MOCAGE is an offline global and regional three-dimensional chemistry transport model developed at CNRM . It is used for various scientific topics, including the impact of climate change on atmospheric composition e.g.,, chemical exchanges between the stratosphere and the troposphere using data assimilation e.g., and the operational production of air quality forecasts for France Prev'Air program; and for Europe (as one of the nine models contributing to the regional ensemble forecasting system of the Copernicus Atmosphere Monitoring Service (CAMS) European project; , https://atmosphere.copernicus.eu/, last access: March 2020).

A special feature of the model makes it possible to include a natural or anthropogenic accidental source, such as volcanic eruptions or nuclear explosions, during a simulation. This feature is used as part of the Toulouse VAAC (Volcanic Ash Advisory Center) of Météo-France, which is responsible for monitoring volcanic eruptions over a large area (including part of Europe and Africa). In order to input an accidental emission, it is required to input the time and place (latitude/longitude), the bottom and top plume heights, the total quantity emitted and the duration of the emission.

The CTM MOCAGE can be used with global or regional resolutions based on its grid nesting capability. Each outer domain forces the inner domain at its edges (boundary conditions). The global domain has a typical resolution of long1∘×lat1∘ (around 110km×110 km at the Equator and 110km×80 km at midlatitudes), while the regional domain resolutions are typically long0.2∘×lat0.2∘ (around 22km×16 km at midlatitudes) and long0.1∘×lat0.1∘ resolution (around 11km×8 km at midlatitudes).

The vertical grid has 47 levels from the surface to 5 hPa (about 35 km), with seven levels in the planetary boundary layer, 20 in the free troposphere and 20 in the stratosphere. The vertical coordinates are expressed in σ pressure, meaning that the model levels closely follow the topography in the low atmosphere and the pressure levels in the upper atmosphere.

Being an offline model, MOCAGE obtains its meteorological fields (wind speed and direction, temperature, humidity, pressure, rain, snow and clouds) from an independent numerical weather prediction model. In practice, they can come from two meteorological models at the global scale, namely the IFS model (Integrated Forecasting System), operated at the ECMWF (European Center for Medium-Range Weather Forecasts; http://www.ecmwf.int, last access: March 2020), or from ARPEGE model (Action de Recherche Petite Echelle Grande Echelle), operated at Météo-France .

At the global scale, anthropogenic emissions from the MACCity inventory are used , while biogenic emissions for gaseous species are from the MEGAN–MACC inventory, also representative of the year 2010 . Note that the difference between 2010 and 2013 emissions is negligible for the purpose of this study as SO2 emissions are only about 1 % higher in 2010 than in 2013. Nitrogen oxides from lightning are based on and are configured dynamically according to the meteorological forcing. Organic and black carbon are taken into account following MACCity . DMS oceanic emissions are a monthly climatology 1∘ horizontal data;. Finally, the daily biomass burning emissions available for each day in 2013 come from the Global Fire Assimilation System (GFAS) daily products . Volcanic emissions are discussed in detail in Sect. .

In MOCAGE, with the exception of the species emitted from biomass burning , lightning NOx and aircraft , all of the chemical species sources are injected in the first five levels of the model (up to approximately 500 m). This configuration is necessary for the numerical stability in the lowest model levels. The injection profile implemented follows an exponential decrease from the surface level of the model (including model orography), where δL=0.5δL-1, with δL being the injection fraction of the mass emitted at the level L of the model. It means that the majority of pollutants are emitted at the surface level and then quickly decrease with altitude. Hereafter, we will refer to the model surface when this configuration is used.

The transport in the model is solved in two steps. A first one explicitly determines the large-scale transport (advection), with the wind input data provided by the numerical weather model. For this purpose, a semi-Lagrangian scheme is used . The second step represents the sub-grid phenomena that cannot be solved explicitly, such as convection and turbulent scattering. The convective transport is configured upon the setup. The scheme of is used to diffuse the species by turbulent mixing.

The previous inventory implemented in MOCAGE is from , which is a study contributing to the work of GEIA (Global Emissions InitiAtive). Measurements ranged over a period of about 25 years, from the early 1970s to 1997, and covered volcanic SO2 emissions at the global scale.

