Principal Components of Short-term Variability in Venus' UV Albedo

TL;DR

This study uses principal component analysis on Venus's UV albedo data from Akatsuki to identify dominant variability modes, revealing known atmospheric waves and new patterns with implications for Venus's atmospheric dynamics.

Contribution

It applies PCA to Venus's UV albedo observations to uncover and analyze dominant variability modes, including known and novel atmospheric patterns.

Findings

Identified six oscillating patterns in Venus's UV albedo.

Observed modes correspond to known atmospheric waves like Kelvin and Rossby waves.

Discovered a hemispheric mode with unclear origin.

Abstract

We explore the dominant modes of variability in the observed albedo at the cloud tops of Venus using the Akatsuki UVI 283-nm and 365-nm observations, which are sensitive to SO2 and unknown UV absorber distributions respectively, over the period Dec 2016 to May 2018. The observations consist of images of the dayside of Venus, most often observed at intervals of 2 hours, but interspersed with longer gaps. The orbit of the spacecraft does not allow for continuous observation of the full dayside, and the unobserved regions cause significant gaps in the datasets. Each dataset is subdivided into three subsets for three observing periods, the unobserved data are interpolated and each subset is then subjected to a principal component analysis (PCA) to find six oscillating patterns in the albedo. Principal components in all three periods show similar morphologies at 283-nm but are much more variable at 365-nm. Some spatial patterns and the time scales of these modes correspond to well known physical processes in the atmosphere of Venus such as the ~4 day Kelvin wave, 5 day Rossby waves and the overturning circulation, while others defy a simple explanation. We also a find a hemispheric mode that is not well understood and discuss its implications.

Equations

$$x_{i,j}^a=x_{i,j}-\frac{{\sum }_{j=1}^n{x}_{i,j}}{n}=x_{i,j}-\overline{x_i}$$

$$c_{k,l}=\frac{{\sum }_{j=1}^n{x}_{k,j}^a{x}_{l,j}^a}{n-1}$$

$$L_{k,j}=\sum _{i=1}^n{ϵ}_{k,i}.x_{i,j}^a$$

$$x_{i,j}=\overline{x_i}+\sum _{k=1}^p{ϵ}_{k,i}{L}_{k,j}$$

$$x_{i,j}^a={ϵ}_{1,i}{L}_{1,j}$$

$$RM{S}_{(n,n-1)}\le 10^{-4}\text{leavevmode}\text{leavevmode}or\text{leavevmode}\text{leavevmode}\frac{|RM{S}_{(n,n-1)}-RM{S}_{(n-1,n-2)}|}{RM{S}_{(n-1,n-2)}}\le 0.1$$

$$x_{i,j}^a={ϵ}_{1,i}{L}_{1,j}+{ϵ}_{2,i}{L}_{2,j}$$

$$x\left(t\right)=x\left(t-1\right)exp\left(-\frac{\Delta t}{\tau }\right)+ϵ$$

$${\sigma }^2=1-exp\left(-\frac{2\Delta t}{\tau }\right)$$

$$G(f)=G_o\frac{1-{\rho }^2}{1-2\rho \ast cos(\pi f/f_{max})+{\rho }^2}$$

$$c(f)=<G_{am}(f)>/G(f)$$

Full text

11institutetext: Department of Complexity Science and Engineering, Graduate School of Frontier Sciences, The University of Tokyo, Kashiwa, Chiba Prefecture, Japan 277-8561 22institutetext: JSPS International Research Fellow 33institutetext: Institute of Space and Astronautical Science (ISAS), Japan Aerospace Exploration Agency (JAXA), Sagamihara, Kanagawa Prefecture, Japan 252-5210

