The soil map of the world used in this study comes from the Food and Agriculture Organization (FAO) of the United Nations soils data set and includes 136 soil units from the FAO–United Nations Educational, Scientific, and Cultural Organization (FAO-UNESCO, 1995) at a 5 min resolution. The global data set of soil clay and silt data are used in this study. Following Claquin et al. (1999) and Nickovic et al. (2012), the illite, hematite, kaolinite, smectite, quartz, feldspars, calcite and gypsum contents are specified for different clay and silt soil types, and the global mineral distribution is presented in Scanza et al. (2015). Some minerals found in dust such as dolomite were not considered by Claquin et al. (1999) and Nickovic et al. (2012) and have also been disregarded in this study due to the lack of data on their distribution.

The elemental compositions of hematite and aluminosilicate minerals used in this study are taken from previous works (Journet et al., 2008, and unpublished data provided by E. Journet, 2012) and were obtained by X-ray fluorescence spectrometry (XRF; Table 1a). Most of the minerals used by Journet et al. (2008) are reference materials from the Clay Minerals Society's Source Clays Repository, i.e., hematite, illite, kaolinite, and montmorillonite. The elemental compositions obtained by XRF are in the range of published values for these reference materials (e.g., Mermut and Cano, 2001; Gold et al., 1983), validating the obtained composition for the unreferenced materials. Moreover, the purity of all mineral samples is estimated by X-ray diffraction. Note that the mineralogical maps used in this study do not distinguish feldspar and smectite subtypes. For feldspars, the elemental composition is mostly averaged based on two subtype minerals: orthoclase (potassic feldspar) and oligoclase (sodium-calcium feldspar). For smectites, the montmorillonite subtype is the most commonly identified smectite in desert dust, particularly for Saharan dust (e.g., Goudie and Middleton, 2006). The chemical composition of montmorillonite is used in this study as an analog for smectite. For calcite, gypsum, and quartz, the natural minerals could contain substitutions or impurities from clays, which are variable depending on origin, formation, contamination, etc., of minerals. Because regional silt samples were not available for spectroscopy, we use the theoretical composition of elements in calcite, gypsum and quartz (Table 1a). The mass fractions of Ca in calcite (CaCO3) and gypsum (CaSO4 × 2H2O) are taken as 40 and 23.3 %, respectively. A mass fraction of 46.7 % Si is used for pure quartz (SiO2).

Following the total element calculation, soluble elemental fractions are estimated based on soluble elemental contents of minerals at pH = 2 reported by Journet et al. (2008) for hematite and the aluminosilicates and are listed in Table 1b. The fractional solubility of Ca used in calcite and gypsum was 7 and 0.56 %, respectively, and that of Si in quartz was 0.0003 % based on the individual solubility product (Ksp) at pH = 2 (Petrucci et al., 2011). Here the mineral-dependent method used to calculate soluble elements is defined as Method 1 (Sol-1). To present uncertainties, another approach (Method 2, defined as Sol-2) is introduced as a reference. It is based on the extractable elemental fractions of in situ 20 µm sieved soil samples reported by Sillanpää (1982; Table S1 in the Supplement) and is combined with an FAO soil data set to get a global soluble elemental inventory independent of soil minerals. It is noted that there is no detailed size distribution for soil samples in Sol-2. Thus, the fractions of soluble elements in clay and silt are assumed to be equal to those of the bulk soils themselves.

One drawback of our approach is that we disregard the large variability of soils included within each defined “soil type”. The range of minerals within each soil type is large (e.g., Claquin et al., 1999), and the range of elemental concentrations in each mineral is also large (Journet et al., 2008). The resolution of our model is such that despite the actual heterogeneity of soils at a particular location, we prescribe an average at each grid box which tends to reduce the variability of the elemental composition in the mineral dust in the atmosphere. This is likely to be the largest source of uncertainty in our approach.