A synergy between the COSPEC surface instrument and the TOMS satellite instrument was used. The COSPEC is a correlation spectrometer initially used in pollution measurements . However, volcanologists have adapted it to measure the quantities of sulfur dioxide in a moving air mass (here the volcanic plume). It works by comparing the amount of solar ultraviolet (UV) radiation absorbed in the plume with a standard (one sample of the background sky and two laboratory-calibrated SO2 concentration cells). It is most commonly used under quiet to moderate eruptive conditions. On the contrary, the space instrument TOMS , operational between 1978 and 2005, was able to detect larger eruptions. The synergy of these two instruments is therefore complementary in the development of the inventory. Although the first instrument is better adapted to the measurement of weak flares and the second to the strongest ones, a campaign dedicated to Popocatépetl in Mexico showed the good correlation between the two instruments .

Measurements were only carried out on sub-aerial volcanoes, i.e., emitting gases directly into the atmosphere. A total of 69 volcanoes are listed in the inventory, divided into two categories, namely 49 continuously erupting volcanoes and 25 sporadically erupting volcanoes. The following five volcanoes belong to both categories because they had a main activity of continuous emissions and also sporadic eruptive events: Mount Aso, Augustine, Kīlauea East Rift Zone, Mayon and San Cristóbal.

Since the beginning of volcanic emission measurements in the early 1970s, the global activity of continuous eruptions has shown relative stability. The fluxes provided in the inventory correspond to a temporal average of all measurements for each volcano. Only three volcanoes are not concerned by this hypothesis, i.e., Mount Etna in Sicily and Kīlauea and the Kīlauea Rift Zone in Hawaii, which are known as being among the largest emitters of SO2. For those volcanoes, fluxes provided by specific studies personal communication supersede the averages.

Since sporadic eruption data in are not recent, it is not possible to take them into account for the recent year chosen for the MOCAGE simulation. Therefore, only continuous eruptions are used in MOCAGE and a global time-averaged SO2 flux of 13 Tgyr-1 is reported.

Since no configuration was developed in MOCAGE to inject volcanic emissions aloft until this study, they were implemented in a similar manner to the other pollution sources. Volcanic SO2 were thus emitted at the model surface (see Sect. ). However, the surface elevation of the model (orography) is mainly below the actual elevation of the volcanoes.

With the improvements in satellite technology, an increasing number of satellites are now able to better detect the sources of volcanic SO2, i.e., plume heights, quantities emitted and location. The most recent instruments with respect to TOMS, such as the Ozone Monitoring Instrument (OMI) and the TROPOspheric Monitoring Instrument TROPOMI;, have a higher sensitivity to detecting small eruptions but also passive degassing. Global coverage gives another considerable advantage over other measurement techniques. As a reminder, COSPEC carries out measurements from the ground and cannot be deployed on hard-to-access volcanoes.

The work of updates and adds complementary information to the study of with a new inventory. The inventory is divided into two parts corresponding to the two types of emissions detectable by satellites.

First, the eruptive emissions data set with data available in , is a synthesis of 40 years of daily SO2 measurements (between 31 October 1978 and 31 December 2018) derived from the following seven satellite instruments: TOMS, OMI and OMPS (Ozone Mapping and Profiler Suite) in the ultraviolet (UV), TIROS Operational Vertical Sounder (TOVS), Atmospheric InfraRed Sounder (AIRS) and Infrared Atmospheric Sounding Interferometer (IASI) in the infrared (IR) and the Microwave Limb Sounder (MLS) in the microwave range. Data from 119 volcanoes and a total of 1502 events over the period are provided. For each of these eruptions, the information given includes the location of the volcano (latitude and longitude), the date, the VEI (Volcanic Explosivity Index), the estimated SO2 mass released (in kilotons) and also the height of the volcano and the height of the plume (measured if possible; estimated if not). Within our study, the additional information from on the injection height is used (see details hereafter), taking into account the height of the volcano as the base of the emissions and the height of the plume as the top of the injection.

Second, the passive degassing data set is the first documented volcanic sulfur dioxide emission inventory made with global satellite measurements . It was retrieved from the observations of the OMI instrument in the UV spectrum during a long-term mission between 2005 and 2015. The high sensitivity of the instrument was a technological breakthrough that made it possible to distinguish low SO2 sources; this means ∼30 ktyr-1 for persistent anthropogenic sources and lower amounts (∼6 ktyr-1) for volcanoes which are located at higher altitudes or at lower latitudes that benefit from more satellite observations and optimal conditions (low solar zenith angle). The volcanic SO2 sources have been identified on the basis of 3-year averages (2005–2007, 2008–2010 and 2011–2014), which implies that, for a source to be characterized as persistently degassing, the emission must be relatively constant on this timescale. Annual mean emissions were calculated for each of the 90 volcanic sources identified over the 11 years of the study. We assume in the model that emission fluxes are constant throughout the year.

