A new method to quantify mineral dust and other aerosol species from aircraft platforms using single-particle mass spectrometry

2.1 Airborne aerosol sampling

Aerosol properties were measured aboard the NASA DC-8 aircraft during three campaigns: DC3, SEAC4RS, and ATom. The Deep Convective Clouds and Chemistry (DC3) campaign was based in Salina, Kansas, in April–May 2012 and targeted convective outflow from isolated storm systems (Barth et al., 2015). The Studies of Emissions and Atmospheric Composition, Clouds and Climate Coupling by Regional Surveys (SEAC4RS) campaign was based in Houston, Texas, in August–September 2013, and sampled a variety of continental environments including regions with high biogenic activity, urban emissions, wildfires, and convective outflow (Toon et al., 2016). The NASA Atmospheric Tomography (ATom) campaign consisted of four seasonal deployments from 2016 to 2018 to map the troposphere with near pole-to-pole coverage in north–south transects along the Pacific and Atlantic basins (Wofsy et al., 2018). Measurements during the New England Air Quality Study (NEAQS) campaign were taken aboard the NOAA WP-3D aircraft based in Portsmouth, New Hampshire, in July–August 2004, with flights targeting anthropogenic emissions from the eastern US (Fehsenfeld et al., 2006). During the NASA Mid-latitude Airborne Cirrus Properties Experiment (MACPEX) campaign the WB-57 aircraft was based in Houston, Texas, in March–April 2011 and sampled tropospheric continental and stratospheric background air near cirrus cloud systems (https://espo.nasa.gov/macpex/, last access: 26 October 2019). Cloudy flight segments are excluded from all aerosol data (Murphy et al., 2004b).

The airborne sampling methodology for ATom DC-8 deployments is detailed in Brock et al. (2019). Instruments are described in Sect. 2.2. For all DC-8 deployments most instruments used the University of Hawaii aircraft inlet operated at isokinetic conditions. This inlet was previously characterized to transmit aerosol particles ≥5.0 µm aerodynamic diameter at low altitude and ≥3.2 µm at 12 km altitude with 50 % efficiency (McNaughton et al., 2007). PALMS and particle size spectrometers subsample a minor flow from the main inlet flow. The PALMS instrument flow was 0.75 L min⁻¹, and particle spectrometer flows were 0.05–0.1 L min⁻¹. Particle spectrometer flows were actively dried using Nafion driers (Perma Pure), typically to < 40 % relative humidity. Residence times between the aircraft inlet and instrumentation were 0.5–3.5 s. The AMS instrument used a dedicated HIMIL aircraft inlet (Stith et al., 2009) with residence times typically < 0.5 s and no active drying. The SAGA filter samplers used the University of New Hampshire aircraft inlet that has similar particle transmission characteristics to the University of Hawaii inlet (McNaughton et al., 2007). Aboard the NOAA WP-3D during NEAQS aerosol particles were sampled using a low-turbulence inlet operated isokinetically (Wilson et al., 2004) and transmitted to size spectrometers inside the cabin. In the WB-57 during MACPEX the FCAS instrument sampled particles using an anisokinetic inlet (Jonsson et al., 1995). PALMS was located inside a wing pod for NEAQS and inside the WB-57 nose for MACPEX, and for both campaigns PALMS sampled aerosol using a forward-facing anisokinetic tube that enhanced large particle concentrations.

A virtual impactor was added upstream of PALMS for the DC-8 ATom deployments to enhance supermicron particle concentration. The design is based on Loo and Cork (1988) and is scaled to achieve an enhancement of at least 50 % of the flow ratio above ∼2.0 µm. The virtual impactor was operated at total-to-minor flow ratios of 5.6–11. Figure S1 in the Supplement shows the virtual impactor design and its concentration enhancement for lab-generated aerosol.

2.2 Aerosol size and composition measurements

The NOAA PALMS instrument (Thomson et al., 2000) characterizes the size and chemical composition of individual aerosol particles from about 0.15 to 5 µm in diameter. Particles pass through an aerosol focusing lens (Schreiner et al., 2002) and enter a vacuum where they pass through two continuous laser beams and scatter light. The transit time between the beams provides the particle velocity, which is used to determine particle aerodynamic diameters based on laboratory calibrations using polystyrene latex sphere size standards (Duke Scientific). A scatter signal triggers a 193 nm pulse from an excimer laser that ablates and ionizes a single particle. Either positive or negative ions are analyzed with a time-of-flight mass spectrometer, with the polarity switched every few minutes during flight. Single-particle mass spectra are post-processed to classify each particle into a compositional type and calculate the relative abundance of particle sub-components (Froyd et al., 2009; Hudson et al., 2004; Murphy et al., 2003).

An important consideration when measuring fractional and absolute abundance from single-particle analysis is the estimation of potential sampling biases due to particle composition or physical properties. In one example, if a certain particle type does not produce detectable ions when hit by the ionization laser, a systematic bias would occur that would underestimate the concentration of that particle type. Additionally, particle mass spectrometers can exhibit a low bias for non-spherical particles due to diverging particle trajectories (Huffman et al., 2005; Vaden et al., 2011). Many aspects of the PALMS instrument design reduce these potential biases (Murphy, 2007). The very close proximity of detection and ionization beams (center separation ∼100 µm) enables PALMS to obtain positive ion mass spectra for > 90 % of particle triggers. In addition, the particle transit distance between the vacuum entrance and the ionization region is shorter than most other SPMS systems. This high targeting efficiency and compact detection region in PALMS minimizes chemical biases from particles of different shape or density that could have diverse trajectories. The PALMS ionization laser produces a mass spectrum for all known particle types in the atmosphere. Even pure sulfuric-acid–water particles, which are notoriously difficult to ionize due to their low absorption properties, generate sufficient ions in PALMS for particle classification. For the data presented here, particles were exposed to > 2500 MW cm⁻² of laser fluence at 193 nm, which is above the ion formation threshold for relatively pure sulfuric acid (Thomson et al., 1997). For organics and sulfate–organic mixtures, ion production is self-limiting due to space-charge repulsion, and total ion current in PALMS is relatively insensitive to laser power. Lastly, particles in the accumulation mode are nearly or completely ablated by the excimer laser (Murphy, 2007). Consequently, PALMS mass spectra represent the composition of the entire particle so that classification routines and relative measurements of chemical sub-components are not biased to physical inhomogeneities such as coatings, phase separation, or surface-enhanced species. It should be noted that although coarse-mode sea salt mineral dust particles do not fully ablate and therefore may give an incomplete picture of the particle composition, the mass spectral signatures are still unique to those particle types, and they are classified accurately. We therefore assume that detection biases due to particle chemical or physical properties yield systematic errors that are small compared to other sources of error (see Appendix A).

Several optical particle spectrometer instruments were used for size distribution measurements. During NASA DC-8 sampling campaigns, the Laser Aerosol Spectrometer (LAS 3340, TSI, Inc) measured concentrations for particles from 0.1 to about 5 µm, above which the aircraft inlet transmission truncated the size distribution. Also on the DC-8, an Ultra-High Sensitivity Aerosol Spectrometer (Droplet Measurement Technologies) measured particles from 0.06 to either 0.5 or 1.0 µm, above which the LAS data were used. On the NOAA P-3 aircraft, the combination of a Lasair model 1001 (Particle Measurement Systems) and a custom-built white light optical particle counter (WLOPC) measured particle concentrations from 0.12 to about 8 µm. On the NASA WB-57 aircraft, a custom-built Focused Cavity Aerosol Spectrometer (FCAS II) measured particles from about 0.07 to 1.5 µm dry diameter (Jonsson et al., 1995; Wilson et al., 2008). All sizes are reported as ammonium sulfate diameters, and all concentrations are reported at standard conditions (1013 hPa and 273.15 K).

