# Another one derives the dust: Ultraviolet dust aerosol properties retrieved from MAVEN/IUVS data

Kyle Connour, Michael J. Wolff, Nicholas M. Schneider, Justin Deighan, Franck Lefèvre, Sonal Jain

► To cite this version:

Kyle Connour, Michael J. Wolff, Nicholas M. Schneider, Justin Deighan, Franck Lefèvre, et al. An-
other one derives the dust: Ultraviolet dust aerosol properties retrieved from MAVEN/IUVS data.
Icarus, 2022, 387 (November), pp.115177. 10.1016/j.icarus.2022.115177. insu-03740758

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https://insu.hal.science/insu-03740758v1

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# Another one derives the dust: Ultraviolet dust aerosol properties retrieved from MAVEN/IUVS data

Kyle Connour<sup>a</sup>, Michael J. Wolff<sup>b</sup>, Nicholas M. Schneider<sup>a</sup>, Justin Deighan<sup>a</sup>, Franck Lefèvre<sup>c</sup>
and Sonal K. Jain<sup>a</sup>

<sup>a</sup>Laboratory for Atmospheric and Space Physics, Boulder Colorado, USA

<sup>b</sup>Space Science Institute, Boulder Colorado, USA

<sup>c</sup>Laboratoire Atmosphères, Milieux, Observations Spatiales (LATMOS), CNRS, Sorbonne Université, UVSQ, Paris, France.

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20 Keywords:

21 Mars

22 Atmosphere

23 Ultraviolet observations

24 Radiative transfer

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## ARTICLE INFO

## ABSTRACT

We derived the ultraviolet complex refractive indices of Martian dust aerosols using data from the Mars year 34 global dust storm (GDS). We used data taken by the Imaging Ultraviolet Spectrograph (IUVS) instrument aboard the Mars Atmosphere and Volatile Evolution spacecraft and surface-based derivations of the column-integrated optical depth from the Mastcam instrument on Curiosity. We first created an explicit microphysical representation of dust to compute dust-scattering properties at wavelengths within IUVS' spectral range for four dust particle-size distributions plausibly present during this GDS. We then used radiative-transfer techniques to iteratively retrieve the single-scattering albedo from IUVS data using the Mastcam-derived column-integrated optical depth as a constraint. We converted the dust single-scattering albedo into its refractive indices and report the refractive indices at the four particle-size distributions. We performed dust optical depth retrievals at another time period using several of these refractive indices and show that our preferred refractive indices produce optical depths which are consistent with optical depths derived from Mastcam data at similar times. These ultraviolet refractive indices will be particularly beneficial for future observational and theoretical studies of Martian dust.

## 1. Introduction

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Atmospheric dust is an important part of the Martian climate. It is ubiquitous in the lower Martian atmosphere, absorbing and scattering incident solar radiation which warms or cools the troposphere depending on local conditions (Kahre, Murphy, Newman, Wilson, Cantor, Lemmon and Wolff, 2017); therefore, the thermal state of the atmosphere is quite sensitive to the abundance and distribution of airborne dust. The resultant temperature gradients further induce surface winds which can sweep large quantities of dust into the atmosphere, particularly during the perihelion season. These dust injections may grow into regional or even global dust storms (GDSs), both of which have an appreciable effect on global atmospheric circulation (Barnes, Haberle, Wilson, Lewis, Murphey and Read, 2017).

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Improvements in our understanding of dust scattering properties can lead to better observational and theoretical studies of the Martian surface and atmosphere. Dust modifies virtually all aspects of the lower atmosphere; consequently, several data analysis techniques benefit from accurate knowledge of dust scattering properties. For example, one can use these properties in remote-sensing studies of the surface to better distinguish dust aerosols from the surface, providing improvements to our understanding of its bidirectional-reflectance properties. Radiative-transfer retrieval algorithms are quite sensitive to aerosol scattering properties and any analysis using these techniques (such as investigating dust climatologies or performing retrievals of other aerosols with dust present) benefits from using accurate dust scattering properties. Martian global climate models (MGCMs) also benefit, as these radiative properties affect the interaction of solar radiation on the lower atmosphere (Kahre et al., 2017) and are a key component in the modeled photochemistry (Lefèvre and Krasnopolsky, 2017).

Ultraviolet (UV) dust scattering properties are not particularly well constrained and are challenging to retrieve. Mateshvili, Fussen, Vanhellemont, Bingen, Dodion, Montmessin, Perrier and Bertaux (2007) retrieved the UV dust single-scattering albedo ($\omega_0$) but their analysis has some assumptions that make their results difficult to generalize to

