Among the available “online” tools, the coupled Weather Research and Forecasting model coupled with Chemistry (WRF-Chem) open-source Eulerian model is distinguished for its capability to simulate atmospheric chemistry, air quality, transport, and deposition of aerosols, including volcanic ash. , , and were the first who include in the WRF-Chem model the capability to simulate emissions from volcanoes and to predict the transport and concentration of ash and SO2. In the model, ash is gravitationally settled, and SO2 undergoes oxidation to sulfate using the prescribed OH vertical distribution. introduced ash size distribution classification and extended the volcanic emission preprocessor with time-variant emissions, which can either be specified directly as mass fluxes or calculated with the formula that relates plume height to the mass emission rate . provided a detailed evaluation of the 2010 Eyjafjallajökull eruption in Iceland and successfully reproduced the observed plume structure. conducted a qualitative comparison of the 2009 Mount Redoubt volcanic clouds using the PUFF and WRF-Chem models together with satellite observations, showing that WRF-Chem and PUFF produced comparable ash transport patterns. simulated the 2010 Eyjafjallajökull volcanic eruption to study ash dispersion and to highlight the importance of the radiative feedback effect on the meteorological fields. In particular, with enabled radiative feedback, a better agreement of volcanic cloud location with radiosonde measurements was achieved. made further extensions of the emission preprocessor introduced by to integrate complex sources. In particular, the volcanic preprocessor was integrated into the WRF-Chem code to allow the temporally and vertically resolved input data for the simulation of the eruption of the Grimsvötn volcano in Iceland in May 2011. Unfortunately, this code is not a part of the official release. simulated a sequence of Mt. Etna paroxysms by coupling WRF-Chem with near-source L-band radar observations and demonstrated improved agreement between modeled and observed plume heights. analyzed tephra fallout and in situ airborne measurements of ash from the 2010 Eyjafjallajökull eruption, providing valuable validation data for volcanic ash dispersion modeling. employed WRF-Chem to simulate ash transport from the 2015 Calbuco eruption in Chile and successfully reproduced the observed regional dispersion and deposition patterns. In , a modified version of the WRF-Chem model was used to evaluate the radiative effects of volcanic ash, sulfate, SO2, and water vapor emitted during the Mt. Pinatubo eruption. They used the Goddard Chemistry Aerosol Radiation and Transport (GOCART) aerosol module to represent ash as mineral dust with a modified complex refractive index (RI). The same approach was used in for inverse modeling of emission rates of ash and SO2. investigated the recent eruption of the Hunga Tonga–Hunga Haapai underwater volcano on 15 January 2022, which released 150 Mt of water vapor into the stratosphere. Water vapor strongly affected the dynamics of the aerosols as a result of the radiative cooling of the water vapor cloud.

Although the WRF-Chem model has been extensively utilized over the past decade and has demonstrated significant efficacy as a tool for forecasting the transport and dispersion of volcanic ash and SO2 , it still lacks a set of parameterizations. Furthermore, the interaction of ash and sulfate with solar and terrestrial radiation for the simulation of the direct radiative effect has not been implemented explicitly into the WRF-Chem code so far. There were only implicit attempts to account for only ash radiation interaction, ignoring the sulfate. In particular, redistributed the three finest ash bins into the PM2.5 3D field, which was used in the calculation of the optical properties. This methodology presupposes a constant size distribution of PM2.5, which constitutes a rather crude assumption considering the variability in the ash size distribution within the cloud, particularly in the initial days. In addition, the standard methodology for preparing volcanic emissions files using the open-source tool PREP-CHEM-SRC is notably cumbersome and not flexible.

