A Global‐Scale Mineral Dust Equation

Abstract

A robust method to estimate mineral dust mass in ambient particulate matter (PM) is essential, as the dust fraction cannot be directly measured but is needed to understand dust impacts on the environment and human health. In this study, a global‐scale dust equation is developed that builds on the widely used Interagency Monitoring of Protected Visual Environments (IMPROVE) network's “soil” formula that is based on five measured elements (Al, Si, Ca, Fe, and Ti). We incorporate K, Mg, and Na into the equation using the mineral‐to‐aluminum (MAL) mass ratio of (K₂O + MgO + Na₂O)/Al₂O₃ and apply a correction factor (CF) to account for other missing compounds. We obtain region‐specific MAL ratios and CFs by investigating the variation in dust composition across desert regions. To calculate reference dust mass for equation evaluation, we use total‐mineral‐mass (summing all oxides of crustal elements) and residual‐mass (subtracting non‐dust species from total PM) approaches. For desert dust in source regions, the normalized mean bias (NMB) of the global equation (within ±1%) is significantly smaller than the NMB of the IMPROVE equation (−6% to 10%). For PM_2.5 with high dust content measured by the IMPROVE network, the global equation estimates dust mass well (NMB within ±5%) at most sites. For desert dust transported to non‐source regions, the global equation still performs well (NMB within ±2%). The global equation can also represent paved road, unpaved road, and agricultural soil dust (NMB within ±5%). This global equation provides a promising approach for calculating dust mass based on elemental analysis of dust.

Key Points

• A global‐scale mineral dust equation with region‐specific coefficients is developed to estimate dust mass

• The global equation reduced regional biases by about 6%–10% compared to the Interagency Monitoring of Protected Visual Environments equation for desert dust in source regions

• Flexible options are developed to expand the global equation for special types of dust containing adsorbed water and salt minerals

1. Introduction

Mineral dust, also referred to as soil (Malm et al., 1994), geological minerals (Chow et al., 2015), and crustal material (Snider et al., 2016), is commonly defined as airborne minerals originating from soil, and is a major component of ambient particulate matter (PM) including PM_2.5 (aerodynamic diameter <2.5 μm) and PM₁₀ (aerodynamic diameter <10 μm). Mineral dust has both natural (e.g., desert) and anthropogenic (e.g., agricultural soil, roads, and industry) sources, affecting visibility (e.g., Ashley et al., 2015; Hand et al., 2014, 2020; Kavouras et al., 2009), human health (e.g., Goudie, 2014; Tong et al., 2017; X. Zhang et al., 2016), the climate system (e.g., Miller & Tegen, 1998; Sokolik et al., 2001; Tegen, 2003), and biogeochemistry (e.g., Jickells et al., 2005; Koren et al., 2006; N. M. Mahowald et al., 2010; Muhs et al., 2012). The dust mass and therefore the dust fraction in PM cannot be measured directly because mineral dust is a complex mixture of many minerals, majorly quartz, feldspars, clays, calcite, and iron oxides (e.g., Nowak et al., 2018), and is often mixed with non‐dust PM species that also contain crustal elements (e.g., Deboudt et al., 2010; Li et al., 2014). The practical and typical way to estimate dust mass is by applying a dust equation to sum oxides of major crustal elements by using measured elemental composition and assuming common oxide forms associated with dust. An accurate dust equation is essential to estimate the dust contribution to measured aerosols (e.g., Andrews et al., 2000; Chow et al., 2015; Malm et al., 1994; Snider et al., 2016), and to serve as a reference to evaluate and improve atmospheric models (e.g., Appel et al., 2013; Kok et al., 2021; L. Zhang et al., 2013) and satellite remote sensing algorithms (e.g., Diner et al., 2018).

Table 1 summarizes dust equations used in previous studies and various sources of error. Most dust equations omit some important dust components such as carbonate. The calcite (CaCO₃) content of dust can exceed 20 weight percent (wt%) in some deserts such as the Sahara (e.g., Scheuvens et al., 2013) and the Middle East (e.g., Ahmady‐Birgani et al., 2015; Awadh, 2012). Thus, neglecting carbonate when estimating dust mass for these areas can cause substantial errors. Some dust equations (e.g., Andrews et al., 2000; Hueglin et al., 2005; Pryor et al., 1997) include K or Mg directly into the equation without excluding the non‐dust component of these elements such as K from biomass burning and Mg from sea salt, which will therefore overestimate dust K or Mg. The U.S. Interagency Monitoring of Protected Visual Environments (IMPROVE) network's “soil” formula (Soil = 2.20Al + 2.49Si + 1.63Ca + 2.42Fe + 1.94Ti) was developed to characterize mineral dust within the United States (Malm et al., 1994), but is used worldwide. The IMPROVE equation assumes that iron is split equally between Fe₂O₃ and FeO in soil according to their abundance in most rock types (Eldred, 2003). Soil K is incorporated as a fraction (0.6) of Fe to avoid the influence of smoke K emitted by biomass burning (Eldred, 2003; Pachon et al., 2013). A correction factor (CF) of 1.16 is applied to all five elements to account for other missing compounds (mainly MgO, Na₂O, CO₂, and H₂O) based on the composition of average sediment (Eldred, 2003; Pettijohn, 1975). Across the IMPROVE network, the elemental composition of PM_2.5 samples is measured using X‐ray fluorescence (XRF) and the above equation is applied to estimate soil (dust) mass. Although the IMPROVE equation is designed to address many of the challenges associated with dust characterization, Malm and Hand (2007) found that dust mass across the IMPROVE network may be underestimated by ∼20%, suggesting that the IMPROVE equation needs further development.

Table 1.

Summary of Dust Equations Used in Previous Studies

Reference	Dust equation	Sources of error
(Macias & Hopke, 1981)	1.89Al + 2.14Si + 1.4Ca + 1.43Fe + 1.2K	Missing carbonate, oxides of Na, Mg, Ti, etc.; K susceptible to biomass burning
(Chow et al., 1994; Solomon et al., 1989)	1.89Al + 2.14Si + 1.4Ca + 1.43Fe	Missing carbonate, oxides of Na, Mg, K, Ti, etc.
(Malm et al., 1994)	[1.89Al + 2.14Si + 1.40Ca + (1.36 + 0.6 × 1.20)Fe + 1.67Ti] × 1.16 = 2.20Al + 2.49Si + 1.63Ca + 2.42Fe + 1.94Ti (IMPROVE)	Accuracy of the correction factor for missing compounds; Developed for the U.S.
(Pryor et al., 1997)	2.2Al + 2.49Si + 1.63Ca + 1.5Fe + 1.4K + 1.94Ti	Accuracy of the correction factor for missing compounds; K susceptible to biomass burning
(Andrews et al., 2000; Kleindienst et al., 2010)	1.89Al + 2.14Si + 1.4Ca + 1.43Fe + 1.67Ti + 1.2K	Missing carbonate, oxides of Na, Mg, etc.; K susceptible to biomass burning
(Hueglin et al., 2005)	1.89Al + 2.14Si + 1.40Ca + 1.43Fe + 1.21K + 1.66Mg	Missing carbonate, oxides of Na, Ti, etc.; K susceptible to biomass burning; Mg susceptible to sea salt
(Terzi et al., 2010)	1.89Al + 2.14Si + 1.95Ca + 1.43Fe + 1.67Ti + 1.2K + 1.66Mg	Missing carbonate, oxides of Na, etc.; K susceptible to biomass burning; Mg susceptible to sea salt
(Ni et al., 2013)	1.89Al + 2.14Si + 1.40Ca + 1.43Fe + 1.67Ti + 1.21K + 1.66Mg	Missing carbonate, oxides of Na, etc.; K susceptible to biomass burning; Mg susceptible to sea salt

Several issues need to be addressed to further develop the IMPROVE equation for mineral dust on a global scale. First, the relationship between soil K and Fe may change in regions outside the US or even within the US because of the variation in dust composition (e.g., Journet et al., 2014). Second, although using Fe as a surrogate for soil K works well for natural dust at IMPROVE sites, for anthropogenic dust in urban areas, Al or Si should be a better choice than Fe given that the Fe concentration is more likely affected by non‐dust sources such as combustion (e.g., Chen et al., 2012). Third, the fraction of missing compounds in dust may also differ inside or outside the US. Fourth, the data of average sediment (Pettijohn, 1975) used to derive the factor of 1.16 might not represent natural dust composition which is usually represented using the data of continental crust from other sources (e.g., Cao et al., 2008; Choi et al., 2001; Contini et al., 2010; Ganor et al., 1991; Gao et al., 2018; Radhi et al., 2010a). Fifth, liquid water (different from crystal water) associated with special types of dust can be non‐negligible. Dust is commonly assumed to be non‐hygroscopic, but high hygroscopicity has been observed for saline dust in some regions (e.g., Gaston, 2020; Gaston et al., 2017; Koehler et al., 2007; Tang et al., 2019), some types of aged dust (e.g., Sullivan et al., 2009; Tang et al., 2016), and some types of anthropogenic dust (e.g., Peng et al., 2020). Sixth, special types of dust such as saline dust (e.g., Gaston et al., 2017), volcanic dust (e.g., Gislason et al., 2011; Taylor & Lichte, 1980), and aged dust (e.g., Tang et al., 2016) may contain salt minerals that are not considered for common desert dust. Some studies have applied the IMPROVE equation to natural or anthropogenic dust measured outside the US (e.g., Ho et al., 2003; K. W. Kim et al., 2001; Matawle et al., 2015; Pant et al., 2015; Z. X. Shen et al., 2007; Wu et al., 2011), yet to our knowledge, none have demonstrated its accuracy for that purpose. The development of a global‐scale dust equation should address the issues discussed above and assess its performance both within and outside the US.

