The calibration procedure starts with identifying the mostly aerosol-free, cleaner days with an AERONET measured AOD (440 nm) < 0.1. The MFRSR instrument measures raw total (full hemispheric view) and diffuse (sun shadowed) voltages [milli-volts] near-simultaneously for seven narrow filter (solid state detector) channels every minute. There are 2 additional voltage measurements with the shadow band blocking the sky radiance in aureole directions on each side of the sun. These measurements are used to correct for the forward scattered solar light around the sun (aureole) (Harrison et al., 1994). The complete cycle takes ∼ 10 s and is repeated every 1 min throughout the day. For on-site MFRSR calibration, we use spectrally and time interpolated AERONET level 1.5 extinction aerosol optical depths, τAER(λrad), where λrad is the radiatively equivalent wavelength for each channel (Krotkov et al., 2005a). The surface pressure adjusted scattering molecular optical depth (i.e., Rayleigh OD, τRay(λrad)P) and the absorption optical depths of trace gases (O₃ and NO₂) are also computed at λrad using satellite or co-located ground-based (e.g., PANDORA) trace-gas column measurements. The total atmospheric column extinction optical depth is then multiplied with the direct-sun air-mass factor, sec(SZA), where SZA is solar zenith angle and combined with the cosine-corrected direct-normal voltage measurement, VdirnMeas/fR, to calculate the calibration constant (V0Clean) for each channel and measurement cycle throughout the day, as formulated in Eq. (1): 1ln⁡V0Clean=ln⁡VdirnMeas/fR+secSZA×τAERλrad+τRayλradP+τgasλrad τAER is interpolated with a 2nd order polynomial from 4 AERONET direct sun level 1.5 AOD (340, 380, 440, 500 nm) in log–log space to λrad (Eck et al., 1999); τRay is the Rayleigh optical depth adjusted to the atmospheric pressure, fR is the laboratory-measured and cosine-normalized angular response (i.e., see Fig. 4 in Krotkov et al., 2005a), and τgas is the combined optical depth of the trace gases of Ozone (O₃) and NO₂ obtained from Aura/OMI sensor for almost entire record, except for the last three months (July through September 2023) during which the total O₃ column densities retrieved from SNPP-OMPS were used. Additionally, the O₃ and NO₂ amounts measured from the collocated ground-based Pandora instrument were used, whenever available, during the same period. Note that all radiative transfer calculations accounting for the Rayleigh, gaseous, and aerosol atmospheres were carried out at the radiatively equivalent wavelength λrad calculated for each measurement and spectral channel, as shown in Krotkov et al. (2005a). Figure 3 shows examples illustrating the Step 1 of the calibration procedure for clean days on 20 and 31 August 2020, when AERONET-measured AOD at 440 nm (AOD₄₄₀) were less than 0.03. The true-color RGB image captured by the MODIS sensor onboard the Aqua satellite visually confirms no dust transport from the Saharan desert on these two dates. The natural logarithm of V0, ln⁡(V0), calculated from Eq. (1) for each 1 min measurement is shown on the left-hand y-axis as red-green-blue-black dots. The different colors show the effect of the iterative removal of outlier measurements with V0 values outside of 3σ standard deviation. The final selections (182 and 184 retained measurements out of original 209 and 211) are shown as black dots, while the black horizontal lines show the daily average 〈ln⁡(V0)〉 values. The red lines show independent Langley intercept calibrations applied to all filtered MFRSR morning measurements between 08:00 and 12:00 UTC (black dots). There is excellent agreement with the AERONET-based calibration on 31 August when the AOD remained approximately constant. On 20 August, the Langley intercept is 1 % lower than the AERONET-based 〈ln⁡(V0)〉 because the AOD systematically increased during the morning Langley calibration period. We do not use Langley calibrations in this work.

Equation (1) was applied to all 1 min MFRSR morning measurement cycles between 08:00 and 12:00 UTC resulting in (after removing outliers using an iterative procedure that discards data points outside 3σ standard deviation) a daily average 〈ln⁡(V0Clean)〉 value of 8.111 and 8.116 on the respective dates. An increase in V0 by 0.5 % from 20 to 31 August is real and attributed to the reduction in the Sun-Earth distance between the two dates. The Step 1 procedure described above was applied to each MFRSR spectral channel for a total of the 223 cleanest days with an AOD₄₄₀ < 0.10 identified during the AERONET-MFRSR combined operation period 2019–2023.