During DC-8 sampling campaigns a high-resolution time-of-flight aerosol mass spectrometer (HR-ToF-AMS; Aerodyne Research; Canagaratna et al., 2007; Nault et al., 2018) measured non-refractory, bulk aerosol mass composition at 1 Hz resolution with 100 % transmission for vacuum aerodynamic diameter 100 < D_va < 500 nm (50 and 770 nm at 50 % efficiency; see DeCarlo et al., 2004, for the definition of D_va). Raw mass spectra were analyzed at 1 min intervals, yielding detection limits for organic and sulfate aerosol mass concentrations of 75 and 10 ng m⁻³, respectively, on average in the free troposphere. During DC-8 campaigns, soluble ions were also measured using the Soluble Acidic and Gases and Aerosols (SAGA) offline ion chromatography from aerosol filters (Dibb et al., 1999). Typical sampling times were 5–15 min with detection limits of ∼10 ng m⁻³. Filter data are excluded when cloudy periods exceed 20 % of the sample time or over altitude ranges exceeding 3 km.

3.1 Composition-resolved size distributions from SPMS combined with particle size spectrometers

The general method of deriving quantitative abundance from single-particle composition data is introduced here and outlined in Fig. 1, with details described in the following sections. The approach combines size-resolved, single-particle composition from the PALMS instrument with a concurrent measurement of size-resolved absolute number concentration. Typically, an optical particle spectrometer (OPS) is used to measure the aerosol size distribution across the accumulation and coarse modes, although other sizing techniques based on electric mobility or aerodynamic diameter, or a combination of techniques, can be employed. Mass spectra of individual particles acquired with PALMS are classified into one of several compositional categories. Aerodynamic diameters, D_a, for each particle are converted to volume-equivalent (geometric) diameters, D_ve, using particle densities and dynamic shape factors to match the OPS data. The particle classes are binned into size ranges that align with the particle size spectrometer. Then the fraction of each particle class within each size bin is multiplied by the average concentration within that bin. The resulting composition-resolved size distribution is integrated to give absolute number, surface area, or volume concentrations for each particle class. Mass concentrations for each particle type are determined by applying particle densities to the volume concentrations. Total sulfate and organic mass concentrations were derived from the non-refractory particle types.

Figure 1Flow chart to derive particle type concentrations and bulk sulfate and organic mass concentrations from SPMS and OPS data.

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Figure 2Quantification of PALMS particle classes. (a, c) Raw PALMS counts for different particle classes (colors) overlaid on the aerosol volume size distribution (dashed black). (b, d) For each diameter bin, the fractional contributions of each PALMS particle class are applied to the total volume. Vertical dashed lines define four broad diameter bins that are used to generate concentration products at higher time resolution (see text). The upper panels are from 39 min of sampling at low altitude over the Gulf of Mexico and contain influences from the marine boundary layer, long-range mineral dust transport, and lower tropospheric pollution. The bottom panels represent the remote upper troposphere with minor influences from continental and stratospheric sources, sampled over 27 min.

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Figure 2 shows two composition-resolved volume distributions measured from aircraft that are representative of two diverse atmospheric environments. Panels a and c give raw spectra counts as a function of size for each PALMS composition class, as well as the OPS volume distribution. The PALMS size bins are then aligned to the OPS, and fractional abundances in each size bin are applied to the OPS volume distribution to generate the panels b and d.

The composition-resolved size distributions in Fig. 2b and d contain a wealth of information and represent a powerful set of tools to investigate atmospheric aerosol properties. PALMS and other single-particle techniques show that the atmosphere consists of an external mixture of particle types, and in Fig. 2 the compositional size modes for these particle types are clearly revealed. Three broad aerosol regions are apparent in the volume distributions: the accumulation mode at D_ve < 0.5 µm consisting of mostly non-refractory particle types, a coarse mode at D_ve > 1 µm dominated by mineral dust and sea salt, and the inter-mode minimum at 0.5 < D_ve < 1 µm that is a mixture of accumulation- and coarse-mode composition. Most particle classes extend to sizes beyond their principal mode. For instance, sea salt and mineral dust can also contribute significantly to submicron aerosol volume. In many environments, an extension of the accumulation mode continues to > 1 µm where non-refractory particle types contribute to supermicron volume (Fig. 2d).

The practical limitations of this method mostly originate from the need in airborne studies to derive statistically significant composition measurements across the atmospherically relevant sizes within a reasonable sampling time (∼1–5 min). The Fig. 2 examples required tens of minutes of sampling to populate nearly the entire accumulation- and coarse-mode size ranges with particle mass spectra. Although PALMS size range encompasses most of the accumulation and coarse volume modes, Fig. 2a and c show how the outer ranges of each mode are not efficiently characterized. The white areas in Fig. 2b and d represent aerosol volume that is not allocated to any particle class. In most cases the unallocated volume is a minor fraction of the total, and the composition can be extrapolated to fill the entire mode, assuming composition remains constant. The following sections describe simplifying assumptions that allow faster measurements of particle type concentration while maintaining reasonable uncertainties. Uncertainties and limits of detection for particle type concentrations are detailed in Appendix A.

Table 1PALMS principal atmospheric particle types.

^a Density at measurement conditions. ^b χ_v, within or near free molecular flow. ^c Mass fraction within the dominant size mode for background tropospheric air.; strat = lower stratosphere, MBL = marine boundary layer. ^d Calculated based on organic-to-sulfate mass ratio. ^e Derived from optical–aerodynamic analysis.

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3.2 Particle composition classes

Each PALMS particle mass spectrum is classified as one composition type, e.g., mineral dust, sea salt, or sulfate–organic–nitrate (SO) mixtures, according to dominant spectral signatures. PALMS particle classification has been described previously (Cziczo et al., 2001, 2004; Froyd et al., 2009; Hudson et al., 2004), and definitions for nine principal atmospheric particle types are updated here. Chemical signatures, sizes, and other properties are listed in Table 1. These particle classes are defined so as to broadly capture the main chemical components or identify a distinct aerosol source. It is important to note that PALMS and other SPMS particle type definitions are flexible and can be tailored to a particular environment or objective. Only positive ion mass spectra are used to categorize particles into these classes. The classification method uses empirical criteria based on relative peak intensities, and a spectra clustering algorithm (Murphy et al., 2003) is then used to refine particle sorting. Figure S2 shows representative particle mass spectra for all classes in Table 1.

The most abundant classes under most tropospheric environments are the sulfate–organic–nitrate internal mixtures and biomass burning (BB) particles. Particles classified as SO can be composed of primary or secondary material from a wide variety of sources but contain no biomass burning or other clear chemical markers that denote a particular source. Biomass burning particles are identified by a distinct potassium signature, abundant organic signatures, and a lack of crustal, marine, or industrial metals, based on the method of Hudson et al. (2004). The crucial potassium signature is stable over weeks of aging, and due to PALMS extreme sensitivity to alkali metals, the potassium signal is observed above organic background peaks even when potassium constitutes ≪0.1 % of particle mass (Cziczo et al., 2001). The identification of these primary biomass burning particles is both highly sensitive and selective and does not deteriorate with particle aging. Single-particle information is critical to differentiating biomass burning potassium from other potassium sources that can confound bulk measurements (Legrand et al., 2016; Sullivan et al., 2019). Although secondary aerosol material is by definition distributed across many composition classes, the SO and BB classes contain the vast majority of sulfate, organic, ammonium, and nitrate aerosol mass.