In this study, we develop a global‐scale dust equation that builds upon the IMPROVE “soil” formula using analyses of the elemental composition and carbonate content of desert dust in different regions compared with that of continental crust. The global equation is evaluated for desert dust over source/non‐source regions, dust in the U.S. IMPROVE monitoring network, and major types of anthropogenic dust. The performance of the IMPROVE equation is treated as a well‐respected benchmark to evaluate the global equation. The goal of this study is to develop a global dust equation with regional parameterization that reduces the regional bias in dust mass estimated using measured elemental data. The reduced bias is especially important to PM mass closure (e.g., Ni et al., 2013; Terzi et al., 2010) and model evaluation (e.g., Appel et al., 2013; Meng et al., 2021; L. Zhang et al., 2013).

2. Data and Methods

2.1. Development of the Global Dust Equation

The five major crustal elements (Al, Si, Ca, Fe, and Ti) of the IMPROVE equation were used in the global equation assuming common oxide forms of Al₂O₃, SiO₂, CaO, FeO, and Fe₂O₃ (in equal amounts), and TiO₂, respectively. However, in contrast to the use of Fe in the IMPROVE equation to estimate soil K, Al was investigated as the new surrogate and used to estimate dust components of K, Mg, and Na by defining a mineral‐to‐aluminum (MAL) mass ratio as (K₂O + MgO + Na₂O)/Al₂O₃. We combined these three elements into one coefficient because they are all major crustal elements that cannot be directly included due to their potentially significant sources from biomass burning and sea salt. We included only dust components of these elements by applying the MAL ratio obtained using dust data with negligible non‐dust sources. The MAL ratio can be converted to:

$$\mathrm{M}\mathrm{A}\mathrm{L}=\left(1.20\mathrm{K}/\mathrm{A}\mathrm{l}+1.66\mathrm{M}\mathrm{g}/\mathrm{A}\mathrm{l}+1.35\mathrm{N}\mathrm{a}/\mathrm{A}\mathrm{l}\right)/1.89$$ (1)

where 1.20, 1.66, 1.35, and 1.89 are the oxide factors that convert elements to oxides for K₂O, MgO, Na₂O, and Al₂O₃, respectively. Thus, with elemental ratios of dust, the MAL ratio can be calculated and compared between regions. The MAL ratio is similar to the Chemical Index of Alteration defined as 100 × Al₂O₃/(Al₂O₃ + CaO + Na₂O + K₂O) and the Weathering Index of Parker represented as 100 × (2Na₂O/0.35 + MgO/0.9 + 2K₂O/0.25 + CaO/0.7) (Price & Velbel, 2003), in the sense of representing the relative abundance of alkalis in dust.

We next examined the contribution from other elements. Although according to the composition of the upper continental crust (UCC) (Shaw et al., 1986), both CO₂ (decomposed from carbonate) and the sum of remaining compounds (mainly crystal H₂O, P₂O₅, and MnO) account for 1 wt% of UCC, for mineral dust in arid areas, the CO₂ content can reach up to 10 wt% or higher (Awadh, 2012; Modaihsh, 1997; Scheuvens et al., 2013). The abundance of bound H₂O, P₂O₅, and MnO is relatively consistent with that in the UCC (N. Mahowald et al., 2008; Mendez et al., 2010; Moreno et al., 2006; Moufti, 2013; Najafi et al., 2014; Zarasvandi et al., 2011). Therefore, we further investigated the regionally resolved CO₂ content at dry conditions but fixed the abundance of remaining compounds as 1 wt%. We derived an overall CF as:

$$\mathrm{C}\mathrm{F}=\frac{100\mathrm{w}\mathrm{t}\%}{100\mathrm{w}\mathrm{t}\%-\left[1\mathrm{w}\mathrm{t}\%+{\mathrm{C}\mathrm{O}}_2\left(\mathrm{w}\mathrm{t}\%\right)\right]}$$ (2)

Including the MAL ratio and CF, we proposed a global‐scale mineral dust equation:

$$\mathrm{D}\mathrm{u}\mathrm{s}\mathrm{t}=\left[1.89\mathrm{A}\mathrm{l}\times \left(1+\mathrm{M}\mathrm{A}\mathrm{L}\right)+2.14\mathrm{S}\mathrm{i}+1.40\mathrm{C}\mathrm{a}+1.36\mathrm{F}\mathrm{e}+1.67\mathrm{T}\mathrm{i}\right]\times \mathrm{C}\mathrm{F}$$ (3)

where 1.89, 2.14, 1.40, 1.36, and 1.67 are the oxide factors for Al₂O₃, SiO₂, CaO, FeO, and Fe₂O₃ (in equal amounts), and TiO₂, respectively. Both the MAL ratio and CF vary regionally. Because the MAL ratio is estimated using dust data with negligible non‐dust sources, the dust mass calculated by the global equation will exclude non‐dust components of K, Mg, and Na when these elements are influenced by non‐dust sources such as wildfire or sea salt. Similarly, we tested a mineral‐to‐silicon (MSI) ratio as (K₂O + MgO + Na₂O)/SiO₂ to examine the feasibility of using Si as the surrogate to estimate K, Mg, and Na.

To include adsorbed water and salt minerals for special types of dust such as saline dust, volcanic dust, and aged dust, we derived an expanded global equation with expanded MAL and CF as described in Text S1 in Supporting Information S1. A water adjustment factor (WAF) was included in the CF based on the single hygroscopicity parameter κ (Kreidenweis et al., 2008; Snider et al., 2016). Although insufficient measured data were available to calculate the coefficients in the expanded global equation for these special types of dust, the expanded equation offers a framework to represent these special cases when detailed mineralogical information and hygroscopicity measurements are available in addition to elemental data. Dust hygroscopicity κ depends on many factors including the dust mineralogy or salinity (Tang et al., 2019), chemical mixing state (Sullivan et al., 2009), emission source (Peng et al., 2020), and particle size (Ibrahim et al., 2018). A review of the literature reveals that the κ of common desert dust is low (<0.1; Gaston et al., 2017; Herich et al., 2009; Koehler et al., 2009; Tang et al., 2019), but for saline dust κ can be higher (>0.8; Gaston et al., 2017; Tang et al., 2019). For dust with high hygroscopicity, for example, κ = 1.0, the resulting WAF will be 1.2, meaning adsorbed water can reach 20 wt% of the dry dust mass. For common desert dust, K, Mg, and Na exist mainly in feldspar or illite with low hygroscopicity (Tang et al., 2019), but they can exist mostly in salt minerals with high hygroscopicity for special types of dust such as saline dust. Salt minerals commonly observed in various special types of dust require the expanded global equation. For example, saline dust can have significant amounts of chlorides and sulfates besides carbonates, such as NaCl and Na₂SO₄ (Gaston et al., 2017). Volcanic dust has non‐negligible sulfates, chlorides, and fluorides, such as MgSO₄, NaCl, and K₂SiF₆ (Gislason et al., 2011; Taylor & Lichte, 1980). Aged dust can contain nitrates, sulfates, and chlorides, such as Ca(NO₃)₂, CaSO₄, and CaCl₂ (Sullivan et al., 2009).