Principal Components of Short-term Variability in Venus’ UV Albedo

Pushkar Kopparla 1122   

Yeon Joo Lee 11   

Takeshi Imamura 11   

Atsushi Yamazaki 33 pushkarkopparla@gmail.com

We explore the dominant modes of variability in the observed albedo at the cloud tops of Venus using the Akatsuki UVI 283-nm and 365-nm observations, which are sensitive to SO2 and unknown UV absorber distributions respectively, over the period Dec 2016 to May 2018. The observations consist of images of the dayside of Venus, most often observed at intervals of 2 hours, but interspersed with longer gaps. The orbit of the spacecraft does not allow for continuous observation of the full dayside, and the unobserved regions cause significant gaps in the datasets. Each dataset is subdivided into three subsets for three observing periods, the unobserved data are interpolated and each subset is then subjected to a principal component analysis (PCA) to find six oscillating patterns in the albedo. Principal components in all three periods show similar morphologies at 283-nm but are much more variable at 365-nm. Some spatial patterns and the time scales of these modes correspond to well-known physical processes in the atmosphere of Venus such as the $\sim$4 day Kelvin wave, 5 day Rossby waves and the overturning circulation, while others defy a simple explanation. We also a find a hemispheric mode that is not well understood and discuss its implications.

††offprints: P. Kopparla,

1 Introduction

The atmosphere of Venus, as seen in ultraviolet wavelengths, is long known to have striking albedo patterns that are indicative of the dynamics and chemistry of the upper atmosphere (Ross, 1928; Del Genio & Rossow, 1990; Markiewicz et al., 2007). Several of these features have been identified and named, for instance: the Y-feature, associated with equatorial Kelvin wave (Del Genio & Rossow, 1990; Peralta et al., 2015); mid-latitude Rossby waves (Del Genio & Rossow, 1990); the equatorial and polar caps and bands (Rossow et al., 1980). The main absorbers in the near UV, SO2 and the unknown UV absorber, seem to vary on multiple timescales, from daily to multi-year (Encrenaz et al., 2012; Marcq et al., 2013; Lee et al., 2015) and their generation, destruction and advection in the atmospheric flow are responsible for the albedo patterns.

The $\sim 4-5$ Earth day period variations are known to be related to the atmospheric background flow and short period Kelvin and Rossby waves (Khatuntsev et al., 2013; Kouyama et al., 2015; Peralta et al., 2015), but not fully understood since the relationship between the UV albedo contrast and the physical quantities describing the wave field (e.g., temperature, pressure, velocity) is not known. The causes for the longer period variability are uncertain, such as 255 days variability in zonal wind speed (Kouyama et al., 2013), and $\sim$270 days in the 365-nm latitudinal contrast (Lee et al., 2015) and mesospheric SO2 gaseous abundance (Marcq et al., 2013). With sustained observations over a 3 year period now available from the Akatsuki Ultraviolet Imager (UVI) instrument (Nakamura et al., 2016; Yamazaki et al., 2018), we have a long enough baseline of observations to find the leading modes of oscillation in the albedo, their periodicities and associated spatial structures. Using observations at 283-nm, which are correlated to SO2 abundance above the clouds (with some absorption by unknown UV absorber and ozone) and at 365-nm (close to the peak absorption by the unknown UV absorber), we attempt to answer two main questions in this paper:

Can we resolve the variable UV patterns into a small number of recognizable components? 2. 2.

What do these components tell us about the physical processes active in Venus’ atmosphere?

The next section details the data reduction, including the handling of missing data and principal component analysis. The following section deals with the leading oscillations that result from the PCA, their physical interpretations and the statistical significance of the results against noise. The final section summarizes the findings and speculates on future applications of such analyses for Venus climate studies.

2 Data and Methods

2.1 Data Reduction and Normalization

The Ultra Violet Imager (UVI) on Akatsuki has two filters at 283 and 365-nm, which correspond to the absorption bands of SO2 and the unknown UV absorber. The field-of-view (FOV) is $12^{\circ}\times 12^{\circ}$ can observe the whole Venus disk except for about 8 hours near the periapsis. The imaging area is composed of 1024x1024 pixels, with an angular resolution of $12\times 10^{-2}$ degrees per pixel, which corresponds to spatial resolutions of about 200 m and 86 km on the cloud top level in the observations from the altitudes of $\sim$1000 km at the periapsis and 60 Venus radii at the apoapsis (Yamazaki et al., 2018). We use the Level-3 (L3) 283-nm data from the UVI, internal release version 20180901. The L3 data from Akatsuki have observed variables mapped onto a regular (equi-spaced) longitude–latitude grid. The resolution of the L3 longitude–latitude map is $0.125^{\circ}\times 0.125^{\circ}$ $(2880\times 1440)$ grids for $360^{\circ}$ longitude and $180^{\circ}$ latitude) (Ogohara et al., 2017). The orbit of the spacecraft is elliptical with a revolution period of $\sim$10.5 Earth days, a periapsis altitude of 1000–8000 km and an apoapsis altitude of $\sim$360,000 km (Nakamura et al., 2016). The data used in this study were taken on the apoapsis side, where the FOV of UVI can capture the whole Venus disk. Since the major axis of the orbit is roughly fixed in the inertial coordinate, the observation condition changes with the revolution of Venus around the Sun. A visualization of the dataset is provided in Fig 1.