A variety of minor but important particle types contributes to the external aerosol mixture of the lower atmosphere. The elemental carbon (EC) class include particles dominated by C${}_n^{+}$ mass spectral signatures and are interpreted as mostly EC by mass (presumably black carbon) since small amounts of internally mixed organics will obscure the EC signatures. Particles with minor EC content are therefore not distinguishable by PALMS and are instead classified as SO. Some EC particles contain potassium, which suggests a biomass burning source, and when accompanied by organic signatures these particles are instead classified as BB. Sea salt is easily distinguished by a dominant sodium signal, often with calcium, strontium, other alkalis, and sodium chloride ion clusters, but without crustal metals. Mineral dust (MD) spectra are identified from multiple crustal metal signatures such as silicon, aluminum, iron, and calcium and often contain trace amounts of alkalis, barium, tin, antimony, or lanthanides. This category is more heterogeneous than other classes and contains many different sub-types of spectra, representing a wide variety of mineralogies. Meteoric material (MT) is identified by iron, nickel, and magnesium within particular intensity ratios (Cziczo et al., 2001) and without other crustal material, and it is usually accompanied by strong sulfate signatures. The alkali salt (KS) category is reported here for the first time. The spectra for this class contain potassium and other alkali metals but no crustal material, and very low organic signatures distinguish them from biomass burning particles. Despite the similarity to biomass burning particles they are not enhanced in smoke plumes. The spatial and vertical patterns of these particles suggest primary continental emissions, but their exact source is still uncertain. Their size is exclusively submicron, which suggests they are not a type of mineral dust. The KS class constitutes 0.1 %–0.5 % of accumulation-mode particles over the US and < 0.1 % in the remote troposphere. Heavy fuel oil combustion particles (FO) are readily identified by strong vanadium signatures mixed with sulfate, organics, and sometimes iron or nickel (Ault et al., 2010; Divita et al., 1996). Spectra not identified as any of the above composition types are compiled into a class labeled as “Other” (OT), which contains a variety of minor particle types. By far the most abundant subtype in OT is a sulfate–organic mixture with possible alkali or metallic signatures that are small and difficult to distinguish from organic peaks. Other examples include spectra with the pyridinium ion and other amine signatures, industrial metals without obvious crustal components, and several types of organic-rich particles with distinct signatures that suggest unique but unknown sources. Primary biological particles are currently identified from negative ion spectra only (Zawadowicz et al., 2017), and a separate particle class is not implemented. In continental air they account for ∼1 % of supermicron particles and < 0.1 % of all detected particles (Zawadowicz et al., 2019).

All particle types acquire secondary material such as sulfate, ammonium, organics, and nitrate during atmospheric transport and aging. This secondary accumulation does not change particle assignments, except that heavy coatings may partially obscure unique signatures, resulting in a particle classified as “Other”. For example, a mineral dust particle that contains secondary sulfate, nitrate, and organic material will still be classified as mineral dust, and the derived dust mass includes the secondary material. Similarly, BB particles may contain secondary material sourced from biomass burning and non-biomass burning emissions. Laboratory calibrations of secondary mass spectral signatures could be used to subtract secondary mass from primary particle types. In some cases, the chemical component that identifies a particle's source is a minor constituent. For example, particles in the meteoric class are mostly sulfuric acid by mass, and the metals from ablated meteorites only account for a few percent of mass. Similarly, particles from heavy fuel oil combustion are composed of mostly sulfate and organic material but also contain traces of vanadium and other metals that denote their unique emission source.

3.3 Simplifying the size distribution

It is infeasible to retain the raw size resolution of the OPS for the integrated concentration analysis, since some common commercial instruments report up to 50 size bins per decade of diameter. For example, to achieve a minimal compositional representation with > 5 particle spectra in each size bin would require > 5000 spectra if acquired evenly across the instrument's size range. Accounting for inefficient acquisition at the extreme size limits of the instrument and with typical single-particle mass spectra data rates of a few hertz, this would require sampling times > 1 h to display composition at the native resolution of the OPS. Therefore, raw size bins of the optical spectrometer must be combined into fewer bins to improve time resolution but at some expense in accuracy of the derived concentrations. Ideally, size bins are defined such that the composition is homogeneous within each combined bin, in which case this simplification is rigorous and introduces no error to the derived number, surface area, and volume concentrations. Induced error should be minimized by defining size bins such that neither the concentration nor particle type fractions have strong gradients across a bin limit. Concentration products cannot be determined if zero PALMS spectra are acquired within any one size bin that contributes significantly to the integrated concentration from the OPS. In practice, composition gradients across size bins and statistical noise at the size range extremes generate systematic error that increases as size bins are combined and the size distribution simplified.

To estimate the systematic errors associated with this approach, integrated volumes were calculated for a number of cases where composition was constant over an extended flight period. For each case PALMS particle class volumes were first determined at a high size resolution of ∼20 bins per decade of diameter. Nearest-neighbor diameter bins were then combined, and integrated particle volumes were recalculated for each particle class at the lower size resolution. When the total number of bins was reduced to three or four, the diameter limits were empirically defined based on volume modes and composition gradients, e.g., one or two bins across the accumulation mode from about 0.06 to 0.5 µm, one across the inter-mode minimum at 0.5–1.1 µm, and one coarse-mode bin at 1.1–5 µm (vertical grey lines in Fig. 2b and d). The high-resolution analysis is treated as a reference value, and the average deviation of derived volumes as a function of final bin count is plotted in Fig. 3a for diverse cases across several flight campaigns. Typical deviations are 5 %–25 % when the size distribution is represented by three or four bins.

For sampling times of a few minutes, reducing the size resolution improves the data coverage (Fig. 3b). For each flight campaign, the number of sampling periods with sufficient statistics to generate concentration products are plotted relative to the two-bin case. To generate concentration products, every diameter bin that contributes significantly to the total volume must include ≥5 PALMS spectra. The three- or four-bin approach offers a good trade-off between reasonable time resolution and data coverage (65 %–85 % for three bins) while still yielding particle volume and mass concentrations whose systematic errors are less than or equal to typical volume uncertainties of a particle spectrometer (Kupc et al., 2018). Small particle detection efficiency (see Sect. 3.6) was worse for DC3 than for SEAC4RS, resulting in a steeper reduction in data coverage between three and four diameter bins. For DC3 the lower sensitivity to small particles results in more sampling periods with less than five particles in the smallest size bin, so that relative data coverage with four diameter bins is 25 %–50 % compared to SEAC4RS with 65 %–75 %.

Figure 3(a) Error in integrated volume introduced by reducing the size resolution of the analysis. Integrated volume was calculated for every PALMS particle class over several long flight segments with externally mixed but constant composition. Volumes computed at full diameter resolution (25–29 bins) provide a reference, and the average deviation for populous particle classes (contributing > 5 % of volume) is plotted as bins are combined. (b) Lines show the relative data coverage, defined as the number of time periods with > 5 particles in every diameter bin, using three different raw sampling times for two flight campaigns.