Here, we rectify the existing imperfections and add new capabilities to the WRF-Chem code v4.8 related to the simulation of volcanic eruptions. In particular, we account for major sinks: wet and dry deposition of ash, SO2, sulfate, and SO2 oxidation by OH and H2O2. We found and fixed an error in the subroutine for ash gravitational settling. Additionally, we establish a mass balance for SO2, sulfate, and ash to ensure conservation of their mass. Moreover, we implemented the capability to simulate direct radiative effects of ash and sulfate aerosols, acknowledging the substantial radiative forcing exerted by volcanic eruptions on the climate system . Recent studies highlight the importance of water vapor in modulating the dynamics of the volcanic plume. Therefore, simulation of emissions of water vapor and sulfate aerosol was also added. In addition, we developed an open-source emission preprocessor called PrepEmisSources . In contrast to the standard PREP-CHEM-SRC utility, our tool enhances the workflow and provides increased flexibility in defining the volcanic eruption process based on the eruption source parameters. More details are presented in Appendix .

We consider the chemical depletion of SO2 resulting from oxidation processes. We replicate the code from the GOCART module, with modifications in the parameters used for the oxidation reaction with OH. The oxidation by H2O2, which had not been previously utilized in modeling volcanic SO2, has been implemented within our study. See subroutine gocart_volc_chem_driver() in module_volc_chem.F for details. The oxidation is activated by setting gaschem_onoff = 1 in the namelist.input file. The OH and H2O2 fields are not computed interactively; instead, they are prescribed based on zonal and monthly mean OH and H2O2 fields derived from the simulation of the Chemical Lagrangian Model of the Stratosphere (CLaMS) and Copernicus Atmosphere Monitoring Service (CAMS) reanalysis , respectively. The “Code and data availability” section includes two Python scripts for interpolating OH and H2O2 fields into the WRF-Chem domain.

Three-body second-order reaction rate coefficient (k) of the SO2-OH oxidation process: OH+SO2+M→sulfates+… is calculated according to Table 2-1 in as follows: 1k=k0⋅M1+k0⋅Mk∞×0.61/1+log⁡10k0⋅Mk∞2(cm3molec.-1s-1), where k0=2.9×10-31×(298T)4.1 (cm6molec.-2s-1) is the low-pressure limit rate, k∞=1.7×10-12×(298T)-0.2 (cm3molec.-1s-1) is the high-pressure limit rate, T is the temperature (K), and M is the air density (molec.cm-3).

The updated SO2 concentration (molmol-1) is calculated as follows: 2SO2=SO2×exp⁡-k⋅OH⋅Δt, where OH concentration is given in (molec.cm-3), and Δt is a time step (s). In general, the production of OH is driven by the photolysis of ozone, which causes a pronounced correlation with the diurnal cycle. To address this variability, the prescribed concentration of OH is multiplied by a scaling factor, which depends on the solar zenith angle.

In-cloud oxidation by hydrogen peroxide (H2O2) is another chemical sink for SO2. Here we replicate the code implemented in the GOCART module. The loss of SO2 due to aqueous-phase oxidation by H2O2 in clouds is parameterized following a simple cloud-fraction-weighted approach. The scheme applies only for grid cells where the temperature exceeds 258 K and the cloud fraction (fc) is nonzero. To avoid excessive depletion when SO2 exceeds the available H2O2, the effective cloud fraction fc* is scaled: 3fc*=fc×H2O2SO2,if SO2>H2O2fc,otherwise.

SO2 and H2O2 are given in (molmol-1). The post-reaction SO2 is: 4SO2=SO2×(1-fc*).

This simple scheme ensures that aqueous SO2 oxidation is limited by both cloud coverage and oxidant availability, without explicit kinetics of dissolution and reaction in cloud water.

The process of ash and sulfate scavenging through convective precipitation is incorporated within subroutine grelldrvct() implemented in module_ctrans_grell.F. This option is activated by setting conv_tr_wetscav = 1. The convective scavenging for SO2 is not calculated, taking into account the assumption that all SO2 undergoes oxidation within clouds. This process was not accounted for before in the simulation of ash and sulfate.