Several parameters can affect the retrieval of volcanic emissions, namely the measurement process, the calculation algorithm or the characterization of the type of emission. Thus, annual uncertainties are given with the mean annual emissions for each volcano and each year. The total uncertainty of the annual sulfur dioxide fluxes are estimated at 55 % and over 67 % for sources emitting more than 100 and less than 50 ktyr-1, respectively. This latter information is exploited in the sensitivity analysis (see Sect. ). Note also that, depending on the instrument used, the retrieval of the plume altitude can differ. Therefore, there are uncertainties on the altitude information provided by the inventory.

Information on the altitude of volcanoes and on the plume height in the inventory is used to implement a configuration to inject volcanic emissions aloft rather than keeping them at the model surface. This is an important improvement because, in some areas, depending on the model resolution chosen, the model orography may differ from the actual topography and have an impact on the transport of volcanic emissions. The new implementation sets the passively degassing emissions at the model level of the volcano altitude. For eruptions, the mass of SO2 emitted is distributed from the model level at the volcano vent to the model level of the plume top height and follows an umbrella profile similar to that used in other chemistry models . During a volcanic eruption, the emitted materials (ashes and gases) are rapidly transported vertically by the convection in the plume, and most of the materials are concentrated at a high altitude, giving an umbrella profile. In practice, the plume follows an almost linear profile, with an increasing altitude from the volcano vent, and then it opens into a parabola containing 75 % of the gases in mass into the top third of the plume.

In summary (see Table ), the updated volcanic sulfur emission inventory now includes about 160 volcanoes (∼110 in the eruptive category and ∼90 in the passive degassing category with 40 volcanoes in common). The availability of plume heights in this inventory allows a better representation of the injection of the volcanic emission in the model.

Meteorological fields are driven by the ARPEGE 3 hourly forecasts. Anthropogenic and biomass burning sources emit SO2, whereas biogenic emissions from the ocean are assumed to occur as DMS. Oceanic DMS emissions are 19.9 TgSyr-1, while anthropogenic emissions are 48.6 TgSyr-1. For 2013, biomass burning emissions from GFAS products were relatively low, at only 1 TgSyr-1.

Concerning volcanic sulfur emission inventories, either or is used. The full eruption emission database is available following Carn (, 10.5067/MEASURES/SO2/DATA405).

In total, four different simulations (Table ) are carried out in order to evaluate the impact induced by the update of the volcanic SO2 inventory in MOCAGE and to analyze its contribution to the sulfur species budget in the atmosphere at the global scale. The four simulations are run at a resolution of 1∘×1∘.

The first simulation, named REF, takes into account the previous volcanic inventory from with the injection at the model surface. The second simulation, named CARNALTI, uses the updated volcanic inventory from and the new configuration to inject volcanic emissions from the volcano altitude, as described in Sect. . By comparing REF and CARNALTI runs, we can analyze the changes brought by the updated volcanic emission inventory with respect to the previous one. These two simulations are evaluated in Sect. , and the associated global distribution of sulfur species is compared in Sect. .

In order to distinguish between the impact of the height of emission and of the quantity of SO2 emitted, another simulation, named CARN, is run and used for the analysis of the differences between the REF and CARNALTI global distribution of sulfur species. Volcanic emissions are from , as in CARNALTI, but they are injected at the model surface, as in REF.

CARNALTI is run to provide a better representation of the global tropospheric sulfur. This is why it is selected for the analysis of the tropospheric sulfur budget in Sect. . In order to quantify the contribution of the volcanoes in the sulfur budget, we compare CARNALTI to the NOVOLC simulation that does not take into account volcanic emissions (only anthropogenic, biomass burning and dust).

The four simulations are run for the year 2013 with a 3 month spin-up period (from October to December 2012). In addition to being one of the years for which a large amount of observational data is available globally, 2013 is chosen as the year with the lowest eruptive emission flux . Figure  shows the volcanic emissions of the different simulations for the year 2013. We notice the monthly variation due to non-volcanic emissions (NOVOLC run in green), with fewer emissions during the Northern Hemisphere summer and the highest values in the Northern Hemisphere winter. Volcanic emissions from are steady throughout the year, as we can see in the REF run (in blue). They are lower than the volcanic emissions of the CARNALTI and CARN runs (in red), with strong constant passive degassing throughout the year and a few sporadically eruptive events. Indeed, SO2 emissions are 13 Tg (or 6.5 Tg S), while the total 2013 annual emissions in are 23.7 Tg of SO2 (or 11.8 Tg S), with 23.5 Tg of passive degassing SO2 and 0.2 Tg of eruptive emissions (<1 % of the total amount of volcanic SO2 emissions, which is almost negligible).