Equation (1) can be inverted to calculate MFRSR aerosol optical depth: τMFRSR(λrad) assuming known daily average calibration constant (i.e., 〈ln⁡(V0Clean)〉), which can be estimated either from Langley intercept (Harrison and Michalsky, 1994) or using our Step 1 calibration procedure. For days with low AOD or fine-mode dominated aerosols (e.g., smoke; Mok et al., 2016), the MFRSR-derived and AERONET measured AOD typically agree within estimated uncertainties, e.g., |τAER-τMFRSR|<0.01 for AOD < 0.5 (Krotkov et al., 2005a). However, for dusty days with large AOD dominated by coarse mode aerosols, the VdirnMeas becomes overestimated due to under corrected aureole effect. On the other hand, AERONET direct sun AOD measurements τAER(λrad) are much less affected by the aureole effect even for coarse dust particles due to CIMEL small field-of-view (∼ 1.2°). Therefore, we calculate corrected direct-normal voltages, VdirnCorr on dusty days with AERONET AOD₄₄₀ > 0.2 using Eq. (2) and the median of the cleaner day calibration constants during each month, 〈V0Clean〉m: 2ln⁡(VdirnCorr)=ln⁡〈V0Clean〉m-secSZA×τAERλrad+τRayλradP+τgasλrad

In the final calibration step, the corrected diffuse voltage, VdifCorr, is calculated by subtracting the corrected direct horizontal voltage, VdirnCorr, from the cosine-corrected measured total voltage, VTotalMeasfT, as given in Eq. (3): 3VdifCorr=VTotalMeasfT-cos⁡(SZA)VdirnCorr Where fT is the effective cosine correction factor applied to the total (direct plus diffuse) raw irradiance measurement (Krotkov et al., 2005a). Figure 4 illustrates the Step 2 and Step 3 of the calibration procedure for 26 August 2020. The three-step calibration procedure described above yields the corrected diffuse voltage, VdifCorr for dusty day observations. Note that while the partition between direct and diffuse irradiance is adjusted according to Eqs. (2) and (3), the total voltage VTotalMeas measured by MFRSR does not change in the calibration process. The dimensionless ratio of the corrected diffuse to corrected direct-normal irradiance is then used in the retrieval algorithm to retrieve the imaginary part of the complex refractive index for each 1 min measurement on dusty days with AOD₄₄₀ > 0.2.

We employ a Gauss–Seidel radiative transfer model, formally referred to as the Arizona RT model, for simulating the at-surface spectral direct and diffuse downwelling planar irradiances. The 1-dimensional RT code accounts for gaseous absorption as well as molecular and aerosol multiple scattering (Herman and Browning, 1965). In this plane-parallel atmosphere, sphericity is included in the incoming solar beam, also known as the pseudo-spherical approximation (Caudill et al., 1997). The model creates a total of 100 vertical atmospheric layers with associated molecular, aerosols, and input trace gases profiles. Absorption cross-sections of ozone and nitrogen dioxide are averaged for each channel using the appropriate bandwidths to derive effective absorption layer optical depths at λrad values used in the RT model. The reflecting surface is modeled as Lambertian with albedo obtained from AERONET Level 1.5 inversion at 440 nm, which also is used at all MFRSR UV channels. The aerosol absorption inversion procedure begins with the availability of the AERONET Level 1.5 direct measurements of spectral AOD and inversion parameters of particle size distribution and the real part of the refractive index (n). Each instance of an MFRSR measurement was temporally collocated with the AERONET direct sun AOD measurements within ±15 min and available closest-in-time inversion products on a daily basis. Note that, no averaging was performed on the MFRSR measurements. Instead, all 1 min MFRSR measurements were assigned to the corresponding collocated AERONET parameters. For each instance of AERONET-MFRSR collocated points, the spectral AODs in the range 340–500 nm are used to derive a quadratic relationship between AOD and wavelengths in log-log space, which then was used to estimate the AOD at the MFRSR radiatively equivalent channel wavelength λrad.

The Izaña Observatory in the Tenerife Island is located in the northwest pathways of long-range dust transport from the Sahara Desert. During such transport events, the mineral dust from the Sahara constitutes the major component of aerosols over the region. Sea salt and locally emitted aerosols might also contribute to the total loading although their contribution is minimal as evident from the very low AOD₄₄₀ (< 0.05) measured by the AERONET on dust-free, cleaner days. Outside the dust transport season (Jun, July, August), Izaña is predominantly under background clean conditions the rest of the year as a consequence of the prevailing westerly flows of the North Atlantic free troposphere at subtropical latitudes, with subsequent transatlantic transport of North American dust, non-sea-salt sulfate and organic matter as main contributors (García et al., 2017; Barreto et al., 2022). Since the focus of the present study is to retrieve spectral aerosol absorption of the transported Saharan dust particles, the mineral dust aerosol is assumed to be the sole component of the aerosol loading.

Dust aerosols are known to be non-spherical in shape, as shown by several studies (Dubovik et al., 2006; Torres et al., 2018). A satellite-based retrieval study, based on the Aura-OMI observations, has shown that assuming spherical dust particles produces large biases in the retrieved AOD (388 nm) between the two sets of scattering angle geometries, i.e., forward and back scattering, over the semi-arid region of Sahara. These results created the necessity to modify the dust aerosol model used in the OMI near-UV aerosol retrieval algorithm.