The Community Earth System Model version 1.0.3 (CESM1.0.3) is coordinated by the National Center for Atmospheric Research (NCAR), and has been used to simulate elemental dust emission, transport and deposition in this study. The bulk mineral aerosol in the Community Atmosphere Model version 4 (CAM4) was adapted to include eight trace elements within total dust (Scanza et al., 2015). In this model simulation, the physical scheme CAM4 is driven by the meteorological data set MERRA (Modern Era Retrospective-Analysis) and is simulated spatially at 1.9 × 2.5∘ resolution for the years 2000–2010. The soil erodibility map used by the dust model has been spatially tuned (Albani et al., 2014). There are four size classes of dust particles used in the dust emission module in the bulk scheme with particle diameters of 0.1–1.0, 1.0–2.5, 2.5–5.0 and 5.0–10.0 µm. The sub-bin size distribution is assumed to follow a log-normal distribution with a mass median diameter of 3.5 µm (Mahowald et al., 2006) and a geometric standard deviation of 2.0 µm (Zender et al., 2003). Combining these log-normal parameters with the brittle fragmentation theory of dust emission (Kok, 2011) yields each bin's partitioning of dust aerosol mass between the soil's clay and silt size fractions (see Table 3 and Scanza et al., 2015). The elements in the dust undergo three-dimensional transport individually in each of the different size bins, identically to bulk dust in the original model. Elemental atmospheric mixing ratios, and wet and dry deposition are updated at each model time step based on actual elemental fields and the corresponding tendencies.

There has been considerable work on improving advection algorithms in atmospheric models, and here we use the finite volume advection algorithm as part of the CAM (Lin and Rood, 1997). While no advection scheme is perfectly mass conserving, monotonic, shape preserving and computationally efficient, this scheme does a good job of balancing these multiple goals and maintaining strong gradients required in modeling atmospheric constituents (e.g., Rasch et al., 2006). By splitting the dust into its different mineral elements, we may add in additional numerical errors, because the advection will not conserve the fraction of elements within dust aerosols due to small numerical errors. For the discussion of the ratios of elements, it would be better to advect the minerals themselves, and evaluate the ratio of elements later, since this would better conserve the ratios. Studies focused on elemental ratios and their distribution in ocean models have suggested there is a relatively small uncertainty associated with these types of numerical errors (e.g., Christian, 2007) and, compared with the errors in the source distribution of the minerals, errors from advection are likely to be small and are neglected here.

An element data set of ground-based aerosol measurements at 17 sites (Table S3) is used to evaluate the elemental dust simulation (Sun et al., 2004a, b; Wang et al., 2010; Chen et al., 2008; Engelbrecht et al., 2009; Carpenter et al., 2010; Cohen et al., 2011; Guo et al., 2014; Formenti et al., 2008; Desboeufs et al., 2010). The sites are close to major dust-producing regions (Fig. 1), including 10 Asian sites (Central Asia: Hetian, Tazhong; East Asia: Yulin, Duolun, Shengsi; South Asia: Hanoi, and Manila; Middle East: Balad, Baghdad, Taji), 5 African sites (West Africa: Cape Verde Atmospheric Observatory (CVAO); East Africa: Eilat; North Africa: Tamanrasset, Banizoumbou, and Douz), and 2 Australian sites (Muswellbrook and Richmond). Generally, these field aerosol samples (total suspended particulates (TSPs), PM10, PM2.5) had 1–3 day collection periods during the period 2001–2010 and were chemically analyzed for elemental composition. No observational aerosol mass concentrations at the Cape Verde station could be used in this study. At this site, the particulate matter (PM) concentrations are estimated by assuming an Al to total dust mass ratio of 0.0804. In order to be certain that only desert dust elements are compared with the model results, only data collected during dust storm seasons are selected. Measurement sites from which data are taken are listed in Table S3, which includes related methodological details.

In addition, the data set of dust deposition at more than 100 sites worldwide is used to evaluate modeled dust deposition fluxes (Albani et al., 2014).

The global distributions of the elements Mg, P, Ca, Mn, Fe, K, Al, and Si in bulk soils as mass percentages in soils are presented in Fig. 2.

