in our simulations

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represents a kinematical description of the atmospheric dynamics of Venus. We do not determine a wind field by solving the equations of motion. Rather, we prescribe a static horizontal wind field that is based on observations. Vertical motions in the constant shear and typical shear cases are simulated via the eddy diffusion coefficient that is determined from the radiativedynamical feedback calculations. Since the vertical motions are treated as eddy diffusion, they do not trigger horizontal motions due to convergence, as a real ascending plume would. Furthermore, horizontal motions driven by the horizontal temperature and pressure gradients that can be generated by the spatially-varying heating rate are not considered. Such dynamical considerations would be better addressed by coupling the present microphysical model to a model of mesoscale dynamics that is designed to handle all of the intricacies of convective dynamics. We initialize the clouds with the results of the one-dimensional feedback model from McGouldrick and Toon (2007). Every column in our two-dimensional model is initialized using the pressure, temperature, air density, specific heat, gas concentration, and particle concentration attained at the end of the base feedback model (with mixing length of 1 km) described in McGouldrick and Toon (2007). To simulate a hole in the cloud similar to the hole that was observed by Crisp et al. (1991), we multiply the particle concentrations (pc) by one period of an inverse raised cosine distribution: ⎧ pc(1), |x − xc |  xh , ⎪ ⎨ c   1+cos( x−x xh π)  pc(x) = pc(1) · 1 − pc · (1) , 2 ⎪ ⎩ |x − xc | < xh , where pc(1) is the nominal particle concentration, pc is the fraction by which the total cloud number is reduced, xc is the location of the center of the hole, and xh is the width of the hole. We choose pc = 0.6, since that is the reduction in particles that Bell et al. (1991) calculated as being necessary to produce the brightness contrasts observed in the holes. We apply this reduction in particle number to all particles at all altitudes below 55 km, since the reduction noted by Bell et al. (1991) applied only to lower and middle cloud particles. Neither the particles of the upper cloud in our model (those above about 55 km), nor the boundary condition at 60 km are affected by this reduction in particle number. This value of pc results in a brightness ratio of about 4.9:1 in the 1.74 µm band in our model, which is consistent with Carlson et al. (1991), who calculated a ratio of about 5:1 at 1.74 µm. The optical depth of the middle and lower clouds in our modeled hole is about τ ∼ 10, compared to about τ ∼ 23 in the modeled nominal cloud. We place the center of the hole in the center of our model domain; but offset it by half a grid cell to limit the effects of numerical diffusion on such a sharp concentration gradient at the peak. We choose xh so that the full width of the hole at half-maximum is approximately 2000 km, consistent with the observations of the cloud made by Crisp et al. (1991). We use a raised cosine because it is a function not quite as sharply peaked as a Gaussian, which helps to limit the effects of numerical diffusion at the beginning of the simulation.

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Table 1 List of 2D shear simulations Shear profile No shear Typical Constant Variable

Dissipation timea

Dissipation timea

(Sim #)

Without feedback

(Sim #)

With feedback

(2) (3) (5) N/Ac

2.8:1b

N/Ac

2.5:1b

(4) (6) (7)

N/Ac ∼21 days ∼15 days ∼15 days

∼12 days N/Ac

a “Dissipation time” is the time required for the simulation to achieve a con-

trast between maximum and minimum flux that is indistinguishable from the background. b In simulations where background level of contrast in not reached, we list the lowest contrast achieved. c Simulations which were not performed are designated “N/A.”

3. Results In this section, we describe each two-dimensional simulation that we ran. We performed seven simulations, as described in Table 1. In the first simulation, there is no horizontal wind, so the model is essentially a series of one-dimensional models as described previously by McGouldrick and Toon (2007), except for the differences in the numerical techniques between that model and this one which are discussed above in Section 2.3. The second simulation includes a spatially and temporally invariant zonal wind, but does not include microphysics or vertical transport. This simulation demonstrates how numerical diffusion can smear out a hole in our model. The third and fourth simulations demonstrate the effects of a vertical shear profile similar to that of Baker et al. (2000) on the holes in the clouds. Simulation 3 demonstrates the effects of shear alone, whereas simulation 4 demonstrates the effects of shear combined with microphysics and vertical transport. Simulations 5 and 6 demonstrate the effects of a profile of constant shear on the holes in the clouds. These simulations are identical to 3 and 4, except for the shape of the wind shear profile. Finally, simulation 7 considers the effects of a variable shear profile that depends upon the static stability. 3.1. Simulation 1: One-dimensional processes Fig. 4 shows the variation in the modeled 1.74 µm upwelling intensity at the top of the atmosphere over the course of our first 30 day simulation. Fig. 4 provides us with an opportunity to check our model against observations (i.e., Fig. 2). The model outputs flux integrated over the wavelength band in units of W m−2 , and we convert the upwelling flux into intensity to generate this figure. The upwelling flux is simply the integral of the intensity over the upward half of a sphere:

2π π/2 Fλ = Iλ cos θ sin θ dθ dφ.

