A detailed description of the current version of the TROPOMI Level 1B radiance product (L1B_RA_BD1), including the data file format in NETCDF-4 and the data fields, is given in the TROPOMI Level 1B product “readme” file (10.5270/S5P-kb39wni, Ludewig, 2023). TROPOMI provides excellent spatial resolution and daily global coverage in the shortwave BUV band 1 (267–300 nm); however, TROPOMI has known radiometric and sensor degradation issues in band 1 (Ludewig et al., 2020), and it has been proved necessary to apply soft calibration techniques to improve the data quality. The TROPOMI soft calibration is computed from characterization of the differences between measured and modelled radiances (absolute residuals), following a similar approach to that described in Mettig et al. (2021). Since this soft calibration is designed to correct input radiances for the TROPOMI ozone profile data product, forward Radiative Transfer (RT) model calculations were performed over the combined spectral range of band 1 and 2 (270–330 nm). Pressure, temperature, and ozone profiles from the Copernicus Atmosphere Monitoring Service (CAMS) were used as inputs to the RT model. Additionally, CAMS ozone profiles were scaled to match total ozone columns derived from the independent OMPS Nadir Mapper gridded column ozone data (Jaross, 2017). The modelled atmosphere does not contain clouds nor aerosols, but particulate scattering effects are compensated through adjustment of the surface albedo. With this in mind, we have fitted the scene albedo in a small spectral window (328–330 nm) and assumed this albedo to be representative for the entire fitting window. Radiance residuals (measurement to model) are computed for single seasonal TROPOMI orbits over the Pacific Ocean. To compute correction parameters, the radiance residuals are compiled separately for each year and then applied to the radiance measurement in that year. Correction parameters are provided as a function of the TROPOMI cross-track position (i.e., CCD detector row number), wavelength and radiance level; they are applied to the uncorrected radiance signal (Runcorr) by subtracting the bias (Rcorr=Runcorr-bias). For TROPOMI orbits 22086 and 22087 affected by Hunga aerosols on 17 January 2022 we apply the fixed correction available for the highest radiance.

One option for constructing the retrieval measurement vector is to use sun-normalized radiances, or the “N-values” (defined as Nλ = -100log10RλFλ where R denotes BUV absolute radiance and F incoming solar irradiance), as shown in Fig. 2 for two TROPOMI orbits (22086 and 22087) overpassing Hunga aerosol plume on 17 January 2022 (eastern orbit 22086 and the following orbit 22087) at four wavelengths, representative of the selected spectral fitting window: λ=287.9, 292.5, 295.1, 297.9 nm.

However, in order to emphasize the Hunga aerosol spectral signal and to reduce its dependence on TROPOMI band 1 calibration and degradation issues, we prefer to use BUV radiance ratios, in which the radiance values from the orbit 22086 and 22087 pixels are normalized to background radiances for the same cross-track pixels from an adjacent Hunga aerosol-free orbit, in this case TROPOMI background orbit 22085. These radiance ratios are plotted in Fig. 3. The advantage of normalizing to background radiances is that this pixel-wise division leads to a partial cancellation of known radiometric and degradation interferences from the TROPOMI band 1, as reported in Ludewig et al. (2020) and reduces sensitivity to ozone absorption. We do account for the ozone profile differences between the background (o22085) and Hunga (o22086 and o22087) orbits using modified MERRA-2 Stratospheric Composition Reanalysis of the Microwave Limb Sounder (MLS) on board NASA EOS Aura satellite as described later in Sect. 2.2. The normalization requires correction for tropospheric clouds if one uses longer band 2 wavelengths (see example for background pixel 1 in Fig. 3). Therefore, in this study we only use a short spectral fitting window from 289 to 296 nm which is not affected by tropospheric clouds.

For the 2-parameter (AOD and aerosol peak height, zp) aerosol retrievals in Sect. 4, we restrict the spectral fitting window from 289 to 296 nm (hereafter, denoted as the “short” window) to reduce interference from bright tropospheric clouds. Figure 3 shows radiance ratios (using TROPOMI orbit 22085 as background) over a large part of Australia, with six- to ten-fold enhancements of the radiance-ratio signal in the presence of stratospheric aerosol. Background pixel ratios show signals from tropospheric clouds, but ratios in the short wavelength window are free of such signals (Fig. 3; this is also seen in Fig. 2d, where cloud signals at wavelength 297.9 nm are apparent in the Australian Bight near the south-central coast).