<figure><img src="image_2.png" /></figure>

<footnote>* Kyle Connour</footnote>

<footnote>kyle.connour@colorado.edu (K. Connour)</footnote>

<footnote>ORCID(s): 0000-0003-0858-2511 (K. Connour); 0000-0002-1127-8329 (M.J. Wolff); 0000-0001-6720-5519 (N.M. Schneider); 0000-0003-3667-902X (J. Deighan); 0000-0001-5294-5426 (F. Lefèvre); 0000-0002-1722-9392 (S.K. Jain)</footnote>
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a range of dust loading conditions. Wolff, Clancy, Goguen, Malin and Cantor (2010) retrieved $\omega_0$ and the associated complex refractive indices ($m$, where $m = n+ik$) of a few plausible dust particle-size distributions ($r_{\text{eff}}$), but their spectral resolution is coarse and does not extend far into the UV. Older works used less sophisticated numerical methods and cruder representations of dust that led to significant uncertainty on their results. In contrast, dust scattering properties have been well studied at visible and infrared wavelengths (Wolff, Lopéz-Valverde, Madeleine, Wilson, Smith, Fouchet and Delory, 2017). To improve upon these properties, one typically retrieves them using radiative-transfer techniques. Performing these retrievals is challenging, as one needs to specify both the dust $\omega_0$ and single-scattering phase function ($p(\theta)$) in a self-consistent manner while also specifying the column-integrated optical depth ($\tau$), surface parameterization, etc. It is usually not feasible to simultaneously obtain all of these parameters from observations, so one must carefully select data from conditions where some of these parameters are known and the retrievals have reduced sensitivity to the unknown parameters, otherwise one encounters situations where the uncertainties on retrieved parameters are large.

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Conditions of the Mars year (MY) 34 GDS, along with a complementary set of observations taken during the storm, provided serendipitous circumstances to derive improved UV dust scattering properties. Under normal conditions dust, water ice, ozone, and $CO_2$ (via Rayleigh scattering) are the only atmospheric constituents that have an appreciable effect on dayside UV spectra of Mars. During this GDS, thin water-ice clouds intermittently formed at high altitudes above the dust as the extreme heating of the GDS prohibited thicker cloud formation (Connour, Schneider, Milby, Forget, Alhosani, Spiga, Millour, Lefèvre, Deighan, Jain and Wolff, 2020). Their optical depth (derived from occultation measurements) rarely exceeded 0.15 after the storm reached its mature phase (Stcherbinine, Vincendon, Montmessin, Wolff, Korablev, Fedorova, Trokhimovskiy, Patrakeev, Lacombe, Baggio and Shakun, 2019) and we assume their $\tau$ could not be significantly larger than this value because the extinction cross section of ice is not significantly larger in the infrared than it is in the UV. Ozone is nearly non-existent during the solar longitudes of this storm (Clancy, Wolff, Lefèvre, Cantor, Malin and Smith, 2016; Lefèvre, Lebonnois, Montmessin and Forget, 2004), indicating UV spectra obtained during this GDS were primarily influenced by the effects of dust and Rayleigh scattering. The Mastcam instrument on the Curiosity rover provided near-daily derivations of the $\tau$ over Gale Crater, which reached 8.5 and sustained very optically thick conditions for dozens of sols (Martian days) (Guzewich, Lemmon, Smith, Martínez, de Vicente-Retortillo, Newman, Baker, Campbell, Cooper, Gómez-Elvira, Harri, Hassler, Martin-Torres, McConnochie, Moores, Kahanpää, Khayat, Richardson, Smith, Sullivan, de la Torre Juarez, Vasavada, Viúdez-Moreiras, Zeitlin and Zorzano Mier, 2019). This thick dust obscured the surface, greatly reducing the effects of the precise details of both the surface reflectance function and the dust $p(\theta)$ on any measured radiances. Together, these facets of the dusty atmosphere suggest that UV measurements taken during this storm should be uniquely valuable for retrieving improved dust scattering properties.

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In this study we report improved UV complex refractive indices of dust for four dust particle-size distributions plausibly present during this storm. We used data taken by the Imaging Ultraviolet Spectrograph (IUVS) instrument (McClintock, Schneider, Holsclaw, Clarke, Hoskins, Stewart, Montmessin, Yelle and Deighan, 2015) aboard the Mars Atmosphere and Volatile Evolution (MAVEN) spacecraft (Jakosky, Lin, Grebowsky, Luhmann, Mitchell, Beutelschies, Priser, Acuna, Andersson and Baird, 2015). We discuss the retrieval methodology and results, and compare these results with previously reported UV dust $\omega_0$ and $m$ values. We used our newly retrieved dust refractive indices to compute sets of radiative properties and then perform retrievals of dust $\tau$ during more diffuse dust loading conditions using IUVS data taken over Gale Crater. We show our preferred refractive indices produce optical depths which are consistent with those derived from Mastcam data. We also discuss the potential impact of these properties on future retrievals from IUVS data, such as water-ice cloud mappings.

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## 2. Observations

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Our analysis focused on a set of spectral images taken by MAVEN/IUVS during the optically thickest periods of the MY 34 GDS.

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### 2.1. The IUVS instrument

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The IUVS instrument is a scanning-slit spectrograph capable of taking recurring images of Mars (McClintock et al., 2015). We used pixels from disk images taken during IUVS' apoapsis observing mode where each nadir pixel subtended about 7 km by 7 km of the Martian surface. We used data from the mid-ultraviolet (MUV) spectral channel where data are binned into 19 spectral bins spanning 205 to 306 nm. During the MY 34 GDS, IUVS took data nearly
<figure><img src="image_3.png" /></figure>

<figure><img src="image_4.png" /></figure>

**Figure 1:** Spectral variability seen in IUVS data over a range of physical conditions. The top image (orbit 3459) shows clear conditions, localized dust storms, and thick water-ice clouds whereas the bottom image (orbit 7414) shows thick dust present during the MY 34 GDS. Both images are enhanced-color projections representing what IUVS observed at apoapsis and north is oriented upwards. During clear conditions IUVS measures relatively featureless spectra, with an increase in brightnesses at shorter wavelengths due to some Rayleigh scattering. Relatively small amounts of dust show similar reflectance values at longer wavelengths but show lower reflectance values at shorter wavelengths as this dust obscures some of the Rayleigh scattering. Optically thick dust continues this trend at shorter wavelengths but produces enough backscatter to increase reflectances at longer wavelengths. Water-ice clouds backscatter much more efficiently than dust and thus are significantly brighter. We can leverage these reflectance values along with the spectral shapes to determine the physical characteristics of aerosols present in IUVS data.

every orbit with a cadence of approximately 4.5 hours. Due to MAVEN's slowly precessing orbit, we observed spatial locations over a wide range of photometric angles.

