Long-term Variations of Venus's 365 nm Albedo Observed by Venus Express, Akatsuki, MESSENGER, and the Hubble Space Telescope

3.1.1. Reflectivity

We converted the observed radiance to a radiance factor, r_F (Hapke 2012), the ratio of bidirectional reflectivity of a surface to the perfectly diffuse Lambertian surface illuminated normally. We calculate the average solar flux at 1 au (Chance & Kurucz 2010) at each of the UV filters of VMC and UVI, S_⊙ (W m⁻² μm⁻¹), and the radiance factor as

$\begin{eqnarray}&&({r}_{{\rm{F}}})=\pi \beta ({R}_{\mathrm{obs}})\displaystyle \frac{{{d}_{{\rm{V}}}}^{2}}{{S}_{\odot }},\end{eqnarray} \tag{ 1 }$

where ${R}_{\mathrm{obs}}$ is the observed radiance (W m⁻² sr⁻¹ μm⁻¹), β is a calibration correction factor of VMC or UVI, and d_V is the distance of Venus to the Sun (in au).

3.1.2. Photometric Corrections

The 365 nm images show a combination of a smooth gradient from the subsolar point to the terminator, and dark features owing to the presence of the unknown absorber. The smooth gradient depends on the incidence (i), emergence (e), and phase (α) angles, which can be described by a photometric law (disk function), D(μ, μ₀, α), where $\mu =\cos (e)$ and ${\mu }_{0}\,=\cos (i)$. We can separate albedo, A(α), and disk function, D(μ, μ₀, α), from the radiance factor (r_F) that is derived from the measured radiance (Shkuratov et al. 2011),

$\begin{eqnarray}&&{r}_{{\rm{F}}}=A(\alpha )D(\mu ,{\mu }_{0},\alpha ).\end{eqnarray} \tag{ 2 }$

This albedo A, the equigonal albedo, depends on α (Shkuratov et al. 2011).

Previous studies showed that the Lambert and Lommel-Seeliger law (LLS) performs better in describing the gradient depending on geometric angles, compared to the Lambert law and the Minnaert laws (Lee et al. 2015a, 2017). Therefore, in this study, we adopted the LLS (Buratti & Veverka 1983; McEwen 1986),

$\begin{eqnarray}&&{D}_{\mathrm{LLS}}=k(\alpha )\displaystyle \frac{2{\mu }_{0}}{{\mu }_{0}+\mu }+(1-k(\alpha )){\mu }_{0},\end{eqnarray} \tag{ 3 }$

where k is a coefficient depending on α,

$\begin{eqnarray}\begin{array}{rcl}k(\alpha ) & = & 0.216004+0.00194196\\ & & \times \,\alpha -(2.11589\times {10}^{-5})\times {\alpha }^{2},\end{array}\end{eqnarray} \tag{ 4 }$

and α is in degrees. Equation (4) is updated from Lee et al. (2017), using more images to find the mean condition along the phase angle.

3.1.3. Areas of Disk-resolved Albedo for a Comparison

Figure 2 shows albedo A at three 5° phase angle bins: 75°–80°, 80°–85°, and 85°–90° (top to bottom). The left four columns are VMC images, having middle-latitudinal views close to UVI's equatorial views in the right two columns. While the UVI data have quality navigation using limb-fitting (Ogohara et al. 2017), the VMC data do not. So, we restricted the VMC data satisfying i < 84°, e < 81°, and r_F > 0.05 (Lee et al. 2015a). The last condition causes a nonsmooth terminator for the VMC images in Figure 2. As shown in these example images, we find no systematic tendency of albedo along local time but temporal variations in the brightness and morphology. We also attempted to search for systematic variations in the albedo along longitude, as the surface topography may affect the 365 nm albedo, particularly over Aphrodite Terra (Bertaux et al. 2016), but the longitudinal coverage of the VMC data is not evenly distributed over time. Additionally, this depends on phase angle selections. A detailed analysis along longitude, latitude, and time requires a different approach from the broad range average utilized in this study. Here we focus on temporal variations using data obtained over a broad range of longitudes. We derive the mean latitudinal albedo from disk-resolved VMC and UVI images, divided into two broad latitude bins: low (0°–30°) and high (50°–70°) latitudes. We also derive a low-latitudinal albedo from the MASCS and STIS spectral data to complete the cross-comparison with the VMC data (Section 3.1.4).