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Figure 3a suggests that induced errors are not a simple function of a particular atmospheric environment. Instead, most of the variability for any given bin count is due to sparse data within a single size bin or composition inhomogeneity across a size bin limit. The choice of size binning and time resolution when deriving integrated products can be altered based on both these conditions. Three size bins, where one bin encompasses the entire accumulation mode, are adequate for many tropospheric sampling environments (Fig. 2b). When certain external mixtures are apparent, it is recommended to split the accumulation mode into two size bins. For instance, biomass burning particles and meteoric or other stratospheric particles occupy the larger end of the accumulation mode, D > 200 nm, whereas secondary sulfate–organic particles typical of the upper troposphere can be smaller, ∼60–150 nm (Fig. 2d).

The PALMS size range encompasses the majority of accumulation- and coarse-mode size ranges under most atmospheric conditions (Fig. 2). Exceptions include the marine boundary layer and strong mineral dust plumes that often contain particles larger than ∼4 µm, and very clean upper tropospheric conditions, where number and volume contributions can be significant for sizes below the PALMS range, e.g., D_ve < 150 nm. In the latter case for example, the lower size bin limits for the concentration analysis can be set to fully include the lower end of the accumulation mode, e.g., D_ve(bin1) =60–250 nm. The PALMS composition averages applied to that bin will be biased to the larger end of the bin (D_ve∼150–250 nm), but PALMS fractions are applied to the entire bin as usual. The total concentration is still accurately measured by the particle spectrometer, but the PALMS composition is effectively extrapolated to sizes outside of the PALMS size range. The inherent assumption is that the composition across the lower half of the accumulation mode is homogeneous. While this extrapolation can be appropriate for many tropospheric and stratospheric environments, care should be taken in cases where the accumulation mode is weak and shifted to small diameters, such as very clean upper tropospheric conditions, or in heterogeneous environments, such as active aerosol emission sources mixing with background air.

3.4 Response of optical particle spectrometers (OPSs) to composition

The optical scattering response of an aerosol particle depends on its size, shape, refractive index, and the light collection geometry of the spectrometer instrument. Size distributions derived from optical particle spectrometers are based on the assumption of a fixed refractive index and spherical shape to translate the optical response of the measured particle population into volume-equivalent diameter, D_ve≡D_opt. A typical atmospheric air mass contains an external mixture of several diverse particle types. Fortunately, the real refractive indices for background tropospheric environments have been observed to fall within a narrow range (n≈1.50–1.56 at mid-visible wavelengths) such that ambient particle size measurements are not strongly affected by this assumption (Hand and Kreidenweis, 2002; Liu et al., 2008; Müller, 2002; Espinosa et al., 2017; Shingler et al., 2016; Yamasoe et al., 1998). Ammonium sulfate and ammonium nitrate (n=1.53 and 1.56 at λ=532 nm, respectively) are common inorganic constituents. Visible refractive indices (n-ki) have been derived for mineral dust aerosol from a variety of field measurements and typically range from about n=1.52–1.58 and k∼0.001–0.01 (Balkanski et al., 2007; Dubovik et al., 2002; Kandler et al., 2011; McConnell et al., 2010; Müller et al., 2010; Petzold et al., 2009; Schladitz et al., 2009), with absorption increasing at shorter visible wavelengths. Pure mineral samples can exhibit higher variability. Many retrievals for ambient organic aerosol material fall within typical inorganic refractive indices (Aldhaif et al., 2018; Kassianov et al., 2014; Espinosa et al., 2017; Shingler et al., 2016), although some laboratory surrogate species and a few atmospheric organics can have a wider range, n≈1.47–1.65 (Dinar et al., 2007; Dubovik et al., 2002; Hoffer et al., 2006; Rizzo et al., 2013; Schkolnik et al., 2007). Sulfuric acid, which is abundant in the stratosphere and sporadically in the troposphere, has a much lower refractive index of n=1.44 at 532 nm (Luo et al., 1996). Sulfuric acid aerosol also retain water (n=1.33 at 532 nm; Daimon and Masumura, 2007) even at low RH, making it a predominant outlier to typical refractive indices. Kupc et al. (2018) investigated the potential systematic error in prescribing the wrong refractive index to a representative upper tropospheric aerosol population. The difference in aerosol volume assuming pure ammonium sulfate (n=1.54) versus sulfuric acid (n=1.44) was only 12 %, which is lower than a typical aggregate volume uncertainty.

Few atmospheric particle types are strongly absorbing, and the complex index of refraction (k) for an ambient population is assumed to be zero. Several exceptions follow. Particles containing elemental carbon (EC), presumably in the form of black carbon (BC), typically account for < 1 % of accumulation-mode mass in the background atmosphere but up to ∼10 % inside wildfire plumes (Andreae and Merlet, 2001). The refractive index of pure black carbon has high variability, e.g., with n-ki =1.74–0.44i (Hess et al., 1998), 1.95–0.79i (Bond and Bergstrom, 2006), and 2.26–1.26i (Moteki et al., 2010). Although their measured diameters can be erroneous by > 10 % (Kupc et al., 2018), the net error on total aerosol number and mass is typically much lower due to their small relative population. Hematite mineral also has a unique refractive index (2.5–1.0i at 405 nm; Sokolik and Toon, 1999), but PALMS data indicate that pure hematite particles are extremely rare in the atmosphere.

Ammonium sulfate and ammonium nitrate are convenient materials to calibrate optical particle spectrometers for use in atmospheric sampling. If generating monodisperse aerosol at coarse-mode sizes is impractical, polystyrene latex sphere (PSL) size standards can be used, but their refractive index (n=1.59 at 532 nm; Ma et al., 2003) is not representative of typical atmospheric aerosol. Therefore, the scattering response of the sizing instrument to PSL particles must be converted to atmospherically relevant particles using Mie theory. Figure 4a shows Mie scattering intensities calculated for the LAS instrument at λ=663 nm for PSL and ammonium sulfate particles. At each diameter, the scatter intensity for a PSL particle is located on the ammonium sulfate intensity curve, and the associated ammonium sulfate diameter is determined. For a given scatter response the calibrated PSL diameter can shift up to 20 % due to the different refractive index of ammonium sulfate. The inset in Fig. 4a shows an expanded region from D=0.8 to 2.4 µm, where oscillations render optical particle sizing more uncertain. These oscillations introduce additional sizing uncertainty that is inherent to all monochromatic particle spectrometers in the range where, depending on the collection geometry, particle diameters are about 1–2 times the laser wavelength. Scattering intensity curves were smoothed so that each PSL diameter yielded one unique ammonium sulfate diameter. A raw PSL calibration curve is shown in Fig. 4b along with an ammonium sulfate-equivalent calibration curve derived using the diameter ratio curve. Also plotted in Fig. 4b are points from laboratory measurements of monodisperse ammonium sulfate particles generated with a differential mobility analyzer for D < 1 µm. Closure between the PSL-derived and measured ammonium sulfate response was not fully achieved. However, rapidly effloresced ammonium sulfate particles are slightly non-spherical, and as a result the volume-equivalent diameter of the monodisperse ammonium sulfate aerosol is smaller than the mobility diameter, D_ve < D_mob. Agreement between measured and derived ammonium sulfate calibration curves improved after correcting the calibration diameters using shape factors of χ_t=1.03 to 1.09, increasing with size (Huffman et al., 2005; Zelenyuk et al., 2006b). We confirmed that the ammonium sulfate particles had fully effloresced in the calibration system by observing an abrupt increase in apparent optical size due to a change in the refractive index when the relative humidity was reduced below the efflorescence point.