Here, large-scale scavenging represents in-cloud removal processes associated with stratiform clouds, as opposed to convective precipitation. The code for large-scale scavenging of ash, sulfate, and SO2 is based on the one used for GOCART aerosols and gases. We implemented the code in the subroutine wetdep_ls_volc() in the module_vash_settling.F file. This option is activated by setting wetscav_onoff to any negative number. The scavenging process is applied to ash, SO2, and sulfate. This scheme has a tuning parameter α, which is the scavenging efficiency. We set α=0.5 for ash and α=1 for SO2 and sulfate, due to their high solubility and efficient removal in cloud water. We added the corresponding diagnostics, which reflect the accumulated amount of scavenged ash, SO2, and sulfate: 5WD_ASH_SC=WD_ASH_SC+∑i=110[dvash_i]⋅ρ⋅Δz⋅10-6(gm-2),6WD_SO2_SC=WD_SO2_SC+[dSO2]⋅ρ⋅Δz/28.97(mmolm-2),7WD_SULF_SC=WD_SULF_SC+[dsulf]⋅ρ⋅Δz/28.97(mmolm-2).

These formulas are applied for each layer of the atmospheric column, where Δz is the layer width, [dSO2], [dsulf], [dvash_i] are the computed fractions of concentrations of SO2 (ppmv), sulfate (ppmv), and ash (µgkg-1) in the ith bin, respectively, subjected to scavenging within the timestep at a specific layer of the atmospheric column. ρ is the dry air density (kgm-3), 28.97 (gmol-1) is the air molar mass. These diagnostic formulas were previously absent in the GOCART module; nonetheless, they can be integrated by adhering to our proposed methodology.

Dry deposition of SO2, sulfate, and ash was implemented by analogy with the GOCART module, where dry deposition is combined with vertical mixing and activated by setting vertmix_onoff = 1. We implemented the code in the module_vash_settling.F file in the volc_ash_sulf_so2_drydep_driver() subroutine. Dry deposition velocity is calculated according to and used as a boundary condition near the surface for the flux of the species. The dry deposition removes aerosols from the lowermost model layer as a dry deposition flux. The accumulated amounts of SO2, sulfate, and ash are computed using the following expressions: 8SO2_DRYDEP=SO2_DRYDEP+[SO2]⋅Vdry,SO2⋅ρ⋅Δt⋅10-6/28.97(molm-2),9SULF_DRYDEP=SULF_DRYDEP+[sulf]⋅Vdry,sulf⋅ρ⋅Δt⋅10-6/28.97(molm-2),10ASH_DRYDEP=ASH_DRYDEP+∑i=110[vash_i]⋅Vdry,vash_i⋅ρ⋅Δt⋅10-9(kgm-2). [SO2], [sulf], [vash_i] are the corresponding concentrations of SO2 (ppmv), sulfate (ppmv), and ash (µgkg-1) in the ith bin, Δt is the timestep (s), and Vdry,SO2, Vdry,Sulf, and Vdry,vash_i are the computed dry deposition velocities (ms-1) for ash particles in ith bin.

As in the GOCART aerosol module, a bulk (single moment) approach is used to represent sulfate aerosols. In this approach, only the mass mixing ratio is tracked, and the assumed size distribution is fixed. Based on observations and , we assume that the volcanic sulfate aerosol number-density size distribution can be approximated by Aitken and accumulation lognormal modes. Aitken mode has a median radius r1=0.09 µm and the geometric width σ1=1.4. The accumulation mode has a median radius r2=0.32 µm and the geometric width σ2=1.6. Volcanic sulfate aerosol droplets in the troposphere have diameters smaller than 0.2 µm. Therefore, in the troposphere, only dry and wet scavenging of sulfate aerosols is usually considered. In contrast, in the stratosphere, the volcanic sulfate aerosol droplets are bigger, air density is lower, and gravitational settling becomes the leading deposition process. Therefore, we implemented the gravitational settling of sulfate aerosols following the same assumptions as in . Sulfate gravitational settling numerical scheme is implemented and adapted from the dust gravitational deposition scheme used in the GOCART scheme . Sulfate aerosol density is 1800 kgm-3. Only sulfate particles in the accumulation mode are gravitationally settled, assuming their wet mean radius of volume size distribution. Firstly, we determine dry radii Rdry,sulf calculated for sulfate aerosol volume median radii: 11Rdry,sulf=r2⋅exp⁡(3⋅log⁡(σ2)2). We obtain that Rdry,sulf=0.62 µm at given parameters of the accumulation lognormal mode. Secondly, sulfate aerosol wet radius (Rwet,sulf) is defined by computed Rdry,sulf, relative humidity RH, and hygroscopic parameter κ: 12Rwet,sulf=Rdry,sulf⋅1+RH⋅(κ-1)1-RH13.

