In this study we followed the regional Nested UM with Aerosols and Chemistry (NUMAC) model configuration described in Gordon et al. (2023). It is based on the NWP (Numerical Weather Prediction) configuration of the UK Met Office Unified Model (UM). For the regional atmosphere model, we used the UM version 12.0 nesting suite coupled with submodels to represent processes including atmospheric chemistry, aerosol microphysics as well as cloud microphysics.

A rectangular regional domain of 3500 km × 2750 km centred at 65.0° N, 20.0° W in Iceland has been set to cover the entire northern North Atlantic. The horizontal resolution within the regional domain (or the nest) is 2.5 km. This nesting suite model uses rotated pole coordinates and therefore the sizes of individual grid cells are approximately constant within the domain. Vertically the model resolves the atmosphere from the surface to 40 km of altitude with 90 layers, 16 layers below 1 km.

The lateral boundary conditions are provided by the Met Office global model (GAL6.1; Walters et al., 2017). The global model has Cartesian coordinates with n216 resolution where grid cells have a size of 0.83° in longitude and 0.55° in latitude.

Both global and regional models are coupled with the United Kingdom Chemistry and Aerosols (UKCA) model to simulate atmospheric transport and chemical processes (Abraham, 2014; O'Connor et al., 2014). Within the UKCA model, atmospheric aerosol processes such as new particle formation, gas to particle transfer, coagulation between particles, cloud processing of aerosols, and dry and wet deposition of aerosols are simulated with the modal version of the GLObal Model of Aerosol Processes model (GLOMAP-mode; Mann et al., 2010).

In the model setup we use in this study, GLOMAP resolves four aerosol components (sulfate, organic carbon, black carbon, and sea salt) in five internally mixed modes (soluble modes in the nucleation, Aitken, accumulation, and coarse size ranges and an insoluble mode in the Aitken size range). Within each mode a lognormal particle number-size distribution is represented. Emissions and atmospheric processes for mineral dust are treated within the CLASSIC bin scheme (Woodward, 2001) and do not interact with other aerosols and clouds.

The Cloud AeroSol Interacting Microphysics (CASIM; Field et al., 2023) scheme prognoses mass and number mixing ratios of five species of hydrometeor (cloud water, cloud ice, rain, snow and graupel), representing the process rates that move mass and number between species and to and from the vapour phase, as well as handling sedimentation. CASIM uses the Abdul-Razzak and Ghan (2000) bulk activation parametrization to convert UKCA-GLOMAP aerosols into cloud droplets when new water is condensed by the cloud fraction scheme (Gordon et al., 2020). The relationships for autoconversion and accretion, which describe the evolution of cloud water into rain, are based on Khairoutdinov and Kogan (2000). This formulation suppresses autoconversion as droplet number increases.

The cloud fraction scheme (Van Weverberg et al., 2021) represents the subgrid humidity distribution and determines when liquid water will condense based on saturation adjustment appropriate for models using timesteps of ∼ 60 s. The humidity in the grid box is represented by a Gaussian distribution (two distributions if the grid box is close to an inversion, to represent mixing across the inversion). The width of the distribution is diagnosed from the turbulence closure given in the model for the boundary layer representation (Lock et al., 2000). The scheme can also account for the presence of ice in a grid box that will lead to a narrowing of the subgrid distribution of relative humidity making it more difficult to form supercooled liquid cloud.

Aerosol related emissions including anthropogenic sulfur dioxide (SO₂), black carbon (BC), and organic compounds (OC) are taken from CMIP6 data for year 2000 through ancillary files. For the natural SO₂ emissions from continually degassing volcanoes, the dataset from Andres and Kasgnoc (1998) is used. The emissions from explosive volcanic eruptions including that from the Holuhraun eruption in 2014 are prescribed separately as described in the next section. Emission of dimethyl sulfide (DMS) from the sea surface is calculated interactively following Nightingale et al. (2000) based on model-predicted surface windspeed and prescribed DMS concentrations in near-surface sea water by Kettle and Andreae (2000). DMS is oxidized to form SO₂ which is a precursor of sulfate aerosol (e.g., Fung et al., 2022). Sea salt aerosol is also calculated interactively within the model based on the 10 m windspeed (Gong, 2003).

The Holuhraun effusive eruption started on 31 August 2014 and lasted until 27 February 2015, and it injected SO₂ into the troposphere at a varying rate. Within our simulations, the strength of the emission has been set to 1.0 × 105 t of SO₂ from 31 August to 13 September 2014 (105 t d⁻¹) followed by 9.8 × 105 t (5.4×104 t d⁻¹) until 30 September (Malavelle et al., 2017).