Figure 4 presents spectral radiance ratio measurements at four selected wavelengths. At wavelengths shorter than 288 nm there is no Hunga aerosol signature because of strong absorption by ozone above the Hunga plume altitude. The major plume signature over Northeast Australia becomes much clearer for the longer wavelengths, 296 to 298 nm, but even at 292 nm (top right) there is evidence of a forward plume streamer at high altitude over Northwest Australia. Also of interest are the tropospheric cloud echoes near the south-central Australian coast, evident at the two longer wavelengths (lower plots), but not present at shorter wavelengths. This indication has allowed us to set a cloud screening spectral threshold at λ=296 nm. In Sect. S1 in the Supplement, we present an animated video of the full spectral scan of TROPOMI band 1 and band 2 combined radiance ratios from 280 to 330 nm in steps of 0.5 nm (10.5446/70186, Choi, 2022).

We contour the Hunga stratospheric aerosol plume using a Cloud Screening Index (CSI), which is defined as a radiance ratio at 296 nm (see Appendix C for the CSI determination). Hereafter, we only consider TROPOMI pixels with CSI > 1.1 for Hunga aerosol retrievals.

Note that we have also considered 3-parameter retrievals, with the third state vector element being the total column SO₂ emitted simultaneously in the Hunga eruption; for this retrieval, we use the larger spectral fitting window (289–310 nm), denoted as the “full” window in Fig. 3. This retrieval takes advantage of strong SO₂ absorption features present in TROPOMI band 2 radiances (306–310 nm) but it does require the application of a cloud-correction step. This retrieval is currently under investigation.

As noted in the Introduction, we are motivated here to discuss the disruption in the BUV stratospheric ozone record due to the Hunga aerosols. Anomalies in a number of total ozone column (TOC) products were observed in the presence of the Hunga eruption plume; notably, enhanced BUV scattering signals due to high-altitude aerosol from the Hunga plume were mistakenly interpreted as TOC depletion in BUV ozone retrievals from all instruments (OMI, OMPS, GOME-2, as well as TROPOMI). Mid-stratospheric aerosols are not represented in the forward models used for the operational TOC retrievals, resulting in artificial TOC depletion during episodes of elevated volcanic aerosol loading. In this regard, it was necessary to re-analyze raw BUV spectra to flag pixels affected by the Hunga aerosols. Indeed, the presence of such “bad-quality” ozone data will contaminate assimilation products that rely on BUV TOC data. For instance, artificially low BUV TOC data affected by Hunga plume resulted in anomalous assimilation outcomes in released M2-SCREAM reanalysis data (MERRA-2 Stratospheric Composition Reanalysis of Aura Microwave Limb Sounder (MLS) produced by NASA's Global Modelling and Assimilation Office using a stratospheric chemistry model and MERRA-2 meteorology (Gelaro et al., 2017; Wargan et al., 2023)), as shown in Fig. 5a.

In contrast, ozone profile measurements from MLS on board NASA Earth Observing System -chemistry (EOS Aura) satellite were not affected by the Hunga sub-micron aerosols with effective radii reff∼ 0.2–0.4 µm (Boichu et al., 2023; Duchamp et al., 2023). Although stratospheric ozone profiles are strongly constrained by MLS, anomalously low OMI total ozone affects the ozone profile to some degree in the assimilated system, because data assimilation distributes the analysis increments in vertical levels according to a prescribed amount of background uncertainty. Also in this regard, there is some evidence (Evan et al., 2023; Zhu et al., 2023) of an actual physical ozone depletion inside the plume within days after the eruption.

For BUV aerosol plume retrievals, it is clear from the above discussion that we cannot use aerosol-contaminated BUV ozone data. Instead, for the air density, temperature, and ozone profiles, we have used specially-processed M2-SCREAM reanalysis data. This special processing involves the removal of erroneous OMI-retrieved total ozone columns in the Hunga plume from this reanalysis (both OMI and MLS are on the Aura platform) for the 10 d period of 15–25 January 2022. Figure 5b presents the total ozone map from special reprocessing, which is smoother than the original assimilated ozone columns that show a low anomaly over Northeast Australia (Fig. 5a). Assimilated ozone profiles also show low anomalies in the stratosphere when erroneous OMI TOC values were included (Fig. 5c). Regarding M2-SCREAM temperature profiles, early-January temperatures may be less reliable due to sparsely assimilated H₂O and partial GPS radio-occultation contamination under conditions of extreme moisture (Randel et al., 2023). To assess the reliability of these temperature profiles, we compared the M2-SCREAM temperature profiles using radiosonde data from stations in Australia and New Caledonia (University of Wyoming archive; https://weather.uwyo.edu/upperair/sounding.shtml, last access: 16 October 2025). We selected eight cases in which the relative humidity exceeded 10 % at least once above 15 km, including the 17 January 2022, 00:00 UTC sounding. The M2-SCREAM temperatures agreed with the radiosonde measurements within ∼ 4 K over 15–30 km range, supporting that the reanalyzed M2-SCREAM temperature profiles are sufficiently reliable for interpreting the early Hunga plume conditions.