To investigate variation in the MAL and MSI ratios of desert dust across different regions, we collected elemental characteristics data (elemental ratios) of mineral dust in six major dust source regions (Sahara, Sahel, Middle East, East Asia, Australia, and Southwest US) as shown in Table 2. Other source regions such as South Africa and South America were not selected because insufficient measured data are available for these regions. Figure S1 in Supporting Information S1 summarizes the median and interquartile range of elemental ratios and MAL for each region. The data we used were obtained from various analysis techniques such as XRF, inductively coupled plasma‐mass spectrometry (ICP‐MS), and particle‐induced X‐ray emission (PIXE). These techniques have different detection limits and analytical errors, which can generate uncertainties on the elemental ratios, an inevitable problem for compiling different published analyses (Scheuvens et al., 2013), so we used the median value to reduce the influence of outliers. For the Southwest US, we used PM_2.5 data with dust mass (SOIL) > 50% of the reconstructed fine mass (RCFM) based on the IMPROVE algorithm (http://vista.cira.colostate.edu/Improve/reconstructed-fine-mass/) measured at IMPROVE rural sites. The measured data in other dust source regions were collected from literature and the Surface Particulate Matter Network (SPARTAN, Snider et al., 2015, https://www.spartan-network.org/). Given that Na and Mg potentially come from sea salt and K from biomass burning, to ensure negligible non‐dust sources of Na, Mg, and K in the collected dust data from literature, we excluded the data affected by sea salt or biomass burning indicated by the dust origin analysis in their literature sources, which removed ∼20 potential data sources. We incorporated different types of dust (aerosol, soil, and sediment) to augment the data set size. We neglected the difference in elemental ratios between different types of dust because insufficient previous studies are available to examine this concern. As a reference, the MAL and MSI ratios for average continental crust were calculated using elemental ratios from commonly cited sources for natural dust (Lide, 1995; Mason, 1952; Taylor & McLennan, 1995; Wedepohl, 1995). We applied the Kruskal‐Wallis test to compare the MAL and MSI ratios in major dust source regions and continental crust. The criterion of a calculated probability with significance level <0.05 (P < 0.05) was used as a measure of statistically significant differences between the groups. When the measurements of any element used in the global equation are not available or not well characterized, the median elemental ratios for each region shown in Table 2 could be applied to estimate the concentration of that element.

Table 2.

Elemental Ratios of Dust in Major Dust Source Regions and Continental Crust

Region	Site	Type	Size (μm)	Si/Al	Fe/Al	Ca/Al	Ti/Al	K/Al	Mg/Al	Na/Al	MAL	K/Fe	Source	Method
Crust	Upper continental crust	Rock		3.83	0.44	0.37	0.04	0.35	0.17	0.36	0.63	0.80	(Taylor & McLennan, 1995)	NA
	Upper continental crust	Rock		3.92	0.40	0.38	0.04	0.33	0.17	0.33	0.60	0.83	(Wedepohl, 1995)	NA
	Continental crust	Rock		3.41	0.62	0.45	0.05	0.32	0.26	0.35	0.68	0.52	(Lide, 1995)	NA
	Continental crust	Rock		3.43	0.68	0.50	0.07	0.25	0.28	0.29	0.61	0.37	(Mason, 1952)	NA
	Median			3.63	0.53	0.42	0.05	0.33	0.22	0.34	0.62	0.66
Middle East	Southwest Iran	Aerosol	0.8–50	NA	NA	1.15	0.08	0.22	0.29	0.13	0.49	NA	(Torghabeh et al., 2020)	ICP‐OES
	Western Iran	Aerosol	TSP	3.57	0.66	2.86	0.07	0.23	0.56	0.11	0.72	0.35	(Najafi et al., 2014)	XRF
	Central Iran 2008	Aerosol	TSP	4.34	0.79	4.28	0.10	0.22	0.44	0.21	0.68	0.29	(Hojati et al., 2012)	ICP‐MS
	Central Iran 2009	Aerosol	TSP	3.29	0.76	5.36	0.14	0.22	0.46	0.32	0.78	0.29	(Hojati et al., 2012)	ICP‐MS
	Ahvaz, Iran 2009	Aerosol	TSP	NA	1.14	4.73	0.02	0.32	0.89	0.21	1.14	0.28	(Zarasvandi et al., 2011)	ICP‐MS
	Israel a	Aerosol	PM2.5	2.71	0.61	0.68	0.06	0.37	0.21	0.37	0.68	0.60		XRF
	Abu Dhabi a	Aerosol	PM2.5	3.05	0.76	2.03	0.06	0.38	0.70	0.23	1.02	0.50		XRF
	Median			3.29	0.76	2.86	0.07	0.23	0.46	0.21	0.72	0.32
Sahara	Northern Algeria	Aerosol	0.1–1	1.85	0.45	1.09	0.06	0.17	NA	NA	NA	0.38	(Gomes et al., 1990)	XRF
	Northern Algeria	Aerosol	1–20	2.12	0.48	0.88	0.06	0.19	NA	NA	NA	0.40	(Gomes et al., 1990)	XRF
	Morocco	Aerosol	TSP	4.97	0.64	5.22	0.09	0.40	0.86	NA	NA	0.63	(Khiri et al., 2004)	XRF
	Khamaseen dust	Aerosol	5–20	4.05	0.73	3.60	0.13	0.25	0.58	0.13	0.77	0.33	(Abed et al., 2009)	ICP‐MS
	Cairo	Aerosol	<20	5.83	0.70	2.00	0.14	0.28	0.57	0.16	0.80	0.40	(Linke et al., 2006)	XRF
	Cairo	Soil	<20	6.33	0.77	4.26	0.21	0.24	0.43	0.20	0.67	0.31	(Linke et al., 2006)	XRF
	Morocco	Soil	<20	7.41	0.57	1.85	0.11	0.38	0.31	0.09	0.58	0.66	(Linke et al., 2006)	XRF
	Western Sahara site 1	Soil	<30	6.26	0.66	1.98	0.08	0.34	0.37	0.15	0.66	0.52	(Moreno et al., 2006)	ICP‐AES
	Western Sahara site 2	Soil	<30	5.82	0.53	3.40	0.07	0.37	0.42	0.15	0.71	0.70	(Moreno et al., 2006)	ICP‐AES
	Western Sahara site 3	Soil	<30	9.88	1.10	3.24	0.20	0.42	0.43	0.23	0.80	0.38	(Moreno et al., 2006)	ICP‐AES
	Hoggar Massif site 1	Soil	<30	3.72	0.54	0.22	0.11	0.26	0.14	0.15	0.40	0.48	(Moreno et al., 2006)	ICP‐AES
	Hoggar Massif site 2	Soil	<30	4.06	0.50	0.20	0.10	0.28	0.13	0.20	0.44	0.56	(Moreno et al., 2006)	ICP‐AES
	Tindouf, Algeria	Soil	<63	4.68	0.65	6.52	0.11	0.34	0.96	0.48	1.40	0.52	(Criado & Dorta, 2003)	ICP‐AES
	Tiris, Mauritania	Soil	<63	7.07	0.53	0.25	0.17	0.42	0.14	0.20	0.53	0.79	(Criado & Dorta, 2003)	ICP‐AES
	Northern Mali	Soil	NA	NA	0.49	7.95	NA	0.27	0.65	0.13	0.84	0.57	(Washington et al., 2009)	NA
	Median			5.40	0.57	2.00	0.11	0.28	0.43	0.16	0.69	0.52
Sahel	Dakar, Senegal	Aerosol	TSP	5.62	0.62	0.25	0.09	0.24	0.15	0.09	0.35	0.38	(Orange et al., 1993)	NA
	Mbour, Senegal	Aerosol	TSP	6.69	0.68	0.14	0.10	0.16	0.16	0.02	0.26	0.24	(Orange et al., 1993)	NA
	Pete, Senegal	Aerosol	TSP	6.59	0.67	0.12	0.10	0.16	0.15	0.01	0.24	0.25	(Orange et al., 1993)	NA
	Zaria, Northern Nigeria	Aerosol	<2	2.23	0.42	0.01	0.06	0.10	0.09	0.00	0.14	0.23	(Møberg et al., 1991)	AAS
	Niger, local	Aerosol	<40	2.50	0.57	0.21	0.11	0.17	0.10	0.04	0.22	0.29	(Formenti et al., 2008)	XRF
	Niger, advected	Aerosol	<40	2.84	0.57	0.39	0.07	0.18	0.16	0.06	0.30	0.32	(Formenti et al., 2008)	XRF
	Agadez, Niger	Soil	<20	6.10	0.23	0.08	0.03	0.49	0.04	0.27	0.54	2.13	(Linke et al., 2006)	XRF
	Niger, Monsoon	Aerosol	<30	5.29	0.50	0.04	0.13	0.16	0.05	0.04	0.17	0.32	(Moreno et al., 2006)	ICP‐AES
	Niger, Harmattan	Aerosol	<30	4.84	0.62	0.18	0.11	0.23	0.08	0.07	0.27	0.37	(Moreno et al., 2006)	ICP‐AES
	Chad Basin	Soil	<30	4.00	0.63	0.13	0.08	0.16	0.10	0.11	0.27	0.26	(Moreno et al., 2006)	ICP‐AES
	Bodélé, Chad	Soil	NA	NA	0.64	0.04	NA	0.16	0.08	0.26	0.36	0.26	(Washington et al., 2009)	NA
	Median			5.07	0.62	0.13	0.09	0.16	0.10	0.06	0.27	0.29
Australia	Birdsville, Queensland	Aerosol	TSP	3.42	0.77	0.11	0.09	0.19	NA	0.24	NA	0.24	(Radhi et al., 2010a)	PIXE, PIGE
	Muloorina station	Aerosol	TSP	3.16	0.96	0.58	0.08	0.26	NA	0.12	NA	0.27	(Radhi et al., 2010b)	PIXE, PIGE
	Ormiston creek site 1	Soil	PM10	NA	0.47	0.09	0.04	0.24	0.10	0.06	0.28	0.51	(Moreno et al., 2009)	ICP‐AES
	Ormiston creek site 2	Soil	PM10	NA	0.44	0.05	0.04	0.17	0.05	0.05	0.19	0.40	(Moreno et al., 2009)	ICP‐AES
	Wilpena pound site 1	Soil	PM10	NA	0.62	0.03	0.05	0.11	0.05	0.01	0.13	0.18	(Moreno et al., 2009)	ICP‐AES
	Wilpena pound site 2	Soil	PM10	NA	0.26	0.03	0.08	0.26	0.07	0.03	0.25	0.99	(Moreno et al., 2009)	ICP‐AES
	Silverton	Soil	PM10	NA	0.53	0.12	0.04	0.28	0.10	0.03	0.29	0.53	(Moreno et al., 2009)	ICP‐AES
	Queensland	Sediment	<80	3.45	0.59	0.09	0.09	0.14	0.10	0.06	0.23	0.23	(Kamber et al., 2005)	ICP‐OES
	Autralian continent	Sediment	<2, 000	8.47	0.53	0.08	0.08	0.23	0.07	0.05	0.25	0.44	(Reimann & de Caritat, 2012)	XRF
	Median			3.44	0.53	0.09	0.08	0.23	0.07	0.05	0.25	0.40
East Asia	Zhenbeitai, China	Aerosol	TSP	4.14	0.52	0.79	0.08	0.25	0.26	NA	NA	0.48	(X. Y. Zhang et al., 2003)	PIXE
	Zhenbeitai, China	Aerosol	PM9	2.79	0.63	0.79	0.05	0.31	0.32	0.19	0.62	0.49	(Alfaro, 2003)	XRF
	Zhenbeitai, China	Aerosol	PM2.5	1.90	0.59	1.00	0.05	0.32	0.35	0.15	0.62	0.54	(Arimoto, 2004)	PIXE
	Yulin, China	Aerosol	PM2.5	NA	0.51	0.81	0.07	0.46	0.24	0.19	0.64	0.90	(Xu, 2004)	ICP‐MS
	Gansu, China	Aerosol	TSP	2.94	0.35	0.74	0.03	0.27	0.31	0.11	0.52	0.77	(Ta et al., 2003)	XRF
	Desert area, China	Soil	<100	7.68	0.54	0.94	0.06	0.34	0.28	0.29	0.68	0.63	(Ta et al., 2003)	XRF
	Gobi area, China	Soil	<100	7.85	0.35	1.17	0.04	0.39	0.18	0.36	0.67	1.09	(Ta et al., 2003)	XRF
	Gansu, China	Soil	<30	4.61	0.49	0.97	0.06	0.32	0.26	0.22	0.59	0.66	(Nishikawa et al., 2000)	XRF, etc. b
	Ningxia, China	Soil	<30	4.76	0.51	0.91	0.08	0.29	0.27	0.23	0.59	0.56	(Nishikawa et al., 2000)	XRF, etc.
	Xi Feng, China	Soil	TSP	4.56	0.78	2.25	0.07	0.41	0.28	0.06	0.55	0.52	(Wu et al., 2011)	XRF
	Xi Feng, China	Soil	PM10	2.03	0.71	2.30	0.06	0.39	0.29	0.08	0.56	0.55	(Wu et al., 2011)	XRF
	Xi Feng, China	Soil	PM2.5	1.78	0.65	1.56	0.05	0.29	0.29	0.07	0.49	0.44	(Wu et al., 2011)	XRF
	Xi Feng, China	Soil	PM1	1.88	0.68	1.77	0.05	0.29	0.29	0.06	0.49	0.43	(Wu et al., 2011)	XRF
	Median			3.54	0.54	0.97	0.06	0.32	0.28	0.17	0.59	0.55
Southwest US c	Jarbidge wilderness	Aerosol	PM2.5	2.86	0.60	0.49	0.05	0.43	0.25	0.30	0.71	0.71		XRF
	Saguaro NM	Aerosol	PM2.5	2.33	0.58	0.68	0.05	0.36	0.22	0.24	0.59	0.61		XRF
	Meadview	Aerosol	PM2.5	2.40	0.63	0.78	0.06	0.36	0.30	0.26	0.68	0.57		XRF
	Owens valley	Aerosol	PM2.5	2.50	0.60	0.78	0.05	0.38	0.37	0.27	0.76	0.64		XRF
	Tonto NM	Aerosol	PM2.5	2.32	0.58	0.63	0.05	0.34	0.26	0.24	0.62	0.59		XRF
	Chiricahua NM	Aerosol	PM2.5	2.36	0.53	0.63	0.05	0.35	0.20	0.27	0.59	0.65		XRF
	Petrified forest NP	Aerosol	PM2.5	2.31	0.60	0.71	0.05	0.32	0.27	0.20	0.58	0.54		XRF
	Canyonlands NP	Aerosol	PM2.5	2.31	0.56	0.88	0.05	0.36	0.32	0.19	0.65	0.65		XRF
	White mountain	Aerosol	PM2.5	2.40	0.57	1.10	0.05	0.33	0.42	0.21	0.73	0.58		XRF
	Capitol reef NP	Aerosol	PM2.5	2.48	0.63	1.02	0.06	0.39	0.38	0.22	0.74	0.62		XRF
	Zion canyon	Aerosol	PM2.5	2.44	0.60	1.01	0.06	0.37	0.40	0.27	0.77	0.61		XRF
	Gila wilderness	Aerosol	PM2.5	2.29	0.55	0.78	0.05	0.34	0.26	0.18	0.58	0.62		XRF
	Median			2.38	0.59	0.78	0.05	0.36	0.29	0.24	0.66	0.61

