Aerosol Total Volume Estimation From Wavelength‐ and Size‐Resolved Scattering Coefficient Data: A New Method

While the importance of supermicron particles on human health and climate is well recognized, knowledge of their size‐related properties remains elusive. Many routine near‐surface in situ measurements of aerosol properties include size spectra of submicron particles and aerosol total scattering coefficient at three visible wavelengths and two size cutoffs. These properties are collected, for example, at the U.S. Department of Energy's Atmospheric Radiation Measurement (ARM) user facility. Our study illustrates how these conventional measurements can be used to predict total particle volume (particle size <10 μm). The well‐known fact that small and large particles scatter sunlight very differently forms the basis of a new method. Our study demonstrates a good agreement between estimated and measured total volumes for five climate‐important locations. The agreement suggests that the new method can be used to predict the total particle volume from the routine data collected at numerous sites around the world.


Introduction
Supermicron particles have several essential impacts on human health, environment, and climate (e.g., Atwood et al., 2017;Feng et al., 2017;Hand et al., 2017;Mahowald et al., 2014). Moreover, concentration of supermicron particles appears to exceed substantially the air-quality guidelines over several regions in the future due to a changing climate (e.g., Monteiro et al., 2018). The comprehensive global study of supermicron particles is hindered by the lack of size-resolved measurements at established air-quality networks supported by international and national organizations (e.g., Vahlsing & Smith, 2012), including the United Nations Environment Programme and the United States Environmental Protection Agency (US EPA), and the relatively sparse coverage of these sites. These routine air-quality data are complemented by measurements of surface-level aerosol properties at instrumented sites focusing on other aspects of the atmospheric research. For example, the U.S. Department of Energy's Atmospheric Radiation Measurement (ARM) user facility (e.g., Mather & Voyles, 2013;Miller et al., 2016) and many Global ©2020 Battelle Memorial Institute This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
Measurements of the size spectra and scattering of both submicron and supermicron particles (PM 10 , particulate matter with aerodynamic particle diameter smaller than 10 μm) are less common relative to those for submicron particles mostly due to well-known sampling issues associated with supermicron particles (Baron & Willeke, 2001). It should be emphasized that PM 10 volume is proportional to PM 10 mass, which represents one of the main health and environmental concerns (e.g., Barthel et al., 2019;Rodriguez et al., 2019). Important qualitative information on the supermicron particles can be provided by the wavelength-and size-resolved values of the total scattering coefficient (e.g., Hansen & Travis, 1974;Schuster et al., 2006). To illustrate this, a strong spectral dependence of SCA 10 suggests that the light scattering is dominated by submicron particles, while the lack of a wavelength dependence of SCA 10 is a good indicator of a large contribution of supermicron particles to the light scattering. The same is true for the size-resolved values of the total scattering coefficient. When comparable values of SCA 1 and SCA 10 at a given wavelength are observed, it suggests that the light scattering is dominated by submicron particles, while SCA 10 values significantly larger than SCA 1 indicate that supermicron particles play a major role in the light scattering.
The outlined qualitative relationship between submicron and supermicron particles and the wavelengthand size-resolved values of the total scattering coefficient is well understood. However, there is a large gap between such understanding and practical quantitative application of this relationship. The main goal of our study is to bridge the gap by taking advantage of available data sets of aerosol size spectra and total scattering coefficients. The selected data sets represent short-term integrated measurements at five sites with distinct aerosol types and environmental conditions. The two major objectives of our study are to (1) introduce a new method for predicting PM 10 volume using two parameters describing the wavelength-and size-resolved measurement of total scattering coefficient and PM 1 volume calculated from measured size spectra and (2) demonstrate an initial application of this method for five representative sites.

Approach
There are two main challenges associated with estimating aerosol volume from the light scattering data. First, the aerosol volume defines the third moment of the aerosol size distribution, while the scattering coefficient is proportional to the second moment of the same distribution (e.g., Sayer et al., 2012). Thus, the aerosol volume and total scattering have different sensitivity to the fraction of supermicron particles. This fraction can modify the spectral behavior of the total scattering coefficient significantly (e.g., Hansen & Travis, 1974;Schuster et al., 2006). Second, the scattering coefficient is influenced by the complex refractive index (RI), which can exhibit strong spectral dependence on aerosol type, mixing state, and composition (e.g., Eck et al., 1999). Therefore, the spectral behavior of the total scattering coefficient is governed by combined impact of two factors considered here (the RI and fraction of supermicron particles). As a result, these two factors must be considered for accurate interpretation of the light scattering spectral behavior.
These challenges suggest that the relationship between aerosol total volume and light scattering data is complicated. Nevertheless, it may still be possible to approximate this relationship by a set of statistical models and demonstrate their practical value as a useful predictive tool. For example, a regression model could express one parameter (the response variable), describing total volume of submicron and supermicron particles, as a function of two other parameters (the independent variables), expressing the wavelength-and size-dependent values of the total scattering coefficient. With this assumption in mind, we introduce the following three dimensionless parameters. The first parameter (the response variable) is a ratio of coarse and fine aerosol volumes: where PM 10,v and PM 1,v are volumes of PM 10 and PM 1 , respectively. The prediction of PM 10,v is the main goal of our approach. The second parameter (the first independent variable) is a ratio of total scattering coefficients measured at two wavelengths: SCA ratio ¼ SCA 10 0:45 μm ð Þ =SCA 10 0:7 μm ð Þ This parameter defines the wavelength dependence of the total scattering coefficient for a given size cutoff (aerodynamic particle diameters below 10 μm). Although the corresponding Ångström exponent can also be applied for describing this wavelength dependence (e.g., Delene & Ogren, 2002), such an alternative is not considered in our initial analysis. It should be noted that the SCA_ratio represents a quite narrow spectral range (0.45-0.7 μm); thus, it is mostly sensitive to the submicron particles (e.g., Atkinson et al., 2018). In other words, the SCA_ratio alone is not well suited for describing a link between the light scattering and PM 10,v . To address this limitation, we include the third parameter (the second independent variable). This parameter is a coarse-mode fraction (CMF) of the total scattering coefficient at a given wavelength: Two parameters (SCA_ratio and CMF_SCA) incorporate both wavelength and size dependence of the total scattering coefficient required for the PM 10,v prediction (section 4).
The proposed PM 10,v prediction includes three steps. The first step is to establish a statistical relationship between the response variable and other two independent variables using a regression model: where the regression coefficients α and β depend on CMF_SCA (section 4).
To do this, we utilize data sets of fine and coarse aerosol size spectra and total scattering coefficient collected at five climate-important locations (section 3). The second step is to apply the established relationship and the independent variables (SCA_ratio and CMF_SCA) for estimating the response variable (PM_ratio). The third step is to calculate the PM 10,v from the estimated PM_ratio and the complementary measurement-based PM 1,v as PM 10,v ¼ PM 1,v × (PM_ratio + 1) (section 4).