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From the equatorial orbit, the UVI images show that cloud-top albedo and contrast patterns primarily displayed north–south symmetry. However, as the example in Figure 3 shows, we also observed cloud-top albedo patterns that were asymmetric across the equator. This asymmetry was observed frequently in 2017 January–February. Wind fields retrieved from cloud motions also detected the similar asymmetry between the northern and southern hemispheres over the same period (Horinouchi et al. 2018). Thus, we restrict our disk-resolved data comparison only for the southern hemisphere, which was observed by all four instruments.

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3.1.4. Cross-comparison of Disk-resolved VMC, MASCS, STIS, and UVI Data

The observed long-term decrease of albedo had been previously attributed to the sensitivity degradation of VMC by Shalygina et al. (2015). Following these authors, we used the 2.32 calibration correction factor (their Figure 12), which was retrieved from the comparison with VIRTIS-IR, and their value for the degradation ratio, k_d (= −16.2 × 10⁻⁵ orbit⁻¹, and one orbit of Venus Express equals 1 Earth day). We correct all VMC data to the value at an initial sensitivity condition (zero orbit number of Venus Express) using the equations given in Shalygina et al. (2015),

$\begin{eqnarray}&&B(t)={B}_{0}(t)\beta ,\end{eqnarray} \tag{ 5 }$

where t is time (orbit); B and B₀ are the corrected and observed radiance, respectively (W m⁻² sr⁻¹ μm⁻¹); and β is the 2.32 calibration correction factor. The temporal sensitivity degradation correction is given as

$\begin{eqnarray}&&B({t}_{2})=B({t}_{1})\left(\displaystyle \frac{1+{k}_{d}{t}_{2}}{1+{k}_{d}{t}_{1}}\right),\end{eqnarray} \tag{ 6 }$

where k_d is the sensor degradation factor (orbit⁻¹). We can get $B(t=0)$ as

$\begin{eqnarray}&&B(t=0)=B(t)\left(\displaystyle \frac{1}{1+{k}_{d}t}\right).\end{eqnarray} \tag{ 7 }$

So the final form is

$\begin{eqnarray}&&B(t=0)={B}_{0}(t)\beta \left(\displaystyle \frac{1}{1+{k}_{d}t}\right).\end{eqnarray} \tag{ 8 }$

Figure 4 shows a comparison of low- and high-latitudinal albedo at the same phase angle bins using the corrected VMC data with Equation (8) (Shalygina et al. 2015). These corrected VMC data are significantly brighter than any of the independently calibrated MASCS, STIS, and UVI observations. The large difference between the 2006 VMC and 2016 UVI is especially noticeable, while the data in 2006 are supposed to have the least sensitivity degradation. We therefore discard this correction on the VMC data due to the inconsistency with other calibrated MASCS, STIS, and UVI data.