Note. NA: not available; XRF: X‐ray fluorescence; AAS: atomic absorption spectrometry; ICP‐MS: inductively coupled plasma‐mass spectrometry; ICP‐OES: inductively coupled plasma‐optical emission spectrometry; ICP‐AES: inductively coupled plasma‐atomic emission spectrometry; PIXE: particle‐induced X‐ray emission; PIGE: particle‐induced gamma emission; TSP: total suspended particulate; NM: national monument; NP: national park.

^a The Israel and UAE data are the ratios of mean element concentrations using PM_2.5 data in 2019 from the SPARTAN network. Only the data with Na/Al < 0.45 and K/Al < 0.5 were selected to avoid the effects of non‐dust sources (Scheuvens et al., 2013).

^b This is a reference material certified using multiple techniques.

^c The Southwest US data are the ratios of mean element concentrations calculated using dust‐dominated (SOIL > 50% RCFM) PM_2.5 data in 2011–2018 from the IMPROVE network.

Measurements of the CO₂ content in dust are commonly omitted, which handicaps the investigation of its regional variability. Thus, an indirect way to estimate CO₂ content is needed. We obtained the worldwide distribution of CaCO₃ content in topsoil (0–30 cm) from the Harmonized World Soil Database (HWSD version 1.21, FAO & ISRIC, 2012). This distribution is generally consistent with the mineralogical maps from several modeling studies (Claquin et al., 1999; Journet et al., 2014; Nickovic et al., 2012). We estimated the average CaCO₃ content in major dust source regions using an embedded query Tool in the HWSD viewer. We also used mineralogical maps for carbonates in the topsoil (A horizon, 5–10 cm) of the conterminous US from the U.S. Geological Survey (USGS, Smith et al., 2019) as a reference. To account for other carbonates in dust, we calculated the mass ratio of total CO₂ to the CO₂ in CaCO₃ using available measured mineralogical data for major deserts worldwide from literature (Boose et al., 2016; Engelbrecht et al., 2016; Z. Shen et al., 2009). Using the inferred total CO₂ abundance and fixing the remaining compounds as 1 wt%, we calculated the corresponding CF in the global equation.