Figure 4Using Mie theory to translate the response of an optical particle spectrometer between particles of different refractive index. (a) Calculated scatter intensities at λ=663 nm for PSL and effloresced ammonium sulfate (AS) particles in the LAS instrument. PSL diameters are translated into ammonium sulfate diameters of the same scatter intensity using the Mie response curves, shown conceptually with grey arrows. The diameter ratio is plotted on the right axis. Smoothing must be applied to the Mie curves (inset in a, dashed line) in order to yield unique diameter translations. (b) A calibration curve derived from PSL particle standards (dashed black) is translated into an ammonium sulfate calibration curve (solid black) using Mie theory. Size-selected AS particles yield a directly measured AS calibration curve (solid red) to compare with the PSL-derived AS calibration curve.

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Highly non-spherical particles such as some mineral dusts and black carbon aggregates have different scattering intensities and phase functions compared to their volume-equivalent spheres. The effect on the angular scattering pattern is not consistent across different shapes and cannot be described by any simple measure of asphericity (Curtis et al., 2008; Mishchenko et al., 1997; Moteki et al., 2010; Peter and Michael, 1988). In general, the wide variety of atmospheric mineral dust morphologies will produce a diverse scattering response for particles with the same D_ve, with the principal effect of increasing the uncertainty in optically measured diameters. The degree to which sizing accuracy is affected depends on the degree and distribution of particle asphericity, surface roughness, the local steepness of the scattering intensity curve, and the angular collection geometry of the spectrometer. For particles that are freely rotating and not aligned with the instrument sample flow, as is the case near atmospheric pressure, optical mis-sizing may be minimized because the scattering response is an average of multiple particle orientations. In the current treatment all particles are assumed to be spheres for the purposes of optical sizing.

3.5 Particle densities and dynamic shape factors

PALMS measures the aerodynamic diameter, D_a, for > 90 % of the chemically analyzed particles. For each particle D_a is converted to a volume-equivalent diameter, D_ve, using the particle density ρ, dynamic shape factor χ, and the Cunningham slip correction factor, C_c.

In the limit of continuum flow β=0.5, and for free molecular flow β=1 (DeCarlo et al., 2004). Particles exit the aerodynamic focusing lens at approximately 35 hPa and accelerate into a vacuum region at ∼0.25 hPa where their aerodynamic size is measured by the time difference in scattering events from two laser beams spaced 33.1 mm apart. During acceleration, particles have Knudsen numbers of 1–20 and therefore experience flow that is near the free molecular regime. A comprehensive model that considers transitional flow is used to convert aerodynamic diameter measured by PALMS to D_ve (Murphy et al., 2004a). For submicron particles the model predicts β > 0.89, such that the measured aerodynamic diameter is near the free molecular limit (D_a∼D_va). As size increases beyond ∼1 µm, particle motion in the PALMS inlet becomes more transitional, e.g., β=0.75 for 3 µm. The dynamic shape factor under these conditions for most particles is close to the vacuum shape factor χ_v, which can deviate significantly from shape factors measured at atmospheric pressure (Alexander et al., 2016; Dahneke, 1973a, b). We further discuss free molecular shape factors for mineral dust below. Dry particle densities and shape factors for each composition class are listed in Table 1. Particle density for each measured particle is determined using one of three methods: (1) prescribed based on literature values for the observed particle type, (2) calculated using prescribed values for pure particle sub-components and their relative component abundance, or (3) estimated here using simultaneous optical and aerodynamic measurements.

Optical scattering intensities are measured in PALMS as particles pass through two detection lasers. Scatter intensities are not directly used for individual particle sizing for several reasons: (1) the particle stream is wider than the laser cross section so that particles experience inconsistent laser intensities, (2) Mie oscillations produce a relatively flat scattering intensity from 0.5 to 1.0 µm, and (3) the photomultiplier signals begin to saturate at D_ve > 0.6 µm. However, when averaged over hundreds of particles, the scattering response yields information about particle density, shape, and refractive index for submicron sizes (Moffet and Prather, 2005; Murphy et al., 2004a). Figure 5 shows simultaneous PALMS measurements of optical scattering intensity (I_scat) and aerodynamic diameter from one scattering laser for several different particle classes. For a given D_ve, a higher particle density translates into larger D_a values, yielding an I_scat–D_a curve further toward the right side of the graph. A larger shape factor will shift curves further to the left.

Figure 5PALMS simultaneous optical and aerodynamic diameter measurements during the SEAC4RS airborne campaign. (a) Raw scatter intensities versus measured aerodynamic diameters for populations of different particle classes. Curves toward the right side represent particle with higher density ∕ shape factor ratios, and a large real refractive index shifts curves upwards for these sizes. Sub-populations of the sulfate–organic–nitrate particle class are plotted for nearly pure (mass fraction > 0.9) organic (green) and sulfate (red) particles. Lines are the average of 100–72000 particle measurements. (b) Aerodynamic diameters are converted to volume-equivalent diameters by prescribing density and shape factors to each particle. Divergence at D > 0.5 µm is due to Mie resonances, which are highly sensitive to refractive index. (c) Calculated Mie scattering intensities at λ=405 nm are plotted for different refractive indices (n-ki) that correspond to composition classes.

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After converting each particle's D_a to D_ve, the scattering curves converge for D_ve < 0.5 µm (Fig. 5b). A single relationship is expected between physical diameter and optical scattering intensity for all spherical particle types with similar refractive index. The I_scat–D_a analysis in Fig. 5b helps validate prescribed densities and shape factors for known particles and also provides guidance for unknown particle types. Particle types with known density and shape factors, such as pure sulfuric acid, ammonium sulfate, and known organic species, act as internal standards.

All particles in the non-refractory classes (SO, BB, MT, FO) are internal mixtures of sulfate, organic material, and other minor components. Density is calculated for each particle in these classes as a weighted average of the pure component densities using the measured organic-to-sulfate mass fraction (see Sect. 3.7). Nitrate content is not considered in deriving density because nitrate is difficult to differentiate from ammonium and other nitrogen species in PALMS positive ion spectra. In regions where ammonium nitrate is the dominant aerosol constituent, particle density and water content can be similarly calculated (Clegg et al., 1998) using an estimated aerosol nitrate or total nitrogen calibration.

Density values for ammonium-sulfate–water and sulfuric-acid–water solutions are calculated at the temperature and RH of the instrument inlet (Clegg et al., 1998; Vehkamäki et al., 2002; Wexler, 2002). Sulfuric acid can retain ∼10 %–20 % water even under very dry (RH ≪ 1 %) sampling conditions, although additional water evaporation will take place in the PALMS low pressure inlet and vacuum region (Murphy, 2007; Zelenyuk et al., 2006a). The density for pure organic material is prescribed as 1.30 g cm⁻³ for SEAC4RS (Fig. 5) and other continental sampling campaigns, approximately the middle of a range of typical values observed in continental air, 1.2–1.45 g cm⁻³ (Cross et al., 2007; Turpin and Lim, 2001; Vaden et al., 2011; Zelenyuk et al., 2010, 2015). Organic density increases with oxidation level (Kuwata et al., 2012) as particles age in the atmosphere. Consequently, for the ATom remote troposphere an I_scat–D_a analysis like Fig. 5 indicates higher average organic densities of 1.35–1.45 g cm⁻³. The density of organic material in biomass burning has a similar range, 1.2–1.45 g cm⁻³ (Reid et al., 2005; Zelenyuk et al., 2015; Zhai et al., 2017), and 1.25 g cm⁻³ is prescribed here for continental US sampling and 1.35 g cm⁻³ for the ATom campaigns.