Of specific interest is the Ca / Al ratio in soil, atmospheric dust and deposited dust as this ratio may be indicative of specific source regions (Fig. 8). Of all considered ratios, the Ca / Al ratio in soils shows the greatest variability in relation to the relevant desert region (e.g., Formenti et al. 2011). The Ca / Al ratio ranges mainly between 0.1–1 in clay fractions of soils and 0.5–5.0 in silt fractions of soils (Fig. 8a, b). The maximum Ca / Al ratios reaches 160 times the global mean Ca / Al ratio of 1.96 in the silt fraction of soils (Fig. 8b), much higher than those of other ratios such as Fe, K, and Mn to Al. Asian desert soils have higher Ca / Al ratios, with values greater than 5 in West Asia and Central Asia. The Ca / Al ratio in dust emissions from Central Asia (1.0–1.6) are higher than in East Asia (∼ 0.5), which is close to Ca / Al ratios (1.0–1.7) derived from source profiles of Asian dust (Zhang et al., 1997, 2003), and also match the observed Ca / Al ratios (0.7–1.3) during Asian dust events (Sun et al., 2004a, b; Shen et al., 2007). In addition, the Ca / Al ratios in dust emissions in North Africa are below 0.5, confirming the application of the Ca / Al ratio of 0.3 (or 3.8 with Al / Ca) as an indicator of North African dust transport to the eastern United States (Perry et al., 1997). Ambient PM2.5 dust measured on the Canary Islands suggests a different ratio (Ca / Al = 1.004; Engelbrecht et al., 2014). However, this ratio could be larger for PM10 or TSP. The high Ca / Al ratio (4.0–10.0) in a range of desert soils in some regions including South Africa, yields a Ca / Al ratio in dust emissions of 1.0, being much larger than those from North Africa. The modeled spatial pattern of Ca / Al ratios in dust emissions from Asia and northwest Africa is consistent with the currently available dust pattern compiled by Formenti et al. (2011) but shows relatively lower values for the Central Asian desert region.

Despite experiencing mixing of airborne dust from various source regions and as a result of dust processing during transport, the Ca / Al ratios still show spatial variations in global atmospheric dust and deposited dust. Relative to the Ca / Al ratio in source regions (Fig. 8a, b), the Ca / Al ratio in atmospheric dust over most of terrestrial Asia ranges mostly between 0.5 and 0.8, with a maximum of 1.8. This is due to the spatial variability of Ca / Al ratios in dust emissions (Fig. 9a) and despite the preferential gravitational settling during transport of the silt fraction which represents the highest Ca / Al variability. The variability in Ca / Al ratios in dust deposited into oceans and onto ice sheets are also shown in Fig. 9b. Near West Asia and western Sahara, higher Ca / Al ratios are noted and the North Indian Ocean and Mediterranean Sea have a Ca / Al ratio above 0.65 in deposited dust. As the combined downwind region of Central Asia and East Asia, the North Pacific has a Ca / Al ratio of around 0.5. The Ca / Al ratio in dust deposited over the Atlantic ranges between 0.3 and 0.4 due to the influence of the southern North Africa desert region and eastern Sahara desert both with low ratios of Ca / Al. Since the soil data set has a high spatial resolution of 5 arcmin (Fig. 8a, b), there is opportunity to increase the model grid resolution (1.9 × 2.5∘ in this study) to a finer resolution. It is expected that Ca / Al ratios will show more spatial heterogeneity when a finer model resolution is used. We conclude that the Ca / Al ratio can be used to identify different source areas and that the model can be used to support the observations.

The averaged modeled fractions of elements in atmospheric dust at each site for the periods for which observations are available are comparable with observations for most of the sites (Fig. 10a, b). It is clear most scatter values of the model and observations are in the range of the 2:1 and 1:2 lines for most elements in TSP except for Mg, Mn and Si. It shows the emission inventories based on mineralogy and elemental compositions are generally consistent with the available data. A large variability in the percentage of different elements is observed at the 17 observational sites for most elements, especially for Ca (Fig. 10). The fraction of Fe in the fine-mode particle (PM2.5) is closer to the observational data than the TSP Fe fraction, implying that simulations of Fe in the clay soils is more accurate than in silt. Since there are only a few reported observations of Si, this element is particularly difficult to verify. Based on averaged elemental fractions in TSP at 13 sites, the correlation coefficients (R) between modeled and observed fractions range widely (Table 3). Ca and Al had the highest correlations (0.75 and 0.72, respectively). However, the correlation coefficients for P, Mn and K were negative. For Fe, if we neglect the three sites in North Africa, the correlation coefficient increases from 0.29 to 0.50; in this area, the observational Fe fractions in TSP are high whereas the modeled ones are low (Figs. 10a, 5). The modeled elemental fractions in TSP are close to the observed data, with most ratios ranging between 0.7 and 1.6 (Table 3).

