Mineral dust aerosol was modelled via the Dust Entrainment and Deposition model (DEAD; Zender et al., 2003), which was previously updated to include the brittle fragmentation theory of vertical dust flux (Kok, 2011) on mineral size fractions (Albani et al., 2014; Scanza et al., 2015). We further improved the emissions of dust in MAM to follow a physically based vertical flux theory (Kok et al., 2014a), which has been shown to significantly improve dust emissions (Kok et al., 2014b). Note that this method allowed for the removal of the soil erodibility map approach previously employed by the DEAD scheme (Table 1) and still provided more accurate simulations of regional dust emissions and concentrations (Kok et al., 2014b). Dust aerosol optical depth (AOD) was calculated using mineralogy-based radiation interactions as described by Scanza et al. (2015). Dust emissions were tuned such that a global annual mean dust AOD of ∼0.03 was attained, as recommended by Ridley et al. (2016) and matching values in Scanza et al. (2015) for a similar model configuration.

Dust mineralogy in MIMI is designed to be comprised of eight separate transported tracers: illite, kaolinite, montmorillonite, hematite, quartz, calcite, feldspar, and gypsum (Scanza et al., 2015). Mineral soil distributions were supplied offline (Claquin et al., 1999) with the emission of each dust mineral species further refined following the brittle fragmentation theory (Scanza et al., 2015).

The simulated life cycle of iron can be grouped into three main stages: (1) iron emission to the atmosphere, (2) physical–chemical iron processing during transport, and (3) final iron deposition and thus loss from the atmosphere. In the following sections, we describe the emissions and subsequent atmospheric dissolution of iron (stages 1 and 2), while the effects of this on the magnitude of oceanic soluble iron deposition (stage 3) in MIMI are examined and compared to BAM-Fe in Sect. 4.

Iron optical properties are currently considered to reflect those of hematite because this mineral contains 97 % of the iron aerosol mass fraction (see Sect. 2.3.1).

MIMI contains three major iron emission sources: mineral dust, fires (defined here as the sum of wildfires and human-mediated biomass burning), and anthropogenic combustion (defined here as the sum of industrial and domestic biofuel burning). In the BAM-Fe version of the model, fire and anthropogenic combustion emissions were combined into a single static monthly mean value. In MIMI, fire emissions of iron were updated to be distinct from other pyrogenic iron sources and were parameterized to track the BC emissions from fires using an Fe : BC ratio. Fire BC emissions were simulated to be time varying on a monthly scale, resulting in a much more pronounced seasonality to fire iron emissions (e.g. Giglio et al., 2013) compared to BAM-Fe wherein seasonality was not imposed.

For all iron species in each mode, the aerosol number emissions (Feemit,num) were calculated from the mass emissions within the same mode (Feemit,mass) using the properties in Table 2 and following Liu et al. (2012): 1Feemit,num=Feemit,massπ6×ρ×Demit3.

An ocean deposition source apportionment sub-study was designed to classify ocean deposition regions according to the dominant atmospheric soluble iron source, rather than ocean basins defined from a more traditional physical oceanographic viewpoint (e.g. Gregg et al., 2003). By incorporating recent model estimates for dust and the importance of pyrogenic iron emissions (Luo et al., 2008; Matsui et al., 2018) the seven large-scale source regions defined in Mahowald et al. (2008) were modified slightly to separate the major dust iron source regions from fire and anthropogenic combustion iron source regions. This resulted in a total of 10 iron emission source regions (Fig. 1; see also Table S1 for details).

Simulations in the source apportionment study used BAM-Fe, as described in Scanza et al. (2018), with slight modification. Briefly, anthropogenic combustion iron emissions were increased by a uniform factor of 5, and iron from fires followed the updated Fe : BC ratio (Table 4) and seasonal variability in the fire BC emissions, all as per MIMI. Aerosols were externally mixed in BAM, and therefore altering the regional aerosol loading did not affect aerosol transport or deposition in the more significant way it could in MAM, in which aerosols are internally mixed. This information was then used in Sect. 4.3 to compare differences in the daily mean deposition of soluble iron between the BAM-Fe and MIMI models within each defined ocean region.