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Instead, we use the star calibration correction factor, 2.0 ± 0.822, for the initial calibration correction factor (β) of the 365 nm channel of VMC (Titov et al. 2012; Shalygina et al. 2015). The large error of 82% results in the ambiguous definition of the absolute radiance. In this study, we improve the calibration of the data using the data points of MASCS in 2007 and STIS in 2011 as a reference to fit VMC values (Table 1). To limit uncertainties that may arise from the influence of the aerosol scattering along the phase angle (α), we utilize only VMC data obtained at the same phase angle as either the MASCS (α = 85°–90°) or STIS (α = 75°–90°) observations. There are differences of 13 and 31 days from the closest VMC image at the time of the MASCS and STIS observations, respectively, at corresponding phase angles. To compensate for possible short-term fluctuations that may have occurred during those time periods, we derive the 80 days mean albedo observed by VMC in the low-latitude bin at the two phase angle bins of MASCS and STIS. We then use the 80 days mean albedo to calculate ratios of A(MASCS)/A(VMC) at α = 85°–90° and A(STIS)/A(VMC) at α = 75°–80°, where A is the mean low-latitude albedo. Using this process, the ratios of 0.74 for A(MASCS)/A(VMC) and 0.84 for A(STIS)/A(VMC) were inferred. Differences in the ratios may result from differences in the latitudinal coverage of the MASCS and STIS observations (Figure 1) and may also incorporate a possible temporal variation of the sensitivity of VMC. Even though the latter is possible, the decreasing trend of low-latitude albedo between 2007 and 2011 changes from 29% to 24% in the low-latitudinal polynomial fit (Figure 5), which is yet a minor effect on the results of this study. Using the mean value of the ratios, 0.79, over all of the VMC data, the VMC and UVI albedo retrievals become reasonably comparable (Figure 5). Thus, we adopt this value and apply a new modified VMC calibration correction factor of 1.58 (β = 2.0 × 0.79) to the VMC data used in our study. As Figure 5 shows, when the modified calibration correction factor is applied, the 365 nm albedo observed by VMC and UVI are reasonably aligned; those in 2008–2009 (VMC) are overlapped data in 2016 (UVI).

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In order to evaluate the robustness of the 1.58 modified VMC calibration correction factor, we employ 82 images taken with UVI in 2011 to compare with VMC. These UVI images were obtained after the first failure of the planned Venus orbit insertion of Akatsuki (Nakamura et al. 2014). In those images, the apparent size of Venus is a few pixels across, but sufficient signal-to-noise ratios were achieved. We calculated the whole-disk albedo, A_whole-disk, which is a function of phase angle (α), following the equation (Sromovsky et al. 2001)

$\begin{eqnarray}&&{A}_{\mathrm{whole} \mbox{-} \mathrm{disk}}(\alpha )=\displaystyle \frac{\pi }{{{\rm{\Omega }}}_{\mathrm{Venus}}}\displaystyle \frac{{{d}_{\mathrm{Venus}}}^{2}{F}_{\mathrm{Venus}}}{{S}_{\odot }},\end{eqnarray} \tag{ 9 }$

where d_Venus is the Venus distance to the Sun (au), F_Venus is the measured disk-integrated Venus flux (W m⁻² μm⁻¹), Ω_Venus is the solid angle of Venus as seen from the spacecraft (sr), and S_⊙ is the solar irradiance at 1 au (W m⁻² μm⁻¹), which is calculated for either UVI or VMC, using each of the transmittance functions.

The observed solid angle of Venus, Ω_Venus, is calculated as

$\begin{eqnarray}&&{{\rm{\Omega }}}_{\mathrm{Venus}}=\pi {\left({\sin }^{-1}\left(\displaystyle \frac{{r}_{\mathrm{Venus}}}{{d}_{{\rm{V}} \mbox{-} \mathrm{sc}}}\right)\right)}^{2},\end{eqnarray} \tag{ 10 }$

where r_Venus is the cloud-top level radius of Venus (6052 + 70 km), and d_V-sc is the distance of the spacecraft from Venus (km). The observed Venus flux, F_Venus, is calculated as

$\begin{eqnarray}&&{F}_{\mathrm{Venus}}=\displaystyle \sum _{r\lt {r}_{o}}{R}_{\mathrm{obs}}(x,y)\times {{\rm{\Omega }}}_{\mathrm{pix}},\end{eqnarray} \tag{ 11 }$

where (x, y) is a location of a pixel in the image, Ω_pix is a solid angle of 1 pixel of either VMC or UVI, R_obs is the radiance (W m⁻² sr⁻¹ μm⁻¹) in the target area (r < r_o), and r is the distance of (x, y) from the Venus disk center (emission angle 0°). Here r_o is the radius range in which the measured radiances are summed, considering the point-spread function of the instrument (5 pixels) that is the required radius of the aperture photometry of the UVI star flux analysis. The whole-disk albedo can be expressed as A_gΦ(α), where A_g is the geometric albedo, and Φ(α) is the phase law of Venus, describing the disk-integrated scattering efficiency as a function of phase angle (García Muñoz et al. 2014, 2017).