(2)

φ=0 θ=0

If we assume that the intensity is isotropic, then the above integral reduces simply to Fλ = πIλ . In this manner, we convert the fluxes from our model into intensities for comparison with Fig. 2. We find that our modeled upwelling intensity is

Fig. 4. Upwelling intensity at the top of the atmosphere in the 1.74 µm band as a function of time in the uniform model (simulation 1). Also shown, for convenience of comparison with later results, is the brightness temperature that corresponds to the value of intensity at the major intervals in the figure.

approximately one-fifth to one-sixth of the intensity reported by Carlson et al. (1991), which we have reproduced in Fig. 2. Thus, our model is consistent with the observations, since our modeled intensity in this simulation emerges from a cloudy atmosphere, whereas the intensity reported in Fig. 2 emerges from a hole in the clouds (we know Fig. 2 is in a hole because the original figure of Carlson et al., upon which ours is based, demonstrates how the emission through the spectral windows could be used to probe the water vapor concentration below the clouds). The ratio between the emitted intensity from the hole in Fig. 2 and the emitted intensity from the cloud in Fig. 4 is consistent with the roughly 5:1 intensity ratio between “clear” and “cloudy” intensities reported by Carlson et al. (1991). The most obvious feature in Fig. 4 is the “sawtooth” quasiperiodicity to the upwelling intensity. This periodicity results because the transport and growth occur on much faster timescales than the radiative heating. Over time, the cloud base is continuously and gradually heated from below. During this time, the middle cloud region is statically stable, so the dominant transport process for the particles is sedimentation (especially for the larger particles). The gradual increase in the upwelling intensity during a single day is due to the slow loss of cloud mass as a result of this sedimentation. Eventually, the cloud base is heated sufficiently to drive the lapse rate unstable, at which time eddy diffusion (which is variable and calculated from the lapse rate, see McGouldrick and Toon (2007) for the details of this calculation) is able to transport particles and vapors quickly throughout the cloud. This mixing results in a rapid increase in cloud opacity, and a rapid decrease in the upwelling intensity. The magnitude of this quasi-periodic intensity variation is rather small. The ratio between the maximum and minimum upwelling intensity is about 1.40:1. This is far smaller than the 5:1 contrasts between the holes and the main cloud deck observed by Carlson et al. (1991). The average period of the oscillation is about 27 h. The variation in total cloud opacity that is driving these variations in intensity is only about one optical depth (the

Modeling the effects of shear on the evolution of the holes in the condensational clouds of Venus

mean total lower and middle cloud optical depth in this simulation is about τ ∼ 23). This simulation is useful in providing an estimate of cloud variability that results from interactions between microphysics and vertical mixing in our simulations. Another characteristic of the evolution of the modeled intensity in Fig. 4 is an apparent upward trend to the intensity over time. In order to determine whether this trend is real, we have run an additional simulation for two model years (not shown), identical to this one but consisting of only a single column. The flux in the wavelength interval being considered for the entire duration of this simulation remained between 0.0022 and 0.0036 W m−2 (between about 20 and 30 erg s−1 cm−1 ster−1 µm−1 ). That is, the subtle trend in Fig. 4 is not persistent, and is consistent with the natural variations that occur in the modeled cloud over timescales longer than one month. 3.2. Simulation 2: Numerical diffusion Numerical diffusion arises when one attempts to solve the advection equations via finite differencing methods. The name derives from the fact that if one were to re-constitute the advection equation from the finite differencing scheme that the machine solves, one finds that an additional diffusive term (with “diffusivity” a function of grid size and time step) has been introduced to the differential equation (see Press et al., 1992, chapter 19, for example). Numerical diffusion cannot be eliminated entirely: it can only be minimized by the choice of differencing scheme. Thus, it is important to characterize the effects of numerical diffusion in one’s model. In order to understand the effects of numerical diffusion in our model, we performed a simulation in which horizontal advection is the only active process. That is, there is no vertical transport in this simulation, either by advection or by diffusion. Furthermore, there are no growth processes acting: neither condensation and evaporation, nor coagulation and coalescence. We initialize the cloud particles as described by Eq. (1), and institute a vertically-constant zonal wind of −83 m/s (so that parcels are advected toward the west, in a retrograde fashion, as they are on Venus). Fig. 5 shows the evolution of brightness temperature of the optical hole as a function of time as the hole and the clouds, carried by the zonal winds, circle the planet. After thirty days, there is little noticeable difference from the brightness temperature of the initial hole. However, it has evolved slightly. The ratio between the maximum and minimum flux at the end of this simulation is only about 2.8:1, down significantly from the 4.9:1 ratio at the outset, but the hole still is quite conspicuous. Most of this reduction in contrast occurs in the first ten days of the simulation. At the end of this 30 day simulation, the hole has an optical depth τ = 14.7, up from its initial optical depth of about τ ∼ 10 (recall that the cloud has optical depth of about τ ∼ 23). 3.3. Simulation 3: Vertical shear This simulation tests the effectiveness of the vertical shear alone in smoothing out the holes. Here, we apply the zonal wind