## 2.2. Reflectance spectra

We created reflectance spectra for this work. We applied a flatfied to the IUVS level-1b data products and then transformed them into reflectance spectra using solar flux measurements from the SOlar Stellar Irradiance Comparison Experiment (SOLSTICE) instrument aboard the Solar Radiation and Climate Experiment satellite. See appendix A for discussion on the flatfield and general calibration of the IUVS data used in this work. We averaged the SOLSTICE data into 1-month-long bins and convolved these spectra by IUVS' point spread function to determine the incident flux. The systematic uncertainty on the flatfield-corrected IUVS data are around 5%, while the systematic uncertainty on the SOLSTICE data are around 3% (Snow, Reberac, Quémerais, Clarke, McClintock and Woods, 2013). The random uncertainty (the pixel-to-pixel scatter) on the IUVS data is no larger than 3%.

See figure 1 for differences between these optically thick, dusty spectra and spectra more characteristic of clear conditions: optically thin dust, clear views of the surface (plus ubiquitous Rayleigh scattering), enhanced Rayleigh scattering, and water-ice clouds. These reflectance spectra allow us to characterize aerosols in conjunction with a model.

## 2.3. Data selection criteria

We exclusively used IUVS data that isolated the effect of the dust $\omega_0$. Specifically, we only used spectra from pixels that met the following criteria:
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1. the pixel center is within Gale Crater,

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2. it was measured at a time when $\tau$ was at least 5, and

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3. its solar zenith and emission angles are both less than 72°.

We restricted ourselves to data taken over Gale Crater primarily to ensure we knew $\tau$ at the times of the IUVS measurements, but it had a secondary effect of minimizing any possible effects of a spatially varying surface reflectance. This $\tau$ was derived from measurements taken by the Mastcam instrument (using its R8 880 nm filter) on the Curiosity rover. We required a large optical depth threshold to ensure we were looking at spectra which maximized the impact of dust properties: the higher the cutoff, the less sensitive the surface phase function and $p(\theta)$ were for our retrievals, but the fewer data points could go into the analysis. We chose a cutoff of 5 because it provided a good balance between reduced parameter sensitivity and sufficient number of data points. The 72° cutoffs allowed us to employ the plane-parallel approximation in our analyses (the majority of the solar zenith angles used in this work spanned 30 to 50 degrees whereas the emission angles spanned 50 to 70 degrees). We applied the above selection criteria and identified 2432 spectra for use in this study spanning 35 sols.

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## 3. Retrieval methodology

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We applied radiative-transfer techniques to iteratively retrieve $\omega_0$ and derive $m$, with the latter being our primary goal. This value can be applied to calculate the radiative properties of any dust particle-size distribution and is therefore applicable to all dust loading conditions. To do this, we retrieved $\omega_0$ from IUVS data using radiative properties for a set of $m$ values, and then derived updated $m$ values from $\omega_0$. Many of the numerical tools, algorithms, and techniques used in this work have been described in previous work (Wolff, Smith, Clancy, Arvidson, Kahre, Seelos IV, Murchie and Savijärvi, 2009; Wolff et al., 2010) but we give an overview of the methodology here.

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### 3.1. Radiative transfer

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We employed DIScrete Ordinate Radiative Transfer (DISORT) version 4.0.99 as the core radiative transfer algorithm (Stamnes, Tsay, Wiscombe and Jayaweera, 1988; Laszlo, Stamnes, Wiscombe and Tsay, 2016). We avoid the complexity of the pseudo-spherical correction and use the plane-parallel mode. By limiting ourselves to solar zenith and incidence angles less than 72°, the error on this approximation is less than 3%(Wolff et al., 2017). We split the model into 14 layers of equal altitude spanning 0 to 80 km and ran the model with 16 streams.

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### 3.2. Rayleigh scattering

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We accounted for Rayleigh scattering in our retrievals by using laboratory measurements of $CO_2$ cross sections. Rayleigh scattering is an important contributor to UV signals as its column-integrated optical depth can reach 1 around 200 nm (about the shortest wavelength used in this work) for realistic Martian pressures and temperatures. We assumed $CO_2$ is the only contributor to Rayleigh scattering, as it comprises 96% of the atmosphere (Mahaffy, Webster, Atreya and et. al, 2013). We assumed an atmosphere in hydrostatic equilibrium with an average vertical temperature profile from Kass, Schofield, Kleinböhl, McCleese, Heavens, Shirley and Steele (2020), a surface pressure of 6.1 mbar (the average surface pressure found in *Laboratoire de Météorologie Dynamique* (LMD) Mars GCM simulations of the storm), and the average vertical pressure profile from these simulations. We then integrated these profiles to obtain the column density in each layer. We combined this value with laboratory measurements of the King factor from Sneep and Ubachs (2005) to obtain the Rayleigh-scattering optical depth in each model layer.