Refractive index differences affect the vertical position of the curves and shift the size where the optical response flattens out. Mie scattering intensity curves are plotted to demonstrate the effect of refractive index in Fig. 5c. For the PALMS wavelength and collection geometry, increasing the real and decreasing the imaginary refractive index gives increased scatter intensity for D < 0.5 µm. Large deviations beyond the typical range of 1.44–1.54 for atmospheric constituents are required to shift the response curve beyond typical variability. Elemental carbon stands out due to its large real refractive index and strong absorption. For most particle types, the I_scat–D_a curves are far more sensitive to density and shape parameters than the refractive index.

Elemental carbon (EC) particles are assumed to be composed of black carbon (BC), and particle density is prescribed at 1.8 g cm⁻³ based on the density for pure BC of 1.8–2.1 g cm⁻³ (Bond and Bergstrom, 2006; Lide, 2016; Park et al., 2004). Shape factors for EC particles in this size range will vary widely depending on the morphology of aggregates. Uncoated BC particles have χ_t values that range from 1.0 to > 3.0 depending on size (Khalizov et al., 2012; Slowik et al., 2007). χ_v=2.0 is prescribed here, based on the assumption that relatively pure EC may exist as chain aggregates that have not fully collapsed into a quasi-spherical shape (Schnitzler et al., 2014). The density and shape factors for EC are less well constrained than other particle classes since the unique refractive index renders the I_scat–D_a analysis ineffective (Fig. 5b), and uncertainties in derived concentrations are accordingly higher.

Sea salt aerosol, when fully dehydrated to anhydrous inorganic salts, has a density of 2.1–2.2 g cm⁻³ (Lewis and Schwartz, 2004; Zelenyuk et al., 2005). However, dried ambient sea salt particles have lower densities due to retention of water even after efflorescence (Cziczo et al., 1997; Shinozuka et al., 2004; Tang et al., 1997; Weis and Ewing, 1999) and to internally mixed organic material. In the marine boundary layer where most sea salt is sampled, particles exist as solution droplets since the ambient RH is greater than the efflorescence RH (ERH) of 40 %–45 % (Cziczo et al., 1997; Tang et al., 1997). Upon sampling, particles are dried to RH ≪ 45 % in the sampling lines, yet water does not fully evaporate. The I_scat–D_a analysis yields a sea salt aerosol density ∕ shape factor ratio of 1.45, which is close to the 1.41 g cm⁻³ density of a spherical sea-salt–water particle at the ERH of ∼45 % (Tang et al., 1997; Zhang et al., 2005). This suggests that efflorescence did not occur during the 0.5 s residence time between sampling and analysis and that most sea salt in PALMS is analyzed as a metastable solution. Sea salt density is prescribed at 1.45 g cm⁻³ with a shape factor of χ_v=1. Occasionally during research flights, particles were sent through a 300 ^∘C thermal denuder for 3.3 s prior to analysis. The I_scat–D_a analysis indicates that the heated sea salt fully effloresced and, assuming a dynamic shape factor of χ_v=1.08 (Beranek et al., 2012), had a density of 1.8 (see Fig. S3). We presume that efflorescence was complete during the 2–3 s residence time in the actively dried transfer tubing prior to sampling with optical particle spectrometers.

Mineral dust particle densities for the large majority of crustal minerals are typically 2.5–2.65 g cm⁻³ (Davies, 1979; Kandler et al., 2009; Linke et al., 2006), with a few subtypes such as hematite having higher values. Shape factors are invariably χ_t > 1 with a typical range of 1.3–1.5 (Davies, 1979; Kulkarni et al., 2011; Linke et al., 2006). χ_t denotes the dynamic shape factor measured at atmospheric pressure, which is in transitional flow but near the continuum flow limit, i.e., χ_t (1 atm) ∼χ_c. Most ambient mineral dust is coated by secondary organic and inorganic material, which reduces both particle density and shape factor. Preliminary PALMS laboratory studies indicate that typical organic coatings add 5 %–10 % to the mass of ambient dust particles, which reduces the density of a 2.65 g cm⁻³ dust particle to 2.4–2.5 g cm⁻³ and will also reduce the shape factor slightly. However, prescribing a density of 2.5 and shape factor of 1.4 yields I_scat–D_a curves for dust that are clearly not consistent with other particle types (Fig. S3). To achieve internal consistency, dust must either be prescribed an implausibly low particle density of ∼2.0 g cm⁻³ or a larger shape factor. Based on the I_scat–D_a analysis a density of 2.5 g cm⁻³ and χ_v of 1.6–1.8 is prescribed to all ambient dust particles. Large shape factors for ambient mineral dust are discussed in Appendix B.

Scattering intensities and sizes for additional particle types from Table 1 are shown in Fig. S3. Biomass burning particles are ∼80 %–90 % organic material by mass soon after emission (Cubison et al., 2011; Levin et al., 2010; May et al., 2014), and they acquire sulfate, ammonium, and nitrate upon further aging, whereby density increases to 1.4–1.5 g cm⁻³. In the stratosphere meteoric particles are nearly pure sulfuric acid (∼1.7 g cm⁻³) with small meteoritic inclusions, and they acquire organic material upon mixing into the troposphere, whereby their density decreases. Particles from heavy fuel oil combustion are mostly composed of mixed sulfate and organic material with trace industrial metals and typically have a density of 1.3–1.6 g cm⁻³. As stated above, for the concentration analysis, individual particle densities for these three classes (BB, MT, FO), as well as sulfate–organic–nitrate particles (SO) are calculated from relative sulfate and organic mass (see Sect. 3.7). Alkali salts have a density ∕ shape factor ratio of approximately 1.5, which, assuming spherical shape, is well below the 2.0–2.6 g cm⁻³ density typical of crystalline alkali sulfates, chlorides, carbonates, or oxides. It is possible that like sea salt, these alkali salt mixtures have not fully effloresced during sampling, and the retained water lowers their particle density.

3.6 Detection efficiency

The efficiency of acquiring single-particle mass spectra from aircraft platforms depends on many factors including sampling biases of the aircraft inlet, losses in sample tubing, transmission through critical orifices and focusing lenses, particle beam dispersion upon entering a vacuum, sensitivity of the optical detection system, and targeting accuracy with the desorption–ionization laser. In practice the detection efficiency at small sizes (D < ∼0.3 µm) is limited by the optical scattering signal-to-noise ratio and is a strong function of size, and large particle (D > ∼1.5 µm) detection is limited by impaction losses in tubing and instrument inlets. Detection efficiency is not used directly in deriving particle type concentrations presented here, yet it is an important diagnostic to assess SPMS performance over the dominant size modes in the aerosol distribution.

PALMS detection efficiencies are calculated for flight segments with fairly constant and low concentration (about < 0.1 µm³ cm⁻³), when the particle rate is not limited by hardware or software and therefore dead time is minimal. Measured D_a is converted to D_ve for all particles, and the total counts in each size bin are converted to an apparent concentration using the PALMS flow rate and sampling time. The PALMS observed concentrations are divided by OPS concentrations to determine detection efficiency. Figure 6 shows detection efficiencies for two airborne campaigns. Although the curves show that average instrument performance is similar across different campaigns, variability within and between individual flights can be large. Within any given flight, the detection efficiency at a particular size routinely varies by ×2–×5, and variations of > ×10 are not uncommon between flights. This variability is due to a variety of the factors listed above, many of which change with ambient pressure. In particular, changes in the overlap between the particle beam and laser beams will dramatically affect the detection efficiency for all sizes or a range of sizes. This variability in detection efficiency affects all particle classes nearly equally for a given particle size. A reduced detection efficiency does not directly impact particle type concentrations, but it can increase the statistical uncertainties and sampling time required to generate concentration products.