To identify spatial structures and time series of oscillations, it is ideal to have continuous observations of the full dayside at high frequency over a long time period. However, due to practical constraints, the fraction of dayside observed varies systematically and there are often long gaps in the time series. The majority of observations have a gap of 2 hours between them, though the longest gap between successive observations is about 40 days which is the time of missing global day side images due to the highly elliptical equatorial orbit. Images that cover less than $80\%$ of the dayside observed are excluded from this analysis and grid points on a given image where the dayside is not observed are referred to as missing data points. The dayside is the region between solar local time 600-1800 hrs, and the fraction of the dayside observed is calculated as the ratio of grid points in this region with observed values to the total number of grid points on the dayside. The exclusion threshold could be relaxed to $10-60\%$, but doing so increased the ratio of missing data to observed data and introduced too many artificial patterns during the interpolation process described in Sec 2.2.2. On the other hand, as the exclusion threshold is increased, the number of images that can be included in the analysis decrease. As a result, the statistics become more uncertain and the time baseline shorter, limiting the longest period oscillation which can be studied. The $80\%$ threshold offers a reasonable balance between these two competing effects.

We convert the radiances to relative albedos based on the Minnaert law described in Lee et al. (2017), using eq. 8 and 10 of that paper for 283-nm and 365-nm respectively. The albedos in each observation thus derived are normalized by dividing by the spatial mean value in each map to give a relative albedo. We have chosen to normalize by the spatial mean instead of the commonly used spatial maximum, since the maximum is very unstable in fields with a large number of missing values. Alternately, another stable measure of the top values of the albedo distribution (such as the 90th percentile) could be used for normalization. Note that this normalization allows for values of albedo above 1 and removes trends in albedo with time, but that is not our primary concern at this time. We are interested in planetary scale patterns in albedo, for which the relative albedos are sufficient. The maps are then centered such that the sub-solar longitude is always at $180^{\circ}$ or 1200 local time. This is equivalent to plotting on a local solar time grid. Grid points where the cosines of the solar zenith angle or the viewer zenith angle are $\leq$0.2 are excluded, since the observing error at such points is rather large compared to natural variability (Fukuhara et al., 2017). The data is regridded to a $2^{\circ}$ resolution (using the resize function from the python library skimage.transform). The region of interest for our study is the dayside, which we define to be between 800-1600 hrs local time. The 283-nm dataset contains 665 images, each with 4476 grid points on the dayside. Of these 2985492 points, $8\%$ are unobserved (”missing data”). The 365-nm dataset contains 652 images, with a similar fraction of missing data.

2.2 Principal Component Analysis

PCA is a powerful dimensionality reduction technique, and is widely used to find oscillations in atmospheric and climate data on Earth (Wilks, 2006). Our PCA will follow this procedure:

The two dimensional (latitude longitude grid) images containing relative albedos are flattened into one dimensional arrays. 2. 2.

A data matrix is created with $p$ variables (here the number of spatial gridpoints, 4476) as rows and $n$ observations (here the number of images) as columns. An element $x_{i,j}$ of this matrix corresponds to the $i^{th}$ gridpoint and $j^{th}$ observation. 3. 3.

The time mean (row-wise mean) of each variable is subtracted to generate the anomalies from the mean.

[TABLE] 4. 4.