Figure  spatially represents the difference between the previous and the new inventories. The red dots mostly show new volcanoes in which are not accounted for by . However, we also notice blue dots, meaning that, in the new inventory, the estimated emission fluxes are reduced. Given the low number of eruptive emissions in 2013, the annual average of volcanic emissions in Fig.  essentially represents passive emissions.

We use satellite-based instruments for the model evaluation since they provide a global sampling. The target chemical species that we evaluate are SO2 and aerosols, since SO2 is the precursor of sulfate aerosols. Concerning SO2, observations in the infrared are not suitable since passive degassing occurs mostly under 5 km, at altitudes where such instruments have reduced sensitivity . Therefore, observations in UV-visible range are chosen. With the Global Ozone Monitoring Experiment–2 (GOME-2) Metop-A (Meteorological Operational satellite) instrument being at the end of its lifetime, data retrievals are not good enough and present strong artifacts, as is the case for GOME-2 Metop-B. Therefore, we choose the OMI, which is the most widely used e.g.,. Moreover, the SO2 tropospheric column estimated from the OMI is the finest resolution and most accurate instrument from 2013 for retrieving SO2 total columns over passively emitted volcanoes with altitudes that are generally around 2–3 km. For aerosols, there is no satellite-derived product providing information on sulfate only. Nevertheless, satellite observations of aerosols as a whole are available. Here, we choose MODIS (Moderate-Resolution Imaging Spectroradiometer) aerosol optical depth (AOD), which provides data at the global scale. MODIS AOD is known as being a robust product and is used in the literature for global evaluation and aerosols assimilation in models (e.g., ). The model comparison with MODIS AOD provides an indirect evaluation for sulfate aerosols since AOD includes sulfate aerosols.

In order to evaluate the model against observation data, we use the fractional bias, the fractional gross error, the root mean square error and the correlation coefficient, following .

The fractional bias or modified normalized mean bias (MNMB) quantifies the mean between the modeled (f) and the observed (o) elements, for N observations. It ranges between -2 and 2 and varies symmetrically with respect to the under- and overestimation of the model. The definition is given by the following: 1MNMB=2N∑i=1Nfi-oifi+oi.

The fractional gross error (FGE) quantifies the model error. It is a positive variable ranging between 0 and 2. The definition is given by the following: 2FGE=2N∑i=1Nfi-oifi+oi.

The root mean square error (RMSE) is the square root of the average of the squared difference between each model and observation value. In other words, it represents a measure of the accuracy in absolute values, while FGE is relative. RMSE is a positive variable, and a value of 0 (almost never achieved in practice) would indicate a perfect fit to the data. The formula is given by the following: 3RMSE=1N∑i=1N(fi-oi)2.

The correlation coefficient (R) indicates whether the variations in the model and the observations are well matched and ranges between -1 and 1. The closer the score is to 0, the weaker the correlation is. The definition is given by the following: 4R=1N∑i=1N(fi-f‾)(oi-o‾)σfσo, where f‾ and o‾ are, respectively, the model and observations mean values, and σf and σo are the standard deviations from the modeled and observed time series.

For the evaluation of the simulations, OMI and the MODIS data set are mapped at the model resolution (1∘×1∘). The model grid points in the simulations corresponding to the filtered observation pixels (as explained in Sect.  and ) are also removed. A different validation strategy is applied, depending on the instrument.

Concerning OMI SO2 total columns, similarly to other SO2 satellite-derived products, their relative uncertainties are large where the signal is low, in particular for background conditions. This is why, in the literature, the SO2 satellite comparisons and the model evaluations focus on specific areas close to SO2 sources e.g.,. Similar to these studies, our strategy is to perform the model evaluation only in the vicinity of the volcanic sources. For each volcano, based on those referenced in , we select nine model grid points (representing a square of 3∘×3∘), with the middle point being where the volcano is located (see Fig. ). Altogether, it corresponds to 633 points. The mask is applied on each daily OMI SO2 total column measurements, and then we perform an annual average for each of the 633 data points. Similar to the abovementioned studies, the results are shown as scatterplots, and the statistical metrics used are the correlation coefficient and the RMSE.