Measurement vectors for the retrieval Mmeasλi are ratios of two BUV radiance spectra measured in discrete wavelength channels, i=1,NS (with associated measurement uncertainties): 1Mmeasλi=RmeasVolcλiRmeasBkgdλi In the following, the RmeasVolc(λi) is a discretized BUV spectrum with a distinct Hunga aerosol signal (e.g., from TROPOMI orbit 22086 or 22087), and RmeasBkgd(λi) is a background BUV spectrum (e.g., from TROPOMI orbit 22085) with similar observational angles and wavelength grid. The dimension of the measurement vector, NS, is variable – this depends on the choice of spectral fitting window and the application of spectral smoothing (if any). For the short spectral fitting window (289–296 nm), there are typically NS=107 spectral points without smoothing. For measurement random errors we use radiance noise levels from the TROPOMI Level 1B product, assuming that individual spectral measurement errors are uncorrelated. The uncertainty in the radiance ratio is then calculated using error propagation, combining the relative uncertainties of each scene in quadrature and scaling the result by the radiance ratio.

The number of retrieved quantities determines the dimension of the state vector, x. The Hunga aerosol loading profile E(z) as a function of altitude z is taken to have a “pseudo-Gaussian” shape (this analytic parameterization is sometimes called a Generalized Distribution Function), characterized by three parameters A0,zp,hw. Here, A0 is the Hunga stratospheric AOD at a fixed reference wavelength λref (taken to be 312 nm), zp is the plume peak height in [km], and hw is the half-width-half-maximum of the plume profile (also in [km]). For a 2-parameter retrieval, the state vector is x=A0,zp, with hw treated as a known model parameter (see Sect. 3.4 for more on this quantity). Appendix A contains a description of this pseudo-Gaussian parameterization, including explicit analytic expressions for Ez;A0,zp,hw in terms of the three parameters of interest, and a determination of analytic derivatives ∂E(z)∂A0,∂E(z)∂zp necessary for deriving analytical layer Jacobian output from the forward model component of the retrieval algorithm.

As noted in Sect. 2.2, ozone, pressure, and temperature profiles are assumed to be accurately known from the re-processed M2-SCREAM reanalysis, independent of Hunga aerosols. We also evaluated the potential impact of air-density variations on Rayleigh scattering (Bodhaine et al., 1999) and ozone absorption (Guo and Lu, 2006), which may not be fully captured by the M2-SCREAM reanalysis during the initial days following the eruption. For a given set of TROPOMI BUV radiances, the following tests were conducted:

The original atmospheric temperature and pressure profiles were perturbed while maintaining a fixed ozone profile.

Next, we consider the forward-model RT simulation of the ratioed BUV spectra. The retrieval algorithm requires forward-model Jacobians with respect to state vector elements; here, the 2-parameter vector x=A0,zp. In general, the forward model will generate simulations Msimλi to match the measured vector in Eq. (1). This requires two RT simulations: RsimBkgdλi is the RT calculation for a background atmospheric scenario, and RsimVolcλi is RT simulation with similar geometry, but including volcanic plume. In addition to Msimλi, the forward model must also generate Jacobians with respect to the aerosol parameters: 2Kλi≡∂Msimλi∂A0,∂Msimλi∂zp=1RsimBkgdλi⋅∂Rsim(Volc)λi∂A0,∂Rsim(Volc)λi∂zp. We use the VLIDORT discrete-ordinate RT model for simulating polarized multiple scattering BUV radiance spectra (Spurr, 2006; Spurr and Christi, 2019) for the two forward-model calculations required. RsimBkgdλi is a simulation for a Rayleigh scattering atmosphere with O₃ absorption, and no aerosols or SO₂; the O₃ profile is from re-processed M2-SCREAM reanalysis as described in Sect. 2.2. The major advantage with VLIDORT is its ability to generate not only the radiance fields, but also any set of analytically-derived layer Jacobians (weighting functions) with respect to atmospheric or surface parameters.

Aerosol optical properties are required for the RsimVolcλi simulation based on a pseudo-Gaussian Hunga aerosol plume loading; for this, we use a linearized Mie scattering model (Spurr et al., 2012) to develop these properties from assumed knowledge of Hunga aerosol microphysical quantities (refractive index, particle size distribution parameters). Details of the aerosol optical property Mie derivations are found in Sect. 3.4, along with a discussion of other atmospheric constituent profiles (in particular, O₃ and SO₂). VLIDORT requires total optical properties (i.e., extinction optical thickness, single scattering albedo, and scattering phase matrix) for each vertical layer and their corresponding linearization to compute the Jacobians (see Appendix B for details).