The covariance matrix is calculated with the dimension $p*p$. An element of this matrix $c_{k,l}$ is the covariance between the observations at gridpoints $k$ and $l$, which is calculated as

[TABLE] 5. 5.

The eigenvalues and eigenvectors of the covariance matrix are calculated (we use the eigsh function from the python library scipy.sparse.linalg). The eigenvectors are called the principal components (PCs) or empirical orthogonal functions (EOFs) which give the spatial structure of the leading modes of variability. Each PC has a dimension of $p*1$ and there are $p$ PCs in total. 6. 6.

The dot product of the mean-removed data with the PCs give the principal component loadings (hereafter referred to as loadings). The loadings give the time series of contribution of each mode of variability to the data, each of which has a shape $1*n$ and there are $p$ loadings in total. The loadings are derived from the EOFs, $\epsilon$, and data anomalies, $x^{a}$ in this way:

[TABLE] 7. 7.

The original data can be fully reconstructed from the PCs and loadings thus:

[TABLE]

The PCs corresponding to the largest few eigenvalues and their loadings give the spatial patterns and the time series of the leading oscillations of the dataset, respectively. The fraction of total data variance explained by each eigenvector is given by the ratio of its eigenvalue to the sum of all eigenvalues.

2.2.1 Calculation of the Covariance Matrix

The covariance of albedo values between two pixels (true covariance or population covariance) has to be approximated using the limited data sample available (sample covariance). However, the existence of missing data means that the sample covariance matrix cannot be calculated immediately from the data. The simplest approaches for dealing with missing data in the calculation of the sample covariance matrix are deletions - removing variables with missing data points (known as list-wise deletion) or the calculation of covariances by considering only data points where data exist for both variables of interest (pair-wise deletion) (for e.g., Carter, 2006; Nakagawa & Freckleton, 2008). List-wise deletion is undesirable, since it discards a grid point entirely even if that point has missing data at a single time step only. Also, use of pair-wise deletion introduces undesirable properties to the sample covariance matrix, such as the existence of negative eigenvalues. This indicates that the sample covariance is not a good estimate of the true covariance of the system being observed and the sample covariance matrix lacks the properties of a true covariance matrix such as positive semi-definiteness (only positive or zero eigenvalues) (Pourahmadi, 2011). Using such bad estimates often results in the first few eigenvalues being biased high. Meanwhile, existence of negative eigenvalues makes the calculation of the variance associated with each eigenvalue hard to interpret, since negative variances do not have a clear physical meaning (Dray & Josse, 2015).

A better way to deal with missing values is imputation, either by interpolation from available data, or the imposition of additional constraints on the structure of the covariance matrix (regularization). Several different techniques have been proposed to regularise the properties of such ill-conditioned sample covariance matrices such as ridge regressions/Tikhonov regularization, banding, tapering (Bickel et al., 2008; Warton, 2008). These methods are primarily focused on eliminating bad behavior in the covariance matrix by introducing constraints such as smoothness or sparsity, where the constraints may or may not be determined from the data set. Other approaches, often used in climate studies, fill in missing data through various interpolations - nearest neighbor regressions followed by smoothing [DCT-PLS] (Garcia, 2010; Wang et al., 2012), optimal interpolation (Burgess & Webster, 1980), singular spectral analysis (Kondrashov & Ghil, 2006) or iterative techniques like regularized estimation maximization [RegEM] (Schneider, 2001), data interpolating empirical orthogonal functions [DINEOF] (Beckers & Rixen, 2003) and several other such variants of PCA based interpolations (Ilin & Raiko, 2010). For our dataset, we need an interpolation technique with the following properties:

The interpolation method must be able to handle large fractions of missing data and continuous data gaps, and must be able to effectively interpolate in three dimensions (as opposed to purely spatial interpolation). It must derive the regression parameters from the data itself, i.e., be non-parametric. 2. 2.

Since the missing values lie on a smooth map, there is a roughness constraint on the interpolated values. This can be enforced in many ways: creating interpolations using low-order principal component truncations (like DINEOF), ridge regularizing the covariance matrix (RegEM) or enforcing a roughness penalty by explicitly specifying a smoothness parameter (DCT-PLS).