Accurate representation of the scattering phase function of large non-spherical particles, such as dust aerosols, requires numerical tools such as T-matrix theory (Waterman, 1971; Bohren and Singham, 1991; Mishchenko and Travis, 1994), geometric optics (Yang and Liou, 1996) or a combination of the two approaches (Dubovik et al., 2006). The simplest and most commonly assumed non-spherical shapes for which exact analytical solutions can be obtained are spheroids characterized by their aspect or axis ratio (ε). While the T-matrix theory applied to the spheroidal shape particles reproduces the laboratory measurements of the scattering phase function significantly better than spheres, it breaks down for highly elongated spheroids of a very large size parameter (Mishchenko et al., 1997). The geometric optics method, on the other hand, documented in Yang et al. (2000) accurately accounts for scattering effects of spheroids of aspect ratios and size parameters beyond the range handled by the T-matrix theory. Dubovik et al. (2006) blended the advantages of the T-matrix theory and Geometric Optics method to create a set of pre-calculated look-up tables (LUT) of phase matrix elements of randomly oriented spheroids at a 1° scattering angle resolution. The associated software package, formally referred to as the Light Scattering Simulations (or popularly referred to as DLS package within the aerosol community), handles a wide range of the real part of the refractive index (1.33–1.6), the imaginary part of the refractive index (0.0005–0.5), aspect ratios (0.3–3.0), and size parameters (0.012–625). Using this package, Torres et al. (2018) simulated the phase matrix elements for the dust aerosol models used in their satellite Aura Ozone Monitoring Instrument (OMI) UV aerosol retrievals (OMAERUV). The aspect ratio distribution assumed in the OMAERUV calculations was taken from Dubovik et al. (2006), which is shown as the black curve in the inset plot of Fig. 5a.

Torres et al. (2018) demonstrated that using a near-UV aerosol lookup table (at 354 and 388 nm), based on phase matrix elements derived from spheroidal aspect ratios proposed by Dubovik et al. (2006), significantly reduced scan bias in the OMI AOD retrievals. This approach improved consistency between retrievals on the west side (characterized by lower backscattering or forward-scattering angles) and the east side (backscattering angles) of the OMI scan over the Saharan Desert. The improvements in the OMI AOD retrievals reflect the effectiveness of the assumed spheroidal aspect ratio distribution over the dust source region. A similar analysis for the Saharan dust transport over the Atlantic Ocean post Torres et al. (2018) publication, however, still showed asymmetry in the retrieved AOD between the East and West sides of the OMI swath. These results necessitated testing different spheroidal distributions to investigate their impacts on the dust AOD retrievals. Three distinct aspect ratio distributions reflecting different adjusting weighting factors were used individually in the OMI-based near-UV aerosol retrievals over ocean. The adjustment in weighting factors between these three distributions was made empirically, while constraining the sum of all factors to be 1.0, by gradually increasing the contribution of spherical particles. The aerosol look-up tables created using the three corresponding sets of phase matrix elements generated using original DLS software tool were used in the OMI aerosol algorithm to investigate the retrieval results. We found that the final set of aspect ratios, characterized with a continuous distribution of weighting factors as a function of axis ratio bins with greater weights given to spherical particles, shown as the red curve in the Fig. 5a, largely eliminated the observed asymmetry in the OMI dust AOD retrievals over the Atlantic Ocean. Figure S1 in the Supplement illustrates the timeseries of monthly mean OMI AOD [388 nm] for the Atlantic Ocean comparing retrievals from westside and eastside of scan derived assuming spheroidal and empirical aspect ratios models. The summertime (June–Juy–August) global distribution of OMI dust AOD derived separately from the data collected on the west and east sides of the scan are presented in Fig. S2. Although these results were not previously published, they were adopted for over-ocean dust aerosol AOD and SSA operational retrievals using near-UV observations by the OMI and TROPOMI sensors (Torres et al., 2020), and EPIC-DSCOVR measurements (Ahn et al., 2021). The over-land dust AOD/SSA retrievals from these sensors still use the original spheroidal aspect ratio distribution proposed in Dubovik et al. (2006). The weighting factors distribution parameter as a function of radius for randomly oriented spheroids proposed in Dubovik et al. (2006) and those used in the over-ocean aerosol retrievals from near-UV sensors are listed in Table 3.