Comparison of dust AOD with regional dust AOD observations (Fig. 2) from the AERONET observational datasets (Holben et al., 1998), as subsampled in Albani et al. (2014), shows good agreement globally (correlation: r2=0.64). This results in MAM annual global mean emissions of 3250±77 Tg dust a-1 (Aitken 16 Tg a-1, accumulation 36 Tg a-1, coarse 3198 Tg a-1), which is at the higher end of literature estimates of ∼500–4000 Tg dust a-1 (Bullard et al., 2016; Huneeus et al., 2011; Kok et al., 2017). Dust emissions in MAM are 84±4 % higher than our previous mean of 1768 Tg dust a-1 in BAM (Scanza et al., 2018) because dust lifetime has proportionally decreased (Table S2), which affects coarse-mode dust aerosol (wherein 98 %–99 % of total dust mass is emitted) more than fine-mode dust aerosol. Globally, both dust concentrations (correlation: r2=0.89) and deposition (correlation: r2=0.83) are simulated well compared to observations within MIMI. A higher correlation of modelled dust concentrations with observations is calculated in the Northern Hemisphere (NH; r2=0.89) compared to the Southern Hemisphere (SH; r2=0.67), but the gradient of the line of best fit is further from 1 : 1 (NH: 1.22 vs. SH: 1.07). Conversely, for dust deposition a lower correlation with observations is simulated in the NH (r2=0.75) compared to the SH (r2=0.60) but with a gradient of the line of best fit closer to 1 : 1 (NH: 1.07 vs. SH: 0.72). Overall, the results presented in this study suggest an improvement on previous dust modelling complications related to underestimating dust deposition when tuned to dust concentration (Huneeus et al., 2011).

Including the parametrization of Kok et al. (2014a) removes the requirement of a soil erodibility map (Table 1). In addition, in previous versions of the model, high-latitude dust sources were zeroed because there were no observations at that time to support high-latitude sources of dust (Albani et al., 2014). However, more recent observations have suggested that high-latitude dust sources do exist (Bullard et al., 2016; Crusius et al., 2011; Tobo et al., 2019), often related to glacial processes (Bullard, 2017) with a higher fraction of bioavailable iron relative to lower-latitude dust sources (Shoenfelt et al., 2017). Thus, for the new version of the model we have allowed for the inclusion of high-latitude dust sources (Fig. 3). In general, aerosol dust and iron concentrations peak closest to the coastlines and during summer. Emissions of dust from >50∘ N are ∼1.3±0.2 % of the global dust total, which is half of the estimates derived from field and satellite data at 2 %–3 % of the global total (Bullard, 2017; Bullard et al., 2016). However, the resulting magnitude and seasonality of dust concentrations have been shown in a recent study to be consistent with observed measurements from Svalbard (Tobo et al., 2019).

There are several propositions explaining sources of soluble iron and the inverse relationship between total iron amount and iron solubility (Sholkovitz et al., 2012). While total iron mass concentrations are dominated by desert dust sources, soluble iron can be a product of mineral dust processed in the atmosphere or emitted from pyrogenic sources (Chuang et al., 2005; Guieu et al., 2005; Ito et al., 2019; Luo et al., 2008; Meskhidze et al., 2003; Schroth et al., 2009). Previous studies have shown that either of these can explain the inverse relationship and that the spatial distribution of data is required to provide more information (Mahowald et al., 2018). Therefore, we explored how to best use the spatial data to compare with the model results. The 5-year (2007 to 2011) mean iron concentration from MIMI is compared to an extensive dataset of observations of total iron and its fractional solubility (Fig. 4). The model captures the global mean observational total iron concentration well; however, relatively low regional correlations (r2<0.4) occur in the south Indian (r2=0.0), South Atlantic (r2=0.34), North American (r2=0.35), and high-latitude (r2=0.06) ocean regions, suggesting that future model improvements can be focused here.