In total, two methods are used in the evaluation strategy. First, we choose to evaluate the model SO2 total column against OMI Column_Amount_SO2 product. However, in order to test if the evaluation is sensitive to this choice, we use another approach which consists of an interpolation of OMI SO2 observations at the altitude where the volcanic emissions are injected in MOCAGE. To do so, we use the OMI products Column_Amount_SO2_PBL, Column_Amount_SO2_TRL and Column_Amount_SO2_TRM, hereafter renamed PBL, TRL and TRM, respectively. Depending on the altitude of the emissions in MOCAGE, either PBL and TRL or TRL and TRM are used for the interpolation.

Concerning the AODs, a spatial validation on the whole global domain is possible against MODIS products. The evaluation at the global scale enables us to quantify the overall aerosol changes in the simulations from the use of the updated inventory with respect to the previous one. Since noticeable changes are also expected at the local scale in the vicinity of the volcanoes, three zones are selected to complete the global-scale evaluation against MODIS. These zones are chosen from among the largest passive SO2 emitters in and are representative of different types of changes between and volcanic emissions inventories.

Zone 1 is centered over central Africa and is under the influence of Mount Nyiragongo and Nyamuragira (altitude of 2950 m). In , this volcano is not listed. In contrast, in , the passive degassing emission represents 2.29 Tg in 2013. No eruption is listed in for 2013.

Zone 2 is located in the northern Pacific Ocean around Hawaii. The volcano, based on the island, is Kīlauea (altitude of 1222 m). In the REF simulation, the volcano emissions in the inventory are 0.45 Tgyr-1 seventh rank of the most SO2-emitting volcanoes in. But, in , the Kīlauea emissions are updated, and it is the second-biggest emitter, with 2.17 Tg. In 2013, no eruptions are recorded in for this area.

Zone 3 is located in the Mediterranean region, under the influence of Mount Etna (altitude of 2711 m in the inventory) and Stromboli (altitude of 870 m in the inventory). In , 1.48 Tgyr-1 is emitted by Mount Etna (the biggest volcanic SO2-emitter referenced), 0.27 Tgyr-1 is emitted by Stromboli and also 0.02 Tgyr-1 by Vulcano. In , only 0.65 Tg of SO2 are emitted in 2013 in zone 3, corresponding to less than 0.04 Tg for Stromboli and 0.61 Tg for Mount Etna. Vulcano is not in the inventories. In 2013, small eruptions occurred at Mount Etna, totaling a little less than 0.06 Tg. Therefore, in the updated , volcanic emissions in zone 3 are weaker than in .

For the evaluation of the simulations against MODIS, the statistical metrics used are the MNMB, FGE and correlation coefficient. Because MNMB and FGE are dimensionless, they are meaningful in all geographical regions regardless of the magnitude of the aerosol column.

Figure a presents the scatterplots of MOCAGE SO2 columns in DUs (Dobson units) from the REF and CARNALTI simulations against OMI observations based on GOES-5 a priori profiles. Each of the points represents an average over the 2013 year. It shows that the previous version of the model (REF) was not good. The correlation coefficient is low (0.13). The bias is high, with a mean SO2 measured by OMI of 0.28 DU and of 0.11 in REF simulation. With the new volcanic inventory in the CARNALTI simulation, the mean SO2 concentration is similar to OMI retrievals (0.27). We can also clearly see an improvement of the model performances with a correlation increased up to 0.67.

To evaluate the impact of the choice of OMI product, we also show in Fig.  (bottom row) the scatterplot when applying the interpolation at the MOCAGE altitude where volcanic emissions are injected. This method provides higher OMI estimates and, therefore, increases the bias with MOCAGE simulations, but it improves the correlation. The conclusion is that the CARNALTI simulation provides by far better statistical results (bias, RMSE and correlation) than REF. The negative bias of MOCAGE CARNALTI with respect to OMI could be due to errors in the plume transport in the model linked to uncertainties in the meteorological inputs, to the limited number of model vertical levels, to the model chemistry and/or aerosol scheme or also to the uncertainties in the SO2 emission estimates from OMI in and in the OMI retrieval products used for the model evaluation.