The measured data assembled from the literature for this study include various sizes of dust. Because the chemical composition of dust can be size‐dependent (Cao et al., 2008; Pettijohn, 1975; Z. X. Shen et al., 2007; Wu et al., 2011; Zarasvandi et al., 2011), we compared the differences of the elemental characteristics and carbonate content between PM₁₀ and PM_2.5 using a data set of surface soil from arid regions (Engelbrecht et al., 2016). Detailed information on data processing is provided in Text S2 in Supporting Information S1.

In addition to employing multiple major crustal elements to estimate dust mass, single crustal elements such as Si have also been used previously (Chow et al., 2015). As a comparison, Si alone with a coefficient M (Dust = Si × M) to account for all the major minerals was also investigated by calculating the coefficient M across dust source regions.

2.2. Reference Dust Mass

To evaluate the performance of the global dust equation, we applied two approximate methods to obtain the reference dust mass since no absolute benchmark is available. One is called the total‐mineral‐mass approach, which is calculated by summing all the oxides of measured major crustal elements (Si, Al, Fe, Ca, Ti, Na, Mg, and K). Elemental concentrations were multiplied by corresponding common oxide factors (Reff et al., 2009) to obtain oxide concentrations. Measurements of Na, Mg, and K can be directly used to calculate dust mass only when they have negligible non‐dust sources. Other dust components such as H₂O and carbonate are not commonly measured, so we applied the same CF used in the global equation to obtain “total mineral mass.” The other method is the residual‐mass approach, which is calculated by subtracting organic mass (OM), elemental carbon, sulfate, nitrate, ammonium, sea salt, and particle‐bound water (PBW) from the measured PM. OM was calculated by multiplying OC with spatiotemporally varying estimates of the OM/OC ratio (Philip et al., 2014). Sea salt was represented as 1.8Cl⁻, or as 1.8Cl when the Cl⁻ concentration was missing (Hand et al., 2012; Malm & Hand, 2007). PBW refers to water associated with sulfate, nitrate, ammonium, sea salt, and OM, which was estimated using a κ‐Kohler framework (Kreidenweis et al., 2008) with specific parameters for each species at different RH conditions from Latimer and Martin (2019). Following the IMPROVE algorithm, we assumed sulfate exists as ammonium sulfate (AS) and nitrate as ammonium nitrate to calculate PBW. For anthropogenic dust such as road dust, non‐dust trace metals were also subtracted because their influence on the residual mass may be non‐negligible (Chow et al., 2015). Both approaches have limitations. The total‐mineral‐mass approach cannot directly test the accuracy of the CF because it is used in both the total mineral mass and the global equation. As for the residual‐mass approach, uncertainties exist in the measurements of each PM component and related assumptions, especially the uncertainty in estimating OM (Philip et al., 2014; Simon et al., 2011). Nevertheless, both approaches offer information to evaluate our global equation. To optimize the accuracy of the reference dust mass, we used dust‐dominated samples where all measurements of mineral elements were well quantified and contributions from organics and other non‐dust species were negligible. The data selection and the method of calculating the reference dust mass applied for different data sources are further discussed in the next section.

To carry out the evaluation, we applied several statistical metrics including the normalized mean bias (NMB), mean fractional bias (MFB), and normalized root mean square error (NRMSE):

$$\mathrm{N}\mathrm{M}\mathrm{B}(\%)=100\times \sum \left(C_j-R_j\right)/\sum R_j$$ (4)

$$\mathrm{M}\mathrm{F}\mathrm{B}(\%)=100\times 1/N\times \sum \left(C_j-R_j\right)/\left[\left(C_j+R_j\right)/2\right]$$ (5)

$$\mathrm{N}\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}(\%)=100\times 1/\sigma \times \sqrt{\sum {\left(C_j-R_j\right)}^2/N}$$ (6)

where C _j represents the calculated dust mass, R _j is the reference dust mass obtained using the total‐mineral‐mass or residual‐mass approach, j represents the pairing of the calculated dust mass and reference dust mass by site and time for N data points, and σ is the standard deviation of the reference dust mass. The NMB and MFB are also calculated with the IMPROVE equation to serve as a benchmark of our global equation. Some results with ratio form were plotted on a log scale so that deviations from unity are visually symmetrical.

2.3. Evaluation of the Global Dust Equation

First, we examined the performance of the global equation for desert dust in source regions and for the average global continental crust using the same data sources as those in Table 2. For the Australian dust data without Si measurements, the median Si/Al ratio (3.44) from available measurements was used. We also evaluated the global equation for desert dust (African and Asian) transported to non‐source regions using measurements from the European Monitoring and Evaluation Programme (EMEP, https://www.emep.int/) and literature. We used dust data measured at southern EMEP sites during summer African dust events. To reduce the influence of sea salt and biomass burning, we selected the data with Na/Al < 0.45 and K/Al < 0.5 reflecting typical elemental ratios for Northern African dust (Scheuvens et al., 2013). After the selection, PM₁₀ data from six sites during three dust episodes (Alastuey et al., 2016; Matassoni et al., 2009) were used for the evaluation. We also applied the global equation to available literature data of African dust over the Atlantic islands (Criado & Dorta, 2003; Engelbrecht et al., 2014; Formenti, 2003; Kandler et al., 2007) as well as Asian dust over Japan (Nishikawa et al., 1991) and Korea (K. H. Kim et al., 2003). We only used data with minimal influence of non‐dust sources suggested in the literature. Because Si measurements were missing in the dust data over Japan and Korea, we used the median Si/Al ratio (3.54) in East Asian deserts from Table 2. For most of the above data, we were unable to apply the residual‐mass approach owing to insufficient measurements of non‐dust PM species, so the total‐mineral‐mass approach was the major method applied for the evaluation. According to the protocol of EMEP measurements, we used 50% RH to calculate PBW for EMEP data.

To further evaluate the global dust equation within the US, we utilized daily‐integrated PM_2.5 speciation data from the IMPROVE network. Mineral elements are analyzed with XRF for samples from IMPROVE sites which are primarily located in rural areas (Solomon et al., 2014). Following the IMPROVE data advisories (http://vista.cira.colostate.edu/Improve/data-advisories/), we used data collected in 2011–2018 to avoid the influence of data anomalies or potential problems such as non‐quantitative Na data prior to 2011 (Hyslop et al., 2015). To balance avoiding uncertainties in the measurements of low dust content data while retaining sufficient data, we used dust‐dominated PM_2.5 data (SOIL > 50% RCFM based on the IMPROVE algorithm). For cases with measured elemental concentration below the minimum detection limit (MDL), we substituted one‐half of the MDL. The spatial distribution of the MAL ratio was investigated by calculating the ratio of the average K₂O + MgO + Na₂O to average Al₂O₃ concentrations. The NMB and MFB for the entire data set and for each site were calculated using both total‐mineral‐mass and residual‐mass approaches. The NRMSE was also provided for the entire data set. For the residual‐mass approach, we adopted the common humidity protocol (35%) for gravimetric mass analysis to calculate PBW. Following the IMPROVE advisory about increased variation of humidity after the weighing laboratory moved in 2011, we applied an RH of 45% for summer (June–August) data after the laboratory move. The average fraction of calculated PBW in measured total PM_2.5 was ∼4 wt%. All IMPROVE sites including rural and urban sites were considered but only the sites with ≥5 daily‐integrated PM_2.5 records that meet the criterion of SOIL > 50% RCFM were used in our maps to ensure representativeness. We neglected the data from the U.S. National PM_2.5 Chemical Speciation Monitoring Network (CSN) given that CSN dust concentrations were inconsistent with collocated IMPROVE dust concentrations, and comparisons between the two networks would be semiquantitative (Hand et al., 2012). Gorham et al. (2021) indicated that CSN has lower flow rate and larger sample deposit area than IMPROVE which makes quantification difficult, and particle size cut point efficiency also varies between the two networks. CSN has higher MDLs for mineral elements than IMPROVE, and therefore some elements are poorly detected (e.g., Al).

We explored the applicability of the global equation for anthropogenic dust by evaluating its performance for paved road, unpaved road, and agricultural soil dust using measured PM_2.5 and PM₁₀ data from the U.S. Environmental Protection Agency's (EPA) SPECIATE 5.0 database (https://www.epa.gov/air-emissions-modeling/speciate) and available data from two studies of paved road dust in Spain and China (Amato et al., 2009; Zhao et al., 2006). Both total‐mineral‐mass and residual‐mass approaches were used to calculate the reference dust mass. All the data we used were dust‐dominated (dust fraction >50 wt%). More details about the data processing are described in Text S3 in Supporting Information S1. Insufficient dust‐dominated data were available to evaluate the global equation for other types of anthropogenic dust including construction, combustion, and industrial dust (Pervez et al., 2018; Santacatalina et al., 2010; Z. Shen et al., 2016).