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### 3.3. Aerosol model

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We chose an electrodynamical approach to self-consistently specify the dust's forward scattering properties. We used a modified version of TMQ, the quad-precision T-matrix code of Mishchenko, Travis and Lacis (2002). Like Wolff et al. (2010), we used cylindrical particles with a diameter-to-length ratio of 1. This code allowed us to self-consistently compute $\omega_0$ and $p(\theta)$—the radiative properties needed to perform retrievals—from a set of $m$ values. This introduced a non-trivial computational cost, but ultimately produced a set of radiative properties that are consistent with IUVS data and are applicable to all dust particle-size distributions (see Wolff et al. (2009) for discussion regarding the potential pitfalls of not using this approach). We combined these computed extinction cross sections with the 880 nm extinction cross sections calculated from the refractive indices of Wolff et al. (2009) to scale the Mastcam-derived $\tau$ to UV wavelengths.

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We considered four dust particle-size distributions ($r_{\text{eff}}$) in our analysis which represent plausible average dust particle sizes relevant to the portion of the atmosphere detected by IUVS during the GDS: 1.4, 1.6, 1.8, and 2.0 µm. Observational and theoretical studies (Lemmon, Guzewich, McConnochie, de Vicente-Retortillo, Martínez, Smith, Bell III, Wellington and Jacob, 2019; Kahre, Hollingsworth, Haberle and Murphy, 2008) indicate the average dust particle size ranges from 1.0–2.0 µm throughout the year, with 1.7–1.8 µm particles being more probable during GDSs when viewed from above (Wolff et al., 2009). We thus considered a conservative range of possible sizes bounding this range. In each case we used a gamma particle-size distribution and fixed the effective width of the distribution ($v_{\text{eff}}$) to 0.3 microns.

We set the dust's vertical distribution using a Conrath profile (Conrath, 1975) that approximated the measured dayside vertical profiles of Montabone, Spiga, Kass, Kleinböhl, Forget and Millour (2020).

## 3.4. Surface parameterization

We used the Hapke UV surface parameterization derived by Wolff et al. (2010). That work fit the surface phase function to a 2-lobed Henyey-Greenstein phase function with a surface single-scattering albedo ($w$) at two UV wavelengths (258 and 320 nm). However, the $w$ values reported in that work are a factor of 10 lower than they intended to report due to a typo. We use the corrected values, which are consistent with the values used in Wolff, Clancy, Kahre, Haberle, Forget, Cantor and Malin (2019).

## 3.5. Fitting algorithm

We used the Nelder-Mead algorithm implemented in Python's Scipy package (Gao and Han, 2012) to fit $\omega_0$ to each spectral bin (approximately 5 nm in width) in each usable spectrum. We chose this algorithm due to its ease of use and robust minimization. We set a tight tolerance ($10^{-4}$%) on the fit $\omega_0$ to ensure that the simulated spectra matched IUVS observations extremely well and thus did not introduce further uncertainties in our results.

## 3.6. Retrieval procedure

The following steps describe our methodology for retrieving $\omega_0$ and deriving $m$. We performed these steps for each of the four considered particle-size distributions (1.4, 1.6, 1.8, and 2.0 µm). These steps are essentially the same as Wolff et al. (2009).

1. We created a look-up-table (LUT) of $k$ as a function of wavelength and $\omega_0$ using T-matrix calculations described in section 3.3. Thus, for a given wavelength and $\omega_0$, we could uniquely determine $k$.

2. We used the ozone-free radiative properties reported in Wolff et al. (2010) as an initial guess for our model (see the top panel of figure 2 for these $\omega_0$ values), and used the nearest neighbor values for 1.4 and 2.0 microns.

3. We derived $\omega_0$ at each of the 19 spectral bins in IUVS data. We fixed the input phase function and extinction cross section but allowed the scattering cross section (and thus $\omega_0$) to vary during this retrieval.

4. We compared the retrieved $\omega_0$ to the $\omega_0$ of the input radiative properties. We knew we were using a self-consistent set of radiative properties—and thus knew $m$—if our retrieved $\omega_0$ was the same as the $\omega_0$ of the input radiative properties. We set a 1% change in $\omega_0$ as our convergence criterion and assumed that if $\omega_0$ converged, $m$ converged as well. If this criterion was not met, we converted $\omega_0$ into $k$ using the LUT from step 1. We then created $m$ from the derived $k$ (using a Kramers-Kronig analysis to derive $n$ from $k$) and used this newly computed $m$ to re-derive radiative properties using T-matrix computations and re-did this iterative process starting from step 3. Thus, our retrieved $\omega_0$ set the initial guess for the radiative properties we used in next iteration of our retrieval procedure.

5.

After each iteration we inspected our retrieved $\omega_0$ values to ensure they were not dependent on any of the major physical parameters. Our retrievals showed no significant changes with emission angle, phase angle, solar longitude, local time, or optical depth; however, we found some changes with solar zenith angle. This could be due to variability in the dust column or surface phase function. We did not have the measurements to distinguish between these possibilities so we eliminated the pixels that exhibited these changes.