3.2.1. Comparison of the Whole-disk Albedo of VMC and UVI

We calculated the whole-disk albedo, A_whole-disk (Equation (9)), of the 82 UVI images in 2011 and all of the disk-resolved VMC and UVI images. The latter is possible because our analysis is restricted to the images for which the observable dayside, defined by the observation elongation angle, is fully captured within the field of view of the cameras (see Figure 2). The 1.58 modified calibration correction factor is applied to the VMC data.

Figure 6 shows the results of the whole-disk albedo versus phase angle. The 82 UVI images taken in February–March (circles) and May 11–20 (triangles) are compared to the VMC images obtained contemporaneously. As a reference, the whole-disk albedo results derived from 2015–2017 UVI data and 2006–2007 VMC data are also included in the plot. The vertical bar of UVI data indicates the 18% error in the absolute radiance (Section 2). The fractions of the disk illuminated by the Sun change with the solar phase angle, from 100% at 0° phase angle to 0% at 180° phase angle, so there is a dominant decreasing trend as the phase angle increases. At small phase angles, a local minimum related to glory is apparent (García Muñoz et al. 2014; Lee et al. 2017). The polynomial fit of UVI's 2015–2017 data shows the empirical phase function Φ(α) in the 40°–110° phase-angle range (brown solid line; the equation is shown in Table 2). We shift this phase function vertically to fit the maximum and minimum VMC whole-disk albedo at a 75°–80° phase angle (cyan lines), assuming a change of geometric albedo A_g over time, whereas the scattering properties Φ are the same. The lower cyan line that fits the VMC whole-disk albedo in 2011 February–March encompasses the UVI data at the same period. This means that the 1.58 modified calibration correction factor for VMC data works well.

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Table 2.  Coefficients of a Polynomial Fit, $y(\alpha )={\sum }_{i\,=\,0}^{n}{c}_{i}{\alpha }^{i}$, Where n ≤ 8, in Figures 6 and 8

	${\bar{A}}_{\mathrm{UVI},\mathrm{low} \mbox{-} \mathrm{lat}}(\alpha )$	${\bar{A}}_{\mathrm{UVI},\mathrm{high} \mbox{-} \mathrm{lat}}(\alpha )$	${\bar{A}}_{\mathrm{UVI},\mathrm{whole} \mbox{-} \mathrm{disk}}(\alpha )$
c0	0.18708465	0.47673713	0.62539023
c1	0.0086404233	0.0029037657	−0.022833883
c2	−0.00017491717	−0.00012465654	0.00063482472
c3	1.1079428 × 10−6	9.7921542 × 10−7	−1.2777032 × 10−5
c4			1.7206082 × 10−7
c5			−1.4916523 × 10−9
c6			7.9181817 × 10−12
c7			−2.3230007 × 10−14
c8			2.8698482 × 10−17

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In addition, our analysis of the 2011 and 2015–2017 UVI whole-disk albedo at 0° phase angle, which is a geometric albedo A_g, increases from ∼0.33 in 2011 to ∼0.40 in 2015–2017. This result confirms the increasing albedo trends from 2011 to 2015–2017 observed at high and low latitudes based on the recalibrated disk-resolved 2011 VMC and disk-resolved 2015–2017 UVI data (Figure 5). The observation of an increasing albedo over these time periods completely opposes the behavior that would be produced by progressive long-term UV sensor degradation (Shalygina et al. 2015). This cannot be used to investigate the influence of surface topography on the 365 nm albedo because for each date, a broad range of longitudes is included in the derivation of the albedo at small phase angles; this includes the 150–315°E range in 2011 March, 180–330°E in 2016 May, and 165–(360)–45°E in 2016 December–2017 January. Additionally, the 2011 UV data have insufficient spatial resolution to segregate specific longitude and latitude topographic regions.