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Fig. 5. Contour plot of evolution of brightness temperatures during the numerical diffusion test (simulation 2). The relatively bright diagonal line is the hole, whereas the black region is the relatively more opaque main cloud. The hole travels to the left in the graph due to the persistent easterly zonal winds. The line becomes less bright and slightly more diffuse as the optical hole spreads in space slightly due to numerical diffusion. The white vertical lines in this figure and subsequent figures demarcate an arbitrary half of the planet. Although there is no difference in terms of the calculations performed, we can consider the area between these white lines in the center of the figure to be the viewable night side of the planet.

Fig. 6. Contour plot of evolution of the brightness temperature in the simulation that demonstrates the effects of “typical” wind shear (simulation 3).

profile described by the dashed line in Fig. 3a; but we do not perform any additional physics. That is, this run is identical to our test of the numerical diffusion, except that we have now introduced vertical shear of the zonal wind. Fig. 6 shows the evolution of the hole in this simulation. The track of the hole around the planet is nearly as obvious as it is in the numerical diffusion simulation. The ratio of the maximum/minimum flux at the end of this simulation is 2.5:1. For comparison, the ratio of the 1.74 µm flux at 455 K to that at 440 K is approximately a factor of two. Since Crisp et al. (1989) reported that about 25% of the night side exhibited 1.74 µm brightness temperatures greater than 455 K and 25% exhibited brightness temperatures less than 440 K, a flux ratio of 2:1 would be recognized as clearly indicating the existence of a hole in the clouds. Since Crisp et al. (1989) were unable to identify their 16◦ latitude, 2000 km feature when it was expected to return to the

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Fig. 7. Time evolution of the maximum/minimum flux ratio. The black line represents simulation 2 (numerical diffusion case); the violet line represents simulation 3 (typical shear: no vertical transport); the blue line represents simulation 4 (typical shear: including feedback); the green line represents simulation 5 (constant shear: no vertical transport); the yellow line represents simulation 6 (constant shear: including feedback); and the red line represents simulation 7 (variable shear). The solid horizontal line indicates the level of the “background” contrast observed in simulation 1 (about 1.4:1); and the dotted horizontal line indicates a ratio of 2:1 (roughly comparable to the ratio of flux at brightness temperatures of 455 and 440 K).

night side after about 16 days, we can assume that the contrast in that particular hole had dropped to at least 2:1. Fig. 7 shows the evolution of the ratio of the maximum/minimum flux as a function of time in the several simulations (the blue curve represents simulation 3). The change in the contrast ratio declines gradually until, after 30 days, the rate of change of the contrast for some of the simulations is essentially zero. We see in Fig. 7 that the wind shear profile that we have applied in this simulation (3) is insufficient to dissipate a hole in the clouds to the point where it would be essentially indistinguishable in fewer than 30 days. 3.4. Simulation 4: Full physics with typical shear Next, we describe a simulation in which we include twodimensional dynamical transport, as well as the full microphysics calculations. The evolution of the brightness temperature is shown in Fig. 8. Here we see an evolution very different than those seen previously in the numerical diffusion simulation (simulation 2: Fig. 5) and the vertical shear (simulation 3: Fig. 6). The contrast between the hole and the cloud already is considerably diminished after only one revolution (about 5.14 days), and the hole is nearly indistinguishable from the background after only three revolutions about the planet (about two weeks). The ratio between the maximum and minimum fluxes in the model drops to a smaller value than anything seen in the previous simulations after only eight days (Fig. 7: blue curve). By the end of the simulation, this ratio has dropped to 1.3:1, which is comparable to the variations seen in the uniform cloud (1.4:1) discussed at the beginning of this section (simulation 1: Fig. 4). In fact, the contrast in this simulation drops to a value of about 1.4:1 in a time of about 21 days. Comparison of the contrast curves for this simulation (Fig. 7: blue) and the previous simulation (Fig. 7: violet) indicates the

Fig. 8. Contour plot of the evolution of brightness temperature in simulation 4: “typical” shear with full physics.