# 4. Results

Here we discuss the data-model fits, the retrieved $\omega_0$, and associated $m$ obtained from the iterative retrieval process.
## 4.1. Data-model comparison

We inspected the simulated reflectances at the end of each iteration to ensure they reliably reproduced the IUVS spectra. In all cases the simulated reflectance was within the tolerance of our fitting algorithm, indicating it always found some $\omega_0$ which produced a reflectance that matched the measurements. We also note our model is monotonic with respect to $\omega_0$: lower $\omega_0$ values produce lower reflectances whereas higher $\omega_0$ values produce higher reflectances. Therefore our retrieved $\omega_0$ values are unique.

## 4.2. Single-scattering albedo

Our best-fit $\omega_0$ after completing the iterative retrieval process is shown in the top panel of figure 2.

The uncertainties in our analysis are due to an approximately equal combination of random and systematic uncertainties. We first consider the random uncertainties present in our analysis, which come in two varieties: variance in the retrieved $\omega_0$ values and the random uncertainty of the data. We assumed horizontal homogeneity in our model, so real deviations from the prescribed dust vertical profile, temperature profile, etc. produced a range of $\omega_0$ values from our retrievals. The root-mean-square error on this scatter was generally around 2%, though it was closer to 4–5% at the shortest wavelengths. Due to the large number of spectra considered in this work, the error introduced by the random uncertainty on IUVS data is much smaller than the error introduced by this scatter. The systematic uncertainty on IUVS data is around 5%. We ran our retrievals with this perturbation to the measured reflectances and found this also changed the retrieved $\omega_0$ by about 2%. Thus our reported uncertainties should be seen as partially due to the radiometric calibration and partially due to the observed scatter in our retrievals.

Errors in any of the model parameters can introduce bias in our retrieved $\omega_0$. We did not consider their effects in the uncertainties reported above but here we discuss biases some key parameters may introduce.

* Dust vertical profile: The dayside vertical profiles of dust exhibit sol-to-sol variability. We used a Conrath profile with $v$ (the parameter that controls the sedimentation timescale) that varied from 0.005 to 0.015, as these profiles approximate the shape and bound the range of profiles from Montabone et al. (2020). Using a $v$ of 0.005 (putting dust at higher altitudes than the profile we used) led to approximately 0.9% larger retrieved $\omega_0$ values whereas using a $v$ of 0.015 (putting dust at lower altitudes than the profile we used) led to a 0.7% decrease in the retrieved $\omega_0$ values.

* Rayleigh scattering optical depth: LMD-MGCM simulations indicate the surface pressure varied between 5.6 and 6.6 mbar during the optically thickest times of the storm. We used these values in our model and found they changed $\tau_{Rayleigh}$ by up to 15% compared to $\tau_{Rayleigh}$ computed from the prescribed 6.1 mbar surface pressure, but they only changed $\tau$ by up to 0.3% because the dust optical depth dwarfed the Rayleigh scattering optical depth during the dust storm. These values negligibly affected the retrieved $\omega_0$.

* Dust optical depth: The majority of the 880 nm Mastcam-derived optical depths have an uncertainty less than 0.04 and nearly all of them have uncertainties less than 0.10 (Lemmon et al., 2019). We perturbed these optical depths by 0.10 and found these retrieved $\omega_0$ values were within 1.5% of our reported $\omega_0$, with lower optical depths producing lower single-scattering albedos and vice versa.

* Surface phase function: In general, retrievals are sensitive to the surface parameterization; however, the high optical depths of this GDS diminished its importance. We ran our retrieval using a Lambert surface parameterization where the surface albedo varied between 0.010 and 0.015 between 200 and 300 nm (Clancy, Wolff and Christensen, 2003) and found almost no difference in the retrieved $\omega_0$. In order to obtain $\omega_0$ changes of 1%, we had to raise the albedo to around 0.90. We also perturbed the Hapke $w$ parameter (the surface single-scattering albedo, which was the most sensitive parameter of our surface phase function) by 50% and found it changed the retrieved $\omega_0$ values by 1.2%.

## 4.3. Refractive indices

Neither *n* nor *k* varied much over the MUV spectral range; therefore we report average values for these quantities in table 1. The imaginary component of the refractive indices is shown in the bottom panel of figure 2. We obtained these values by transforming $\omega_0$ into *k* using the LUT described in section 3.6. We transformed the highest and lowest values on the $\omega_0$ uncertainties to set the uncertainty on *k*. We then obtained *n* from *k* via Kramers-Kronig analysis.
<figure><img src="image_5.png" /></figure>

**Figure 2:** (top) Retrieved dust $\omega_0$ of the four particle-size distributions considered in this work. The shaded region shows the uncertainty on the 1.4µm curve, though the magnitude of the errors are nearly identical for all four particle-size distributions. These values are in excellent agreement with those values derived from MRO/MARCI data (Wolff et al., 2010) at the two particle sizes considered in that work, and continue the trends shown by Wolff et al. (2009) using MRO/CRISM data (see the inset plot). (bottom) The imaginary index of refraction corresponding to the retrieved $\omega_0$. We converted $\omega_0$ at its highest and lowest uncertainties to set the uncertainty on $k$. As with $\omega_0$, the uncertainty of $k$ is nearly the same for each of the particle-size distributions so we only plotted the uncertainty for the 1.4µm case.
Ultraviolet Martian dust aerosol properties

<table><thead><tr><th>r<sub>eff</sub> (μm)</th><th>1.4</th><th>1.6</th><th>1.8</th><th>2.0</th></tr></thead><tbody><tr><td>n</td><td>1.48</td><td>1.49</td><td>1.49</td><td>1.49</td></tr><tr><td>k</td><td>0.0180</td><td>0.0154</td><td>0.0135</td><td>0.0122</td></tr></tbody></table>

**Table 1**

Average *n* and *k* (the real and imaginary parts of the refractive indices, respectively) values at the four particle-size distributions (*r*<sub>eff</sub>) we considered in this work over the wavelength range considered in the LUT. The *r*<sub>eff</sub> values represent the most frequently occurring size in the distribution.