We use a one-dimensional line-by-line radiative transfer model (SHDOM; Evans 1998, 1998) in the 0–100 km altitude range and the 2000–50,000 cm⁻¹ (=0.2–5 μm) range to estimate the abundance of the unknown absorber that fits the observed 365 nm albedo and to calculate the solar heating rate at low latitudes at the local noon time. The configurations are the same as those used in Lee et al. (2015b, 2016). The CO₂ line parameters were taken from a combined HITEMP2010 (Rothman et al. 2010) and one developed by Wattson & Rothman (1992) and Pollack et al. (1993), as described in Lee et al. (2016). We included collision-induced CO₂ absorption in the near-infrared and that of H₂O (Lee et al. 2016). Line parameters of other gases, N₂, SO₂, OCS, HCl, CO, HF, and H₂S, were taken from HITRAN2012 (Rothman et al. 2013), and vertical profiles of gaseous abundances were taken from Titov et al. (2007). We included Rayleigh scattering (Pollack 1967; Hansen & Travis 1974) and UV-range absorption cross sections of SO₂ (Wu et al. 2000). The microphysical properties of the cloud aerosols (modes 1, 2, 2', and 3) were taken from Zasova et al. (2007). We took the vertical structures of the clouds' extinction coefficient from Crisp (1986), as shown in Figure 7. For the unknown absorber, we assumed Crisp's (1986) absorption coefficient (Q_abs) of the mode 1 particle (0.15 μm mean radius cloud particles; Kawabata et al. 1980; Knollenberg & Hunten 1980; Wilquet et al. 2009; Luginin et al. 2016) in the 0.3–0.8 μm spectral range in the upper cloud layer (57–71 km). This assumed vertical location of the unknown absorber has been widely adopted in previous solar heating calculations (Crisp 1986; Lee et al. 2015b; Haus et al. 2016).

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The albedo A (Equation (9)) is phase angle α dependent due to strong backward and forward aerosol scatterings (García Muñoz et al. 2014; Lee et al. 2015a; Shalygina et al. 2015). Therefore, we restrict a comparison of A(α) to data obtained at near-equivalent phase angle bins. Figure 5 shows the temporal evolution of Venus's low- and high-latitudinal mean albedo obtained at phase angles of 75°–80° and 85°–90°. In this figure, a strong and steady decline in the albedo occurs between 2006 and 2011, from 0.4 to 0.25 at low latitudes and from 0.6 to 0.3 at high latitudes. Albedos at low and high latitudes in 2015 December–2017 May are restored to the 2008–2009 values.

While direct comparison of the mean A should be done using data at a specific phase angle bin, often there are missing data over time due to regular changes in phase angles along the orbit of the spacecraft. In order to have better temporal coverage of the mean A variations, we calculate the percent deviation of A from the 2016–2017 mean phase curve, ${\bar{A}}_{\mathrm{UVI}}(\alpha )$, which is derived as a polynomial fit of UVI data in 2016–2017 in the 50°–100° phase angle range (Figure 8). Table 2 shows the coefficients of the polynomial fit to the mean phase curves at low and high latitudes. Deviations from the UVI phase curve are defined as

$\begin{eqnarray}&&\mathrm{Deviation}\,( \% )=\displaystyle \frac{A(\alpha )-{\bar{A}}_{\mathrm{UVI}}(\alpha )}{{\bar{A}}_{\mathrm{UVI}}(\alpha )}\times 100.\end{eqnarray} \tag{ 12 }$