The retrieval inverse model is an iterative damped non-linear least-squares minimization using a modified version of the Levenberg-Marquardt (L-M) algorithm (LMA) (Marquardt, 1963) with variable step-size (see e.g., Chong and Zak, 2001). If xm is the state vector at iteration m, then the estimate for the state vector at the next iteration is given by: 3xm+1=xm+αmKTSϵ-1K+μmI-1KTSϵ-1ymeas-F(xm) Here, K is the Jacobian matrix which has row vector Kλi for wavelength λi in the fitting window as seen in Eq. (2), ymeas is the measurement vector with entries Mmeasλi (Eq. 1), F(xm) is the forward-model simulated measurement vector with entries Msimλi of the same form as that in Eq. (1), Sϵ is the measurement and forward-model error covariance matrix (here considered diagonal), and I is the identity matrix. The “T” superscript denotes matrix transpose. This inversion scheme is a form of the maximum-likelihood (ML) method (Rodgers, 2000).

The L-M damping parameter μm is adjusted as needed at each iteration in order to ensure the approximation to the Hessian matrix (KTSϵ-1K+μmI) in Eq. (3) remains positive definite. This ensures that the shape of the cost-function approximation we are seeking to minimize during that iteration is “bowl-shaped”, and that the negative of the gradient KTSϵ-1(ymeas-F(xm)) in Eq. (3) points in a direction to descend into the bowl.

The step-size αm is sometimes determined by a line search, in order to guarantee the cost function approximation is minimized at each iterative step; however, this procedure would be too numerically expensive in our retrieval. Instead, in order to ensure that A0 and zp remain in physical parameter space at each iteration step, we simply halve the step size repeatedly until this physicality condition is satisfied (starting at αm=1).

Convergence is reached when relative differences in state-vector elements between adjacent iterations are all below a threshold criterion (10⁻² in our case), and/or when the cost-function itself reaches a clear minimum in fitting space. Spectral points are λi,i=1,…Ns, where the number of points Ns depends on the selection of TROPOMI measurements in UV band 1. With two parameters (A0 and zp), matrix K in Eq. (3) has dimension Ns×2.

In addition to the above, to obtain better estimates of uncertainties on the retrieved state vector elements A0 and zp, a facility was implemented to modify the original standard deviations from the measurement and forward-model error covariance matrix Sϵ used in retrieval (which is often based initially on measurement characteristics alone such as signal-to-noise ratio (SNR)). This was done as follows. As part of each original retrieval, a chi-square diagnostic χ2=[ymeas-F(x)]TSϵ-1[ymeas-Fx] is produced. If the value of chi-square for the retrieval is too large – indicating that the estimated mismatch in actual measurements ymeas versus forward-model-simulated measurements Fx is generally too large relative to that assumed using the original standard deviations in Sϵ – then the expected value of chi-square for the retrieval (i.e., the number of measurements Ns used in the retrieval minus one), along with ymeas, the final values of Fx from the original retrieval, and the original standard deviations used in Sϵ, are used to compute an additional contribution to the estimated standard deviation of measurement/forward model error for each measurement. These contributions account for the influence of unknown sources of measurement and/or forward model error. These values are then added to the original measurement standard deviations on the diagonal of Sϵ and the retrieval is then re-run using the more realistic combined standard deviations of measurement and forward-model error. With this procedure, retrieved values of the state vector elements often do not change significantly, but their estimated uncertainties are often more realistic (i.e., larger), along with improved chi-square diagnostics.

We calculated Hunga BUV synthetic radiances using the NASA OMI spectral simulator software, based on geophysical conditions for 17 January 2022. Simulations were performed with and without aerosols to develop synthetic radiance ratios, which were then used as input to the Hunga inversion tool, the purpose being to evaluate the impact of changing the ozone profile and the Hunga aerosol layer height and AOD. These tests helped to develop confidence in the forward and inverse models used in the real Hunga retrievals.

In addition, a number of tests were carried out to obtain a sense of the retrieval's sensitivity to (1) the half width at half maximum (HWHM) of the ascribed aerosol plume profile, (2) profiles of atmospheric density and ozone, (3) parameters governing the aerosol particle size distribution [e.g. mode fraction (assuming a bimodal particle size distribution), mode radius, refractive index (real & imaginary parts)], (4) the spectral window chosen for retrieval, and (5) the influence of the initial state vector guess on retrieval convergence. These tests were used as a guide to aspects of the retrieval which demanded further attention during the process of refining the retrieval algorithm.

To further verify the fidelity of the retrieval algorithm itself, we performed a set of closed-loop validation tests using synthetic radiance spectra generated by the forward model. Each test used a pre-defined state vector xtrue={AOD,zp} to represent typical Hunga plume conditions. Two cases were examined: (1) a retrieval based on noise-free synthetic spectra to ensure that the algorithm could reproduce the known state (xret≈xtrue), and (2) a retrieval using spectra with added random noise levels representative of TROPOMI UV band 1 measurements to assess retrieval robustness under realistic conditions. In both cases, the retrieved parameters converged closely to the true inputs, demonstrating that the Hunga retrieval framework is stable and internally consistent. The noise-added tests also showed slightly larger retrieval uncertainties, as expected, but without systematic bias in AOD or zp. Overall, the results increased confidence in the forward and inverse model configurations used in the actual Hunga plume retrievals.