The evaluation of MOCAGE performances against the OMI SO2 total column and MODIS AOD shows an improvement in the CARNALTI simulation compared to REF. The previous inventory lacks some volcanic sources, which leads to a global underestimation of sulfur dioxide concentrations and aerosol concentrations in the tropics (e.g., in zone 1). With the new inventory used in the CARNALTI simulation, volcanic emissions are larger. Even if in some areas the scores are deteriorated, e.g., in zone 2 where the model is already overestimating aerosol concentrations, the scores at the global scale and in the vicinity of most of the volcanoes are improved.

The global sulfur budget simulated in CARNALTI is shown in Table . Annually and globally averaged SO2 emissions, SO2 and sulfate aerosols burdens, as well as sulfur wet and dry depositions, are used to calculate the sulfur budget.

Volcanic emissions are 11.8 Tgyr-1. This estimation remains in the range of previous studies which estimated volcanic emissions to be between 7 and 14 Tg updated in , . However, due to lower anthropogenic emissions compared to those studies because of the recent year chosen (2013), the 15 % contribution from volcanic emissions to the total sulfur emissions in CARNALTI is higher.

The global SO2 burden is 0.30 Tg, similar to other studies whose values range from 0.2 to 0.52 Tg . In our simulation, 34.69 Tg S are directly removed by the dry and wet deposition of sulfur dioxide, representing a percentage of almost 43 %. Thus, the transformation rate of SO2 to sulfate is about 57 %, which is consistent with the studies reported above (from 50 % to 66 %).

The global vertical sulfate column is 0.70 Tg S, comparable with other studies, i.e., 0.53 Tg S in , 0.78 Tg S in , 0.81 Tg S in and 0.64 Tg S in .

These results confirm the nonlinear contribution of the different SO2 sources emissions to the sulfate burden. Indeed, volcanic sources represent almost 15 % of the total SO2 emitted into the atmosphere, but they contribute 25 % to the sulfate burden. The transformation of SO2 into sulfate from the other sources is not as efficient. We can note a higher efficiency for the volcanic sources, at around 1.75, compared to the other sources, at 0.87.

The total sulfur deposition is around 82 Tg S, including 35 Tg S of SO2, a little less than the total sulfur deposition in of 94 Tg S, and also including 22 Tg S of SO2. The difference comes from the aerosol deposition which depends on the deposition scheme and the meteorological fields, which can vary depending on the considered time period. In our study, the sulfur deposition is mainly wet deposition. Precisely, the partitions of each deposition flux are 55 % for wet deposition, 35 % for dry deposition and 10 % from sedimentation. But sulfur deposition due to volcanic emissions is weaker than for the other sources, i.e., 35 % for wet deposition, 24 % for sulfate aerosol sedimentation and only 5 % for dry deposition. Due to the higher altitude of injection, the atmospheric residence time for volcanic sulfur species is longer, and the deposition rate is lower, especially for the dry deposition. Even though there is a lower contribution, we still note the strong contribution of volcanoes to wet deposition and sedimentation, which is much greater than the contribution to the emissions.

Figure  shows the global and annually averaged vertical profiles for sulfur dioxide and sulfate concentrations for 2013. Anthropogenic and volcanic sources are separated to highlight the main differences between them.

Non-volcanic SO2 dominates the entire vertical column, with a maximum at the surface linked to anthropogenic emissions emitted at the model surface. On the contrary, the vertical distribution from volcanic SO2 shows variations. There is no contribution below 950 hPa, but there are three maxima above, i.e., one at 850 hPa (about 1500 m), due mostly to passive degassing, another around 680 hPa (about 3300 m), due to passive degassing from high-altitude volcanoes and eruptions, and the last one around 450 hPa (about 6000 m), due to high-altitude eruptions. It is noteworthy that, even with few eruptive events during the year 2013, the volcanic SO2 vertical distribution is affected by them.

Concerning sulfate aerosols, volcanic emissions are also not dominant over the entire vertical column. Non-volcanic sulfate aerosol have the highest values, around 950 hPa, near the surface. For volcanic sulfate, the maximum is between 850 and 450 hPa but 4 times smaller than for other sources and without any specific peak associated to passive degassing or eruptive emissions. These results are different from , which shows that the vertical distribution of volcanic sulfate aerosols is comparable to anthropogenic and biomass burning sulfate and is even dominant between 800 and 300 hPa (the altitude of volcanic emissions, mainly from eruption). This difference between our study and can be explained by the quantity of SO2 emitted by eruptions. In 2013, only a few eruptive events occurred, while almost 30 % of volcanic emissions in are eruptive. Therefore, with a greater volume of volcanic emissions injected at higher altitude in , the potential to form sulfate aerosols is greater than in our study. This can explain the greater efficiency of 2.63 in the tropospheric sulfate burden in compared to 1.75 in our study.