# 5. Discussion and Applications

## 5.1. Comparison to previous work

Here we compare our retrieved $\omega_0$ and derived *m* to values found in the literature. The sophistication of the retrieval methods in this area has evolved substantially over time: early works used the single-scattering approximation to report $\omega_0p(\theta)$ (which is proportional to the reflectance) whereas later works used more powerful numerical methods (such as incorporating multiple scattering and electrodynamical techniques) and more consistent microphysical representations of dust. Consequently, earlier works tended to focus on the scattering properties rather than the refractive indices.

### 5.1.1. Single-scattering albedo

Our analysis is most readily comparable to analysis by Wolff et al. (2010) and we show good agreement (see the top panel of figure 2). They used MARs Color Imager (MARCI) data from the Mars Reconnaissance Orbiter (MRO). Both of our works used the same microphysical representation of dust, the same basic radiative transfer algorithms, and similar observational datasets so it provides additional confidence that our works show agreement at the single overlapping bandpass. At longer wavelengths our analysis appears to show somewhat lower $\omega_0$ values than values obtained by linearly interpolating between the MARCI results; however there is no guarantee that $\omega_0$ does not rapidly change when transitioning to visible wavelengths so we do not ascribe much significance to this disagreement. These $\omega_0$ values are approximately what one would obtain when extrapolating the results Wolff et al. (2009) obtained from Compact Reconnaissance Imaging Spectrometer (CRISM) data to UV wavelengths.

Our analysis generally agrees with works from other Martian-based instruments, though the differing techniques employed make direct comparison difficult. Early work in this area by Pang, Ajello, Hord and Egan (1976) used data from Mariner 9's Ultraviolet Spectrograph (UVS) to retrieve $\omega_0p(\theta)$ for a range of phase angles. Our results generally agree with these simplified retrievals. Ockert-Bell, Bell III, Pollack, McKay and Forget (1997) later used whole disk spectra and reported $\omega_0$ of 0.72 at 210 nm and $\omega_0$ of 0.61 at 300 nm, though their work did not account for atmospheric effects like Rayleigh scattering. This, in addition to their assumption that all reflectance is due to surface reflectance, leads to significant uncertainty on their $\omega_0$ values. More recently, Mateshvili et al. (2007) used spectra of a regional dust storm taken by the Spectroscopy for the Investigation of the Characteristics of the Atmosphere of Mars (SPICAM) instrument on the Mars Express spacecraft and retrieved $\omega_0$ of 0.60 ± 0.05 at 213 nm and $\omega_0$ of 0.64 ± 0.04 at 300 nm. They did not fix $\tau$ and used a single LUT instead of performing the same iterative process that we did, but our results are in agreement.

Our analysis also somewhat agrees with results from the Hubble Space Telescope (HST). Wolff, Lee, Clancy, Martin, Bell III and James (1997) used the Faint Object Spectrograph to derive $\omega_0$ of 0.57 at both 210 and 300 nm with Wolff et al. (2010) conservatively estimating the uncertainty at ± 0.06. This relatively large error is due to the observational geometry of the HST and the use of simplified treatment of aerosol scattering. Nevertheless, our $\omega_0$ values are within each others' uncertainties.

### 5.1.2. Refractive indices

The complexity of radiative modeling makes it difficult for us to directly compare our refractive indices to previous results because the refractive indices used in a first-principles model will produce different scattering properties depending on the choice of particle shape, particle size, and particle-size distribution. The first attempts to observationally derive UV complex refractive indices used UVS data and found *n* to be at least 1.8—significantly higher than our findings of 1.5—and *k* of 0.02 at 268 nm and *k* of 0.01 at 305 nm (Pang et al., 1976). This shows rapid variability over the UV that is not seen in our analysis. Mateshvili et al. (2007) found sets of refractive indices that matched SPICAM spectra, with *n* ranging from 1.4 to nearly 2.0 and *k* ranging from 0.010 to 0.025. Both of these ranges are
significantly larger than the nearly constant *n* and *k* values we derived, with some points having *m* values consistent with ours, though they used different particle shapes and sizes than we used in this work. The most recent approach (Wolff et al., 2010) used the same aerosol model and approach described in section 3.3, to derive the refractive indices from MARCI data. Our $\omega_0$ values agree so it is unsurprising that our *m* values also agree.

## 5.2. Applications

There are a number of potential, broad applications of our results. For example, GCMs can use these refractive indices to more accurately prescribe photolysis rates in their microphysical computations. Our results can also help improve our understanding of the Martian surface in the UV by helping to remove atmospheric effects and isolate surface effects. Analyses of Martian data in the UV using radiative transfer techniques will benefit from this work as well.