significance of the vertical mixing in dissipating the hole in this shear case. Simulation 3 loses contrast steadily, due to the effects of vertical shear of the zonal wind and numerical diffusion. This simulation (4), considering the effects of vertical transport as well, experiences a sharper drop (and more variability) in the contrast ratio. Furthermore, the vertical mixing in the vicinity of the hole is enhanced relative to the mixing that occurs in the nominal cloud. Fig. 9 compares the verticallyaveraged eddy diffusion coefficient in the middle cloud region (48 to 55 km) as a function of horizontal index. The horizontal index is the value of the horizontal grid cell, assuming a frame that moves with the clouds (i.e., east-to-west at a speed of 83 m/s). Thus, the location of the hole is constant with respect to the horizontal index. We compare the eddy diffusion coefficient averaged over the first 21 days (while there still remains an identifiable hole) to the eddy diffusion coefficient averaged over the last nine days (after the hole has been dissipated). To generate these curves, we find the average eddy diffusion coefficient between 48 and 55 km for each column at the time of each model output. We are interested in the magnitude of the vertical mixing generated by the radiative-dynamical feedback, so we ignore all columns at all times at which there is no mixing other than the pre-defined background level of mixing (i.e., we consider only columns that have an average eddy diffusion coefficient greater than 2 m2 s−1 ). We then find the average of the remaining column-averaged eddy diffusion coefficients. We see in Fig. 9, that the average eddy diffusion coefficient in the vicinity of the hole (which is centered at horizontal index 49.5), through the first 21 days (i.e., during the time that the hole still exists) is about 15% larger than the whole-model mean eddy diffusion coefficient. For comparison, also shown in Fig. 9 is the eddy diffusion coefficient averaged over the final nine days of the run (i.e., after the hole has dissipated). There is not any significant enhancement to the eddy diffusion coefficient anywhere in the model, averaged over these final nine days, as the excursions both above and below the whole-model mean are about the same. Also indicative of the role of the radiative-dynamical feedback in the more rapid dissipation of the holes is the behavior of the layer optical depth in the lowest kilometers of the cloud.

Modeling the effects of shear on the evolution of the holes in the condensational clouds of Venus

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of the cloud (which, as we recall from simulation 3, has a very small effect on the total cloud opacity and upwelling infrared flux), the enhanced opacity in the lowest kilometer of the hole causes a heating of that layer, triggering the vertical mixing via the radiative-dynamical feedback which leads to an increase in cloud opacity. Thus, there is an interaction between the vertical shear and the radiative-dynamical feedback that hastens the dissipation of the hole, relative to the situation with shear alone. 3.5. Simulation 5: Constant value of vertical shear (a)

(b) Fig. 9. Eddy diffusion coefficient averaged over altitudes from 48 to 55 km, and averaged over the time, for simulation 4 (typical shear: with feedback). We assume a frame that travels with the middle cloud deck at −83 m/s, so the center of the initial hole is always at a horizontal index of 49.5 (i.e., the center of the domain). The first plot represents the average eddy diffusion over the first 21 days of the simulation (while there still exists a clearly identifiable hole); the second plot represents the average eddy diffusion over the last 9 days of the simulation (after the hole has been dissipated). Each curve has been smoothed with a “boxcar” average with a horizontal index width of 6. The dotted line in each panel represents the model-wide average eddy diffusion coefficient.

In Fig. 10, we show the evolution in time of the extinction coefficient in three layers in the lower cloud region of simulation 3 (typical shear: no vertical transport) and simulation 4 (typical shear: with feedback) as a function of time at one particular location on the planet. We have plotted the evolution of the extinction coefficient for layers in our model centered at 47.5 (within the sub-cloud shear region), 48.5, and 49.5 km (the latter two are in the region of the velocity profile that does not exhibit shear). We can see clearly the significant change in the extinction coefficient that occurs as the hole passes “overhead.” The total opacity in each layer is reduced by about 50% with a periodicity of about once every 5.14 days in the nonfeedback case. Note that the location of the hole at 47.5 km, in the simulation without vertical transport, travels relative to the hole in the layers above it as a result of the difference in the zonal velocity between these two altitudes. However, in the case of the simulation which includes vertical transport via the radiative-dynamical feedback, the relative location of the hole at all three altitudes remains unchanged throughout the simulation, traveling, at all altitudes, at the zonal velocity characteristic of the middle cloud (−83 m/s). Thus, as shear at the cloud base fills in the edges of the hole at the lowest kilometer