Hunga aerosol peak heights zp were retrieved using both lower (nr=1.39) and upper (nr=1.47) bounds of the real part of the refractive index; these values provide an uncertainty range for Hunga zp retrievals. Figure 7a shows zp retrieved using the upper-bound index (nr=1.47). The highest values of zp > 30 km were retrieved in the western part of the plume from orbit 22087. The lower zp values (∼ 25 km) were retrieved in the eastern part from orbit 22086. This west–east contrast is consistent with previous studies distinguishing the western aerosol- and water-rich cloud (C1) and the eastern SO₂-rich cloud (C2) (Carn et al., 2022; Legras et al., 2022). The C1 cloud likely experienced faster SO₂-to-sulfate conversion and stronger water-driven radiative cooling, which contributed to its more rapid descent compared to that for C2, as noted in previous analyses (Legras et al., 2022; Sellitto et al., 2022). This difference is largely explained by the strong stratospheric easterly wind gradient in the 20–40 km altitude range. This interpretation is supported by the trajectory analysis presented in Appendix D, which uses assimilated wind data from the MERRA-2 reanalysis. The higher the altitude, the stronger the easterly winds, so those parts of the C1 cloud at zp ∼30±1 km were advected westward more quickly than the lower parts (Sadeghi et al., 2025). By contrast, the C2 cloud, centered near zp∼25±1 km in the eastern sector, showed slower westward advection consistent with a weaker easterly wind field at these lower stratospheric levels.

We compared the TROPOMI aerosol peak heights zp retrieved from orbit 22086 at ∼ 03:30 UTC and orbit 22087 at ∼ 05:00 UTC with the CALIOP daytime overpass at 05:27–05:29 UTC (Fig. 7b) and later nighttime overpass at ∼ 16:16 UTC (Fig. 7c). Examining the daytime CALIOP data, we see that the average height of the C1 cloud is close to 30 km. The zp heights retrieved from TROPOMI orbit 22087, ∼ 30 min prior to the CALIOP observations, match within ∼ 1 km. A second validation was obtained with the CALIOP nighttime overpass at 16:16 UTC (solid magenta line), where matchup between CALIOP and TROPOMI pixels within the C2 part of the Hunga plume (shown with the dashed magenta line) can be achieved with 13-h back trajectories (Appendix D).

TROPOMI zp ∼ 30 km over the Northeastern part of Australia also agrees with the geometric top height retrievals from the Multi-angle Imaging Spectro-Radiometer (MISR) aboard NASA's Terra satellite. On 17 January 2022, MISR observed the Hunga aerosol plume off the Northeast coast of Australia at ∼00:25 UTC, with retrieved height of 27–30+ km a.s.l. (30 km is the maximum allowed retrieval height in the MINX (MISR INteractive EXplorer) stereo-height retrieval (Kahn et al., 2024)).

Figure 7d shows the absolute difference in zp retrieved using the lower-bound refractive index (nr=1.39) relative to nr=1.47 scenario. The average difference is 0.03 ± 0.8 km, indicating generally low sensitivity to the refractive index assumptions. Notably, in the central dense part of the plume, most areas fall within a ± 1 km difference range (shaded in gray). However, larger localized differences of up to ± 2 km were observed in the eastern part of the plume above the Coral Sea. These discrepancies may be due to the low altitude of the Eastern part of the plume, close to the assumed plume boundary (24 km). The differences in zp up to ∼ 4 km were found in areas with thin aerosol layers, likely due to reduced sensitivity in such cases. Overall, differences in zp values retrieved using extreme refractive index assumptions fall within the expected range.

Without prior information about Hunga aerosol sulfuric acid (H2SO4/H2O) aqueous solution concentration we repeated AOD retrievals using low (nr=1.39) and high (nr=1.47) values of the real part of the refractive index, nr, which correspond to a plausible range for sulfuric acid concentrations (∼ 26 wt % to ∼ 79 wt %) (Beyer et al., 1996; Toon and Pollack, 1973). Figure 8 shows TROPOMI-retrieved AOD at reference wavelength λ0=312 nm for the upper limit of the refractive index (nr=1.47) and the percentage difference in results between the two nr scenarios. The highest AOD values (up to ∼ 5.0) were retrieved over the Coral Sea (C2 cloud), where the densest portion of the volcanic plume was concentrated at lower plume altitudes around 25 km (see Fig. 8a). As the plume was transported westward across northern Australia, a secondary maximum in aerosol density was located over Western Queensland (C1 cloud), with AOD values as high as 3. Further westward, AOD values gradually decreased over Northeast Australia coinciding with a higher zp values (>30 km).