A tempting alternative to the method presented here (combining SPMS data with coincident size distribution measurements) is to determine the SPMS particle detection efficiency as a function of size under controlled conditions, and then multiply this curve by the airborne size-dependent data rate to yield a quantitative particle concentration, similar to SPMS scaling methods used at ground sites (Bein et al., 2006; Jeong et al., 2011; Pratt et al., 2009b; Shen et al., 2019). However, this approach is not recommended due to many possible pitfalls and large, unquantifiable errors. The key drawback is that the detection efficiency curve for PALMS and other SPMS instruments is extremely steep as it ascends several orders of magnitude across the accumulation mode from D∼ 0.1 to 0.5 µm, where particle number concentrations are also changing by orders of magnitude. The multiplication of these two strong functions, combined with the inherent variability over different ambient conditions and instrument alignment, will produce large and intractable uncertainties, e.g., > ×10 in mass. Other problems include the following.

• Both the measurement of detection efficiency and its application to derive concentrations are only valid when the particle data rate is not artificially limited by software or hardware or when instrument dead time can be accurately determined. In practice, aerosol concentrations in many lower tropospheric conditions and particularly inside plumes are high enough that SPMS systems will far exceed their maximum acquisition rate and generate erroneously low concentrations.

• Small changes to the alignment of the particle beam with the detection lasers, ionization laser, and ion extraction optics, which are not uncommon on airborne platforms, have a large effect on particle detection efficiency. Detection efficiency must also be re-determined after any routine alignment adjustments. For PALMS the second detection laser beam is only ∼150 µm wide.

• The flow characteristics of pressure reduction orifices change with upstream (ambient) pressure, changing particle trajectories downstream of the orifice in ways that are very sensitive to physical alignment and may not vary smoothly with pressure. One example is that pressure-controlled inlets can act as virtual impactors that enhance concentrations above a certain particle size that is both difficult to define and changes with pressure.

• Upstream pressure reduction orifices routinely accumulate small amounts of aerosol material that subtly change particle trajectories with large impacts to detection efficiency (Fig. 6).

The approach described in Sect. 3.1, mapping the PALMS composition measurements to independently measured size distributions without the need to determine size-dependent detection efficiencies, circumvents these complications.

Figure 6Detection efficiency curves for the PALMS instrument in flight. Detection efficiency was calculated for several cases, identified as clean flight segments when the particle data rate was not actively limited by software or hardware. Thick lines and shading are geometric means and standard deviations over all cases. Higher efficiencies for D_ve > 3 µm during ATom are partly due to addition of a virtual impactor upstream of PALMS. Thin black lines are five individual cases during one ATom-1 flight. Variations in altitude, particle composition, inlet performance, and unknown factors result in detection efficiencies that vary by > ×10 within and between flights. The lowest thin line was a case where a buildup of aerosol material on the pressure reduction orifice altered particle trajectories inside the inlet.

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3.7 Sulfate and organic mass concentrations

In addition to deriving concentrations for individual particle classes, the subcomponents of internally mixed particles can also be quantified. Signal intensity ratios in PALMS mass spectra for components of interest are calibrated to known mass fractions in laboratory-generated aerosol standards. By combining these calibrations with the particle class concentrations described here, absolute mass fractions for aerosol subcomponents such as sulfate and organic material can be determined. For instance, the average sulfate mass fraction is first determined for all non-refractory particle classes using mass spectral signal ratios, and then this mass fraction is multiplied by total mass concentration of those particle classes to yield an aerosol sulfate mass concentration. The resulting mass concentrations for sulfate, organic material, metals, or other components can be compared directly to bulk composition measurements from instruments such as the AMS, SAGA, or a variety of offline analytical methods (see Sect. 4.1).

Murphy et al. (2006) derived sulfate and organic mass fractions from PALMS negative polarity spectra by calibrating airborne data to a quadrupole AMS. New calibrations for sulfate and organic mass fraction were performed on positive mass spectra for the current study using realistic atmospheric surrogate particles, shown in Fig. 7. Aqueous solutions were nebulized to generate a submicron aerosol population that was dried to RH < 40 % and sampled with PALMS. Solutions were composed of ammonium sulfate mixed with varying amounts of sulfuric acid, sucrose, and mixed dicarboxylic acids (see Table S1 in the Supplement). Positive spectra were very similar to free tropospheric aerosol spectra in the SO particle class, confirming that the ionization environment for calibration particles is representative. Another set of calibration solutions contained ∼1 % potassium and generated particle spectra that were very similar to biomass burning aerosol in the atmosphere. Relative intensities were summed for C⁺, CH⁺, CO⁺, and ${\mathrm{C}}_{\mathrm{3}}^{+}$ ions to represent the total organic signal. In PALMS, these ions comprise > 90 % of the total organic ion intensity in positive spectra for nearly all non-refractory particles in the atmosphere. This efficient conversion of organic material into a few simple ion species demonstrates a weak dependence of the principal mass spectra signatures on organic aerosol species and facilitates calibration across different particle types. The ${\mathrm{C}}_{\mathrm{2}}^{+}$ ion was excluded here due to interference with Mg⁺ in the meteoric class. The sulfate signal is the sum of S⁺, SO⁺, and ${\mathrm{SO}}_{\mathrm{2}}^{+}$ ion intensities, and it is similarly consistent across non-refractory particles.

Figure 7PALMS calibration of organic mass fraction for atmospheric aerosol surrogates composed of neutralized and acidic sulfate mixed with a variety of organic compounds (see Table S1). Blue points are ammonium sulfate–sucrose–adipic-acid solutions, and red points are ammonium-sulfate–sulfuric-acid–dicarboxylic-acid solutions. (a) Raw signal fractions (dashes) are fit to the solution organic mass fraction data (dotted line). Symbols are averages of 130–1900 spectra. (b) Calibrated organic mass fractions from PALMS (red and blue) confirm a linear response, with averages that exhibit similar deviations to a quadrupole AMS. The dotted line is a linear fit to PALMS data forced through zero. (c) Relative error (standard deviation ∕ mean) for all calibration points as a function of the population size used to calculate the average.

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Figure 7a shows the PALMS response as a function of aerosol organic mass fraction. The organic signal fraction, sf_org, defined as the intensity ratio of organic peaks ∕ (organic + sulfate peaks), is fit to the organic mass fraction mf_org using the following functional form.

The single parameter α represents the relative ionization efficiency (RIE) of organic material to sulfate. No systematic differences were found in the PALMS response to organic and sulfate mixtures with and without potassium, indicating that organic and sulfate ionization is fairly consistent across different ionization environments in non-refractory particles. The calibration fit is applied to the signal fractions in Fig. 7b. The organic mass fraction for individual particles can have large errors due to the inherent particle-to-particle variability in SPMS spectra. However, errors are quickly reduced when averaging over a population of particles. To estimate precision uncertainty, particles were arranged into groups of increasing size, and the average organic mass fraction for each population was compared to the solution mass fraction, Fig. 7c. The relative standard deviation converged to 8 % when averaging ≥15 spectra, and errors exhibited no trend with mass fraction (not shown). Coincident with PALMS, an Aerodyne AMS using a quadrupole mass analyzer (Jayne et al., 2000) measured sulfate and organic mass of the generated aerosol. In Fig. 7b, average mass fractions from the AMS show similar deviations from the 1:1 line to the PALMS averages.