To determine whether the particular wind profile we used was responsible for the persistence of the hole in the case with no vertical transport (Section 3.3), we performed another simulation in which horizontal transport occurs, but cloud physics and vertical transport do not. In this case, however, we assume a linear vertical profile of zonal velocity with a constant shear of −2.5 m/s km−1 (solid line in Fig. 3a). This “constant” shear profile is identical to the “typical” shear profile used in simulation 3 and simulation 4 at all modeled altitudes below 48.5 km. The zonal velocity reaches −83 m/s at 48.5 km in this simulation. The constant shear profile and the typical shear profile also have approximately the same zonal velocity at the top (60 km) of the model. As can be seen in Fig. 11, maintaining a constant shear throughout the model domain results in a rather quick dissipation of the hole. By the second revolution about the planet (less than ten days), the initially relatively compact central peak is absent. The maximum contrast in the model at 1.74 µm has dropped below 2:1 after only about five days; and below 1.4:1 after only about twelve days (Fig. 7: green curve). Clearly, a constant shear profile is more effective at smoothing out the holes in the clouds than the “typical” shear profile we used in simulation 3 (Fig. 6, and the violet curve in Fig. 7), in which shear only occurs near cloud top and cloud base. A constant shear profile, even without vertical transport driven by the radiative-dynamical feedback, also is more effective at dissipating the hole than is the typical shear case with radiative-dynamical feedback (simulation 4). This is not terribly surprising since vertically-adjacent layers of a 2000 km wide hole, experiencing a difference of zonal wind of 2.5 m/s, 6 m will be sheared completely in a time of 2×10 2.5 m/s ≈ 10 days. 3.6. Simulation 6: Full physics with constant shear Next, we consider the evolution of a hole experiencing the constant shear profile in a simulation that includes vertical transport and cloud physics. In Fig. 12, we see that the hole has disappeared after barely one revolution around the planet. This is considerably more rapid than the dissipation of the hole observed by Crisp et al. (1991). The ratio of the maximum/minimum flux drops below 2:1 after only six days (compared with simulation 4, which took about twelve days). The hole is barely distinguishable from the background, exhibiting a contrast of less than 1.4:1 after only about 15 days (Fig. 7: yellow curve).

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Fig. 10. Comparison between the behavior of the lower cloud in response to shear in the presence (upper panel) and absence (lower panel) of vertical motions driven by the radiative-dynamical feedback. Each curve represents the evolution of the extinction coefficient of a layer in the atmosphere at a given location, relative to the nominal optical depth. The lowermost curve in each panel indicates the behavior of the 47 to 48 km layer; the middle curve indicates the behavior of the 48 to 49 km layer; and the topmost curve indicates the behavior of the 49 to 50 km layer. The latter two curves have been offset from the former by +1 and +2 optical depths, for clarity.

Fig. 11. Contour plot of the evolution of brightness temperature in simulation 5: constant shear.

Fig. 12. Contour plot of the evolution of brightness temperature in simulation 6: constant shear, including vertical transport and microphysics.

In contrast with the typical shear cases, however, the additional consideration of vertical transport and cloud physics has little effect on the dissipation of the cloud in the constant shear case. There is increased variability with time in the case with the cloud physics included (just as was the case with the typical shear simulations), but the contrast ratio diminished at the same overall rate in the two simulations with constant shear, regardless of any influence of vertical mixing. This is not to say that there is a lack of enhanced vertical mixing caused by the shear; but rather that the change in cloud opacity induced by the horizontal motions dominates that caused by vertical motions, in this case.

3.7. Simulation 7: Stability-dependent shear Finally, in Fig. 13, we show the results of a simulation in which the value of the vertical shear of the zonal wind is dependent upon the stability conditions. In a true physical situation, vertical motions or convection driven by local instability tend to suppress the vertical shear. The contrast between the maximum and minimum flux in this simulation diminishes nearly as quickly as it does in simulation 6 (constant shear, with feedback). The contrast reaches a value of 2:1 after about seven days, between the times required by the previous two cases that included feedback. The contrast drops nearly as low as 1.4:1 af-

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train air from adjacent columns via mass continuity, inducing horizontal motions that might have an effect on how the zonal winds evolve. On Earth, vertical shear of the horizontal wind can affect the morphology of convection, for example, in the formation of “cloud streets.” Furthermore, the timescale for the dissipation of shear due to convection in the Venus atmosphere is not well known. Nor is the timescale for the restoration of zonal flow once vigorous convection ceases. In our model, we arbitrarily assume that these two timescales are essentially zero, since we switch instantaneously between the two shear profiles. Finally, the processes which generate and sustain the Venus zonal super-rotation are poorly understood and beyond the scope of this model. Fig. 13. Contour plot of the evolution of brightness temperature in simulation 7: variable shear.