Following , we assume a hygroscopicity parameter of κ=1.19 for sulfate particles, which contrasts with κ=0.5 used in the calculation of sulfate optical properties (see Sect. ). We found that κ=0.5 produced unrealistically small Rwet,sulf values, resulting in slower gravitational settling and artificial accumulation of sulfate in the troposphere. In contrast, using κ=1.19 increased Rwet,sulf, and, consequently, the gravitational deposition velocity, yields a more realistic vertical distribution and removal rate of sulfate aerosols. Furthermore, we verified that κ=1.19 results in an H2SO4–H2O binary solution weight fraction in the range of 60 %–90 %, consistent with observational estimates for stratospheric sulfate aerosols.

The sulfate gravitational settling is implemented in module_vash_settling.F subroutine sulf_settling_driver(). The accumulated amount of gravitationally settled sulfate is computed as follows: 13SULF_GRAV_SETL=SULF_GRAV_SETL+[SULF]⋅Vsettling,Sulf⋅ρ⋅Δt⋅10-9(kgm-2), where [SULF] sulfate concentration (µgkg-1), and Vsettling,Sulf is the computed settling velocity (ms-1) of sulfate particles.

For convenience, we also added diagnostic output containing computed PM2.5 and PM10 surface concentrations. We modified PM10 and PM2.5 calculations by analogy with . The subroutine sum_pm_gocart() in module_volc_chem.F calculates PM2.5 and PM10 surface concentrations using the following formulas: 14PM2.5=ρ⋅(1.375⋅sulf+0.672⋅vash_10),15PM10=ρ⋅(1.375⋅sulf+vash_10+vash_9+0.356⋅vash_8),

Factor 1.375 compensates for missing NH4, which neutralizes sulfate and produces ammonium sulfate. sulf is sulfate concentration converted from ppmv to µgkg-1, ρ is the dry air density (kgm-3), vash_8,9,10 are the mixing ratios (µgkg-1) of the ash in the smallest three bins. Coefficients 0.672 and 0.356 are computed assuming that ash volume size distributions are functions of the natural logarithm of the particle radius, see for details.

The gravitational settling of aerosols is a key driver of their removal from the atmosphere. The modeled volcanic ash is subdivided into different bins representing the size spectrum of the particles. In WRF-Chem, ash particles are categorized into 10 size bins based on their radii, ranging from 0.01955 to 1000.0 µm, see Table . Ash can be modeled using 4 or 10 ash bins (chem_opt =403 or chem_opt =400,402, respectively). For the ash gravitational settling, the terminal velocities are calculated for the mean arithmetic radii (Rm) within each bin size. Ash density is assumed to be 2500 kgm-3, see Table .

The treatment of optically active ash and sulfate is vitally important. In particular, absorbing solar radiation, ash heats the atmosphere and is lofted . Ash has a relatively short lifetime and does not affect the climate much. While sulfate aerosols scatter solar radiation, have a longer lifetime, and play a primary role in aerosol–climate interactions.

By analogy with the subroutine optical_prep_gocart() being called for the calculation of volume-averaged refractive index (RI) when the GOCART aerosol module is being used, we implemented the subroutine optical_prep_volc() in module_optical_averaging.F file. This subroutine computes the volume-averaged RI needed for Mie calculations. The RI of ash=1.550+i0.001 in the shortwave spectral range has been chosen to approximate ash optical properties . The larger imaginary part of the RI corresponds to the stronger absorption of solar radiation, enhancing atmospheric heating.