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Figure 9 shows the percentage of deviations of mean A from ${\bar{A}}_{\mathrm{UVI}}(\alpha )$ at low and high latitudes as a function of time, where phase angles from 50° to 110° are represented according to the color bar at the top of each panel. The overall decline in the 365 nm albedo from 2006 to 2011 remains apparent. Additionally, relatively sharp albedo declines are observed at the ends of 2009 and 2010, and the beginning of 2013 that remain constant over short time periods (∼months) before returning to the ${\bar{A}}_{\mathrm{UVI}}(\alpha )$ level. The robustness of the darker albedo conditions observed at the beginning of 2011 is confirmed by the overlap with the 2011 January STIS data. At high latitudes, periods of albedo decrease are less pronounced and appear to be shorter-lived than those at low latitudes. This may be an indication of the combined influence of the unknown absorber abundance and the meridional circulation (Hadley circulation). In particular, the latter would remove older aerosols downward below the cloud-top level, following the descending branch at high latitudes (Imamura & Hashimoto 2001) and leaving behind only the bright, newly formed aerosols that support the existence of Venus's bright high latitudes.

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We apply also Equation (12) for the whole-disk albedo A_whole-disk and use the mean phase curve (Figure 6 and Table 2) to get the percent deviations of A_whole-disk from the 2016–2017 mean phase curve. Figure 10 shows the result as a function of time. The same albedo decreases inferred from the disk-resolved data from 2006 to 2011 are shown in this whole-disk albedo analysis. The independent UVI data obtained in early 2011 (dots with error bars) are well overlapped with those of VMC, including the same short-term albedo variations between 2011 March and May. A darker 365 nm albedo in 2011 than in 2006–2007 or 2016–2017 is a common feature in both the disk-resolved latitudinal and disk-integrated data, implying that the 365 nm darkening that occurred between those dates was a global phenomenon.

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Because of the influence of the unknown absorber on the solar heating rate near the cloud-top level (Crisp 1986; Titov et al. 2007; Lee et al. 2015b) owing to the broad absorption spectrum from UV to visible (Crisp 1986; Pérez-Hoyos et al. 2018), the long-term 365 nm albedo variation we present here should have had a significant effect on Venus's solar heating rate. We use the radiative transfer model (Section 3.3) to determine a required abundance of the unknown absorber, which is assumed to be fixed to the mode 1 particles in the 57–71 km altitude range (Section 3.3), and to estimate the resulting solar heating rate changes at low latitudes. We incorporate the observed low-latitudinal 365 nm albedo variations into our model using a scaling factor f that is multiplied by the assumed initial absorption coefficient Q_abs taken from Crisp (1986) for the unknown absorber. Here f = 1.0 means the initial value, and f > 1.0 means the more abundant unknown absorber, which results in a darker albedo, and vice versa. So we control only the single scattering albedo of the mode 1 particles, but not the size of the particles. In order to fit the observed A, we calculate five sets of emission (e) and incident (i) angles that satisfy α = 88°—(e, i) = (28°, 60°), (38°, 50°), (48°, 40°), (58°, 30°), and (68°, 20°)—to simulate different combinations of e and i. The resulting radiance factors are corrected using the same photometric law that was applied to the calculation of the albedo (Section 3.1.2), and the mean value is used to find f values that match the observed albedo.

Figure 11 shows the relationship of f and the mean value of the calculated 365 nm albedo for the 88° phase angle conditions (Figure 5). The mean albedo observed at low latitudes is 0.33 and requires f = 1.18. This is close to the initial value, f = 1.0, that results in a calculated albedo, (A) = 0.35. The approximate maximum albedo observed at low latitudes, A = 0.40, requires f = 0.65, and the minimum albedo, A = 0.25, requires f = 2.51. We employ these f values in net solar flux profile calculations at 15° latitude, which is the middle of the low-latitude bin, at local noon time. Figure 12 shows the net solar flux divergence spectrum as a function of altitude z, $-{\rm{\nabla }}\cdot {F}_{\mathrm{net}}=-({{dF}}_{\mathrm{net}}/{dz})$, where F_net is the net solar flux. The strongest influence of the unknown absorber appears around 400 nm, where decreasing absorption and increasing solar irradiance overlap.