The SO₂ is injected into the atmosphere centred at the location of Holuhraun (64.85° N, 16.83° W) and between the altitudes of 800 and 3000 m. The initial plume is assumed to have a horizontally concentric distribution, with the SO₂ concentration highest at the centre and decreasing radially with distance following a Gaussian distribution with a standard deviation of 30 km. SO₂ concentration is assumed to be vertically uniform across the injected altitudes.

Following the injection of SO₂ into the atmosphere, the plume will evolve as the gas is converted into aerosols, as described in the following sub-section.

The key processes for this work are summarised here. More comprehensive descriptions of aerosol processes can be found in Yoshioka et al. (2019).

SO₂ is oxidized to form sulfuric acid, which is then transferred to the particle phase within the free troposphere through binary homogeneous nucleation. The boundary layer nucleation is turned off in the default version of the model. This process is mediated by secondary organic material (Metzger et al., 2010) that is a product of biogenic volatile organic compounds from land plants (especially forests). Because of this, we have assumed that this process would not be particularly important for our largely oceanic domain and the barren terrain of much of Iceland. Therefore, this process is switched off for the default simulations, but it is included in additional simulations.

Particle growth occurs through sulfuric acid condensing onto existing particles in the atmosphere and through coagulation between particles. Particle growth is represented by an increase of geometric mean diameter and aerosol particles are transferred to a larger aerosol mode once the diameter exceeds the threshold of the mode. When sulfuric acid condenses onto insoluble particles such as BC and OC they become hydrophilic and are transferred to a soluble mode of the appropriate size.

Soluble particles can absorb water from the atmosphere, increasing in size (hygroscopic growth) and can serve as cloud condensation nuclei (CCN) to become cloud droplets when the size, composition (solubility), relative humidity and vertical velocity combine favourably. This is simulated with the Abdul-Razzak and Ghan (2000) bulk activation parametrization.

Aerosol particles are removed from the atmosphere through dry deposition (gravitational settling and turbulent mixing near the surface), nucleation scavenging (activated to form cloud drops and rained out through autoconversion) and impaction scavenging (washed out by rain drops; Slinn, 1982; Mulcahy et al., 2020).

The global model was spun-up for 60 d before starting the regional simulations to ensure that the aerosol fields had reached a steady state. Regional simulations were started from 12:00 UTC of 30 August 2014 using the output fields from the spun-up global simulation at this time as their initial conditions. The lateral boundary conditions were provided from the global model that was run in parallel with each regional simulation. The meteorology of the global model was initialized at 12:00 UTC every day from Met Office UM operational analysis and both global and regional simulations were run for 36 h in each iteration. We discarded the first 12 h as spin-up and used the simulation output from t=12 to 36 h (00:00–24:00 UTC of the next day) from each iteration. The next iteration starts at 12:00 UTC using the meteorological fields from operational analysis of the corresponding date and the aerosol fields inherited from the previous iteration.

We ran regional simulations for two scenarios: Volc is the simulation that includes Holuhraun SO₂ emission as described in Sect. 2.4 and NoVolc does not include this emission. Simulations were run to 28 September 2014 and we analyzed the simulations from 1 September.

Since the original simulation underestimated the observed cloud droplet number concentrations as will be shown in Sect. 3, we modified some of the model settings and parameter values to enhance the background aerosols and clouds. Table 1 shows the changes between the default model and the enhanced aerosols and clouds configuration of the model. The model assumes that 2.5 % of SO₂ is emitted as primary sulphate particles, and this modification changes the modes of these emissions to the smaller Aitken mode from larger size modes in line with Yoshioka et al. (2019). However, this does not affect the Holuhraun volcanic emission for which no primary sulphate emission is assumed.