Vertical profiles of aerosol optical properties such as aerosol optical depth, single-scattering albedo, and asymmetry factor are computed by the parameterized Mie theory at 4 wavelengths (300, 400, 600, and 1000 nm). Wavelength interpolation based on Angstrom coefficients for these 3 quantities is used as input for the Rapid Radiative Transfer Model (RRTMG) for shortwave and longwave radiation options (ra_lw_physics = 4 and ra_sw_physics = 4). The Mie parameterization was modified by and for the sectional representation of the aerosol size distribution, such that the Mie subroutine requires input of ash and sulfate concentration presented in eight intervals. These intervals are identical to those used in the MOSAIC microphysical module . Therefore, we further refer to them as MOSAIC bins (MOS_{1,2,3,4,5,6,7,8}), see Table .

As mentioned above, ash mass can be redistributed between 4 or 10 bins (see Table ). Sulfate aerosol is prescribed by two log-normal distributions, which describe Aitken and accumulation modes. Parameters of these two distributions are given in Sect. . Following , we assume that the accumulation mode comprises 95 % of the sulfate mass, and the Aitken mode 5 %.

Mass of ash and sulfate is divided between MOSAIC bins before being passed into the Mie routine. Calculation of mapping coefficients for ash is done by analogy with the method in . The following formula is used to calculate the mapping coefficient fri for sulfate aerosol for the ith MOSAIC bin with boundaries ri and ri+1 listed in Table . 29fr(1,2)i=∫riri+1r2⋅1ln⁡σ1,22πexp⁡-(ln⁡r-ln⁡r1,2)22ln⁡2σ1,2dr∫0∞r2⋅1ln⁡σ1,22πexp⁡-(ln⁡r-ln⁡r1,2)22ln⁡2σ1,2dr.

The computed mapping coefficients for ash and sulfate are presented in Table . Ash bin vash_8 is only partially accounted for in MOS₈ MOSAIC bin, while the contribution of bin vash_10 spans across MOS₁ and MOS₇. We do not include in the Table  the contributions of the ash bins vash_1,2,…,7 as they are out of the MOSAIC size range and therefore not accounted for in the mass redistribution. Sulfate in Aitken mode only contributes to the MOS_1,2,3,4,5 bins; MOS_3,4,5,6,7,8 bins are affected by larger particles belonging to the accumulation mode.

Aerosol optical properties computed using the volume averaging mixing rule (aer_op_opt = 1) that assumes internal mixing of aerosol composition that averages the refractive indices for each MOSAIC bin . Within each bin, aerosol particles of each species are simplified as spheres undergoing hygroscopic growth. Volume of the water in ith bin (Volh2o,i) computed following to : 30Volh2o,i=RH1-RH⋅Volsulf,i⋅κsulf+Volash,i⋅κash, where RH is the relative humidity, Volsulf,i and Volash,i are the volumes of sulfate and ash, respectively, in the ith bin. Ash hygroscopicity κash=0.1 , sulfate hygroscopicity κsulf=0.5 . Aerosol optical depth (AOD) at 300, 400, 600, and 1000 nm, as well as shortwave (SW) and longwave (LW) fluxes at the bottom and top of the atmosphere (BOA and TOA, respectively), are available in the WRF-Chem output. Calculation of volcanic aerosol radiative feedback is activated by setting aer_ra_feedback = 1 in the namelist.input file.