3. Results and Discussion

3.1. Characteristics of Regional MAL and CF Coefficients

The use of Si alone is explored first given its dominant abundance in dust. Figure S2 in Supporting Information S1 shows that the single Si coefficient M can vary by more than a factor of two within a region especially East Asia and Sahara where the standard deviation of M was 27% and 21% of the mean respectively. This high variability in the soil composition within the selected regions will result in undue errors in dust estimated using a single tracer, such as Si. Only the multi‐component dust model is examined further.

We subsequently examine the use of regional MAL ratios. Table 2 shows dust data with negligible non‐dust sources. The corresponding K/Fe ratios of desert dust in the southwestern US and eastern Asia are ∼0.6 as used in the IMPROVE equation (Malm et al., 1994), but tend to be lower (∼0.4) in other regions, providing evidence that the K/Fe ratio varies regionally. Figure 1 shows the variation of the MAL ratio in six different dust source regions and the MAL ratio for the average global continental crust using the data in Table 2. The median MAL ratio is significantly different (P < 0.05 for the Kruskal‐Wallis test) across regions. Australia and the Sahel have low MAL ratios (<0.3) due to high chemical weathering (Kamber et al., 2005; Moreno et al., 2006, 2009; Reimann & de Caritat, 2012), while the MAL ratio in other regions is close to the crustal MAL ratio. Dust with relatively high MAL ratios (∼0.8) in the Sahara (Linke et al., 2006; Moreno et al., 2006) and the Middle East (Hojati et al., 2012) is enriched in dolomite and palygorskite leading to their high Mg/Al ratios (>0.4). Figure S3 in Supporting Information S1 shows that the MSI ratio varies more widely than the MAL ratio both across and within regions, indicating that the sum of (K₂O + MgO + Na₂O) may associate better with Al than Si. This could be because Si has an additional major mineral source besides aluminosilicate, that is, quartz, which makes the MSI ratio sensitive to the variation of quartz content across and within regions (Nickovic et al., 2012) as well as the significant mineralogical fractionation effect on quartz (Ahmady‐Birgani et al., 2015; Formenti et al., 2014; Jeong et al., 2014). Therefore, we used the MAL ratio instead of the MSI ratio to develop the global equation. No consistent difference of the MAL ratio among aerosol, soil, and sediment was observed. Thus, all the data were used to develop regional MAL ratios. The particle size effect is discussed below. The median values in Table 2 were used to represent regional MAL ratios in six dust source regions and the crustal MAL ratio listed in Table 3.

Figure 1.

The mineral‐to‐aluminum (MAL) ratio of (K₂O + MgO + Na₂O)/Al₂O₃ in six dust source regions and the average global continental crust shown on a log scale. The dashed line indicates the median MAL ratio (0.62) in continental crust of four data sources. Each symbol represents a data record in Table 2.

Table 3.

Region‐Specific Mineral‐to‐Aluminum Ratio and Correction Factor for Natural Dust

Type	Region	Regional MAL	95% CI of MAL a	CaCO3 (wt%)	CO2 (wt%)	Regional CF
	Crust	0.62	(0.60, 0.68)		1	1.02
Source region	Middle East	0.72	(0.68, 1.00)	22	11	1.14
Source region	Sahara	0.69	(0.56, 0.80)	22	11	1.14
Source region	Sahel	0.27	(0.23, 0.35)	8	4	1.05
Source region	Australia	0.24	(0.19, 0.28)	8	4	1.05
Source region	East Asia	0.59	(0.54, 0.63)	18	9	1.11
Source region	Southwest US	0.66	(0.58, 0.71)	22	11	1.14
Within the US	East b	0.27				1.05
Within the US	West	0.66				1.14
Non‐source region	South Europe and the Atlantic islands	0.48				1.10
Non‐source region	Korea and Japan	0.59				1.11

^a The 95% confidence interval of the median MAL ratio for six dust source regions (deserts) and the average global continental crust are calculated.

^b Eastern and western regions are defined based on the dividing line shown in Figure 3.

The regional carbonate content and CF are thereafter investigated. Figure S4 in Supporting Information S1 demonstrates that CaCO₃ of topsoil is predominantly distributed in arid areas with variation in amounts across different deserts. The approximate content of CaCO₃ in topsoil for the six dust source regions is shown in Table 3, which generally agrees with available dust measurements in previous studies. Desert dust in the Middle East is commonly rich in carbonate due to abundant calcite and dolomite in local soils (Ahmady‐Birgani et al., 2015; Awadh, 2012; Modaihsh, 1997). Saharan dust is considerably more carbonate‐rich than Sahelian dust that is largely originated from the Chad Basin (Moreno et al., 2006; Scheuvens et al., 2013). The carbonate content of Australian dust is relatively low most likely linked to extensive and intense weathering of Australian soils (Moreno et al., 2009; Reimann & de Caritat, 2012). Asian dust in the Taklimakan Desert and Gobi area contains large amounts of carbonate (Cao, 2005; Wang et al., 2005). USGS reports somewhat higher calcite contents than the HWSD but they both show soils in the Southwest US are primarily carbonate‐rich. Figure S5 in Supporting Information S1 shows that the mass ratio of total CO₂ to CO₂ in CaCO₃ is not significantly different across regions (Kruskal‐Wallis test, P > 0.05). Hence, we applied the median ratio (1.11) of total CO₂ to CO₂ in CaCO₃ to account for other carbonates of dust in all the regions. Sensitivity tests using 25th percentile (1.06) or 75th percentile (1.20) for this mass ratio show that this variation does not significantly change the CF. The resulting dust CO₂ content and the calculated CF across six dust source regions and the average global continental crust are shown in Table 3. Although regional‐scale variation in MAL and CF is included, microscale or synoptic‐scale variation cannot be resolved without sufficient measured data.

We then examine the effects of particle size on the elemental ratios and CO₂ content. Figure S6 in Supporting Information S1 shows that using surface soil data from arid regions worldwide, the particle size of dust has a significant effect (paired‐sample Wilcoxon test, P < 0.05) on Si/Al, Fe/Al, Ti/Al, and K/Al, but not on Ca/Al, Mg/Al, and Na/Al. As natural mechanical weathering can have various effects on minerals with different properties (Boose et al., 2016), the size effect is expected to differ among elemental ratios. However, Figure 2 indicates that the size effect is not significant for the MAL ratio (paired‐sample Wilcoxon test, P = 0.14) and the CO₂ content (paired‐sample Wilcoxon test, P = 1.00) which are used in the global equation. A size‐dependent dust equation appears unnecessary based on the available data. Nevertheless, more available data sets of measured size‐fractionated elemental composition and carbonate content of dust samples are needed to assess the size effect and possibly develop a size‐dependent global dust equation.

Figure 2.

Particle size effect on the mineral‐to‐aluminum ratio and CO₂ content of dust using a data set of surface soil from arid regions (Engelbrecht et al., 2016). Inset P‐values are the results of the paired‐sample Wilcoxon test.

The coefficients used within the US are further investigated. Figure 3 shows the distribution of the MAL ratio at IMPROVE sites. Most of the western sites have a similar MAL ratio with deserts in the Southwest, while the MAL ratio at eastern sites is close to that of Sahelian dust (∼0.27). A previous study (Perry et al., 1997) found that African dust transported to the US has a characteristic Ca/Al ratio of <0.26, similar to that of Sahelian dust (median Ca/Al = 0.13 shown in Table 2). Thus, we applied the coefficients of Sahelian dust (MAL = 0.27, CF = 1.05) to eastern sites and those of the Southwest (MAL = 0.66, CF = 1.12) to western sites using the longitude (103.2°W) of the Big Bend national park (NP) site in Texas as an approximate dividing line based on the data pattern shown in Figure 3. Because we only use dust‐dominated data to investigate the MAL pattern, using the Sahelian MAL may underestimate dust mass for months without the influence of African dust but the dust contribution to total PM_2.5 is small in those months.

Figure 3.

The mineral‐to‐aluminum ratio of (K₂O + MgO + Na₂O)/Al₂O₃ at Interagency Monitoring of Protected Visual Environments (IMPROVE) sites using daily‐integrated dust‐dominated (SOIL > 50% of reconstructed fine mass) PM_2.5 speciation data in 2011–2018 from the U.S. IMPROVE network. Only the sites with ≥5 data points were used to ensure representativeness. The number of selected IMPROVE sites is 95. The dashed line indicates the dividing line (103.2°W) through the Big Bend National Park site.