For this comparison (above mentioned), we calculate the elemental fractions and average the fractions temporally for each site and compare to observations but, alternatively, we could average the elemental concentrations and divide by the elemental dust concentrations instead, and this will make a difference in our interpretations. For example, taking site 2-Tazhong, the averaged fraction is 3.5 % when we calculate the fractions of iron firstly and average those temporally. However, when we calculate the averaged iron mass and dust mass separately, their ratio is 2.3 %. For site 3-Yulin, the ratios are 3.6 and 3.1 % for the first method and the second method, respectively. This difference may be due to dust storm events. For this comparison, we use the first method, as we think it is more suitable for our goal of simulating the percentage of each element correctly.

The averaged fractions of Mg and Mn in dust are underestimated by the model at all observational sites. It should be noted that there are some uncertainties when comparing elemental fractions. When the elemental concentration is divided by particle mass concentration to obtain the elemental fraction, the errors are amplified due to error propagation associated with the combination of the error on the particle mass and that of the element concentrations. Even though the available observational data are chosen from source sites or dust events in non-source regions, the contribution from other sources could be important, especially for fine-mode particles. The modeled fraction of Mn and Al in fine particles show a larger inconsistency than those in TSP when compared with observations. Some of the discrepancies may be because the model only includes particles up to 10 µm in diameter, while the observations include larger particle fractions in TSPs. In South Asia, the elemental fractions in dust, with the exception of Mn, are always much lower than at other sites, perhaps due to anthropogenic contributions to elemental particulate matter concentrations. In particular, many metals in insoluble forms in dust particles could be from other sources such as the refractories and steel industries, construction, biomass burning or volcanic emissions (Castillo et al., 2008; Gaudichet et al., 1995; Hinkley et al., 1999; Paris et al., 2010).

The daily elemental fractions across all times and sites where there is data show that while the mean of the model was similar to the mean of the observations, there are some systematic differences (Fig. 11a, b). The modeled elemental fractions are not as variable as the observations. This could be due to several issues. First there is a greater variability in the soil mineralogy and elemental composition of minerals than those included in the model (we only include the average values). Secondly, the dust model could introduce systematic errors (through advection, although this is likely to be small, as discussed in the methods Sect. 2.1), or there could be some unaccounted anthropogenic particulate sources, modifying the dust aerosol. Also, inconsistencies in the collection methods and differences in aerosol sampling periods and times could yield the observed variations in elements as concluded by Lawrence and Neff (2009).

However, the ranges of the modeled fractions of P, Ca, Fe, K and Al are close to the dominant range of the observational fractions (Fig. 11a, b). The measured fractions of elements in dust are reported to be 0.5–2.3 % for Mg, 0.065–0.2 % for P, 1.0–10.2 % for Ca, 0.028–0.124 % for Mn, 1.3–7.8 % for Fe, 1.2–4.6 % for K, 3.7–12.7 % for Al, and 22.4–35.7 % for Si (Wilke et al., 1984; Reheis and Kihl, 1995; Stoorvogel et al., 1997; Zhang et al., 1998; Yadav and Rajamani, 2004; Goudie and Middleton, 2006; Moreno et al., 2006; Jeong, 2008; Lawrence and Neff, 2009; Formenti et al., 2008; Desboeufs et al., 2010). The modeled elemental fraction in dust for P, Ca, Fe, K, Al and Si were similar to observations. However, the modeled fractions of Mg and Mn are lower (3.4 and 3.5 times, respectively; Table 3) than the observed ones for samples used in this study or of the above-cited results. Underestimation of Mg and Mn could be due to a deficiency of minerals containing high concentrations of Mg and Mn in our model, as dolomite (MgCO3) or palygorskite ((Mg,Al)2Si4O10(OH) × 4(H2O)) are often identified in dust particles for Mg (e.g., Diaz-Hernandes et al., 2011; Kalderon et al., 2009). Moreover, it is known that the chemical composition of minerals could be variable according to the regional origin of minerals and possible impurities. For example, the Mg content in calcite ranges from 0 to 2.7 % in the natural environment (Titschack et al., 2011). But in this study, the assumed fraction of Mg in calcite is zero because we took calcite as a pure mineral (see Table 1). So the underestimation of Mg in dust could be a propagation of errors in previous compositions in minerals considered in this study.

For reference we show the comparison of the modeled dust deposition versus observed deposition (Fig. 12). The modeled dust deposition flux agrees well with observations. The correlation coefficient between modeled and observed dust deposition is 0.86. The median of model to observation ratio is 1.15. Overall, the model has been tuned to represent dust deposition, concentration and aerosol optical depth (AOD; Albani, et al., 2014); however, the model has difficulty matching both deposition and concentration observations, similar to other models (Huneeus et al., 2011), suggesting more work on dust emission, transport and deposition processes is needed.