Since our ultimate goal is to perform a PCA on this dataset, two of the above methods, RegEM and DINEOF, iteratively create imputed datasets that converge on a set of PCs. But RegEM uses a 2d spatial-only linear regression which is unsuited for our data (since missing values are primarily located near the edges of the region of interest rather than in the center), so we use the DINEOF method (Beckers & Rixen, 2003). It is closely related to other spatio-temporal methods like singular spectral analysis and optimal interpolation and produces comparable results (Allen & Smith, 1996; Alvera-Azcárate et al., 2005).

2.2.2 Data Interpolating Empirical Orthogonal Functions

The DINEOF method is based on the descriptions from Beckers & Rixen (2003); Alvera-Azcárate et al. (2005) and is implemented as follows:

All missing values in the time-mean subtracted dataset are filled in with zeros and the covariance matrix is calculated. 2. 2.

The PCs, eigenvalues and loadings of this zero filled covariance matrix are calculated as described in Sec 2.1. 3. 3.

The missing values are imputed using a reconstruction consisting only of the first leading PC and corresponding loadings like this:

[TABLE] 4. 4.

The imputed dataset is again used to calculate a new covariance matrix, and the previous step is repeated to find better imputation values. This procedure is iterated till the imputed values converge. Convergence is defined to occur when the root mean square difference in imputed albedo values from two successive iterations differ by less than $10^{-4}$ or 10$\%$ over three successive iterations, computed thus.

[TABLE]

where RMS*(n,n-1)* is the root mean square difference in imputed values between iterations $n$ and $n-1$. 5. 5.

The next set of iterations then uses two PCs for the imputation:

[TABLE]

and is repeated to convergence. 6. 6.

Thus we can arrive at a converged imputed dataset for any given number of eigenvectors.

Since it is possible to create an imputed dataset with any $k$ PCs, where $1\leq k\leq p$, the optimal number of PCs is determined through a generalized cross validation procedure. Following Alvera-Azcárate et al. (2005), we choose $1\%$ of the existing data points randomly and set them as artificially missing. This number of points is often used for cross-validation procedures (for e.g., Wilks, 2006). The imputed datasets are reconstructed using 1,2,3 .. 100 PCs using the convergence criterion above. The artificially missing data is not included in the convergence calculation as described in Step 4 above. For each converged imputed dataset, the root mean square error of the reconstruction of the artificially missing data is calculated. The optimal imputation is the one for which this RMS error is minimum. For our data set, this minimum occurs at $N\sim 25$ PCs.

3 Results and Discussion

3.1 Dominant Modes and Statistical Significance

The question of how many PCs are significant and should be retained has been widely discussed, and many different stastical and rule-of-thumb approaches exist (Jackson, 1993; Peres-Neto et al., 2005; Cangelosi & Goriely, 2007). Of these we use a very simple criterion that looks for an inflection point in the eigenvalue spectrum to find the break between signficant and noisy PCs. This is known as Catell’s Scree test (Cattell, 1966), and is a commonly used heuristic significance metric. From Fig 2, we see that our interpolated datasets have an inflection point around 5 or 6, indicating a dimension of 6. We therefore retain only the first 6 spatial PCs, and these are shown in Figs 3 and 5.

The Lomb-Scargle periodograms of the time series corresponding to each PC are shown in Figs 4 and 6, with a minimum period of 1 day and a maximum of half the total length of the window (typically each window is about 40 days). The periodograms show several peaks, but their significance must be first confirmed. The spectral analyses of atmospheric data are affected by red noise (for e.g., Allen & Smith, 1996; Meinke et al., 2005), where the noise contribution increases with period as opposed to a flat spectrum for white noise. This leads to spurious long period peaks in periodograms. This noise is usually approximated by an autoregressive process with a time lag of one (AR1) (Gilman et al., 1963), however irregular time sampling prevents estimation of the autocorrelation coefficient directly from the data. We therefore use existing methods in the climate science literature (Mudelsee, 2002; Schulz & Mudelsee, 2002) for variable spaced time series data. We do not use the programs made available by these studies, but only use the methods as described in the text with some minor modifications. Our implementation is summarized below:

The AR1 process is modeled as

[TABLE]

where $x\left(t\right)$ is the time series value at time $t$, $\Delta t=\left(t\right)-\left(t-1\right)$ is the time step, $\tau$ is persistence timescale of the time series and $\epsilon$ is the Gaussian noise component. 2. 2.