Coefficients for desert dust transported to non‐source regions are assumed to be the same as those used for source regions. Elemental ratios (e.g., Al/Ca, K/Fe) are used as dust source tracers in many studies and the elemental ratios used to calculate MAL (i.e., K/Al, Mg/Al, and Na/Al) can remain similar during long‐range transport (e.g., Cao et al., 2008; Hand et al., 2017; Mori et al., 2003; VanCuren, 2002), so we used the MAL ratio of source regions for non‐source regions. Previous studies show that CaCO₃ may be converted to Ca(NO₃)₂ or CaSO₄ by reacting with acidic species if the dust plume passes over highly polluted regions (Huang et al., 2010; Scheuvens et al., 2013). Asian dust transported eastwards passing over urban areas of China can become aged (Heim et al., 2020), which may require a higher CF than that for Asian dust in the source region given the formation of secondary salts and adsorbed water due to increased hygroscopicity. The expanded expression of the global equation can be used in this case, but insufficient mineralogical information and hygroscopicity measurements are available to calculate the coefficients. Therefore, for Asian dust transported to Japan and Korea (K. H. Kim et al., 2003; Nishikawa et al., 1991), we still utilized the MAL ratio (0.59) and CF (1.11) of its source region. The loss of carbonate during long‐range transport is not severe for African dust (Coz et al., 2009; Denjean et al., 2015; Scheuvens et al., 2013). African dust traveling to southern Europe (Alastuey et al., 2016; Escudero, 2005; Sánchez de la Campa et al., 2013; Stuut et al., 2009) and the Atlantic islands (Criado & Dorta, 2003; Engelbrecht et al., 2014; Formenti, 2003; Reid, 2003) can originate from both the Sahara and Sahel, so we employed the average MAL ratio (0.48) and average CF (1.10) of the two regions.

With limited data for different types of anthropogenic dust in various regions, we estimate the coefficients for anthropogenic dust more simplistically than for natural dust. The crustal MAL ratio (0.62) was applied to both paved road and unpaved road dust. Given that the road dust data are from areas (Texas, Illinois, northeastern Spain, and northern China) where local soils are enriched in carbonates or places affected by dust storms (Amato et al., 2009; Smith et al., 2019; Zhao et al., 2006), we used a high CF of 1.12 for both paved road and unpaved road dust. For agricultural soils, mobile elements (Na, K, and Mg) and carbonates can be leached by irrigation (Chow et al., 2003), so we applied a lower MAL ratio of 0.31 (half the crustal MAL) and the crustal CF (1.02).

3.2. Evaluation of the Global Dust Equation

Figure 4 shows the performance of the global equation and the IMPROVE equation for desert dust in six source regions and for the average global continental crust. The estimates by the global equation are consistent with the “total mineral mass” with a small NMB of −0.7%–0.2% and a small MFB of −0.7%–0.3% for all the source regions as well as the continental crust, while both the NMB and MFB of applying the IMPROVE equation are −6%–10%. Because the same CF was used in both the global equation and “total mineral mass,” the comparison between the two estimates indicates the accuracy of applying the region‐specific MAL ratio. Although the MAL ratio can vary by more than a factor of 4 within a region (Figure 1), the resulting bias in using a median MAL in each region is within ±1%. The underestimation of US desert dust by the IMPROVE equation is also observed in previous studies (Hand et al., 2019; Simon et al., 2010, 2011). Therefore, it is necessary to consider the variation in dust composition to improve the accuracy of estimating dust mass. Using an equation with region‐specific coefficients (MAL and CF) is found to be an effective approach, which reduced the regional bias by about 6%–10% compared to the IMPROVE equation with universal coefficients. This reduction in bias matters to PM mass closure and model evaluation especially when dust mass is high during dust events. Although the global equation agrees well with the “total mineral mass,” the total‐mineral‐mass approach cannot be used when Na, Mg, and K are significantly influenced by non‐dust sources because they are directly added to the total dust mass. Thus, the advantage of the global equation is that it accounts for only the dust component of these elements by applying an average MAL ratio obtained from analyses of dust data with negligible non‐dust sources.

Figure 4.

The ratio of the dust mass calculated by the global equation and the Interagency Monitoring of Protected Visual Environments (IMPROVE) equation to the “total mineral mass” for desert dust in source regions and for the average global continental crust.

The performance of the global equation for the IMPROVE network is shown in Figure 5. Both equations show a small bias compared to the “total mineral mass” (NMB and MFB within ±4%), which is within experimental uncertainties for the five elements (Al, Si, Ca, Fe, and Ti) measured in the IMPROVE network (Gorham et al., 2021; Hyslop & White, 2009). The global equation shows a slightly smaller NRMSE (8.5%) than the IMPROVE equation (10%). Applying the bootstrapping method, the mean estimates from the two equations have no statistically significant difference (P = 0.30). We also attempted to use the residual‐mass approach for evaluation but were stymied by possible biases in gravimetric and speciated measurements as well as related assumptions. The relative humidity is not rigorously controlled in the weighing laboratory (Simon et al., 2011), especially after the laboratory was relocated in 2011, and RH generally increased after 2011 (Hand et al., 2019). Opposing biases from the residual‐mass approach were observed before and after the IMPROVE weighing laboratory move in 2011, with no net bias as shown in Figure S7 in Supporting Information S1. Over the high dust mass range (>10 μg/m³), the “residual mass” tended to be larger than estimates from the global equation after 2011, likely related to underestimated PBW, and tended to be smaller before 2011, possibly attributable to overestimated OM/OC ratio and the assumption of fully neutralized AS as discussed in Hand et al. (2019). The analytical changes in 2011 on dust could also contribute to the bias. Based on the IMPROVE advisory, the attenuation effect for light elements at high sample loadings was not corrected after the switch to the PANalytical XRF system and the implemented correction before 2011 could overcorrect the attenuation.

Figure 5.

Comparison of the dust mass calculated by the global equation and the Interagency Monitoring of Protected Visual Environments (IMPROVE) equation with the “total mineral mass” using dust‐dominated (SOIL > 50% reconstructed fine mass) PM_2.5 data in 2011–2018 from the U.S. IMPROVE network. Inset statistics are the normalized mean bias (NMB), mean fractional bias (MFB), and normalized root mean square error (NRMSE) of using the two equations for the entire data set. N is the number of speciation profiles.

Despite the overall systematic, yet unquantified, bias in the residual mass approach at IMPROVE sites, comparison across sites remains instructive because all sites are similarly affected by laboratory protocols. Figure 6 presents the performance of the global equation at individual U.S. IMPROVE sites including the Virgin Islands NP site which is known to be impacted by African dust (Perry et al., 1997). Compared to the “total mineral mass,” the global equation performs well at almost all sites (NMB within ±5%) and reduces the variable performance found for the IMPROVE equation. The residual‐mass approach shows similar improvement after using the global equation, although overestimation or underestimation was observed at some sites possibly related to the heterogeneity of soil carbonate content on a small scale (Smith et al., 2019). Soils in the West Coast region of the US are carbonate‐poor due to Mediterranean climates (Machette, 1985; Smith et al., 2019), which may explain the overestimation at some sites in that region. The underestimation at the Pasayten site (48.4°N, 119.9°W) in the Northwest may be attributable to the influence of transported Asian dust (Hand et al., 2012, 2017). For the Virgin Islands NP site, the global equation shows a much lower bias (NMB = 5.7%) than the IMPROVE equation (NMB = 15.9%). The overall improvement at IMPROVE sites is owing to the use of distinct MAL and CF for eastern and western sites in the global equation. Similar maps for MFB are shown in Figure S8 in Supporting Information S1.

Figure 6.

Normalized mean bias (NMB) for the dust mass calculated by (a and b) the global equation and (c and d) the Interagency Monitoring of Protected Visual Environments (IMPROVE) equation compared to (a and c) the “total mineral mass” and (b and d) the “residual mass” at IMPROVE sites using daily‐integrated dust‐dominated (SOIL > 50% of reconstructed fine mass) PM_2.5 speciation data in 2011–2018 from the U.S. IMPROVE network. Only the sites with ≥5 data points were used to ensure representativeness. The number of selected IMPROVE sites is 95.