Comparisons between observations and the model simulations presented here suggest some bias in the model results (Fig. 11, Table 3); subsequently the model deposition values are adjusted to better match observed measurements by the tuning ratios (Table 3; Fig. 13). Of course, improving our elemental estimates in the source region would be preferred in future studies. From the observations, we have found a wide range in fractions of elements at individual sites and at the sites together; the ratio of the maximum and minimum in measured fractions could reach more than 700 for element K, and more than 200 for Ca and Mn. Because of the limited observations, we use a global tuning factor, based on the median elemental percentage, and contrast this result with our default modeling approach (Table 3). It is noted that both the median of observed (3.10 %) and modeled (2.9 %) Fe was lower than 3.5 %, which was thought to be the fraction of Fe in dust (e.g., Luo et al., 2008; Mahowald et al., 2008).

This study suggests significant variability in the elemental fractions in dust deposition (Fig. 13, Table 4) and shows that the assumption that the fixed composition of dust being deposited over oceans is unlikely to be correct. Consistent with Mahowald et al. (2008), most dust deposition occurred downwind of dust generating regions bordering the North Atlantic, North Pacific and North Indian oceans. The Greenland ice sheet accounted for the dominant part of elemental deposition to ice sheets regions, which is equal to the total amount of elements deposited in the whole of the South Atlantic. Fe and P are key elements in the marine ecosystem, with 6.3 Tg Fe and 184 Gg P added annually to all oceans and ice sheets (Table 5).

Also, the amounts of soluble dust element deposition are determined over different regions (see Sect. 2.1; Fig. 14). No atmospheric processing of natural dust or other sources of particles (e.g., anthropogenic sources) is included in this simulation. To better understand the uncertainties of soluble element deposition, estimates from two methods are used (Sect. 2.1) in simulating soluble elemental emission, transport and deposition. Fractional solubility of elements could not be estimated due to the lack of total element data from Method 2 (Sillanpää, 1982). Spatial variations in fractional solubility of elements are identified by Sol-1 (mineral method; Fig. 14). Fractional solubility of Ca increases with distance from source regions because its solubility is higher in clay than in silt (Table 1b). Fractional solubility of modeled P in deposition ranges from 5 to 15 %, with Saharan and Australian dust sources having solubilities averaging ∼ 10 %, consistent with Baker et al. (2006a, b). Previous observations suggest a fractional solubility for P of 7–100 % (e.g., Graham and Duce, 1982; Chen et al., 1985; Bergametti et al., 1992; Herut et al., 1999, 2002; Ridame and Guieu, 2002). Fractional solubility of Fe is 0.8–1.2 % in regions (Fig. 14) where clay minerals such as illite play an important role (Journet et al., 2008) with a mean value of 1.17 % of fractional Fe solubility (Table 1b). There is an obvious north–south gradient in the distribution of fractional solubility for Fe and Al but with opposing magnitude (Fig. 14). The fractional solubility could not be calculated using Sol-2 (Sillanpää method) since total elemental fractions in soil were not reported in Sillanpää (1982). Thus, the proportions of soluble Fe and K in total dust using two methods are compared with each other. This shows similar distribution patterns but the values are different (Fig. 15). The mineral method resulted in lower soluble Ca deposition and higher soluble Mg, P, and Mn (Fig. 15). Our results suggest significant differences in the spatial distribution of solubility depending on which data set is used to estimate soil solubility of elements. It should be noted that the solubility measurements by Sillanpää (1982) were performed at different pH values (pH of 7 vs. 2) and media of extraction (acidified ultrapure waters vs. organic ligand solutions). It is known that pH and organic complexation greatly influence the fractional solubility, at least for Fe (e.g., Paris et al., 2010). Thus, that would explain the differences in elemental solubility that we computed for the dust. The soluble elemental deposition values over ocean basins and ice sheets are determined using two methods and are listed in Table 5. Annual inputs of soluble Mg, P, Ca, Mn, Fe and K from mineral dust using method Sol-1 (Sol-2) were, respectively, 0.30 (0.28) Tg, 16.89 (7.52) Gg, 1.32 (3.35) Tg, 22.84 (6.95) Gg, 0.068 (0.06) Tg, and 0.15 (0.25) Tg to oceans and ice sheets.