The comparison (Fig. 8b) shows that retrieved AODs for low aqueous sulfuric acid solution concentration (nr=1.39) are generally higher than those AODs for high solution concentration (nr=1.47), with a mean percent difference of ∼ 30 %; this provides an estimate of the AOD systematic retrieval error associated with uncertainties in the refractive index assumptions. The largest differences were found in regions with optically thick plumes, particularly over the Coral Sea, where the aerosol peak height was close to the assumed low limit of min⁡zp∼ 24 km – that is, close to the ozone density peak.

To validate our TROPOMI AOD retrievals, we compared them with AERONET direct-sun AOD measurements (Holben et al., 1998) from the Lucinda coastal site (18.5198° S; 146.3861° E; elevation: 8.0 m) during the Hunga plume overpass from ∼ 21:00 UTC on 16 January to ∼ 03:00 UTC on 17 January (Fig. 9). The Lucinda site is located ∼ 6 km offshore in the tropical coastal waters of the Great Barrier Reef, and background AOD at this site is typically very small. Based on AERONET values of aerosol microphysical parameters and assumed values of refractive index, we used the Mie code to convert our retrieved TROPOMI AOD at 312 nm to corresponding quantities at 412 nm; this is the shortest AOD wavelength for AERONET measurements at Lucinda (Fig. 9b). We also subtracted tropospheric AOD contributions of 0.1, as measured by AERONET on previous days to the Hunga plume overpass.

Using the NASA Goddard trajectory model (see Appendix D), we calculated the backward movement of air parcels starting from TROPOMI AOD retrievals from orbit 22087 (overpass at 05:00 UTC) and from 22086 (overpass at 03:15 UTC). We averaged all TROPOMI AOD retrievals from those parcels that pass within 10 km of the Lucinda site and compared them with the AERONET AOD measurements averaged over a 15-minute interval (Fig. 9a). We see that average retrieved AOD values show good qualitative agreement with the AERONET AOD measurements. Quantitatively, the retrievals assuming nr=1.47 (black dotted curve) showed a median difference of 0.25 (mean: 0.3) relative to AERONET. For the nr=1.39 (black solid curve) case, the median difference is similar 0.3 (mean: 0.3). Both TROPOMI and AERONET AODs reached a maximum (over 2) during the local-time morning hours (21:45–23:00 UTC on 16 January) and dropped to ∼ 0.5 after the main part of the Hunga aerosol cloud passed over the station.

TROPOMI AOD retrievals also agree qualitatively with MISR-retrieved AOD558∼0.7±0.2 (1σ) (Kahn et al., 2024), accounting for spectral differences in the aerosol extinction between short UV and mid-visible wavelengths (Fig. 9b). Recent AOD₅₃₂ retrievals from CALIOP nighttime Hunga overpasses estimate somewhat larger AOD₅₃₂ values of ∼1.24±0.13 (1σ) for C1 and ∼1.01±0.12 (1σ) for C2 on 17 January (Duchamp et al., 2025). These CALIOP-derived AOD₅₃₂ values are also consistent with TROPOMI AOD results, considering the spatial heterogeneity of the Hunga plume, the temporal differences between the satellite overpasses, and the spectral differences between the retrievals. A more comprehensive comparison with CALIOP will be conducted in a follow-up study.

We estimated AOD retrieval uncertainties εAOD theoretically using different approaches: (1) taking error estimation from the Hunga retrieval algorithm diagnostic and comparing retrievals using low and high limits of nr=1.39 and 1.47 as shown in Fig. 10, and (2) comparing AOD retrievals for each Hunga pixel using short (289–296 nm) and extended (289–310 nm) spectral fitting windows (see Fig. 3). We note the following:

Retrieval εAOD uncertainties were initially based on TROPOMI radiance measurement noise (SNR) but were later refined incorporating additional contributions derived from chi-square diagnostics accounting for discrepancies between measured and simulated radiance ratios (see Sect. 3.3). Figure 10 shows the normalized probability density distribution of the updated εAOD for all pixel retrievals in Hunga plume; this distribution has a long non-Gaussian tail; therefore, we use the median and the interquartile range (IQR; 25th–75th percentile) statistics rather than the mean and the standard deviation to describe an overall AOD uncertainty. The relative εAOD greatly increases for small AODs. When restricted to cases with AOD > 0.2, the median εAOD∼0.06 and the corresponding IQRs are 0.02(0.03)–0.13 for both nr cases (Fig. 10). Then normalizing to the retrieved AOD, this median absolute error corresponds to a median percentage error of ∼ 15 %.