In the absence of iron atmospheric process modelling, ocean biogeochemistry models with an iron component (e.g. Aumont et al., 2015; Moore et al., 2004) have estimated iron solubility from offline dust modelling by means of an assumption that it contains 3.5 % iron by weight, of which 2 % is soluble. Iron solubility is highly temporally and spatially variable, however, and in the absence of spatial atmospheric emission information, pyrogenic iron sources, and atmospheric processing of iron, an estimate of 2 % solubility leads to underestimates of observed iron solubility in nearly all HNLC ocean regions (Fig. 4).

Aggregating observations onto a lower-resolution grid (sometimes termed super-obbing) compared with the model can help reduce the representation error when comparing with such limited observations (Schutgens et al., 2017). Fig. 5 uses an observational resolution one-third that of the model, and the model-to-observation comparison of the mean state is thus improved. Persistent observation-based features of the local environment become more obvious, while less frequent ones conversely diminish. At this observational resolution, the low total iron concentrations in the North Atlantic ∼30∘ N, as seen in Fig. 4, are perhaps not a common feature, and the model much more precisely represents the climatological state here than Fig. 4 might suggest. However, examining the North Pacific reveals that the model imprecisely represents the mean state here. Potential missing iron sources in remote regions, such as the North Pacific, include the following: (1) shipping emissions (Ito, 2013), which have a high soluble iron content from oil combustion (Schroth et al., 2009); (2) volcanic emissions, which provide a localized “fertilizer” to the surface ocean owing to the macronutrients and trace metal nutrients contained within them (Achterberg et al., 2013; Langmann et al., 2010; Rogan et al., 2016); and (3) low Asian and South American aerosol concentrations, either through underrepresenting combustion emission sources (Matsui et al., 2018) or in the transport and deposition of aerosol within these regions (Wu et al., 2018). These are discussed in more detail in Sect. 5.1 and 5.2.

In terms of iron solubility (soluble iron concentration / total iron concentration), the model is not capturing the observational mean state in many regions (Fig. 5). A detailed examination of the observation point at 18∘ N and 330∘ E (anomalous green point surrounded by blue points in the North African outflow plume in Fig. 4) and the nine model grid cells co-located with it in Fig. 6 shows how a single high observation (155 % percent solubility) is causing a representation issue (see also Sect. 4.3 regarding soluble iron deposition). Both model and observation histogram distributions are similar, as are the median (model: 1.8, observation: 0.9) and geometric mean (model: 2.1, observation: 1.3) values. However, the arithmetic means are not similar (model: 2.5, observation: 9.6) and while a high observation value of 155 % is likely to be an outlier and should be at most 100 %, it still informs us about what is possible, and simply discounting it (even at an adjusted 100 %) would require strong justification. It is therefore advisable to instead alter the estimator of the average. Comparing model to observation differences calculated using the median or geometric mean reveals that they are similar in magnitude, as one would expect for log-normally distributed data (Fig. 6 insert). Although the median is robust with respect to outliers, the model results may not exhibit a uniform Gaussian distribution (Fig. 6 insert; solid compared to dashed lines), and often the number of available observations is also low (Fig. 7), suggesting that its use also requires careful consideration. An equivalent methodology to the geometric mean in Fig. 7 would be to first log transform the data before calculating the arithmetic mean. Arguments pertaining to the appropriate methodology for comparing model results to temporally limited observations extend beyond the iron aerosol examination in this study to all aerosol comparisons with limited observations.

It is interesting to note the effect that the order of operations (taking the average of ratios compared to the ratio of averages) has when calculating iron solubility (Fig. 8). Throughout this study, the percent of iron solubility was calculated at each model time step (30 min) and then the daily mean output was analysed (online; Eq. 6) at an annual or 5-year mean time resolution. It is also acceptable to use the simulated soluble and total iron concentrations to generate the annual or 5-year mean iron solubility in a post-processing step (offline; Eq. 7). The resulting differences between methods are not insignificant (Fig. 8); however, the offline method creates a distribution in which low iron solubility is generally lower and the highest (>18 %) iron solubilities are generally higher. Overall, the global annual mean iron solubility calculated online is one-third (34 %; NH = 40 %, SH = 29 %) higher than when calculated offline.