We can also use these refractive indices for aerosol studies using IUVS data. Perhaps the most straightforward application is to create a dust climatology from IUVS data. This might be useful when compared to climatologies derived from datasets that have different spatial and temporal coverage (e.g. Montabone, Forget, Millour, Wilson, Lewis, Cantor, Kass, Kleinböhl, Lemmon, Smith and Wolff (2015)). Our derived refractive indices are anchored by the Mastcam-derived optical depths and should allow us to uniquely examine the spatial and temporal evolution of dust. We are also particularly interested to incorporate radiative properties derived from these refractive indices into our retrievals of water-ice clouds using IUVS data, as the diffuse dust component is an important aspect of this modeling.

In the section below, we demonstrate the feasibility of using these optical properties in dust optical depth retrievals. We performed a few targeted retrievals of diffuse dust optical depths using some of our retrieved refractive indices and demonstrate our preferred set of refractive indices yield reasonable agreement with Mastcam-derived optical depths.

### 5.2.1. Dust climatology over Gale Crater

Up to this point we have been agnostic regarding particle sizes present during the storm but we need to select a set of refractive indices that best represents the dust. We obtained simulations from the *Laboratoire de Météorologie Dynamique* (LMD) Mars GCM run with the MY 34 dust scenario. A representative particle-size gradient over Gale Crater during the GDS is shown in figure 3. If we consider the average particle sizes sampled by IUVS during this storm assuming this vertical profile, we obtain $\langle r_{eff} \rangle = \int r_{eff}(z) \, d\tau(z) \approx 1.8$ µm. Thus we hypothesize this set of refractive indices best represents the dust, but we can only confirm this hypothesis by testing the relevant set of refractive indices in a retrieval. We used these refractive indices to compute the radiative properties for 1.5 µm dust particles as this size is more representative of the particle sizes seen during diffuse dust loading conditions (Lemmon et al, 2019).

We tested most of these retrieved sets of refractive indices on a targeted set of observations with a “ground truth” to ensure some set performed well. We selected pixels from IUVS data over Gale Crater during diffuse dust loading conditions, retrieved $\tau$ from these pixels, and compared our results to Mastcam direct solar-imaging results. We found a few sequences of IUVS images that included Gale Crater when Mastcam also had good coverage, and chose one around a solar longitude of 180° during MY 33. We selected this sequence because the aphelion cloud belt is largely dissipated around this season so our images are less likely to be contaminated with water-ice clouds. Additionally, this season is before local dust storms become more common, allowing us to perform the desired retrievals of diffuse dust. We identified three images that showed obvious signs of water-ice clouds over Gale Crater and removed these images from our analysis. We identified no dust storms over Gale Crater in these images.

The shortest UV wavelengths are the best wavelengths to use for these dust retrievals. The impact of ozone on these IUVS data is most significant around 255 nm and remains impactful throughout much of the MUV but it has nearly no effect towards the ends of the MUV spectra. Rayleigh scattering is relatively insignificant at longer MUV wavelengths but is significant at shorter MUV wavelengths. Dust thus presents a higher contrast against the Rayleigh scattering at shorter wavelengths than against the surface at longer wavelengths. Dust aerosols have a featureless spectra over this range so if no water-ice clouds are present, the shortest wavelengths provide the best opportunity to retrieve dust optical depths, though we note that these signals are still sensitive to the details of the Rayleigh scattering and surface phase function.

Our retrieval process was very similar to that described in section 3 so we briefly highlight the changes. We prescribed the dust vertical profile using a Conrath distribution with $v$ of 0.1, as that vertical profile is similar to those seen in the Mars Climate Database (MCD) around this season. These lower optical depth retrievals are much more
Ultraviolet Martian dust aerosol properties

<figure><img src="image_6.png" /><figcaption>**Figure 3:** Average dust particle sizes over Gale Crater during the thickest times during the GDS as simulated by the LMD-MGCM using the MY 34 dust scenario.</figcaption></figure>

sensitive to Rayleigh scattering than our $\omega_0$ retrievals so we also set the surface pressure and vertical temperature profiles with values from the MCD at the corresponding solar longitude and local times of these images. We used our newly created radiative properties and retrieved $\tau$ at 205 nm, and then scaled it to 880 nm using a ratio of the extinction cross sections for direct comparisons with Mastcam-derived optical depths. We performed this analysis using radiative properties derived from the 1.6, 1.8, and 2.0 refractive indices.

The result of these retrievals are shown in figure 4. As predicted, the 1.8 micron refractive indices perform the best and show agreement with the trends shown in the Mastcam results (Lemmon et al., 2019). As with the $\omega_0$ retrievals, there are a number of sources of bias: deviations from the real vertical dust profile, errors in the pressure and temperature profiles, etc. Nevertheless our preferred radiative properties give sensible results and we conclude that our selected radiative properties are well-suited for future retrievals involving dust.

## 6. Conclusion

We used IUVS data from the MY 34 GDS to derive UV complex refractive indices of dust using radiative transfer techniques. We chose data taken over Gale Crater during the optically thickest times of this storm and combined these data with Mastcam-derived optical depths to perform retrievals of $\omega_0$. With this method we were able to minimize the uncertainty associated with several of the key inputs to our radiative transfer-based approach. We used a first principles methodology for the dust model, which produced a self-consistent set of radiative properties. We derived $\omega_0$ from the IUVS spectra and converted that into a set of refractive indices and recalculated the dust radiative properties. We repeated this process until the $\omega_0$ values changed by less than 1%. The resulting refractive indices were nearly constant in the UV and their averages can be found in table 1. These refractive indices are in good agreement with the values derived by Wolff et al. (2010) and extended the analyses to shorter wavelengths, which is key for providing contrast between dust and Rayleigh scattering.