Simulated cloud properties such as cloud droplet number concentration (CDNC), effective radius (Reff), liquid water path (LWP) and cloud fraction (CF) are compared with the satellite observation data from the MODerate resolution Imaging Spectroradiometer (MODIS) onboard the Aqua satellite. Peace et al. (2024) used the MODIS COSP 1 degree resolution data set (Pincus et al., 2023) to compare with coarse-resolution models. For the higher-resolution simulations presented here, the same retrieved variables are taken from a higher-resolution satellite dataset, namely the MODIS Aqua Level-2 Collection 6.1 products (Platnick et al., 2015, 2017). Reff, cloud water path, cloud optical thickness and cloud phase are retrieved at 1 km spatial resolution. Cloud fraction is retrieved at 5 km resolution. CDNC is calculating from Reff and cloud optical thickness assuming adiabatic clouds following Quaas et al. (2006). The Level 2 swath data was aggregated to a 0.5 × 0.5° resolution grid for each day. Cloud fraction was obtained from the cloud mask fraction rather than cloud retrieval fraction (Peace et al., 2024). The cloud properties are examined for marine liquid cloud with cloud top heights between 1 and 5 km. This 5 km threshold was chosen to separate lower-tropospheric liquid clouds from upper-tropospheric ice clouds such as cirrus. In our simulations, more than 99 % of liquid water resides below 4 km, so varying this threshold within a reasonable range (e.g. 4–6 km) would not substantially affect the results.

Satellite observations of cloud properties are subject to uncertainties due to various factors. A comprehensive overview of the uncertainties in the satellite retrieval of CDNC is given in Grosvenor et al. (2018) where the uncertainty of pixel-level CDNC is estimated to be approximately 78 %, although the overall uncertainty is likely to be reduced for area-averaged values. In the MODIS Aqua dataset we used, only data pixels with cloud optical thickness between 4 and 70, and Reff between 4 and 30 µm were retained as these retrievals are most reliable (Quaas et al., 2006).

We masked both simulation outputs and satellite derived data based on column SO₂ loading and separated the region into three categories; in-plume, out-of-plume, and regions outside the analysis domain.

In the satellite data, we followed the general methodology of Peace et al. (2024) but with the higher resolution data. Column amounts of SO₂ were retrieved from the Ozone Mapping and Profiler Suite (OMPS) Nadir Mapper (NM) onboard the NASA-NOAA Suomi National Polar-orbiting partnership (SNPP) satellite (Flynn et al., 2014; Seftor et al., 2014). The region categorized with SO₂ loading higher than 1 DU (Dobson Unit) from OMPS was identified as “in-plume”. A 3 × 3-pixel median filter was then applied to minimise the inclusion of isolated grid cells with SO2>1 DU that were not likely to be part of the plume. The median filtering approach has been used to remove random classification errors when detecting methane plumes (Varon et al., 2018). Next, we introduced a rectangular boundary enveloping the in-plume region. Grid points outside this boundary were excluded from the analysis, while those inside the boundary but outside the plume were classified as out-of-plume. We ignored regions over land to avoid potential biases in satellite retrievals and a larger region around the British Isles to avoid contamination from land sources of SO₂.

To create plume masks for the simulations, the simulated SO₂ fields were first regridded to a horizontal resolution of approximately 0.5°, comparable to that of the satellite data. In-plume regions were defined based on simulated column SO₂. Following Peace et al. (2024), a rectangular analysis domain was then constructed using the minimum and maximum east-west and north-south extents of the plume. Within this domain, grid points outside the in-plume regions were classified as out-of-plume.

When a 1.0 DU threshold of simulated column SO₂ was applied, the resulting in-plume and out-of-plume regions were smaller than those derived from the satellite data. To improve the comparability between the simulated and satellite-derived plume masks, a threshold of 0.5 DU was therefore adopted for the main analysis. Plume masks based on a 1.0 DU threshold are also constructed for sensitivity analyses.

Another sensitivity experiment was performed using hybrid masks, in which the in-plume regions are defined using the same 0.5 DU threshold on simulated SO₂ as in the main analysis, whereas the extents of out-of-plume regions follow the satellite-derived 1 DU threshold. The impacts of using the differently defined plume masks and the validity of the results from the main analyses are examined in Sect. 3.3.

In the following sections we will apply satellite derived plume masks to satellite data and simulation derived masks on simulation data to compare the cloud properties in in-plume and out-of-plume regions. Figure 1 shows the plume masks from the satellite and the model from 1 to 6 September 2014 (day 2–7 of the Holuhraun eruption). The masks for the rest of the simulation period (7 to 28 September) are shown in Fig. S1 in the Supplement. The masks created from the simulation agree well with those from the satellite data.

Column mean CDNCs in the simulations were calculated by vertically averaging CDNCs within grid boxes using liquid water contents as weights to account for the vertically varying amounts of cloud condensate. This approach will weigh the value towards cloud top to be more comparable with the satellite view of the cloud. Cloudy-sky LWPs were obtained by dividing column LWPs by column cloud fraction. Column volume mean cloud droplet radii were calculated by dividing column LWPs by total column CDNCs, dividing by the density of water and converting from the resulting volume to a radius assuming spherical droplets. The volume mean radius was converted to Reff by multiplying by 1.24. This follows from CASIM assuming the cloud droplet distribution follows a gamma distribution with a shape factor of 2.5. The ratio of effective radius (ratio of third and second moments of the droplet distribution) to the volume mean radius (ratio of third to zeroth moment all to the third power) is then 1.24.