Figure 5 shows the scattering phase function F11 for the 440 nm wavelength for a single set of MFRSR-AERONET collocated measurements of mineral dust aerosols acquired on (a) 26 August at 10:10 UTC, (b) 27 August at 10:19 UTC, and (c) 28 August at 15:09 UTC of 2020 corresponding to randomly oriented spheroids proposed in Dubovik et al. (2006) (black), empirically derived distribution (red) used in the present study, and that from AERONET inversion product (blue). F11 (except retrieved from AERONET) was simulated using the refactored DLS software package (named as the API and described in Appendix A). The differences in F11 between the two aspect ratio distributions are quite small for scattering angles smaller than 120°. However, they deviate increasingly at large scattering angles, where the use of the randomly oriented spheroidal model of Dubovik et al. (2006) produces substantially lower F11 values than the empirically derived aspect ratio distribution representing a mixture of spheroids and spheres. Despite these differences, the corresponding SSAs (black and red) show a close agreement – indicating that the choice of aspect ratio distribution didn't play a significant role in the inversion for these three dust events. A sensitivity analysis quantifying the change in the derived SSA due to different dust shape factor distributions is presented in Sect. 4 and also included in Table 4.

The aspect ratio distribution of the Saharan mineral dust inferred from electronic microscope and in situ measurements as reported in the published literature shows a great deal of variability. Reid et al. (2003) sampled the African dust during the Puerto Rico Dust Experiment and found dust to have a significantly higher aspect ratio near 1.9 with standard deviation of 0.9 after long-range transport. Huang et al. (2020) compiled the aspect ratio of the mineral dust aerosols representative of the Saharan and Asian deserts published in the literature, and showed a trend of increasing aspect ratios for northern African dust after transatlantic advection. Specifically, the median aspect ratio increased from 1.60 ± 0.07 in the dust source regions of North Africa to 1.66 ± 0.03 for short-range transported dust and 1.90 ± 0.04 for long-range transported dust. This increase in particle non-sphericity or aspect ratio during transport is attributed to the preferential settling of spherical particles, which have a greater terminal fall speed than aspherical particles of the same volume. Overall, the aspect ratios reported for North African dust were in the range 1.4–2.0.

More recently, Panta et al. (2023) reports high non-sphericity of dust particles collected during the FRontiers in dust minerAloGical coMposition and its Effects upoN climaTe (FRAGMENT) field campaign in the Moroccan Sahara in September 2019, with mean and median aspect ratios of ∼ 1.55 ± 0.38 and 1.46, noting that it does not vary strongly with particle diameter. Aryasree et al. (2024) found that the aspect ratio of the Saharan air layer measured at the Capo Verde and Caribbean sites did not change significantly and remained in the range 1.5–2.0.

Accurately representing the true aspect ratio distribution of dust airmass observed by the MFRSR during absorption inversion at the study site remains a challenging problem. As a first approximation, we adopted an empirically derived model previously used in satellite-based Aura/OMI AOD retrievals in UV. It is important to note that improved aerosol retrievals from satellite observations do not necessarily confirm the presence of a mixture of spherical and spheroidal particles. Rather, this improvement suggests that such a mixture best reproduces the observed solar backscattered UV (BUV) radiances, even though real dust particles are typically angular and irregular, not smooth and spheroidal as represented in the model. Driven by the improved OMI AOD retrievals over land and ocean using two distinct models of spheroidal aspect ratio distribution, the over-ocean dust retrievals in the near-UV aerosol algorithm applied to OMI (Torres et al., 2018), S5p-TROPOMI (Torres et al., 2020), and DSCOVR-EPIC sensors (Ahn et al., 2021) was also updated.

Both AERONET and satellite retrieval algorithms assume spheroidal particle shapes primarily because: (1) computationally efficient scattering algorithms for irregularly shaped particles are not readily available, and (2) the spheroidal approximation captures some of the key scattering phase matrix angular features of randomly oriented desert dust particles reasonably well. More importantly, in the context of this study, incorporating these empirically derived aspect ratios into the aerosol LUT significantly improved the agreement in SSA at 440 nm between MFRSR and AERONET inversions. The results of such comparison on a much larger retrieval dataset are discussed in Sect. 5.1.

During the summer months, the Izaña observatory on Tenerife Island observes transported dust that originated in the Saharan Desert. Although suspended dust particles are complicated in shape and size that are practically difficult to model in RT simulations, we hypothesize that the dust airmass measured at the site is composed of a mixture of spheres and spheroidal particles for the reasons explained above. The phase matrix associated with the adopted empirically derived aspect ratio distribution was simulated using a modified, substantially faster version of the Light Scattering DLS package for all RT calculations (Lyapustin et al., 2021; Korkin and Lyapustin 2023). See Appendix A for a detailed description of how the original DLS package was modified with a specific aim to shorten the computational time without losing accuracy. A test performed to evaluate the differences in the simulation between the original and refactored DLS software tools revealed minor differences of ∼ 0.001–0.002 in the simulated SSA for the dust aerosol inversion measurements at the Izaña site. Such small differences in the SSA simulations are negligible compared to the expected uncertainties in the spectral SSA due to the uncertainties in the measurement calibration and other assumptions made in the inversion procedure.