Evaluation of the global equation for Europe is challenging due to the paucity of complete analyses of PM speciation and the strong effect of sea salt and biomass burning on the data (Manders et al., 2010; Sigsgaard et al., 2015), as well as the transport of dust from both the Sahara and Sahel with different dust mineralogy. We identified a campaign in Italy with sufficient characterization to contribute to the evaluation of the global equation. Figure 7 shows that both the global equation and the IMPROVE equation perform well for African dust transported to Italy using the total‐mineral‐mass and residual‐mass approaches. The global equation shows a somewhat lower NMB (−0.3% and −0.9% respectively) than the IMPROVE equation (2.8% and 2.1% respectively) for both approaches. The MFB of using the global equation (−0.2% and −0.0% respectively) is also somewhat lower than the IMPROVE equation (2.8% and 3.0% respectively) for both approaches. The performance of the global equation at EMEP sites during other African dust episodes is shown in Figure S9 in Supporting Information S1. The high correlation between the estimates by the global equation and “total mineral mass” indicates that the MAL ratio (0.48) in the global equation used for African dust transported to southern Europe is appropriate for data examined in Figure S9 in Supporting Information S1. The small difference between the estimates by the global equation and IMPROVE equation indicates that the fractions of missing compounds considered in both equations are close to each other in this case. However, for desert dust significantly depleted or enriched in mobile elements and carbonate, the difference will be larger as shown in Figure 4.

Figure 7.

Comparison of dust mass calculated by the global equation and the Interagency Monitoring of Protected Visual Environments (IMPROVE) equation with the “total mineral mass” (left) and the “residual mass” (right) for dust‐dominated PM₁₀ data (SOIL > 50% of reconstructed fine mass) measured at Montelibretti, Italy during an African dust event (20–30 June 2006). Data with Na/Al > 0.45 or K/Al > 0.5 are excluded to reduce the influence of non‐dust sources. Inset statistics are the normalized mean bias and mean fractional bias of using the two equations.

We evaluated the global equation for transported African dust over the Atlantic islands as well as transported Asian dust over Japan and Korea shown in Figure S10 in Supporting Information S1. For African dust, the global equation shows a slightly lower bias (NMB = 1.4%, MFB = 1.6%) than the IMPROVE equation (NMB = 2.0%, MFB = 1.7%). As for Asian dust, the global equation (NMB = −1.2%, MFB = −1.2%) performs similarly to the IMPROVE equation (NMB = −1.0%, MFB = −1.0%). The good performance of the global equation for desert dust over both source and non‐source regions confirms that long‐range transport does not substantially alter the MAL ratio of desert dust. However, the dust mass could be underestimated because the potential secondary salts and adsorbed water due to chemical aging are not included. Sufficient mineralogical information and hygroscopicity measurements are needed to better estimate transported dust that likely undergoes significant chemical aging.

Figure 8 shows the performance of the global equation and the IMPROVE equation for several major types of anthropogenic fugitive dust including paved road, unpaved road, and agricultural soil dust. Using the total‐mineral‐mass approach, the NMB for the global equation is similar to the IMPROVE equation for paved (3.3% vs. 2.4%) and unpaved (−0.05% vs. 1.1%) roads, while the bias for the global equation is much lower than the IMPROVE equation for agricultural soils (1.9% vs. 15%). Similar results were found using the residual mass as the reference, although more noise was observed which is attributable to greater uncertainties in calculating the residual mass. The results suggest that the previously recognized overestimate by the IMPROVE equation of agricultural soil (Simon et al., 2010, 2011) can be remedied by accounting for the depletion of mobile elements and carbonates by irrigation. Because the evaluation is based on data with limited regional coverage, more measured data of anthropogenic dust in different regions are needed to further examine the performance of the global equation. It is difficult to derive general coefficients (MAL and CF) for other types of anthropogenic dust because their chemical composition can vary widely depending on the source and the area. However, an accurate dust equation is still important to estimate the concentration of different types of anthropogenic dust if the missing compounds are not measured or some crustal elements have significant non‐dust sources.

Figure 8.

The ratio of the dust mass calculated by the global equation and the Interagency Monitoring of Protected Visual Environments (IMPROVE) equation to the “total mineral mass” (left) and the “residual mass” (right) for paved road, unpaved road, and agricultural soil dust using PM_2.5 and PM₁₀ data from the U.S. Environmental Protection Agency's SPECIATE database and collected literature data (Amato et al., 2009; Zhao et al., 2006). Ratios are presented on a log scale. Data points are jittered to avoid overlap. The number of asterisks indicates the significance level (**P < 0.01, ****P < 0.0001) of the difference between two groups using the paired‐sample Wilcoxon test.

4. Conclusions

This study develops a global‐scale mineral dust equation used to estimate dust mass by building upon the IMPROVE equation that was designed for the U.S. The IMPROVE equation is widely used to calculate dust mass but prior work finds general underestimates in dust mass across the IMPROVE network, and had not been evaluated globally. Developing a global dust equation needs to address several issues especially the variation of dust composition across different regions. Three important mineral compounds, K₂O, MgO, and Na₂O, are usually either missing from previous dust equations or directly included without excluding biomass burning or sea salt sources. Our global dust equation incorporates the three compounds using Al as a surrogate by defining the MAL ratio as (K₂O + MgO + Na₂O)/Al₂O₃ that is specific to the dust components of K, Mg, and Na. Analyses of dust data from major dust source regions of the world with negligible non‐dust sources indicate that the MAL ratio is significantly different across regions with Australian and Sahelian dust exhibiting much lower MAL ratios than dust in other regions. A CF is used to account for other missing compounds, mainly CO₂ which is an important mineral compound but is commonly not measured and not included in previous dust equations. The amount of CO₂ in dust inferred from CaCO₃ content in topsoil and mineralogical data also varies substantially across regions. We provide flexible options for expanding the global equation to include adsorbed water and salt minerals in special types of dust such as saline dust, volcanic dust, and aged dust.

Applying the global dust equation with the region‐specific coefficients (MAL and CF) to major dust source regions and using the IMPROVE equation as a benchmark demonstrates that the global equation provides evident improvement for estimating the dust mass. Compared to the reference dust mass, the resulting NMB and MFB of the estimates from the global equation are within ±1%, while those from the IMPROVE equation are −6%–10%. The global equation also performs well (NMB and MFB within ±2%) for desert dust transported to non‐source regions using coefficients that depend on their source regions. For major types of anthropogenic dust (paved road, unpaved road, and agricultural soil), the global equation generally performs well (NMB within ±5%) by applying the crustal MAL ratio and a high CF for road dust as well as a low MAL and CF for agricultural soil dust. Applying different coefficients to eastern and western IMPROVE sites, the global equation estimates the dust mass well (NMB within ±5%) at most sites.

Further improvement of the global equation would benefit from more complete and accurate measurements of mineral elements and CO₂ content in dust. More accurate estimation of OM, sea salt, and PBW can decrease the uncertainties in calculating the reference dust mass using the residual‐mass approach. Assigning the coefficients on a finer spatial scale could further reduce the bias but would require much more data. Further examining the link of the MAL ratio and carbonate content between soil and aerosol is beyond the scope of our work but worthy of further study. Characteristics of different types of anthropogenic dust over various regions deserve further investigation. Despite the limitations, the global equation with region‐specific coefficients has an absolute advantage over the IMPROVE equation with universal coefficients because it considers the variation in dust composition across different regions which is important for accurate estimation of dust mass on a global scale.

To our knowledge, this is the first study to develop and evaluate a region‐specific global dust equation, which is challenging given the limitation of insufficient complete measurements of dust composition on a global scale and the lack of an absolute benchmark for reference dust mass. The use of regional coefficients for MAL and CF yields a promising method for estimating the dust mass not only outside the US but also within the US. This global equation can help future studies assess the measured dust contribution to aerosols more accurately when performing PM mass reconstruction and better understand the dust impacts on the environment and human health. More accurate representation of ground‐based dust measurements can also benefit the development of atmospheric models and satellite remote sensing algorithms.

Supporting information

Supporting Information S1

Liu, X. , Turner, J. R. , Hand, J. L. , Schichtel, B. A. , & Martin, R. V. (2022). A global‐scale mineral dust equation. Journal of Geophysical Research: Atmospheres, 127, e2022JD036937. 10.1029/2022JD036937

Data Availability Statement

The elemental composition data from the U.S. Interagency Monitoring of Protected Visual Environments network is available at http://vista.cira.colostate.edu/Improve/improve-data/. The elemental composition data from the SPARTAN network can be downloaded at https://www.spartan-network.org/data. The elemental composition data from the EMEP sites can be accessed at http://ebas-data.nilu.no/default.aspx. The U.S. EPA's SPECIATE 5.0 database is available via https://www.epa.gov/air-emissions-modeling/speciate-2. The Harmonized World Soil Database can be found at https://webarchive.iiasa.ac.at/Research/LUC/External-World-soil-database/HTML/index.html?sb=1. All the collected data from literature with detailed data selection and processing are compiled into a data set available at https://data.mendeley.com/datasets/55vd6p28gk/1 (Liu, 2022).