4. Discussion

ter about 15 days, the same time that simulation 6 took to reach this level; but the contrast ratio in the variable shear simulation remains slightly greater than the ratio in simulation 6 through much of the remainder of the simulation. As mentioned in Section 2.4, the magnitude of the vertical winds that arise from the horizontal shear of the zonal wind in this simulation is on the order of a few cm/s. While Imamura and Hashimoto (1998) have shown that a persistent vertical wind on the order of a few mm/s (i.e., the Hadley circulation) is capable of affecting the distribution of the cloud mass, the vertical winds arising from the horizontal shear of the zonal wind in this simulation is not persistent. As evidenced in Fig. 4 the vertical mixing is characterized by brief periods of significant activity, followed by longer periods of relative quiescence. Thus, the vertical winds that are generated by this process in the variable shear simulation also are intermittent. For the most part, there is very little horizontal shear of the zonal wind; hence the cloud behaves largely as though it were in the constant shear case. In the instances where the instability is significant enough to trigger vertical motions, which are experienced as an enhanced eddy diffusion coefficient, the calculation of a vertical velocity is performed only to satisfy mass continuity. While this simulation does account for the suppression of shear by vertical motions driven by instability and convection, it does so in a somewhat unphysical manner. In our model, the mixing that is driven by the radiative-dynamical feedback usually first manifests itself as an enhanced eddy diffusion coefficient at cloud base, brought about by the radiative heating there which drives an unstable lapse rate in the lowest kilometer of the cloud. In the first dynamical timestep in which this feedback occurs, the enhanced eddy diffusion coefficient enables the mixing of much of this heating up to the next layer, and only the next layer, of the model. This processes repeats until the propagated heating no longer drives the next layer unstable. This is why we use the typical shear profile if there exists instability at any altitude. In our model, an enhanced eddy diffusion coefficient present anywhere in the column is an indication of convective overturning at work. Unlike our model, a real atmosphere will exhibit an interaction between the vertical and horizontal winds. A rising (or sinking) plume might en-

It is important to note that our simulations assume that the processes that lead to the formation of the holes have ceased to act. Thus, the lifetimes quoted here are lower limits to the expected cloud lifetime under each set of conditions. Furthermore, the formation of the large hole observed by Crisp et al. (1991) was not seen. Thus, the lifetime of that particular hole also could have been longer than the 11 to 16 days that the hole was observed. Nevertheless, the combination of the simulations presented here and the observations of the large hole made by Crisp et al. (1991) can be used to partially constrain the mechanisms for the dissipation of holes in the clouds of Venus. For example, if a hole is observed to dissipate in a shorter time than the holes in these simulations, then it is likely that a process other than the radiative-dynamical feedback and the typical vertical shear of the zonal wind is responsible for the filling of the holes. Conversely, a considerably longer-lived hole, compared with the lifetimes in the present simulations, could indicate the long-term persistence of the hole-forming mechanism. Careful, long-term observations—such as can be made by Venus Express, now in orbit, or by Venus Climate Orbiter, due to be launched by the Japanese Space Agency in a few years—that can capture the entire life cycle (or at least the formation and ultimate dissipation) of holes in the clouds of Venus, can provide the observational evidence that, when combined with simulations such as these, can identify the formative and dissipative mechanisms of these features. While both of the “full physics” simulations (simulation 4: Fig. 8; and simulation 6: Fig. 12) illustrate holes in the cloud that rapidly diminish to a level of contrast consistent with normal variations in the cloud opacity in a time consistent with observations of hole dissipation, there are differences between the results of these simulations which can help to identify which case is more representative of a particular situation in the clouds of Venus. The Pioneer Venus descent probes observed a correlation between wind shear and static stability (Schubert et al., 1980), in which regions of greater stability tended to occur in regions of greater wind shear, and vice versa. Furthermore, most of the descent probes observed an alternation between regions with high and low wind shear in the Venus atmosphere. Thus, the shear profile we employ in simulations 3 and 4 is likely typi-

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(a) Fig. 14. Morphology of the hole in simulation 4 (full physics with typical shear: lower panel) and of the hole in simulation 6 (full physics with constant shear: upper panel) after two full revolutions about the planet (about 10.25 days). The horizontal dotted line is the mean “background” brightness temperature in each case, defined as the average of the brightness temperature in the half of the modeled domain that is farthest from the peak. Note the difference in the brightness of the hole itself, as well as the more asymmetric shape of the curve in the constant shear simulation.

cal of the atmospheric situation we have assumed both here and in McGouldrick and Toon (2007), namely, there is a neutrally stable region with vertical transport driven by the radiativedynamical feedback in the lower clouds. However, not all of the descent probes observed this alternation between regions of high and low shear. The Pioneer Venus north probe observed a fairly consistent (but gradually increasing with altitude) average shear of about −2.5 m/s km−1 . Thus, holes that develop under conditions similar to those experienced by the Pioneer Venus north probe might experience dissipation in a manner more like our simulation 6. Both compact, “blocky,” holes (such as we see in simulation 4), and zonally-elongated holes (such as we see in simulation 6) have been observed in the clouds of Venus (Belton et al., 1991). Simulation 4 (“typical” shear) requires about 11 to 16 days to effect a nearly complete dissipation of the hole, whereas simulation 6 (constant shear) requires barely half that time. The physical characteristics of the dissipating hole also differ subtly between these two cases. In Fig. 14, we display the brightness temperature as a function of position in the model domain for each of the “full physics” simulations, at a time of 10.25 days: two circuits around the planet at 16◦ latitude at a speed of −83 m/s. Most obvious is the difference in maximum brightness temperature that has already been addressed in the previous sections. There also is a suggestion of a difference in symmetry between the two curves. The brightness temperature in the hole in the lower panel (which depicts the simulation with full physics and the typical shear profile) is still sharply peaked and appears to be somewhat horizontally symmetric. The brightness temperature in the hole in the upper panel (which depicts the simulation with full physics and the constant shear profile), appears to be slightly more asymmetric, with the peak in the brightness temperature displaced to the