We applied several sets of newly derived refractive indices in a retrieval using IUVS data taken above Gale Crater during more diffuse dust loading conditions. This allowed us to evaluate the utility of these indices and distinguish which set is most applicable to future retrievals involving dust. We retrieved $\tau$ from the IUVS data and compared it to Mastcam direct-imaging derivations of $\tau$ at similar times at most sets of refractive indices. The result showed a very reasonable agreement between the Mastcam and IUVS results for the 1.8 micron refractive indices. As a result, these indices and their corresponding radiative properties will be particularly beneficial to future retrievals using IUVS data.

## Acknowledgements

NASA supported this work through the MAVEN project. MAVEN/IUVS data files used in this work are identified as “apoapse”, version 13, of the level 1b data and are available on the atmospheres node of the Planetary Data System.
<figure><img src="image_7.png" /></figure>

**Figure 4:** Comparison between IUVS retrievals and Mastcam results for a time period during MY 33. We performed these retrievals at each usable pixel between MAVEN orbits 3400 and 3499 and report a single value for each orbit containing Gale Crater. We performed all retrievals using IUVS' 205 nm data and scaled our results to 880 nm (the spectral bin used by Mastcam). We performed this analysis using radiative properties of 1.5 micron dust computed from the refractive indices of 1.6, 1.8, and 2.0 microns. The errors in all cases are approximately the same; thus, we only plotted the errors for the 1.8 micron case. The 1.8 micron refractive indices best reproduce the trends seen in the Mastcam retrievals and we believe these are the most applicable indices to dust.

We thank Mark Lemmon for providing the Mastcam optical depths used in this work. We also thank Ehouarn Millour and the entire LMD team for providing the simulations from the MY 34 GDS. Additionally, we thank Zac Milby for assistance creating select graphics in this paper.

## A. IUVS calibration

The results in the current work employ a flatfield correction to the IUVS MUV spectrograph images. We constructed this flatfield using only standard apoapse disk integrations acquired with an approximately evenly illuminated slit, effectively using Mars as a reflectance screen. The data used were collected between MAVEN orbits 3470 and 3488 (corresponding to solar longitudes between 183.8 and 185.7 in MY 33). These data were collected at a time when Mars was relatively geographically homogeneous in its reflectance properties, being outside both the cloudy season and the most active part of the dust storm season.

These data were filtered to only include integrations in which the entire slit field of view was on the dayside disk with solar zenith angles and emission angles both less than 80°, and variation in both angles along the length of the airglow slit did not exceed 20°. In addition, data were constrained to latitudes between 45° and -45° in order to
<figure><img src="image_8.png" /><figcaption>**Figure 5:** The flatfield used in this work for the 133 spatial binning and 19 spectral binning scheme.</figcaption></figure>

avoid regions with ozone absorption signatures. We averaged together detector images from the integrations meeting these criteria, rejecting outlier values that fell outside of 4.45 median absolute deviations of the mean (equivalent to 3 standard deviations for a normal distribution). We produced a slit-averaged spectrum by taking the median of the averaged detector image along the spatial dimension. Finally, we produced the flatfield by using this spectrum to normalize the spectrum at each spatial element of the averaged detector image.

The flatfield derived in this manner is shown in figure 5. We interpret the horizontal striping is due to multiple reflections in the beam splitter that partitions dispersed light between the far-UV and MUV channels (McClintock et al., 2015). The magnitude of the variation is generally smaller at the short wavelength end of the detector (bottom) and larger at the long wavelength end of the detector (top).

We investigated special measurements of bright stars taken by IUVS' airglow slit to independently validate the flatfield. We simulated a local slit filling source at each position sampled along the length of the slit by scanning the airglow slit in the dispersion dimension across a stellar point source while integrating the detector continuously. We acquired 60 integrations for each position sampled along the length of the slit, enabling us to compute the standard deviation of the mean from the variance of the integrations. We selected stars based on serendipitous availability within the IUVS field-of-regard during nominal science operations, and it was not always possible to sample the entire length of the airglow slit with every star. These calibration data are publicly available in the “calibration” collection at the PDS with the file observation label type “star”. They differ from the standard IUVS stellar occultation campaign data, which only use the keyholes at the edges of the detector.

We show a comparison between the stellar calibration data and the flatfield derived from the filtered observations of the Martian disk at two selected wavelengths on the detector in figure 6. The error bars on each symbol represent the one-sigma uncertainties for each stellar observation. The flatfield information derived by disk and stellar methods are generally consistent. Two notable differences are (1) that the disk derived flatfield includes stray signal from the IUVS “keyholes” located at the top and bottom of the airglow slit, and (2) that the disk derived flatfield is aligned with the stellar results but is slightly less extreme in magnitude. The latter effect is likely due to the fact that the disk data represents a truly slit filling sources, while the stellar data are spatial point sources. In other words, the disk derived flatfield is somewhat smoothed by the instrumental spatial point spread function relative to the star derived flatfield.

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