In order to verify the modifications introduced in the code and to assess the mass balance of ash, sulfate, and SO2, a hypothetical 2 h-long Mt. Pinatubo eruption was modeled, with the total simulation period extending to 30 d (15 June to 15 July 1991). Domain dimensions are 75×40 grid-cells in zonal and meridional directions, respectively. The domain is centered at 9° N, 95° E. Grid resolution is 100 km2. The meteorological initial and boundary conditions for WRF-Chem are also calculated using the ERA-Interim reanalysis product provided at 0.75°×0.75° horizontal and 6 h temporal resolution. We emitted 65 Mt of ash and 15 Mt of SO2. The emissions were redistributed following an umbrella profile spanning from 1 to 15 km, with 95 % of the mass contained within the umbrella cloud. The total emitted ash mass was evenly distributed among the ten ash size bins, with each bin assigned 10 % (fraction =0.1) of the total ash mass refer to example3.py in. The prepared emission file is being read every two hours. To avoid the volcanic debris loss through the boundary, periodic boundary conditions were imposed by setting the following parameters in the namelist.input: specified = .false., periodic_x = .true. and periodic_y = .true. .

We conducted two 3 month simulations of the Mt. Pinatubo eruption at a 100 km grid resolution: with radiative feedback disabled (RADOFF) and enabled (RADON). Both simulations start on 15 June 1991 at 00:00 UTC. The eruption starts at 01:40 UTC and finishes at 15:40 UTC on 15 June 1991. All sinks for SO2, sulfate, and ash mentioned above are accounted for. The dimensions of the domain are 376×111×60 points in longitude, latitude, and altitude directions, respectively, extending up to 1 hPa. The domain for the simulation is within ≈30° S–60° N latitude belt, see Fig. . Periodic boundary conditions on the longitudinal direction are applied by setting periodic_x = .true. in the namelist.input.

Emissions of ash and SO2 were prepared using the developed tool PrepEmisSources see example2.py in. We used inverted time-varying emission rates of ash and SO2 from , with 66.53 Mt of ash, 15.54 Mt of SO2 in the RADON run, and 62.67 Mt of ash, 16.73 Mt of SO2 in the RADOFF run. Sulfate is not emitted in this experiment. We emit 100 Mt of water vapor, with 75 Mt distributed according to a parabolic profile between 17 and 12 km, and the remaining 25 Mt distributed linearly between 12 and 1 km, following . We inject water vapor to account for its radiative influence on the volcanic plume, as water vapor can modify buoyancy and radiative heating. Although we do not analyze water vapor evolution in this paper, it is included to ensure physically consistent plume thermodynamics. To determine the ash mass fractions for each bin, we follow , assuming that the ash particle size is log-normally distributed with a median radius of 2.4 µm and a geometric width of 1.8. We employed the same method as utilized for sulfate mass redistribution across MOSAIC bins, as referenced in Sect. . The computed ash mass fractions are the following: 0.0 %, 0.0 %, 0.0 %, 0.0 %, 0.5 %, 7.3 %, 32.6 %, 42.2 %, 15.8 %, 1.7 % for vash_1, vash_2, …, vash_10 bins, see Table . In and we obtained the following mass fractions: 0.1 %, 1.5 %, 9.5 %, 45 %, and 43.9 % for ash bins 1 to 5, respectively.

Spectral nudging has been applied above the PBL (>5.0 km) to horizontal wind components (u and v) for the European Centre for Medium-Range Weather Forecasts Era-Interim reanalysis fields. The nudging coefficient equals 0.0001 s-1. Only wavelengths larger than 450 km are nudged. This setting accounts for the realistic phase of the Quasi-Biennial Oscillation and keeps the large-scale motions close to the reanalysis, letting the model develop smaller-scale disturbances freely.

The volcanic cloud after the Mt. Pinatubo eruption was observed by several remote sensing instruments, including the total ozone mapping spectrometer (TOMS) and stratospheric aerosol and gas experiment (SAGE) . SAGE is a limb-viewing instrument that measures aerosol extinction in the stratosphere at different altitudes. The original SAGE observations have multiple gaps. filled these gaps using various techniques. We further refer to this data set as SAGE/ASAP. Infrared satellite SO2 data provided by the TOVS/HIRS/2 (TIROS (Television Infrared Observation Satellite) Optical Vertical Sounder/High Resolution Infrared Radiation Sounder/2) sensor .