(b) Fig. 15. (a) Morphology of the hole in simulation 5 (constant shear: no feedback) after two full revolutions about the planet (about 10.25 days). (b) Vertical profile of the extinction coefficient of the Venus clouds in the simulations.

left of the center of the hole (where the hole is taken to be the region enclosed by the locations where the brightness temperature curve first crosses the dotted line that indicates the average background brightness temperature). This apparent asymmetry in the profile of the brightness temperature in the constant shear simulation is possibly an artifact of the increased “noise” that results from the peak brightness temperature similar to the background. Recall the one-dimensional simulation shown in Fig. 4, which indicates that variations in 1.74 µm brightness temperature on the order of about 3 K are a typical response to the onset of the mixing due to the radiative-dynamical equilibrium in our simulations. The magnitude of the variation seen in Fig. 14 is only about three times greater than this. In Fig. 15a, we see that the hole in the case of simulation 5 (constant shear without feedback) is significantly skewed to the downwind direction of the center of the feature. This asymmetry occurs because of the particular distribution of the opacity in the Venus clouds. In Fig. 15b, we see that the cloud is thickest between about 47 and 50 km, while the extinction [km−1 ] be-

Modeling the effects of shear on the evolution of the holes in the condensational clouds of Venus

comes smaller with increasing altitude above ∼50 km. Since the zonal velocity increases with altitude, the comparatively thinner parts of the cloud are advected farther to the west (i.e., downwind) than the comparatively thicker parts of the cloud. Hence, in the case of constant shear, the vertical shear, by itself, causes the hole to become skewed to the downwind side. However, the hole in simulation 6: constant shear, with feedback (upper panel in Fig. 14) is skewed in the opposite direction as the hole in Fig. 15. This difference in the of the hole between simulation 6 (constant shear, with feedback) and simulation 4 (constant shear, without feedback) is further evidence for the effect of the radiative-dynamical feedback on the dissipation of the hole. That the downwind portion of the hole is less dissipated than the upwind portion of the hole indicates that the radiative-dynamical feedback, which has greater effect on the lower parts of the cloud, plays an important role, even in the dissipation of features that experience relatively constant vertical wind shear. Perhaps the morphological evolution of the holes can tell us something about the nature of the shear structure there; and by proxy, tell us something about the stability profile and the convective qualities of the clouds. For example, the north probe observed a fairly constant vertical profile of wind shear. From our simulation 6, holes in such regions will become considerably elongated, and not be as bright as holes which experience a shear profile more like our typical shear profile used in simulation 4. Alternately, significant elongation of the holes could also be indicative of meridional shear of the zonal wind. The Venus Express mission may have high-resolution images of the evolution of the holes in the clouds of Venus. If real, the symmetry differences between these two simulations might be used to interpret the morphological differences in such potential observations. Repeated, high-resolution imaging of the larger holes in the clouds of Venus by Venus Express can confirm the processes by which the holes are destroyed. Since the vertical mixing by convection is likely more intermittent than the horizontal mixing by shear, observations of the evolution of the larger holes in the clouds of Venus (especially, observations of the edges of the holes, where subtle shear near cloud base coupled with the feedback will be most apparent) can help to demonstrate which of the processes investigated in this paper is at work. 5. Conclusions We have run a series of simulations of the middle and lower cloud decks of Venus with a two-dimensional microphysical model that includes vertical motion via the radiative-dynamical feedback and zonal flow via a pre-determined zonal wind profile. We have performed these simulations in order to better understand the processes that cause the destruction or fillingin of the holes in the clouds of Venus that are associated with variations in the lower and middle cloud decks. The typical vertical shear of the zonal wind is capable of reducing the contrasts observed in the brightness temperatures at 1.74 µm. However, even after thirty days, shear alone reduced the contrasts only to about a factor of 2.5:1. This is still a greater contrast than that between the flux in the top quartile and the