To estimate the upper limit of the εAOD, we repeated TROPOMI Hunga retrievals using the extended spectral fitting window (289–310 nm) (see Fig. 3) and assuming upper limit of nr=1.47. With this long fitting window, we obtained AOD values ∼ 16 % lower than those obtained with the “short” window. This reduction is possibly due to increased sensitivity to tropospheric clouds and uncertainties in assumed gas-phase absorbers such as O₃ and SO₂. These comparisons indicate the importance of varying the spectral fitting window to estimate the upper limit of uncertainty of our Hunga aerosol retrievals. On the other hand, using an extended spectral fitting window would permit retrieval of additional aerosol parameters (e.g., effective radius) or gases (e.g., O₃, SO₂), but would require a more complex forward RT model (e.g., including tropospheric cloud correction).

Furthermore, to estimate potential instrument-specific biases we carried out an inter-sensor comparison against the NOAA-20 OMPS Nadir Profiler (NP) based Hunga retrieval; this was conducted using the same short spectral fitting window (289–296 nm) and specially assimilated O₃ profiles (see Appendix E). The retrieved NOAA-20 OMPS-NP AOD values were approximately ∼ 20 % higher than those from our TROPOMI retrievals collocated within six OMPS-NP pixels over Northeast Australia. Based on these estimates, we adopt εAOD±20 % as the total percent uncertainty, considering both retrieval and instrument specific errors.

To convert the retrieved AOD to aerosol column mass maer (g m⁻²) we need to know particle mass density, ρ (g cm⁻³), effective radius reff (µm), and extinction efficiency Qext=<Ext><G>, where <Ext> and <G> are particle size distribution weighted average extinction and geometric cross-sections (Krotkov et al., 1999a, b; Duchamp et al., 2023; Sellitto et al., 2024): 4maer=43ρreffQextAOD We assume that the AERONET-retrieved fine-mode effective radius reff∼0.22 µm at Lucinda (Fig. 9b) is representative of the whole Hunga plume. To compare with the satellite infrared IASI retrievals, we first assume the same mass density ρ=1.75 g cm⁻³ (Sellitto et al., 2024). This density corresponds to a high sulfuric acid mass fraction w=0.765 at temperature T=233 K (Myhre et al., 1998) and a high value of nr=1.47 at ∼ 300 nm (Beyer et al., 1996). These values are used in Eq. (3) to produce the spatial distribution of Hunga column aerosol mass maer shown in Fig. 11. The column mass spatial distribution has similar features to those in the AOD map (Fig. 8a). Using a BUV radiance ratio filter at 296 nm (CSI > 1.1) to define the plume, we estimate a total plume area Atotal∼4×106 km², and a corresponding total wet aerosol mass Maer=0.47 Tg, where “wet” denotes aqueous sulfuric acid solution droplets including water uptake at temperature T∼233 K. The maximal maer∼0.8 g m⁻² was found over the densest part of the plume over the Coral Sea, as discussed in Sect. 4.2, given that the aerosol column mass values are proportional to the AOD. In the aerosol-rich (C1) part of the plume over Northeast Australia, maer increased in value to ∼ 0.5 g m⁻², then decreased to maer ∼ 0.05 g m⁻² over the Northwestern part of Australia.

Both droplet mass density, ρ, and the refractive index nr are linked to the assumed sulfuric acid (H₂SO₄) mass fraction (w) in the aerosol solution droplets. Higher sulfuric acid content results in both higher nr and ρ, and vice versa. To quantify the range of the total wet aerosol mass Maer, we compared the retrieved maer using two limiting (nr, ρ) pairs:

for nr=1.47 and ρ=1.75 g cm⁻³ (wmax=0.765), the integrated total wet aerosol mass Maer is ∼ 0.47 Tg.