The next day after the eruption, the TOMS detected high levels of SO2 loading and positive aerosol index (AI) values. The AI indicates the presence of UV-absorbing aerosols, derived from the contrast between measured and modeled radiances at two ultraviolet wavelengths. Positive AI values correspond to absorbing aerosols such as volcanic ash, whereas near-zero or negative values represent scattering aerosols or clear skies . The AI and AOD are linearly related if the volcanic cloud is relatively thin (i.e., AOD <5) . Figure  compares AI from the TOMS retrieval at 03:45 UTC on 16 June and AOD at 550 nm computed in the RADON and RADOFF runs at 04:00 UTC on 16 June. The spatial patterns of the AI and AOD are not similar for both runs. In , a better agreement between these fields was achieved. This discrepancy may be due to different ash bin size ranges and, as a result, different redistribution of ash mass between MOSAIC bins used for the calculation of optical properties, see Sect. . However, AOD from the RADON run slightly better resembles the observed AI field in comparison with the AOD from the RADOFF run.

Figure  compares observed and simulated SO2 column loadings on 18 June, three days after the volcanic eruption. The absorption of solar radiation by volcanic ash warms the surrounding air within the ash plume, enhancing its buoyancy. This heating also modifies the plume's vertical and horizontal structure. This dynamical response in the RADON run (Fig. b) results in a broader SO2 plume compared to the RADOFF run (Fig. c). The altered temperature gradients also modify local wind fields, slightly shifting the transport pathway of SO2 cloud. The TOMS observations in Fig. a depict a dispersed SO2 plume extending westward from the volcano, with maximum column loadings of approximately 250–300 DU. The plume shows a broad latitudinal spread, with the highest concentrations situated between 5 and 12° N. The RADON simulation (Fig. b) reproduces the observed westward transport of the SO2 plume more realistically compared to the RADOFF run (Fig. c). The spatial extent and position of the plume in RADON align reasonably well with TOMS data, particularly in terms of latitudinal and longitudinal spread and peak loadings. However, the RADON's plume western and northern extents are slightly overestimated relative to observations. In contrast, the SO2 plume from the RADOFF simulation (Fig. c) displays significant deviations from the observed plume. In particular, the RADOFF plume is split into two distinct parts: the northern part with maximum values between 400 and 450 DU, and the southern part with maximum values up to 200 DU. Overall, in contrast with the RADOFF run, the RADON experiment demonstrates a better match to the TOMS data, both in SO2 loading magnitude and spatial distribution.

Figure  presents the temporal evolution of SO2, sulfate, and ash mass during the first 3 months following the eruption, along with the contributions of major sinks. These diagnostics were computed for the RADON run. The initial SO2 mass of 15.54 Mt is decreasing steadily over time. This decline is primarily driven by atmospheric oxidation processes converting SO2 into sulfate aerosols, with an effective e-folding time ≈34 d. Minor contributions to SO2 removal arise from dry deposition and precipitation scavenging, but these represent a small fraction of the overall loss compared to chemical transformation. The simulated rate of decay is close to the TOVS and TOMS estimates.

Sulfate mass increases as SO2 is oxidized primarily by OH, see Fig. a. Sulfate mass reached about 14 Mt by the end of August. This growth reflects sustained conversion of SO2, with a minor fraction of sulfate removed by deposition and precipitation. Ash mass dynamics (see Fig. c) differ from those of SO2 and sulfate. The ash column loading shows a rapid initial decline within the first few weeks. Ash mass loss is dominated by gravitational settling and, to a lesser extent, by precipitation and dry deposition.