The average relative Z score (Eqs. 8 and 9) is around zero for most model grid cells (Fig. 9), indicating that they mostly followed similar temporal and relative magnitude trends. However, even if the average relative Z scores are around zero and the ratio of relative standard deviations is around one, the ratio of online- to offline-calculated iron solubility is most likely >1. Temporal differences in the soluble and total iron concentration might therefore be controlling the overall solubility at each model grid cell. We also find that the ratio of online and offline solubility is >1 for most of the cases when the ratio of the relative standard deviations of soluble and total iron is <1 (Fig. S2), indicating that the differences in both methods of iron solubility calculation are sensitive to the differences in the relative size of the tails of the distribution. That is, if soluble iron has narrower tails compared to total iron at any grid cell, it is highly likely that a higher solubility will be obtained in the online method compared to offline. The extreme ratio of the tails of soluble and total iron is only found in specific regions with the highest temporal variability in emissions and modelled solubilization of insoluble iron (Fig. S2).

Field measurements have generally suggested an inverse relationship between total and soluble iron concentrations (Myriokefalitakis et al., 2018). This means that high total iron concentrations are generally accompanied by low soluble iron concentrations and vice versa. By assuming that the field measurements faithfully represented the actual average values of soluble and total iron concentration at those locations, we implicitly assume that all the measurements have a Z score of zero. In Fig. 9 we show that this is not the case with the modelled results, and the two variables can be relatively farther from their respective means even when averaged over the modelled time period.

The sensitivity of a result to the order of operations extends beyond iron solubility to any variable that is calculated in a similar manner, and current multi-model intercomparison project (MIP) protocols do not explicitly account for this. However, the effects of outliers, in both online and offline methods, can be reduced by employing the geometric mean and has been used in some MIPs (e.g. Mann et al., 2014). It will also be important to consider differences in the solubility of iron induced by the choice of the order of operations as ocean biogeochemical models move away from using offline results from global climate or chemistry transport models to online results within Earth system models, which are designed to couple the two components at each time step. For short-term interactions between deposited iron and ocean biota, shorter-term averaging may be more important (e.g. Guieu et al., 2014), but for the long-term accumulation of iron that is (re)cycling in the oceans, the longer-term average may be more appropriate (Moore et al., 2013). One should be aware, however, that iron is readily removed from the ocean mixed layer, and thus the lifetime of iron may well be short enough for the online calculation to be more appropriate much of the time (Guieu et al., 2014).

Globally averaged emissions of dust (3200 Tg a-1) and its iron component (126 Tg a-1) are within the current multi-model range (Table 7). The simulated annual mean iron in dust percentage is 4.1 %, with the highest percent occurring in the coarse mode at 6.5 % and the lowest percent occurring in the Aitken mode at 1.1 %. Accounting for dust mineralogy therefore increases the global mean iron percent by weight above the currently well-used global mean estimate of 3.5 % (e.g. Jickells et al., 2005; Shi et al., 2012).

Compared to BAM-Fe, MIMI dust emissions are ∼80 % higher and the iron it contains is ∼120 % higher (Table 7). Although both the BAM-Fe and MIMI models are globally tuned to a similar dust AOD (∼0.03) and based within the same host model (CESM), changing from a bulk aerosol scheme (e.g. Albani et al., 2014; Scanza et al., 2015) to a modal aerosol scheme reduces the aerosol lifetime significantly (Liu et al., 2012 and Table S2). The spatial distribution of dust emissions is also different following the move to the Kok et al. (2014a, b) parameterization (Table 1), resulting in the spatial distribution of dust AOD also being altered (Fig. S3). Total pyrogenic iron emissions (sum of fires and anthropogenic combustion activity) in MIMI are higher than previous estimates by a factor of between 2 and 3 (Table 7), reflecting the growing evidence that they have been previously underestimated (Conway et al., 2019; Ito et al., 2019; Matsui et al., 2018).