The calibration is applied to positive spectra for all non-refractory particle classes, including SO, BB, MT, and FO. The organic or sulfate mass concentration for an individual particle class can be calculated by multiplying the mass concentration by the organic or sulfate mass fraction. Similarly, total organic and sulfate mass concentrations are calculated as the sum of organic and sulfate mass concentrations from all non-refractory particle classes. These mass concentrations are conceptually comparable to bulk aerosol analysis of organic and sulfate made by common online (e.g., aerosol mass spectrometry) and offline (e.g., ion chromatography) techniques. By truncating the PALMS size range accordingly (Hu et al., 2017), direct comparisons between PALMS and these other measurements can be made. Total uncertainties in PALMS sulfate and organic mass concentrations are estimated from uncertainties in the simplified size distribution (Sect. 3.3) combined with errors in mass fraction, OPS volume, particle classification, and particle density (see Appendix A). For ATom campaigns using 3 min sample periods, estimates of total relative uncertainties (1σ) are 40 %–50 % for mass concentrations ≤0.01 µg m⁻³ and 20 %–35 % at higher concentrations. Any potential biases due to extrapolation of accumulation-mode composition to sizes below the PALMS size range (Sect. 3.3) are not included.

Primary sulfate on sea salt or mineral dust, as well as secondary sulfate accumulated on other particle types, is not included in the calibration because sulfate ionization on refractory particles is complicated by interferences and stronger matrix effects. The analysis assumes that dry aerosol mass is composed entirely of organic and sulfate material. Constituents like ammonium, nitrate, chloride, and alkali metals are disregarded. In most free tropospheric environments these components account for a small fraction of the aerosol mass. In the continental boundary layer or under polluted conditions, higher levels of ammonium and nitrate will introduce a high bias to the derived organic and sulfate mass concentrations. Future calibration studies can address the aerosol total nitrogen content from positive spectra or nitrate content using negative spectra.

Figure 8Comparison of PALMS with other speciated aerosol mass measurements. (a) PALMS derived sulfate mass at 3 min time resolution compared to co-located AMS and SAGA filter samples during the ATom-1 airborne campaign. Sea salt sulfate ($\mathrm{0.25}\times {\mathrm{Na}}^{+}$) is subtracted from SAGA data. SAGA filters taken over an altitude range > 3 km are excluded. Small points are 3 min averages (blue) or represent one SAGA filter measurement (orange). Large symbols are medians with interquartile error bars. The solid black line is 1:1, and grey dashed lines are 1:1.5 and 1:2. The inset graph is a histogram of PALMS ratio to AMS or SAGA for all individual samples. PALMS sulfate (b) and mineral dust (c) mass are compared to nearby IMPROVE ground station data for three airborne campaigns. Each point is the average of airborne data for non-targeted flight segments in the continental boundary layer within 0.5^∘ latitude and 1^∘ longitude of an IMPROVE site that reported data that day. IMPROVE data are 24 h averages, and airborne segments are typically ∼3–30 min duration during daytime. Error bars are estimated statistical uncertainty calculated as described in Appendix A. Dashed lines are weighted linear fits.

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4.1 Comparison to other aerosol composition measurements

Figure 8 compares PALMS mass concentrations for sulfate and mineral dust with other online and offline techniques during routine airborne measurements. PALMS sulfate mass is calculated as the sum of all non-refractory particle types (SO, BB, MT, and FO), accounting for the sulfate mass fraction of each particle type (Sect. 3.7). PALMS sulfate mass concentration shows excellent agreement with other airborne sulfate measurements over several orders of magnitude (Fig. 8a). For the AMS comparison the PALMS and LAS size ranges are truncated using the AMS size-dependent lens transmission efficiency, which is similar to that reported in Hu et al. (2017).

Few standard methods exist to derive accurate mineral dust aerosol concentrations. The Interagency Monitoring of Protected Visual Environments (IMPROVE) program performs routine aerosol composition measurements at over 200 ground sites throughout the US. Particles are collected on filters over a 24 h period every few days. Bulk concentrations of aerosol components are measured using particle-induced X-ray emission (PIXE), X-ray fluorescence (XRF), and other offline analytical techniques. Sulfate is derived from sulfur measurements assuming partial neutralization by ammonium. Soil dust concentration is derived from crustal metal concentrations and by applying a basic mineralogy. In Fig. 8b and c, PALMS sulfate and mineral dust mass concentrations are compared to IMPROVE data for airborne sampling in the continental boundary layer near an active IMPROVE site. PALMS airborne data are truncated to D_a < 2.5 µm to match the IMPROVE size range. Spatial and temporal variability render this an indirect comparison. Nevertheless, the sulfate measurements are strongly correlated, suggesting that measurement colocation is reasonable and that for sulfate, the snapshot obtained during short airborne segments can often be representative of the daily average. Mineral dust is also positively correlated but exhibits higher variability than sulfate. The variability is large compared to estimated uncertainties, suggesting that real atmospheric variability rather than measurement error is the cause. This is not surprising given the different sources of sulfate and mineral dust. Dust resuspension from land surfaces is a strong function of wind speed, and localized wind patterns give ground-level dust a high variability at small spatial scales, whereas secondary sulfate sources are more regional in scope. Additionally, the different size ranges for sulfate and dust can lead to different loss rates due to precipitation scavenging or gravitational deposition. Despite the imperfect sampling overlap, the qualitative agreement and positive correlation in Fig. 8c furthers confidence in the ability of PALMS to measure absolute mineral dust mass concentrations.

Figure 9Vertical profiles of PALMS mineral dust mass (a) and mass fraction (b) over the continental US for D_ve > 0.1 µm. Lines are campaign average concentrations binned at 1 km intervals from products generated at native resolutions of 3 min (SEAC4RS, DC3, NEAQS) or 5 min (MACPEX). Biomass burning plumes and clouds are excluded. By truncating the size range using a typical cyclone impactor transmission curve with D_a (50 %) =2.5 µm (http://www.urgcorp.com/, last access: 26 October 2019), these mass concentrations are equivalent to a PM_2.5 measurement. The MACPEX size range is limited by the optical particle spectrometer to D_ve < 1.5 µm. Positive error bars are one standard deviation.

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4.2 Examples of mineral dust mass over the US

To demonstrate the utility of the new quantification method, we calculate the average mineral dust mass over the continental US. Figure 9 compares PALMS mineral dust mass concentrations for four airborne campaigns that span different regions and seasons. In general, the large majority of dust mass was present in the coarse mode, D_ve > 1 µm. For the summertime campaigns, concentrations decrease steadily with increasing altitude, suggesting that dust was emitted from regional sources and removed during vertical transport. For the DC3 campaign the dust maximum occurred in the mid-troposphere. This profile is consistent with Asian dust sources contributing significantly to springtime US dust loadings (Chin et al., 2007) and also to convective lofting of dust. The MACPEX campaign targeted large-scale convective systems. The dust mass increase at 11–12 km is consistent with deep convective outflow. For the SEAC4RS, DC3, and NEAQS campaigns, the aircraft inlets and aerosol instrumentation measured sizes up to 4 µm and captured nearly the entire coarse mode. An exception was a weak Saharan dust plume encountered over the Gulf of Mexico, where external cloud–aerosol probes showed particles up to 20 µm. Future publications will explore mineral dust abundance and geographic distributions over continental and remote regions.