$\tau$ is estimated by a least-squares fit of the AR1 equation to the loadings (using the function curve_fit from the python library scipy). There is one $\tau$ for each principal component loading in each window. 3. 3.

1000 artificial time series are generated using the AR1 process described above with the initial value and the time steps being the same as the PC loading. The Gaussian process is taken to have a variance of

[TABLE] 4. 4.

Each artificial time series is scaled so that the periodogram has the same area under the curve as the original time series. The mean, $<G_{am}(f)>$, and the standard deviation, $<G_{as}(f)>$ , of the set of all the artifical time series’ periodograms are calculated, where $f$ is the frequency. 5. 5.

The analytical expression for the power spectrum in the periodogram of an AR1 process is given by

[TABLE]

where $f_{max}$ is the highest frequency in the periodogram (often taken to be the Nyquist frequency, but here set to $1/day$), $G_{o}$ is the mean spectral power, $\rho$ is the mean autocorrelation coefficient calculated as $\rho=exp(-\Delta t_{mean}/\tau)$ where $\Delta t_{mean}$ is the arithmetic mean of the time steps in the time series. 6. 6.

Correction factors are calculated for the deviations of the mean artificial periodogram from the analytical value

[TABLE]

These correction factors account for biases resulting from taking periodograms of irregularly spaced data. 7. 7.

The unbiased periodogram of the original series is calculated as $G_{ts}(f)/c(f)$, where $G_{ts}(f)$ is the power spectrum of the original time series. The standard deviation is scaled similarly, and plotted in Figure 4. Assuming a Gaussian distribution, the $95\%$ confidence level is taken to be 2 standard deviations from the mean. The periods of the significant peaks are labeled.

The results are shown in Figs 4 and 6.

3.2 Physical Interpretations of the Oscillations at 283-nm

The first column in Fig 3 shows a (roughly) longitudinally-uniform latitudinal gradient from the equator to the poles. This likely reflects the Hadley circulation which lifts SO2 from the lower atmosphere to the cloud tops at the equator, from where it is advected to the poles while being lost to photodissociation and conversion to sulphuric acid (Marcq et al., 2013) and polysulphur (Mills et al., 2007). The corresponding periodicities in Fig 4 show a major periodicity of around 10 days, which is likely due to the spacecraft orbital period (Nakamura et al., 2016). The synchronization with the orbital motion might indicate a solar-locked component, i.e., a contribution of thermal tides. The approximately four day period can be attributed to the atmospheric rotation around the planet, and the eight day peak is probably a subharmonic of this period. However, GCM studies indicate the existence of barotropic or baroclinic waves with periods ranging from 6-23 days (Lebonnois et al., 2016) in the cloud layer, which is another possibility for the 8 day signature. An $\sim$ 8 day period wave was observed a little deeper than cloud top level in near-infrared observations ($\sim$1.7 micron), and is also thought to result from the interaction of Kelvin and Rossby waves with the mean flow (Hosouchi et al., 2012).