There is a much lower aerosol pH in the fine aerosol modes (Aitken and accumulation) in MIMI compared to that in BAM-Fe (Fig. 10). This is due to a combination of resolving pH in each aerosol size mode in MIMI and the subsequent lowering of the pH value (1) being applied in the two fine aerosol modes (Aitken and accumulation). Conversely, dust dominating the coarse aerosol mode provides more of an opportunity for [calcite] > [SO4] in this aerosol size fraction, resulting in most continental areas having a high coarse-mode aerosol pH in MIMI compared with the higher pH being much more localized to the major desert regions in BAM-Fe. Acidic processing of iron in MIMI therefore proceeds faster globally in the fine-sized aerosol modes (Aitken and accumulation) compared to the BAM-Fe fine-sized bin (0.1–1 µm), but it is generally slower over continental regions in the coarse mode than in BAM-Fe coarse-sized bins (1–10 µm).

Comparison of Fig. 10 to modelled pH estimates by Myriokefalitakis et al. (2015) shows generally good agreement in the NH, but in the SH MIMI simulates less acidic coarse-mode aerosol over continental regions and more acidic aerosol over marine regions. As iron models are unable to capture the high observed iron solubility (>10 %) over SH marine regions (Myriokefalitakis et al., 2018) and in the absence of remote pH aerosol observations, we suggest that our basic parameterization captures an aerosol pH which is suitable for use in Earth system models

Model physics, and hence simulated cloud cover, are significantly different between CAM4 and CAM5. Figure 11a shows the relative model difference in the oxalate distribution between MIMI, which also includes an increase in the tuning factor by an order of magnitude (from 15 to 150; Table 5), and BAM-Fe by normalizing by the simulated cloud fraction in each model. The effect of oxalate on iron dissolution is therefore larger in MIMI over extratropical ocean regions, where iron models underrepresent solubility (Myriokefalitakis et al., 2018), and land regions which are dense in tropical vegetation or industry (both centres of large aerosol precursor gas emissions). Compared to observations (Myriokefalitakis et al., 2011; Table S3) modelled oxalate concentrations are well represented at high observed concentrations but are biased low when observed concentrations are low (Fig. 11b). The low model bias is stronger within remote observational regions (marine vs. urban observation sites), suggesting that the removal of secondary organic aerosol may be too strong within the model and/or that there is a missing marine aerosol precursor gas emission source (Facchini et al., 2008; O'Dowd and de Leeuw, 2007) in this model which significantly lowers simulated secondary organic aerosol, and thus oxalate, concentrations.

Comparison of mineral dust and pyrogenic sources of modelled soluble iron (sum of emissions and atmospheric dissolution; Fig. 12) with the four iron models (including BAM-Fe) reported by Myriokefalitakis et al. (2018) shows that the spatial distribution in MIMI is broadly similar for most regions of the world. A notable difference exists in the North Pacific region, where the soluble iron source in MIMI is lower than all other iron models, similar to total iron concentrations when compared to observations (Figs. 4 and 5). Future development of MIMI should thus be focused on the North Pacific, including the addition of shipping soluble iron emissions, which are relatively concentrated in this region (Ito, 2013). An improvement for MIMI can be seen over the Atlantic region directly downwind of Saharan soluble iron sources. In general, iron models are overrepresenting iron solubility close to dust sources compared to observations (Myriokefalitakis et al., 2018), and in order for BAM-Fe to reach better agreement with observed iron solubility in this region dust emissions of soluble iron had to be scaled downwards (Conway et al., 2019). We suggest that this improvement is linked to the improved modal representation of aerosol pH in MIMI (Fig. 10).