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Figure 13 shows the calculated local noon time solar heating rate at 15° latitude, derived from Figure 12. This represents that the solar heating rate varied from −25% to +40% from the mean (2006–2017), which is a significantly large range. The peak of the solar heating rate is 36 K (Earth) day⁻¹ for the mean albedo condition, 49 K day⁻¹ for the minimum albedo, and 27 K day⁻¹ for the maximum albedo at this local noon time.

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We note that the vertical structure of the upper clouds may affect the solar heating rate (Lee et al. 2015b), but the structure of the upper clouds at low latitudes from near-infrared observations is shown to be rather stable during the time of Venus Express (Ignatiev et al. 2009; Cottini et al. 2015; Fedorova et al. 2016), validating the use of a fixed cloud structure. Other analyses suggest that the vertical distribution of the unknown absorber may sometimes extend vertically above the cloud-top level (Molaverdikhani et al. 2012; Lee et al. 2015a). However, the upper haze and vertical locations of the unknown absorber are not changed in our calculations, as these are beyond the scope of this study. Further sensitivity studies on solar heating rate would explore in depth the effects of variable vertical and latitudinal distributions of the unknown absorber on Venus's global solar heating rate.

The observed 365 nm albedo variations should result in solar heating variations near the cloud-top level as shown in Section 4.3. We note that two long-term trends occurred in parallel. In the period when the 365 nm albedo had declined, leading to increases in solar heating, the long-term cloud-top zonal wind was observed to increase from 80–90 to ∼110 m s⁻¹ between 2007 and 2012 around local noon at 20°S (Khatuntsev et al. 2013; Kouyama et al. 2013; Hueso et al. 2015). Likewise, between 2014 and 2016, when the 365 nm albedo had increased, leading to decreases in solar heating, the zonal wind speed was observed to slow down from 110 to 100 m s⁻¹ (Horinouchi et al. 2018). This wind speed variation is qualitatively consistent with the expected change in vertical shear associated with cyclostrophic balance. As the strongest solar heating occurs at low latitudes, the low-latitudinal heating can alter the pole-to-equator gradient of temperature. The increased low-latitudinal solar heating inferred from the 2011 to 2013 period should have increased the meridional temperature gradient, which then increases the equilibrium vertical shear, leading to an increase of wind speed. Additionally, there would be contributions of change of momentum flux associated with the thermal tide, which has been expected to participate in the angular momentum budget. To test these ideas, a simulation was run with the latest version of the Institut Pierre Simon Laplace (IPSL) Venus Global Climate Model (GCM; Garate-Lopez & Lebonnois 2018). Starting from the reference simulation (see the Appendix for details), the solar heating rate was modified as a function of time, slowly reducing it (the whole profile at the same time, a simple test adjustment) over 20 Venusian solar days, i.e., 2340 Earth days or 6.4 Earth yr. The rate of solar heating change is −40% in 6.4 yr (from 7.5 to 4.5 K day⁻¹ in zonal mean solar heating rate), consistent with the evolution proposed in this study. The time evolution of the zonally averaged solar heating rate in the latitudinal band between 10°S and 20°S and at 30 mbar (∼70 km, near the cloud-top level) is plotted in Figure 14, together with the simultaneous evolution of the temperature and zonal wind in the same region. There is a clear correlation between these variables with an amplitude only slightly higher than the observed zonal wind variations. This correlation is caused by a reduced meridional circulation that directly affects the transport of angular momentum upward and poleward, resulting in a reduction of the cloud-top zonal wind peak. A detailed analysis is given in the Appendix.

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There are many intervening agents that may act in combination to produce the observed albedo variations, for example, the chemical composition and reaction rate of the unknown absorber, its interaction with or dependency on the chemical state of other atmospheric constituents, and the variability of the cloud and haze structure as a function of time. We note that the SO₂ abundance above the cloud-top level was observed to decline from 2007 to 2012 (Marcq et al. 2013) and then subsequently increase around 2016 (Encrenaz et al. 2019). Since the 365 nm albedo will become relatively brighter with more abundant pure sulfuric acid aerosols that are formed through photolysis of SO₂, it is plausible that the observed albedo trend is linked to the long-term trend of SO₂ abundance.