Figure a represents the annual zonal mean sulfate concentration. Most of the sulfate aerosols reside in the Northern Hemisphere (between 15 and 30∘ N) due to anthropogenic influence, and the highest values are around 800 hPa. The sulfate concentrations due to volcanic emissions (Fig. b) are located at higher altitudes. On both sides of the Equator, volcanic sulfate is found between 900 and 650 hPa. Over the tropical region, the volcanoes' contribution to the sulfate aerosol concentrations is larger, with a maximum of 50 %–60 % around 650 hPa (see Fig. c). We also notice that sulfate aerosols are transported by the general atmospheric circulation, up to the UTLS (upper troposphere lower stratosphere) and even into the stratosphere and from the Equator to the poles, especially in the Southern Hemisphere where there are more volcanoes.

The volcanic contribution to the global surface SO2 concentrations is relatively low, around 2 %, but it is much higher close to the source points (see the top of Fig.  for SO2). This is mainly due to the high altitude of emissions from volcanoes. Similarly, Fig.  (bottom for sulfate aerosol) shows a greater influence of volcanic emissions on the sulfate aerosol concentration at the surface, which is almost larger than other sources in the vicinity of volcanoes. Globally, the mean contribution is of 10 %, but with a rather low, almost zero, contribution over continental areas in the Northern Hemisphere. Considering that, within the boundary layer, anthropogenic SO2 emissions are dominant, the sulfate aerosols formed in this environment come largely from anthropogenic rather than from other sources. However, in areas with small anthropogenic sources (Indonesia, Hawaii and central Africa), the volcanic contribution is large.

For the total column, volcanic emissions contribute a great to the sulfur species burden, i.e., 12 % to SO2 and 19 % to sulfate aerosols. In Fig. , we can see that the highest sulfate burden is located over polluted areas (eastern North America, Europe, the Middle East, India and China) and near some volcanoes and particularly over oceanic volcanoes. By looking at the volcanic contribution, we note that the sulfate aerosols due to volcanic emissions are mainly distributed over the oceanic environment in the tropics (also corresponding to volcanoes of lower altitudes). The highest contribution, 85 %, is found over Indonesia.

The annual global depositions of sulfur species due to volcanic emissions are 23 %, 11 % and 10 % for wet deposition, dry deposition and sedimentation, respectively. Figure  represents the total sulfur deposition at the global scale and shows higher deposition fluxes over anthropogenic polluted areas, where volcanic contribution is low (see Fig. b). The only exception, where there are a high deposition flux and a high volcanic contribution, is Indonesia. Details on the proportion of each type of deposition (wet, dry and sedimentation) are shown in Fig. S5, where we notice a weak influence of sedimentation, consistent with Table , compared to wet and dry depositions.

In total, three additional simulations are conducted to analyze the sensitivity of the MOCAGE model to the uncertainty of volcanic passive emissions. The first one, named CA_MIN, takes into account, for each volcano, the lowest estimation of SO2 emissions. In other words, for each volcano, we remove the annual emission uncertainty to the annual mean emission as follows: EV,Y=EV,Y‾-UV,Y. In contrast, the second simulation, named CA_MAX, takes into account the highest estimation of SO2 emission; we add the annual emission uncertainty to the annual mean emission as follows: EV,Y=EV,Y‾+UV,Y. Thus, both CA_MIN and CA_MAX experiments do not have daily variations due to passive degassing but only due to eruptions. For the last one, named CA_RAND, emissions are randomly determined on a daily basis within the annual emission uncertainty interval, [EV,Y‾-UV,Y,EV,Y‾+UV,Y], following a continuous uniform distribution. Thus, daily variations are not only due to eruptions but also to passive degassing, as expected in reality. The reference simulation used, CARNALTI, is called CA from now on.

Figure  presents the 2013 temporal evolution of SO2 total emission for each simulation. As in Fig. , we note the annual variation due to anthropogenic emissions, representing a common basis of around 70 TgSyr-1 for all simulations, as well as the daily variation due to eruptions, which is shown by the large peaks and representing a value of 0.10 Tg S in 2013. Therefore, the differences are only due to passive degassing SO2 emissions. In the CA simulation, the annual total passive degassing emission is 11.74 Tg S. In the CA_MIN, CA_MAX and CA_RAND experiments, it is 10.60, 12.95 and 11.75 Tg S, respectively. Thus, there is a relative difference of 10.6 % with respect to the annual mean volcanic emissions for CA_MIN simulation but a difference of 1.4 % when considering all sulfur emissions. Similarly, volcanic emissions in CA_MAX and CA_RAND simulations are 9.3 % and 0.1 % higher than in CA, which represents a difference of 1.5 % and <0.01 %, respectively, with respect to the total sulfur emissions.