The wet aerosol mass Maer retrieved in our study remains nearly constant: Maer∼0.5 ± 0.05 Tg for a broad range of assumed sulfuric acid (H2SO4/H2O) solution concentrations in Hunga aerosol droplets. Therefore, it is interesting to independently estimate the spatially-averaged sulfuric acid (H₂SO₄) mass fraction w and H2SO4/H2O solution density ρ. For this, we assume conservation of the total Hunga stratospheric sulfur (S) mass MS0 initially emitted in the gas phase as SO₂, and an exponential SO₂-to-sulfate conversion rate with an e-folding time of τ, to estimate the expected S mass in the aerosol phase MS,aer at time t (∼ 2 d) after the main eruption on 15 January: 5MS,aer=MS01-e(-t/τ) We use reported Hunga gaseous sulfur (S) emissions on 15 January: MS0∼0.21–0.24 Tg S (i.e., half the SO₂ mass produced by 15 January eruption) and an e-folding time of τ∼6 d as reported in Carn et al. (2022) to calculate the expected S mass converted to aerosols after ∼ 47 h of transport to be MS,aer∼0.061–0.068 Tg S and a gaseous S mass (in SO₂) to be MS,gas∼0.15–0.17 Tg S. Within uncertainties, the latter estimate agrees with independent operational TROPOMI stratospheric SO₂ retrievals (Theys et al., 2017) integrated within the Hunga aerosol plume on 17 January (∼ 0.14 Tg S; CSI > 1.1). The average sulfuric acid (H₂SO₄) mass fraction w can be estimated from the ratio of the MS,aer to the retrieved total wet aerosol mass Maer∼0.5 Tg, by accounting for their molar weight ratio: (MWS∼ 32 g mol⁻¹) and H₂SO₄ (MWH2SO4∼98 g mol⁻¹): 6w=MS,aerMaerMWH2SO4MWS Applying this approach, we estimate the Hunga sulfuric acid mass fraction to be w∼0.37–0.42 with an average value of w∼0.4 and corresponding H2SO4/H2O solution density: ρ∼1.34 g cm⁻³ at Hunga temperature T∼233 K based on laboratory measurements of Myhre et al. (1998). These new estimates based on Hunga stratospheric S mass balance are consistent with the physics-based sulfate (H₂SO₄) weight percent (wt %) simulation of Hunga aerosols using the NASA Goddard Earth Observing System Chemistry Climate Model (GEOS CCM) with the Community Aerosol and Radiation Model for Atmospheres (CARMA) similar to Case et al. (2023): H₂SO4∼40 wt %–60 wt % (i.e., w∼0.4–0.6) and ρ∼1.3–1.4 g cm⁻³ (see details in Appendix F).

Sellitto et al. (2024) reported retrievals of SO₂ and sulfate aerosol mass in the Hunga plume based on mid-IR IASI measurements. Their study noted that SO₂ and sulfate aerosol have overlapping spectral signatures in the IR, which can lead to large uncertainties in the co-retrieval of these species in volcanic plumes; however, the potential impact of collocated water vapor on the IR retrievals was not addressed. In their paper, the equation used to derive sulfate mass from IASI measurements of mid-IR AOD is identical to that used here (Eq. 4) but is based on the measured mid-IR AOD and average extinction efficiency (Qext) calculated at mid-IR wavelengths (∼8.5 µm). Sellitto et al. (2024) also assumed a sulfate aerosol mass density of ρ=1.75 g cm⁻³ which corresponds to the upper limit of the sulfuric acid solution concentration w=0.765 at temperature T=233 K (Myhre et al., 1998). Additional uncertainties arise from the range of possible particle size distributions (reff∼0.25–0.45 µm) in the Hunga aerosol plume (Boichu et al., 2023; Duchamp et al., 2023).

These authors report a maximum Hunga sulfate aerosol mass loading of 1.6±0.5 Tg, but the peak loading was measured later in the year (August-September 2022). On 17 January 2022, the IASI-derived sulfate aerosol mass reported in Sellitto et al. (2024) is ∼ 0.2 Tg, with a large uncertainty (estimates range up to ∼ 0.8 Tg). Our BUV-based wet aerosol mass of Maer∼0.5 Tg is thus broadly consistent with these IR retrievals, given the uncertainties on the assumed particle size distribution. In contrast, a larger discrepancy is apparent in the SO₂ retrievals: on 17 January, the IASI-based SO₂ mass is ∼ 0.75 Tg (range: ∼ 0.4–1.1 Tg), compared to a total BUV SO₂ mass of ∼ 0.4 Tg (note that this is the total retrieved SO₂ mass on 17 January, not the SO₂ collocated with the Hunga aerosol plume discussed in Sect. 4.4). Furthermore, the IASI-based SO₂ mass reached a maximum of ∼ 1 Tg (range: ∼ 0.7–1.2 Tg) on 19 January 2022 (Sellitto et al., 2024), whereas the BUV SO₂ mass was observed to decrease after 17 January (e.g., Carn et al., 2022).

Sadeghi et al. (2025) also retrieved Hunga SO₂ mass using CrIS IR measurements in combination with the VOLCAT (VOLcanic Cloud Analysis Toolkit) framework and HYSPLIT-based trajectory analysis to assess SO₂ transport and decay patterns. On 16 January 2022, Sadeghi et al. (2025) reported a CrIS-derived SO₂ mass of ∼ 0.4 Tg, which is consistent with the BUV SO₂ mass reported in Carn et al. (2022).

The reasons for these discrepancies remain unclear. It is possible that the BUV operational SO₂ measurements were more strongly impacted by the presence of optically thick aerosol; we also propose that the impact of Hunga water vapor on the IR SO₂ and sulfate mass retrievals merits further consideration.