The matchup procedure of the AERONET-MFRSR measurements deals with the three kinds of datasets: 1 min MFRSR measurements of diffuse and direct-normal voltages, AERONET Level 1.5 almucantar combined with hybrid sky scan inversion dataset, and AERONET Level 1.5 direct spectral AOD measurements. While the AERONET Level 1.5 almucantar scans are mostly performed during the early morning-late afternoon hours, ensuring an adequate sky signal at higher solar zenith angles (> 50°), hybrid scans are made once per hour throughout the day. Direct measurements of spectral AOD are made typically at 5 min intervals at the Izaña site. To maximize the usage of the MFRSR's 1 min hemispheric sky observations, each of these measurements were temporally collocated with the nearest available AERONET inversion instance, either almucantar or hybrid, within a specific day. For instance, near-noon MFRSR measurements could be matched with either morning or afternoon AERONET inversion data, whichever is closest in time. Similarly, the nearest-in-time direct AERONET AOD measurements were also assigned to each MFRSR data points. This simple temporal collocation procedure provided a matchup dataset which begins with an instance of the AERONET inversion dataset (the real and imaginary part of the refractive index, particle size distribution, and other related parameters) followed by a number of collocated MFRSR measurements that include diffuse and direct-normal voltages and corresponding AERONET spectral AODs. This procedure was performed for each wavelength of the MFRSR independently.

The MFRSR-AERONET merged file contains each instance of the AERONET direct and inversion data product values and a corresponding number of collocated MFRSR 1 min measurements for a specific day. For the 440 nm wavelength measurements, the real and imaginary parts of the refractive index and the particle size distribution parameters provided by AERONET were used to create input files for the refactored DLS (the API) package. A total of 21 bins of aspect ratio distribution ranging from about 0.4 (oblate) to about 2.5 (prolate) are prescribed with associated weighting factors shown as the red curve in Fig. 5a. The AERONET volume size distribution defined at fixed 22 radii bins was used as direct input to the API. Using these parameters as input, the phase matrix elements were simulated at a total of 181 scattering angles at a 1° resolution. The resultant phase matrix values along with the total AOD measured by AERONET and trace gas absorption optical depths were then ingested into the ARIZONA RT code to simulate the diffuse and direct surface irradiance at the prescribed atmospheric pressure. The vertical profile of aerosols is assumed to follow the Gaussian distribution with the peak concentration at 3 km above ground.

We adopted a look-up table-based approach in which the simulation of the ratio of diffuse to direct-normal (DD) irradiance was created using the phase matrix calculated for a total of 15 node values of the imaginary part of the refractive index. The measured diffuse to direct ratio was then fitted linearly to an array of simulations to derive the imaginary part of the refractive index and SSA. The Jacobians quantifying the sensitivity of the retrieved imaginary part of the refractive index to the simulated DD ratio and the SSA to the imaginary part of the refractive index were also calculated. These Jacobians are useful to estimate uncertainty in the derived SSA due to prescribed uncertainty in the DD ratio measurements. The entire inversion procedure was applied to each of the five wavelengths of the MFRSR independently.

The aerosol absorption inversion procedure described above essentially follows the method described in Krotkov et al. (2005b), except that (1) the aerosol phase matrix for the coarse mode dust aerosols is simulated externally and ingested into the ARIZONA RT model instead of using the Mie theory calculations for spherical particles, and (2) adoption of a LUT-based approach to find the solution in the imaginary part of the refractive index, which is more efficient than an original iterative procedure, which fails for certain observations. A simplified flowchart of the AERONET-MFRSR synergistic algorithm is illustrated in Fig. 6.

The entire MFRSR multi-wavelength observations record at IZO was processed with the present algorithm. The inversions were attempted for all observations at all five wavelengths with AOD₄₄₀ > 0.2 and solar zenith angle < 70°. “Successful” retrievals are defined as those in which both k and SSA are derived for each 1 min MFRSR observation at a given wavelength independently of other wavelengths. If a retrieval fails at one wavelength but succeeds at others, the successful results are not discarded but retained and reported for the corresponding wavelengths. Consequently, the number of successful retrievals may vary across wavelengths. Table 2 lists the total number of processed observations and valid inversions performed for different wavelengths and years. It was noticed that the inversion success rate for the 440 nm wavelength is noticeably lower compared to other shorter wavelengths. The majority of these failed retrieval attempts corresponds to either lower AOD conditions (0.2 < AOD₄₄₀ < 0.4) and/or larger solar zenith angles (65–70°), and higher AERONET SSA (440 nm) of ∼ 0.98. Under such conditions and at the minimum node value of 0.0005 in the imaginary part of the refractive index, the measured DD ratios, even after accounting for 1 % uncertainty in the measurements, were found to be significantly higher compared to the RT simulations at the minimum node value of 0.0005 in the imaginary part of the refractive index, below which DLS simulations are not recommended. Another source of uncertainty in retrieving aerosol properties at lower AOD conditions at the Izaña site is the lower boundary reflectance with bi-directional reflectance distribution function (BRDF) of the mountain slope. Additionally, clouds and the Rayleigh-aerosol radiative interactions from the atmosphere below the station can also modify the spectral sky radiance measured by both MFRSR and AERONET sensors. Accounting for these effects in the inversion algorithm is complicated, which makes retrievals on higher altitude mountain slope stations more complicated, difficult, and uncertain than those at stations with relatively a flat surrounding landscape/terrain.