The second column shows a pattern broadly described as a hemispheric oscillation, showing an oscillation with opposite directions of change between the two polar regions. A polar asymmetric brightening/darkening was observed by a ground-based telescope (Dollfus, 1975), and it was thought to be caused by polar clouds independently evolving in either hemisphere. The pattern identified here is somewhat different, in that the two hemispheres do not evolve independently, rather they evolve together in opposite directions, that is, one brightens while the other darkens. Notably, Fig 4 shows no significant periods associated with this pattern other than the spacecraft orbital period. This can mean either that the phenomenon is aperiodic, or more likely, that the period is longer than the observational window considered here (approximately 40 days). Such a large scale pole-to-pole pattern could indicate the existence of an atmospheric teleconnection. Another interpretation might be that the period comparable to the spacecraft orbit might indicate a contribution of asymmetric components of thermal tides. Alternatively, it may also arise from the non-equatorially symmetric component of the meridional circulation. However, further observations are required for confirmation, as completely symmetric polar features were observed from the mid-infrared ground-based observations (Sato et al., 2014). A very recent study of IR1 (900-nm) images from Akatsuki revealed an asymmetric pattern in the middle clouds at low latitudes with a periodicity of 4-5 days (Peralta et al., 2018). It is unclear at this time if this IR pattern is directly related the hemispheric mode we find at the cloud tops. Analysis of mid-infrared images (LIR, Fukuhara et al., 2011) from the same time period as the UV images studied here, using PCA, may confirm this oscillation and offer clues to robust physical interpretations in near future. Notable hemispheric dichotomies have also been observed in CO concentrations below the clouds (Arney et al., 2014; Marcq et al., 2006, 2008). Higher concentrations were found to variably occur either on the Northern and Southern hemispheres during observations separated by several months. SO2 hemispheric dichotomies were also studied, but an unambiguous detection was only made once in 2010. It is unclear at this time how these long-term variations are related to the short-term mode we find.

We interpret the third, fourth and fifth columns to be combinations of atmospheric wave patterns. They often show short-period variabilities of approximately 5 days. Waves with periods of a few days have been observed (Del Genio & Rossow, 1990; Kouyama et al., 2015; Imai et al., 2016) and simulated in Venus GCM models (Yamamoto & Takahashi, 2006). In particular, the 5 day wave has been interpreted as a Rossby wave and the four day wave as an equatorial Kelvin wave (Rossow et al., 1990; Kouyama et al., 2012; Imamura, 2006). It must be noted also that several subplots do not show any notable periodicity even similar spatial patterns are associated with waves in other windows. For example, in column three, row one shows no periodicity except for the spacecraft orbit and some high frequency noise around the 1-2 days range. But rows two and three clearly show five and four day periods respectively. It is interesting that similar spatial patterns appear to form from different wave configurations in different periods.

The sixth column clearly shows the famous Y-feature (Boyer & Camichel, 1961; Rossow et al., 1980), and is clearly associated with a strong periodicity of about four days. This is also consistent with the interpretation of the major cloud features of the Venus atmosphere interpreted as a trapped Kelvin wave (Del Genio & Rossow, 1990; Kouyama et al., 2012; Peralta et al., 2015). It is interesting that the order of PCs in each window is slightly variable and needs rearrangement to align similar patterns under each column. This indicates that different processes dominate albedo variability in different periods, which is consistent with the previous finding that the dominant periodicity of atmospheric waves in the Venus atmosphere varies on a timescale of several months (Del Genio & Rossow, 1990; Kouyama et al., 2013; Imai et al., 2016).

A joint PCA of data in all windows combined together was also attempted. The periodograms of that study were dominated by peaks at about 220 days and its harmonics at 110, 55 etc days, which are functions of the changing orbital orientation of the spacecraft relative to the Venus dayside, the observational window frequency and other factors rather than interesting atmospheric phenomenon. Also, the dominance of these observational periodicities in the data caused peaks from the 4 and 5 day waves to become statistically insignificant. As such, results from that analysis are not discussed in this paper since they are dominated by systematics.

3.3 Physical Interpretations of the Oscillations at 365-nm

The 365-nm PCs are comparatively much more variable across the three windows than the 283-nm PCs as shown in Fig 5. However, they can still be approximately classified into a few broad categories. Two PCs in each window can be placed into the first category, which is similar to the latitudinal gradients seen at 283-nm. The periodicities, as seen in Fig 6, are also similar to those seen at 283-nm. This is generally consistent with the understanding that the overturning circulation is responsible for increased UV absorber concentrations leading to low albedos at the equator at 365-nm (Titov et al., 2008; Molaverdikhani et al., 2012). However, latitudinal gradients are much weaker than those seen at 283-nm, suggesting that choatic variability in morphology is perhaps more important at this wavelength. Spatial distributions are in general far more complicated at 365-nm, with significant ambiguities in classification. This can be understood on the condition that the 365-nm observations are sensing an altitude level slightly below the cloud top, while 283-nm is at a higher altitude (Horinouchi et al., 2018). Therefore, the 365-nm features are affected by both the absorber and bright sulfuric acid cloud aerosols, which are formed through photochemical process (Mills et al., 2007; Parkinson et al., 2015), whereas the 283-nm would reveal the absorbers above the clouds so atmospheric flow patterns are more apparent. The latter would be also affected by photodissociation of SO2 (Mills et al., 2007) and the upper haze (Luginin et al., 2016), but our results suggest that these influences may be less effective than at 365-nm.