Similar to the previous study by Scanza et al. (2018), we report the amount of total and soluble iron deposited in each of the major ocean basins (Table 8) as defined by Gregg et al. (2003). We find that in MIMI the amount of total iron deposited to all ocean basins is approximately double that estimated in BAM-Fe (26 vs. 12 Tg Fe a-1, respectively), while soluble iron deposition is similar (∼ 0.5 Tg Fe a-1 in both models). The larger mineral dust emission flux in MIMI (3200 Tg dust a-1 compared to BAM-Fe dust emissions of 1800 Tg dust a-1) is driving most of the increases in total iron deposition because it is the primary iron source (Table 7). In general, the magnitude of soluble iron deposition to the oceans is more evenly distributed across hemispheres in MIMI owing to a major reduction (approximately one-half) in the equatorial north–central Atlantic basin deposition flux and increases to SH ocean deposition fluxes of a factor of 2 to 4. In MAM4 dust is treated as internally mixed aerosol with sea salt, leading to higher rates of wet deposition than when dust is externally mixed aerosol (Liu et al., 2012) as it is in CAM4. The internally mixed treatment of dust aerosol in MAM4 is thus an important factor leading to the lower simulated dust lifetime when compared to BAM-Fe (Table S2). Over the north–central Atlantic region, the combination of a lower soluble iron source (Fig. 12 compared to Fig. S4b by Myriokefalitakis et al., 2018), dust atmospheric lifetime (Table S2), lower aerosol pH (Fig. 10), and lower relative organic ligand processing (Fig. 11) will all work towards reducing the magnitude of atmospheric soluble iron deposition flux in MAM4 compared to BAM-Fe. There are significant increases in anthropogenic combustion iron deposition in all equatorial and NH ocean basins driven by the fivefold increase in combustion emissions implemented in MIMI. The percent contribution from pyrogenic iron to total iron deposition between MIMI and BAM-Fe is, however, more similar for all northern and equatorial oceanic regions than southern oceanic regions. Beyond the correction to anthropogenic combustion emissions, which are NH dominated, this could be due to differences in the emissions of both dust and fire aerosol, structural differences between models relating to the aerosol size and composition, which alters aerosol deposition rates, or a lower soluble iron source (Fig. 12); it is most likely to be a combination of all three.

The fraction of fire aerosol which is injected above the boundary layer is crucial for determining its capacity for long-range transport (e.g. Turquety et al., 2007). Vertically distributing fire iron emissions in MIMI, as compared to emitting all iron from fires at the surface as in BAM-Fe, increases the long-range transport of iron aerosol to remote ocean regions (Fig. 13). In general, vertically distributing fire emissions results in small increases in soluble iron deposition (between 0 % and 20 %) in SH ocean regions and a larger increase (between 20 % and 40 %) in NH oceans, with converse lower land deposition close to the major regions of fire activity. The exception is in the sub-Arctic North Pacific, an HNLC region, where iron deposition from fires significantly increased until it was more than double that when surface fire emissions are used.

The dry deposition flux is sensitive to aerosol properties, surface roughness, and modelled turbulence. Although increasing the vertical resolution has been shown to increase surface PM10 concentration (Menut et al., 2013) and better simulate the dust vertical profile (Teixeira et al., 2016), it is not yet clear if this would correspondingly increase the dry deposition flux.

Downwind of significant mineral dust sources iron models generally overestimate the observed amount of total iron (Myriokefalitakis et al., 2018), and soluble iron comparisons are highly sensitive to the assumed initial solubility of mineral dust iron at emission (Conway et al., 2019). Conversely, in remote ocean regions, improving the representation of combustion emissions has been shown to be a necessary step towards more accurate representations of observed high iron solubilities at low iron concentrations (Ito et al., 2019).

An examination of aerosol dry deposition in CAM5 by Wu et al. (2018) showed that the deposition velocity for Aitken- and accumulation-sized BC particles is potentially an order of magnitude too high. It is highly likely that this will also be the case for dust. As the largest discrepancies between models and observations are in remote ocean regions, improving the model long-range transport of iron by investigating deposition rates is an important constraint to be applied to the model.