In Fig. 10a, we compare the MFRSR-derived SSAs at 440 nm against those of AERONET for a transported Saharan dust event observed between 26–28 August 2020. The SSAs are compared for the coincident AOD ranges 0.2 < AOD₄₄₀ < 0.4 (blue circles) and AOD₄₄₀ > 0.4 (red circles). Vertical gray bars represent 1-standard deviation of MFRSR SSAs retrievals at a 1 min frequency collocated within ±30 min of the AERONET inversion. The resulting statistics of the comparison are included within the plot. The remaining three panels of Fig. 10 (Fig. 10b, c, d) show the true-color satellite images, visually illustrating the dust transport, captured from the VIIRS sensor onboard Suomi-NPP satellite over the Tenerife Island for the respective days. We find that all matchup data points were contained within the ±0.03 error limits, which is the expected uncertainty in the AERONET SSA inversions at AOD₄₄₀ = 0.4. Sinyuk et al. (2020) have shown that the uncertainty in AERONET SSA decreases significantly for AOD₄₄₀ greater than 0.4. Furthermore, the data points (in red) corresponding to higher aerosol loading conditions (AOD₄₄₀ > 0.4) showed a relatively lower SSA in the range ∼ 0.91–0.95; lower AOD conditions (< 0.4) result SSA in the range ∼ 0.93–0.95. Figure 11 displays the intraday evolution of the spectral SSA derived from the MFRSR (colored circles) and the AERONET SSA at 440 nm (black circles). Each circle represents 30 min averaged SSAs from the two respective sensors. Vertical lines show the expected uncertainty or total error in the MFRSR-derived SSAs calculated as εAOD2+εDD2.

Here, εAOD and εDD are the systematic uncertainties in SSA caused by uncertain AERONET AOD by ±0.01/±0.02 and random uncertainties due to 1 % error in the measured diffuse-to-direct irradiance ratio, respectively. The 30 min averaged AOD for each interval is printed next to the respective circles. The daily-averaged spectral AOD and SSA are printed below each plot. The Saharan dust transport over the Tenerife Island resulted in higher aerosol loading (AOD ∼ 1.0) on 26 August, followed by relatively lower aerosol loading (AOD ∼ 0.5–0.4) on the following 2 d. Despite a significant reduction in the total aerosol loading above the Izaña site on 26 and 27 August, the derived spectral SSA from the MFRSR shows a similar intraday pattern and magnitude, indicating the stability of the inversion at lower and higher aerosol loadings. The spectrally dependent SSA follows the behavior of the known dust aerosols exhibiting decreasing SSA at shorter wavelengths (Di Biagio et al., 2019). On all 3 d of dust transport, the SSA at all wavelengths (325 to 440 nm) from near noon to late evening, especially at shorter wavelengths, show an increasing trend. This is also indicative in the AERONET SSA inversions at 440 nm, albeit with a smaller increase relative to the shorter UV wavelengths.

The impact of the choice of the aspect ratio distribution of the spheroidal dust on the retrievals of SSA has also been examined. Figure 12 compares the MFRSR-derived k (Fig. 12a, b) and SSA (Fig. 12c, d) at 440 nm under two scenarios: (1) AERONET-like “mixing” approach combining sphericity-weighted randomly oriented spheroids (Dubovik et al., 2006) and spheres and (2) employing an empirically derived distribution used in space-based aerosol retrievals over the ocean from near-UV sensors. In the first approach, the diffuse-to-direct irradiance ratios were simulated assuming spheroid and sphere separately and then linearly mixed by using the sphericity parameters of AERONET as follows:

4DDRatioLUT=DDRatiosphere×Sphfrac+DDRatiospheroid×(1-Sphfrac) Where DDRatioLUT is the sphericity-weighted simulation of diffuse-to-direct (DD) ratio simulation (LUT), DDRatiosphere is the simulation for purely spherical particles, and DDRatiospheroid is the simulated DD ratio simulated using the Dubovik et al. (2006) aspect ratio, and Sphfrac is the AERONET-provided sphericity fraction. The DDRatioLUT as a function of the nodes in the imaginary part of the refractive index are then used to retrieve k and SSA.