Figure  displays the ash, SO2, and sulfate domain-averaged concentrations as a function of altitude and time computed for the RADON and RADOFF experiments. Solid lines and shading in Fig.  show the volcanic cloud boundary from the RADON experiment; dashed lines correspond to the RADOFF experiment. The threshold concentrations are at the color bar's lowest value. In Fig. a and c, ash and SO2 are present from the beginning of the experiments. It takes about 2–3 d to produce a significant amount of SO4. The RADON run shows a more pronounced and sustained presence of ash, SO2, and sulfate compared to the RADOFF run, suggesting that lofting caused by the radiative heating resists gravitational settling. Despite the gravitational settling, the ash cloud rises initially before descending into the troposphere, see Fig. a. The SO2 cloud, driven by buoyancy generated by the radiative heating of eruption products, moves up. In the RADOFF run, the stratospheric updrafts also move SO2 and SO4 up, but at a much slower pace. The gravitational settling of sulfate aerosols restricts the SO4 cloud's upward motion. Eventually, sulfate deposition velocities define the level of neutral buoyancy for the SO4 cloud. Differential radiative heating and gravitational settling lead to a separation of ash, SO2, and sulfate clouds. In the RADOFF simulation, sulfate converted from SO2 below the tropopause undergoes a separation and is rapidly deposited. During the initial two months, the sulfate cloud experiences an ascent; subsequently, it becomes diluted and stabilizes as the buoyancy weakens due to cloud dispersion. In the RADOFF experiment, the SO2 and SO4 clouds end up 3–4 km lower than in the RADON experiment.

Figure  presents the accumulated deposition of ash and sulfur over 3 months following the eruption. The ash and sulfur deposition includes dry deposition, gravitational settling, and washout by large-scale and convective precipitation. The spatial pattern of ash fall is concentrated over Southeast Asia and the western Pacific, where values exceed 1 gm-2. In general, the spatial distribution of tephra-fall deposits is in agreement with and . Ash accumulation also occurred along the equatorial zone in the Indian Ocean, central Africa. It reached the west coast of the Americas, although deposition amounts decreased progressively with distance from the source. Minimal ash fall is seen over the North Atlantic and Central Pacific, as most of the coarse ash particles settled within the first few thousand kilometers downwind. The total mass of ash deposited over the domain is 54.18 Mt, confirming that nearly 80 % of the injected ash (54.18 out of 66.53 Mt) was removed from the atmosphere within three months. This removal primarily reflects the gravitational settling of coarse ash particles >1 µm;, whereas submicron particles remained aloft for a longer period. The accumulated sulfur deposition sums to 0.38 Mt over the same period. Given that sulfate mass reached about 14 Mt by the end of August (see Fig. b), and that most SO2 had been oxidized, the deposition of 0.38 Mt of sulfur represents only a small fraction of the emitted SO2. The deposition pattern of sulfur is more dispersed than that of ash, reflecting the widespread transport, see Fig. b. Sulfur fall is generally lower in magnitude, as most of the sulfate aerosol remains suspended at high altitudes and contributes to the long-lived stratospheric sulfate layer rather than being removed by deposition processes. Sulfur deposition occurred broadly across the tropical belt. Noticeable sulfur fall affected the Pacific Ocean, Central America, and Central Africa. In these areas, we expect the precipitation to be more acidic.

Figure  compares the observed (SAGE/ASAP) and simulated in RADON and RADOFF runs zonal mean stratospheric aerosol optical depth (SAOD), which includes contributions from ash and sulfate. In the RADOFF run, during the first week, a significant amount of aerosol moves to the Southern Hemisphere, reaching 10° S, but the maximum SAOD remains in the Northern Hemisphere. In contrast, the SAOD structure in the RADON run is close to that observed by SAGE, including the position of maximum SAOD, latitudinal spread, and pattern. But in the RADON run, the SAOD pattern is shifted by 10° to the north compared with the SAGE/ASAP observations. The maximum SAGE/ASAP SAOD is in the 10° S–0° range, whereas in the RADON run, the SAOD maximum is within the 0°–10° N range. This suggests that the RADON simulation slightly overestimates the transport of aerosols into the Northern Hemisphere, which was also observed in our previous study .