To carry out comparisons with satellite observations (MODIS AQUA), the horizontal resolutions of simulated cloud properties were reduced to about 50 km by horizontally averaging the values within the box of reduced resolution. To account for the insensitivity of the satellite instrument to thin clouds, all data where column LWP is less than 10 g m⁻² were excluded.

The data were split into four one-week periods for comparing to the satellite data following Peace et al. (2024).

We split observed and simulated data into in-plume and out-of-plume using the plume masks as described above. For the observations and the Volc simulation we call the difference between a cloud property in and out of the plumes as the “TOTAL effect”. We calculate this either as the difference between two arithmetic means or the quotient between two geometric means depending on the distribution of the variable. This is the effect that can be observed with satellites.

In simulations we can use the counterfactual NoVolc scenario to estimate the effects of different background meteorology and other environmental factors depending on the location of the plume. We call this the “LOCATION effect” and calculate it as the difference between arithmetic means, or the quotient between geometric means, inside and outside the plumes in the NoVolc simulation.

The difference between total effect and location effect is considered to be caused by the volcanic plume. In our model we only take into account sulphate aerosol produced by SO₂ as the impact of the volcanic emission. We call this the “AEROSOL effect” and calculate it as the difference or the quotient, where appropriate, between the TOTAL effect and the LOCATION effect. We also look at the difference between the Volc in-plume and NoVolc in-plume to obtain the “ERUPTION effect”. This allows us to see if there is an impact of the aerosol on the cloud fields and avoids any impact of the meteorology acting to mask any effects in the satellite data. The AEROSOL effect converges to the ERUPTION effect if the region outside the plume remains unaffected by the volcanic eruption (i.e., there is no “REMOTE effect”). Reasons for these values being different include diffuse plumes below the given threshold, changes in circulation caused by modifications to heating rate profiles in the plume region that impact cloud fields outside of the plume, or the presence of large amounts of additional water vapour in the plume that is not included here. TOTAL, LOCATION, ERUPTION, REMOTE, and AEROSOL effects are summarised in Fig. 2 and Table 2.

We will discuss the results in the following order. First, the aerosol is perturbed by the volcanic plume and is expected to feed through directly to CDNC. Secondly, changes in CDNC control the process that converts cloud water to rain affecting the LWP, which is therefore examined next. Thirdly, Reff, that impacts the radiation, is diagnosed from the primary characteristics predicted by the model (liquid water mass and droplet number concentration). Finally, the emergent behaviour of the cloud cover that results from all of the changes is examined.

Figure 3 shows the values of observed and simulated CDNCs at three quartiles (25th, 50th and 75th percentiles) as well as the 5th and 95th percentiles within and out of the volcanic plumes during the four weeks from the start of the eruption. The probability distribution functions for the same data are shown in Fig. S2. CDNC is underestimated in the simulation including volcanic emissions (Volc; red) both within (dark colours) and out of (light colours) the plume by factors of 2–4 compared to the observation (grey). General underestimation is considered likely due to biases in background aerosols or an underestimate in the treatment of the activation of cloud droplets than a bias in the Holuhraun volcanic emission implemented in the model. The use of alternate activation schemes is a subject of ongoing investigation. Enhancement of CDNC within the plume compared to outside of the plume can be seen in both the observations and in the Volc simulation in all but the third week. Since CDNC is underestimated outside the plume and the magnitudes of enhancements within the plumes are about right, the general underestimation is considered likely due to biases in background aerosols and clouds rather than a bias in the Holuhraun volcanic emission implemented in the model.

Following the relatively large underestimates in simulated background CDNC, we modified the model settings as described in Sect. 2.6 and all the subsequent results use this new configuration. Figure 4 replicates Fig. 3 but for the simulations with enhanced settings (Volc: V and NoVolc: N). The background values of CDNC have been improved and the underestimates in the Volc simulation are within a factor of ∼ 2 and in most cases less than 1.5 (50 %).