When compared against AERONET inversion data, k (SSA) retrievals at 440 nm derived following the AERONET-like mixing approach show a positive (negative) bias of 0.0011 and 0.0005 (0.022 and -0.011) for AOD₄₄₀ ranges of 0.2–0.4 and > 0.4, respectively. In contrast, k (SSA) inversions made assuming the fixed, empirical distribution yield significantly lower biases of 0.0005 and -0.0001 (-0.014 and -0.002) for the respective AOD ranges. Root-mean-square-difference (RMSD) and number of SSA matchups falling within ±0.03 uncertainty limits also show noticeable improvement from 58 % to 87 % and 86 % to 98 % for the two AOD ranges, respectively. A limited comparison of the scattering phase function F11 for the three dust events displayed in Fig. 5 showed close agreement in SSA between the two approaches. On the other hand, when applied to a much larger set of observations, the use of fixed, empirical aspect ratio provides improved comparison of MFRSR retrievals against AERONET.

Given the similar assumptions of PSD, real part of refractive index, AERONET-like spheroid and sphere mixing approach, and surface albedo, one would expect a close agreement between AERONET and MFRSR. Despite consistent assumptions, the MFRSR-derived SSAs are found to be biased lower by 0.02. Several factors, including dust shape factor, could have contributed to these observed discrepancies. Surface is assumed to be a Lambertian reflector against Ross–Li BRDF implemented in AERONET, which is not explicitly addressed in the present work. Other factors, such as iterative versus LUT-based retrieval approaches produced even smaller SSA differences, typically within 0.005. Moreover, the LUT nodes in the imaginary part of the refractive index are closely spaced, reducing the effect of non-linearity in the inversion. Such changes in the original inversion code were primarily made for improving computational efficiency.

We adopted the empirically derived continuous dust aspect ratio distribution, shown as the “red curve” in Fig. 5a, in the present work because of two supporting reasons: (1) the location of the ground instrument on Tenerife Island is more representative of the over-ocean dust retrievals, for which the same distribution model used in the near-UV satellite aerosol retrievals showed improvements, and (2) resulting level of agreement between the MFRSR- and AERONET-derived SSA at 440 nm, as shown in Fig. 12. However, we do not claim that this empirically derived aspect ratio distribution is applicable globally and, therefore, we don't intend to suggest replacing the distribution proposed in Dubovik et al. (2006).

A year-by-year comparison of the derived SSA at 440 nm between the two sensors is presented in Fig. 13. A notable finding is the strong agreement observed in 2020 and 2021, with mean biases of -0.003 and 0.007 and RMSD of 0.013 and 0.011, respectively. In contrast, MFRSR SSA for 2022 and 2023 exhibits relatively larger positive biases of 0.021 and 0.010 and RMSD of 0.024 and 0.017, respectively, in cases with higher aerosol loading (AOD₄₄₀ > 0.4). This interannual variability in the apparent bias suggests that the elevated SSA values in 2022 and 2023 may be linked to remaining calibration issues in the MFRSR retrievals. Specifically, the current calibration method for direct and diffuse irradiance is based upon relatively clean conditions (AOD₄₄₀ < 0.10) and subsequently applied to days with higher aerosol loading (AOD₄₄₀ > 0.2) on a monthly basis. Any changes in the instrument's performance during specific months between cleaner and aerosol-laden conditions, therefore, may introduce systematic errors in SSA retrievals.

The observations recorded by MFRSR Head 582 at Izaña have been processed individually at all wavelengths to create a multi-year dataset of spectral aerosol absorption. Figure 14 displays the monthly times series of spectral SSAs, in the format of a box and whisker plot, at all five wavelengths of MFRSR. Grey boxes and whiskers represent the 25th–75th percentile range and 1.5 times the interquartile range, respectively; circles and horizonal lines are mean and median of the data for each month. Only the best SSA retrievals corresponding to the AERONET AOD > 0.4 at the respective wavelengths and AERONET Extinction Ångström Exponent < 0.6 (440–870 nm) were included in the timeseries charts. SSA datasets at all five wavelengths, specifically at shorter UV wavelengths, show distinct interannual and intraseasonal variations. First, the SSA at UV wavelengths during the summer months of 2020 and 2023 are found to be lower in magnitudes (more aerosol absorption) as compared to those during the years 2021 and 2022. A large spread in the SSA data was also noticed in the month of July 2020. Second, a well-defined intraseasonal pattern in the SSA can be seen during the summer months, especially in 2021 and 2022, where SSA are found to be lowest in June and gradually increasing until October. An exception to this pattern is the month of August, where the spectral SSA at all wavelengths show a slight dip in the magnitude. Both the interannual and intraseasonal variations in spectral SSA are of prime interest for the estimation of dust radiative forcing, its influence on the atmospheric stability, and aerosol-cloud interactions. The interannual and intraseasonal variations in spectral SSAs, beyond the range of their expected uncertainty of 0.02–0.03, are indicative of diverse sources of dust emissions having distinct absorption properties.