The second category is the hemispheric asymmetry, represented by two PCs each in the first two windows, but appears to be absent in the third. PC 3 in window 3 shows something like a hemispheric mode, however, it is associated with a strong wave peak of around 4 days in Fig 6, which is characteristic of the Y-feature. Window 3, PC 4 may also qualify for this category, but is somewhat ambiguous because the pattern is not purely hemispheric. The hemispheric mode typically does not show any strong periodicities apart from the spacecraft orbital period, as seen at 283-nm, though hints of the 4 and 5 day periods are seen when the asymmetry is strong (window 1, PC 5 and window 2, PC 6). The large variability between windows could be attributed to concealment of gradients by transient cloud features, as for the previous category.

The third category shows a very clear transition region around 50∘ N/S, from dark low-to-middle latitudes to the bright polar hood (Titov et al., 2012), sometimes symmetric across both hemispheres. The structure is associated with drastic changes in cloud tracked 365-nm winds, slowing down poleward of about 50∘ (Kouyama et al., 2012), in cloud top altitudes which also decrease poleward (Ignatiev et al., 2009), and in thermal structure, presenting colder temperatures near the cloud top level (Tellmann et al., 2009). This means that winds, cloud top structure, and thermal structure are closely linked with the 365-nm patterns, implying overlapped vertical locations each other. The morphology bears a resemblance to model simulations of Rossby wave patterns at the cloud top (Kouyama et al., 2015). The periodicities always show a peak at around the 5 day mark confirming the signature of midlatitude Rossby waves. This can be interpreted as features arising from the perturbation of the midlatitude bright bands or the ”cold collar” (Titov et al., 2008, 2012) by Rossby waves. Interestingly, such a clear Rossby wave signature is not apparent in the 283-nm data.

The fourth category is the Y-feature, associated with a period of $\sim 4$ days with some other waves at 4.5, 9 and 12.3 days occasionally contributing. The absence of the Y-feature in window 2 does not mean that this feature did not occur during this time, since it is clearly seen at 283-nm for the same window. It maybe that the feature was sufficiently obscured at 365-nm that it is not represented in the first six PCs considered here.

4 Conclusions

We performed a PCA of the Akatsuki UVI 283-nm and 365-nm data taken over about 1.5 years, subdivided into three observational windows each. The first six PCs over each window are considered significant and show similar morphologies at 283-nm, but are more variable at 365-nm. The difference can be understood if the 365-nm observations are sensitive to altitudes below the cloud top which are affected by transient cloud variability, while 283-nm probes the atmosphere above the cloud tops. Additionally, since the unknown UV absorber is the result of unidentified chemical reaction chains, the kinetics of those reactions may also be responsible for some of the observed differences. The signatures of the overturning circulation, Rossby and Kelvin waves are apparent from the spatial patterns and associated periodicities. We also note that similar spatial patterns are sometimes associated with different waves, and the relative importance of different waves change across the different observing periods as seen by the changing order of PCs with similar spatial patterns.

A hemispheric asymmetry mode is also apparent from this analysis. To be sure of its existence and to understand its dynamics, the same mode will need to be studied in other atmospheric observations of Venus. The analysis technique described here is general, and has potential for use in other gridded atmospheric datasets from Akatsuki, Venus Express and Pioneer Venus, and can be applied to other planetary atmospheric image analysis with a long-term monitoring dataset.

5 Acknowledgements

We thank Takehiko Satoh and the anonymous referee for comments that improved the paper. PK acknowledges generous funding support from the grants-in-aid program of JSPS. Codes used in this study are available on request and Akatsuki data will become publicly available at https://darts.isas.jaxa.jp/pub/pds3/staging/.