We expect a greater sensitivity to the annual emission uncertainty at volcanoes where the proportion of the annual uncertainty with respect to the annual mean emission is close to 100 %. Figure  represents the percentage of uncertainty on the annual measurement of volcanic emission per volcano in . The darker and bigger the circle is, the more important is the uncertainty compared to the mean emission.

As in Table  for CA, Table  presents the annual mean global sulfur budget for the CA_MIN, CA_MAX and CA_RAND simulations. Even if the total sulfur species burdens are similar in all simulations, with the SO2 burden around 30 Tg S and the sulfate burden between 0.69–0.72 Tg S, the contribution of the volcanic emissions to the total budget varies. In the CA experiment, the volcanic contribution to the sulfate aerosol burden is 25.40 %, but it ranges from 23.73 % in the CA_MIN experiment to 27.15 % in the CA_MAX experiment. This implies a variation in the efficiency of the model MOCAGE in producing sulfate aerosols from volcanic SO2 emissions. The greatest efficiency score is 1.78 for the CA_MIN simulation, meaning that smaller amounts of SO2 emitted can form sulfate more efficiently. This illustrates the nonlinear relationship between the volcanic SO2 emission and the sulfur budget.

Figure  illustrates the spatial difference in volcanic SO2 contribution between CA and CA_MIN, CA_MAX and CA_RAND. The differences with CA_MIN or CA_MAX (Fig. a and b) are similar but of the opposite sign. As expected, differences are located in the vicinity of volcanic point sources but especially near volcanoes with a high UV,Y/EV,Y‾ ratio (see Fig. ).

The contribution of volcanic SO2 to the SO2 burden is larger (less important, respectively) in the CA_MAX simulation, with 19.19 % (the CA_MIN simulation, respectively, with 15.69 %), than in the CA simulation, with 17.40 %. The difference between CA and CA_RAND is weaker. Daily variations in SO2 emissions of volcanoes (CA_RAND) do not significantly change the annual mean contribution of the volcanic SO2 tropospheric column. The same conclusions are shown in Fig. S6 for the sulfate tropospheric column.

The differences between the simulations are mostly in the deposition fluxes. Regardless of the sensitivity simulation, the dry sulfur deposition is higher than in the CA simulation. The sulfur wet deposition is 43.90 Tg in the CA simulation but 43.92, 44.65 and 45.41 Tg in the CA_MIN, CA_ALEA and CA_MAX simulations, respectively. It represents a contribution of 33.00 % for CA and 33.03 %, 34.13 % and 35.25 % for CA_MIN, CA_MAX and CA_RAND, respectively. On the contrary, regardless of the sensitivity simulation, the sulfur dry deposition is lower than in the CA simulation. In the CA simulation, the dry deposition is 29.34 Tg (representing a volcanic contribution of 4.80 %), but the dry deposition is 29.34 (4.80 %), 29.17 (4.27 %) and 29.02 Tg (3.78 %) in CA_MAX, CA_ALEA and CA_MIN simulations, respectively. Sedimentation (only due to aerosols) behaves in the expected way; the more volcanic emissions there are, the more sulfur is deposited by sedimentation. The variations in deposition are, thus, due to variations in the deposition of sulfur gases and, more particularly, of SO2. To conclude, sulfur deposition does not react linearly to both the quantities of volcanic SO2 emitted (with respect to CA_MIN and CA_MAX simulations) or to the temporal variability in these emissions (with respect to CA_RAND).

Finally, in the CA_MAX experiment, with the highest estimation of volcanic emissions, we find, as expected, a higher sulfur burden and higher sulfur deposition quantities. However, the CA_MIN simulation assumes the lowest estimate of volcanic SO2 emissions and gives only a slightly lower total sulfur deposition (81.13 compared to 81.60 Tg S in CA) but with a different partition. Even when applying a daily variation, with nearly the same total annual quantity of volcanic SO2 emitted (the CA_RAND simulation), we notice slight changes in the MOCAGE sulfur budget.