The period of low 365 nm albedo in this study overlaps the known maximum time of the solar activity cycle (Jiang et al. 2018), as shown in Figure 15. This resembles the correlation of Neptune's reflectivity and the solar activity cycle (Aplin & Harrison 2016). Since solar EUV radiation might affect photochemical reactions involving SO₂ that are necessary for aerosol formation on Venus (Mills et al. 2007; Parkinson et al. 2015), further study is required to explore the influence of the solar activity cycle on the Venusian atmosphere. It is also possible that the production rate of sulfuric acid aerosols is altered by galactic cosmic rays via ion-induced nucleation. Electrostatic interactions between ionized acid molecules can enhance new aerosol formation by reducing the critical size and increasing the collision possibility (Lovejoy et al. 2004; Kirkby 2007), and there are observations of H₂SO₄–H₂O ultrafine aerosols of less than 9 nm in diameter in Earth's upper troposphere and stratosphere that were explained by the ion-induced nucleation (Lee et al. 2003). The peak of the ion production rate in the Venusian atmosphere due to galactic cosmic rays is predicted at 62.5 km (Nordheim et al. 2015) with the 46–58 ion pairs cm⁻³ s⁻¹ range of variations between solar minimum and maximum. So, the upper haze aerosol formation might be effectively triggered by such ion-induced nucleation and vary following the solar activity. Figure 15 shows comparisons of the 365 nm albedo at low latitudes, neutron cosmic rays detected from the Oulu station,¹⁸ and Ly-α flux at the Earth location.¹⁹ A 5 day mean is applied to compare the 365 nm albedo and cosmic rays to compensate for the atmospheric rotation rate on Venus. The solar rotation rate (25 days) mean is applied for the comparison of the 365 nm albedo and Ly-α flux to take into account the different locations of Venus and the Earth with respect to the Sun. The results show that the 365 nm albedo A has a negative correlation with Ly-α flux and a positive correlation with neutron cosmic rays, but these may act together with the mesospheric SO₂ gas influences.

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Regardless of the cause of the observed albedo changes, the range of albedo variation on Venus is surprising. On the Earth, clouds play a considerable role as a buffer of possible climate variations and are also a regulator of the solar energy distribution (Stephens et al. 2015). However, the clouds on Venus are different; rather than supporting a stable solar heating rate, drastic variations of solar heating seem to occur as inferred from the 365 nm albedo. The astounding nature of the albedo variation results we present here is further emphasized by results derived from other planetary albedo studies in the solar system, where weaker long-term albedo variations were observed. For example, at Neptune, the observed magnitude varied by ±0.02 (corresponding to ±2% changes in flux) at the blue (472 ± 10 nm) and red (551 ± 10 nm) filters over 1972–2014 (Aplin & Harrison 2016), and at Mars, the surface albedo varied by 10% at the red filters (575–675 and 550–700 nm) from 1976–1980 to 1999–2003 (Geissler 2005).

In addition to the impact of the solar heating rates at the cloud-top level, the vertical profile of solar flux on Venus, down to the surface, should also be altered by the observed cloud-top albedo changes. Such solar flux variations may explain the unbalanced net radiative energy below the clouds (Lee et al. 2017); therefore, further investigation is needed to understand the true impact of the albedo changes on the entire lower atmosphere of Venus.

Our study focuses on the observed 365 nm albedo and its direct impacts on solar heating at the equator. This does not cover detailed modeling of net radiative forcing, such as cooling rate changes (Haus et al. 2017), that would impact the microphysical and photochemical processes. Such studies must be completed to accurately infer the true impact of the solar heating on cloud formation and climate. The work we present here provides a foundation for future in-depth studies of links between Venus's 365 nm albedo and the processes that directly impact Venus's climate.