47

flux in the bottom quartile of the observed night side of Venus. Thus, typical shear can reduce the brightness temperature contrasts between holes and clouds, but not by sufficient magnitude to be consistent with observations of hole evolution. A constant vertical shear, similar to that observed by the Pioneer Venus north probe, is capable of dissipating the hole rather quickly and significantly. The ratio of the maximum to minimum brightness was reduced to levels comparable to the natural variations in less than two weeks’ time. However, such a constant vertical shear profile is physically implausible in a region with neutral lapse rates. There are identifiable differences between the “full physics” simulations with different shear profiles. Holes in the “full physics” simulation with constant shear were dissipated in less than a week, which is considerably shorter than what has been observed. This result is consistent with the fact that constant shear across the neutrally stable region is unlikely to exist. In contrast, the holes in the “full physics” simulation with a typical shear profile lasted about two to three weeks, as has been observed. Also, the shape of the dissipating hole differed between these two simulations. The hole in the constant shear case experienced greater “spreading” over a wider horizontal area and appeared to exhibit a subtle horizontal asymmetry. The hole in the typical shear case was comparatively more symmetric and more localized throughout the dissipation process. These observable differences may be useful in determining the physical and dynamical conditions that exist in the neighborhood of a particular hole. The inclusion of vertical transport and microphysical processes served to accelerate the dissipation of the hole in each shear profile case. Vertical shear of the zonal wind combined with vertical mixing and transport due to the radiativedynamical feedback was capable of reducing the brightness contrasts in the clouds of Venus much more quickly than shear alone. Regardless of our choice of shear profile, in simulations which accounted for both vertical shear of the zonal wind and vertical motions driven by the radiative-dynamical feedback, the ratio of the flux between the hole and the cloud was reduced a level consistent with normal variations in a time of two to three weeks. Vertical mixing is enhanced in the vicinity of the hole relative to the mixing that occurs elsewhere in the model, in the absence of a hole. Thus, we conclude that the interaction between shear and the radiative-dynamical feedback is responsible for the dissipation of the holes in the clouds of Venus. The main conclusions of this paper, summarized above, coupled with the conclusions from McGouldrick and Toon (2007), lend clarity to some of the unresolved questions about the middle and lower cloud decks on Venus. The ability of our simple, parameterized radiative-dynamical feedback simulation, described previously in McGouldrick and Toon (2007), to reproduce the observed characteristics of the clouds of Venus indicates that the condensational clouds of Venus are probably sustained by such a feedback, similar to the feedback that sustains terrestrial marine stratocumulus. This feedback generates convective motions, which, according to the work of Baker et al., must be compressible in nature. One characteristic of compressible convective processes is the presence of

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broad upwellings with smaller vertical velocities than the narrower downwellings. Though there is a significant difference in the scale of the downdrafts noted in the models of Baker et al. (∼10 km) and the observed large holes on the night side of Venus (∼103 km), the processes could still be similar in nature. A consequence of the difference between the nature of the upwellings and the downwellings is that the convective updrafts cannot necessarily be counted upon to fill in the holes once they have been formed. Thus, shear processes must be invoked to dissipate the large holes in the Venus clouds. Though observations indicate that the shear within most of the middle cloud deck is negligible, the shear that exists near to the base of the cloud deck is sufficient to draw enough cloud mass into the hole that the feedback is again stimulated, resulting in significant mixing throughout the hole, which fills it in. Repeated, highresolution imaging of the larger holes in the clouds of Venus by Venus Express can confirm the processes by which the holes are destroyed. Since the vertical mixing by convection is likely more intermittent than the horizontal mixing by shear, observations of the evolution of the larger holes in the clouds of Venus (especially, observations of the edges of the holes, where subtle shear near cloud base coupled with the feedback will be most apparent) can help to demonstrate which of the processes investigated in this paper is at work. Acknowledgments We thank two anonymous reviewers and the editor for their helpful comments and suggestions for the improvement of this paper. This work was supported by NASA’s Planetary Atmospheres Program under Grant NNG05GA53G. References Allen, D.A., Crawford, J.W., 1984. Cloud structure on the dark side of Venus. Nature 307, 222–224. Baker, R.D., Schubert, G., Jones, P.W., 2000. Convectively generated internal gravity waves in the lower atmosphere of Venus. Part II. Mean wind shear and wave-mean flow interaction. J. Atmos. Sci. 57, 200–215. Bell, J.F., Crisp, D., Lucey, P.G., Ozoroski, T.A., Sinton, W.M., Willis, S.C., Campbell, B.A., 1991. Spectroscopic observations of bright and dark emission features on the night side of Venus. Science 252, 1293–1296. Belton, M.J.S., Gierasch, P.J., Smith, M.D., Helfenstein, P., Schinder, P.J., Pollack, J.P., Rages, K.A., Ingersol, A.P., Klaasen, K.P., Veverka, J., Anger, C.D., Carr, M.H., Chapman, C.R., Davies, M.E., Fanale, F.P., Greeley, R., Greenberg, R., Head III, J.W., Morrison, D., Neukum, G., Pilcher, C.B., 1991. Images from Galileo of the Venus cloud deck. Science 253, 1531– 1536. Bullock, M.A., Grinspoon, D.H., 1996. The stability of climate on Venus. J. Geophys. Res. 101, 7521–7529. Carlson, R.W., Baines, K.H., Encrenaz, Th., Taylor, F.W., Drossart, P., Kamp, L.W., Pollack, J.B., Lellouch, E., Collard, A.D., Calcutt, S.B., Grinspoon,

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