Figures 15, 16, and 17 summarize the combined spectral retrievals from 2019 to 2023 for the imaginary part of the refractive index, the single-scattering albedo, and the aerosol absorption optical depth respectively. The data are presented separately for the summer months of June through September as box and whisker plots, where orange and light-blue boxes represent retrievals from the MFRSR (440 to 325 nm) and AEROENT (440 to 1020 nm), respectively. Retrieval instances with AERONET-measured AOD > 0.4 and Extinction Ångström Exponent (440–870 nm) < 0.6 are included in the plots to restrict the analysis to moderate to higher dust aerosol loading, thus minimizing the uncertainty in the aerosol absorption inversion at lower AODs in both AERONET and MFRSR datasets. During the peak months of Saharan dust transport to the Atlantic Ocean and over the Izaña site (June through September), the imaginary part of the refractive index and AAOD both exhibit a weak spectral trend in the visible to near-IR region (AERONET) but a distinct increasing trend towards shorter UV wavelengths – a typical and expected spectral absorption behavior of coarse-mode dust aerosols (Kandler et al., 2007; Wagner et al., 2012). The SSA shows weak absorption with SSA values in the range 0.98–1.00 at red (675 nm) and longer wavelengths but decreases rapidly at 440 nm followed by a sharp decline at the UV wavelengths. The aerosol Absorption Ångström Exponent (AAE) values calculated for the MFRSR UV to visible light range (325–440 nm) are found to be noticeably larger than that calculated using the AERONET visible to near-IR dataset (440–870 nm). Seasonally, the AAE values are found to be largest in June (4.52), with a monotonic decrease as the season advances, reaching to the lowest value (2.02) in September. The intraseasonal variations in all three retrieved quantities show the largest absorption, but with significant variability in July and August, followed by relatively moderate absorption in June, and the lowest absorption strength (SSA > 0.9) with minimal variability in September.

The spectral imaginary part of the complex refractive index retrieved from both MFRSR and AERONET observations is compared with laboratory-based k measurements of dust samples reported in the literature. Wagner et al. (2012) conducted a detailed retrieval analysis of five different Saharan dust aerosol samples representing diverse mineralogical compositions collected from locations such as Burkina Faso, Cairo, and during the SAMUM field campaign. Using an inversion scheme based on a spheroidal particle model, the study retrieved refractive indices over the 305–955 nm wavelength range. The retrieved k exhibited significant variability across the different samples, with k values ranging from approximately 0.005 to 0.02 at ∼ 450 nm, and from ∼ 0.01 to 0.03 at ∼ 350 nm, with overall uncertainties in the range of 0.002 to 0.01. Another Izaña-specific study by Kandler et al. (2007) derived the chemical composition and complex refractive index of transported Saharan mineral dust during July and August 2005, based on a mineralogical model derived from electron microscopy. The study reported a k value of 0.009, which closely aligns with the k value of 0.007 at the same wavelength obtained from the direct optical measurements by Patterson et al. (1977).

Di Biagio et al. (2019) conducted extensive in situ measurements of the imaginary part of the refractive index k and SSA over the spectral range 370–950 nm of mineral dust aerosol samples collected from 19 globally distributed dust sources, including the Saharan and Sahelian Deserts. Of particular interest to the present study, the Saharan Desert was represented by soil samples collected from eight locations, where k values at 370 nm ranged from 0.0011 to 0.0088, with mean values of 0.0033 and 0.0049 for the North Africa-Saharan and Sahelian samples, respectively. The corresponding in-situ measurements of SSA at 370 nm for those soil samples were found in the range 0.85–0.92. The MFRSR-retrieved k values at 380 nm in the present study, on an average, range between 0.003 to 0.006, depending on the month of observations, with an upper bound value of ∼ 0.009 observed in July. The corresponding monthly mean SSA values at 380 nm lie between 0.86–0.88 during June through August. While the averaged dust spectral absorption obtained in Di Biagio et al. (2019) was consistent with that retrieved from AERONET-based inversion (Dubovik et al., 2002) and Balkanski et al. (2007) for dust with a 1.5 % volume fraction of hematite content, the spectral k and SSA values across near-UV to near-IR wavelengths were systematically lower than those reported in several earlier in situ and satellite-based studies. Nonetheless, we find that the MFRSR-retrieved k and SSA values at the Izaña site align closely with the equivalent in-situ based measurements reported in Di Biagio et al. (2019) for the North African-Sahara and Sahel desert areas.

The spectral k values retrieved from the MFRSR and AERONET in the UV and visible ranges in this study (see Fig. 15), and those obtained by Di Biagio et al. (2019), are significantly lower than those reported in previous studies discussed above. A key factor contributing to this discrepancy, beyond the inherent uncertainties in both in-situ and remote sensing techniques, may lie in the fundamental differences in measurement approaches. Laboratory measurements are typically performed on particles extracted from aerosol samples under controlled conditions, whereas ground-based and satellite remote sensing retrievals represent effective column-averaged aerosol properties in their ambient atmospheric conditions. Additionally, the dust aerosols observed at the Izaña site could be originated from different sources depending on wind directions and speed, potentially leading to observations that reflect either the optical characteristics of a dominant dust source or a mixture of multiple sources.