CDNC is enhanced within the plumes in both the observations and the Volc simulation except for during the third week. As shown in Table 3 and Fig. 8, Student's t-tests indicate a statistically insignificant (at 0.01 level) difference between the CDNC in-plume and out-of-plume (TOTAL effect) for the third week for both the model and observations. Note that t-tests were performed on the base 10 logarithms of the values and a lagged autocorrelation has been performed to estimate the degrees of freedom by assessing the scale at which the field becomes decorrelated (e.g. Field and Wood, 2007). The ERUPTION effect for the model (Fig. 4, Table 3, Fig. 8) shows that the aerosol perturbation in the plume region always leads to an enhancement of CDNC (factors of 2.4–4.2). The LOCATION effects are significant for weeks 1 and 3 but no significant differences for weeks 2 and 4. In contrast, the REMOTE effects are significant in all weeks.

Cloudy-sky LWP (Fig. 5) is also underestimated by factors up to ∼ 2 compared to the satellite observations, although MODIS LWP can be in error due to various factors, such as effective radius and optical depth retrieval errors, and assumptions regarding the degree of adiabaticity used to estimate LWP. Notwithstanding systematic errors in the MODIS LWP retrieval, Table 3 shows that observed differences between in-plume and out-of-plume (TOTAL effect) are significant in the first 3 weeks with increased LWP in the plume for weeks 1 and 2 but decreased LWP in the plume for week 3. In the model, on the other hand, the TOTAL effect is not deemed significant for any of the weeks. The ERUPTION effect (V.in versus N.in) is about +20 % and statistically significant in the first week at the 0.05 (but not 0.01) level, while the other weeks indicate changes of ∼ 5 % that are not deemed significant. The LOCATION effect is significant in the first week at 0.01 level (significant at 0.05 level in the third week), while the REMOTE effect does not show any significance.

Background Reff (Fig. 6) are underestimated by up to about 30 % (O.Out vs. V.Out). But the differences between in-plume and out-of-plume values (TOTAL effect) for models and observations are similar, including the weak response for the 3rd week. This mirrors the CDNC response since, for a constant LWP, Reff will scale inversely with CDNC^1∕3 and in-plume and out-of-plume LWP values are very similar in the model. For the observations there are LWP increases in weeks 1 and 2, but there is still a reduction in Reff for these weeks indicating that the increase in CDNC dominates over the LWP increase in terms of causing the Reff response. Following the change in CDNC, Reff is also significantly reduced for the eruption effect (factors of 0.65–0.77). As was the case for the CDNC, Reff shows a non-zero remote effect of up to -15 % that is deemed significant. The location effect again follows the CDNC response with significant differences in the 1st and 3rd weeks.

Figure 7 indicates that there is 3 %–5 % increase in observed CF in the in-plume region compared to the out-of-plume region, except in the 3rd week. On the other hand, the model shows smaller changes in CF. Even when only considering the liquid cloud fraction (see Fig. S8) there is no significant change in the cloud fraction due to the volcano with the exception of the 3rd week in direct contrast to the observations. The ERUPTION, LOCATION and REMOTE effects all exhibit no significant change.

As described in Sect. 2.8, we examine the sensitivity of our results to different definitions of plume masks. In the preceding sections, a 0.5 DU threshold of simulated column SO₂ was used to define in-plume and out-of-plume regions. Here, we instead apply a 1.0 DU threshold, consistent with the SO₂ criterion used to construct the satellite-derived plume masks. This choice yields smaller in-plume regions and, consequently, smaller associated out-of-plume regions compared to the satellite-derived masks.

Figure S9 shows that using the 1.0 DU criterion leads to a slightly higher contrast in CDNC between in-plume and out-of-plume regions than in the main analysis (compare Volc.In vs. Volc.Out in Figs. 4 and S9). This indicates that the main results, based on the 0.5 DU threshold, provide a conservative estimate of the magnitude of volcanic plume effects on clouds. Consequently, the statistical significance of the volcanic effects identified in the main analysis is strengthened.

A second sensitivity experiment was performed using hybrid plume masks, in which the in-plume regions are identical to those in the main analysis, while the boundaries defining the out-of-plume regions follow the satellite-derived masks from Peace et al. (2024). Figure S10 shows the resulting CDNC distributions, which are identical to those in Fig. 4 except for the simulated values in the out-of-plume regions (V.Out and N.Out). CDNC values in both V.Out and N.Out increase in week 1, decrease in weeks 2 and 3, and remain nearly unchanged in week 4. The largest deviation occurs in week 3, when the LOCATION effect increases by 22 % and the AEROSOL effect decreases by 14 % (Table S1 in the Supplement). Although these differences are not negligible, they do not alter the overall conclusions of this study.