Observations
We use data collected during four Intensive Observational Periods (IOPs) supported by the ARM user facility (https://www.arm.gov). The selected IOPs with relatively short duration (4-6 weeks) were part of four major atmospheric field campaigns, which examined the temporal and spatial variability of the aerosol microphysical and optical properties over climate-important continental, alpine, coastal, and marine locations ( Figure 1 and Table 1), among other important topics. Similar suites of instruments, with state-of-the-art capabilities, sampled properties of the atmospheric aerosol, such as aerosol size distributions and total scattering coefficient (Table 1). In addition to the IOP-based aerosol properties, we include in our analysis related aerosol data with similar duration collected during summer and winter at the midcontinental ARM's Southern Great Plains (SGP) site (Table 1). Detailed reviews of the integrated aerosol measurements and corresponding instruments are given in the corresponding papers (Table 1). Here, we use the data to show site-dependent contribution of supermicron particles into aerosol volume and total scattering coefficient and to illustrate the strong covariability of parameters representing the coarse aerosol volume and the wavelength and size dependence of total scattering coefficients over variety of locations and seasons.
Similar to Kassianov et al. (2012), we calculate CMF of aerosol volume as a ratio of the coarse-mode volume (PM 10,v − PM x,v ) over the total volume (PM 10,v ), where PM x,v is either PM 1,v or PM 2.5,v (aerodynamic particle diameter below 2.5 μm). We define the corresponding fractions as the CMF_PM 10-1 (aerodynamic particle diameter range 1-10 μm) and CMF_PM 10-2.5 (aerodynamic particle diameter range 2.5-10 μm), respectively. These two fractions illustrate relative contributions of supermicron particles with different size ranges to the total volume. The selection of the upper size cutoff (10 μm) for the aerosol volume is made to match the upper size cutoff (10 μm) for the aerosol total scattering coefficient. Also, we calculate the corresponding CMFs of the aerosol total scattering coefficient at three wavelengths (0.45, 0.55, and 0.7 μm) and denote them as CMF_SCA 0.45 , CMF_SCA 0.55 , and CMF_SCA 0.7 , respectively. Finally, we assess the contributions of coarse particles to aerosol volume and total scattering following a probabilistic description (Kassianov et al., 2012). Our description involves cumulative percentages, which describe the percentage of time (or frequency) when the CMF of a given aerosol property exceeds a specified threshold (or magnitude).
Both CMF_PM 10-1 and CMF_PM 10-2.5 depend strongly on the location and season (Figure 1). To illustrate, we consider two extreme examples with the smallest and largest values of the CMF_PM 10-1 . Its smallest 10.1029/2019EA000863

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values take place during summer at the continental location (the SGP site): The CMF_PM 10-1 exceeds about 15% for 50% of time ( Figure 1a). In contrast, its largest values occur during winter at the marine location (the ENA site): The CMF_PM 10-1 exceeds 87% for 50% of time ( Figure 1b). In other words, the coarse-mode contribution to the aerosol volume has strong spatial and seasonal changes, and its largest value (87%) is about 6 times larger than the corresponding smallest (15%) value at the selected frequency threshold (50% of time). Relative to the CMF_PM 10-1 , the PM_ratio exhibits even larger changes (more than 1 order of magnitude) with season and location (section 4). For this reason, we use the PM_ratio for the PM 10,v prediction (section 4).
In contrast to the CMF_PM 10-1 and CMF_PM 10-2.5 , the coarse-mode fractions of the total scattering coefficient show weaker spatial and seasonal changes. For example, their largest values occur during winter at the marine location (the ENA site): The CMF_SCA 0.45 and CMF_SCA 0.7 exceed 67% and 75% for 50% of time, respectively (Figure 1b). These largest values (67% and 75%) are about 4 and 2 times higher than the corresponding values (18% and 31%; Figure 1a) observed during summer at the typical continental location (the SGP site). Since the spatial and seasonal changes of the CMF_SCA 0.45 (67% vs. 18%) in comparison with those of the CMF_SCA 0.7 (75% vs. 31%) are stronger, we use the CMF_SCA 0.45 in our consequent analysis.

Results
Here we demonstrate that the joint application of two parameters (CMF_SCA 0.45 and SCA_ratio) allows reasonable prediction of the PM 10,v values. A scatterplot, which pairs up values of the PM_ratio and SCA_ratio (Figure 2a), illustrates three important points. First, the upper limit of the PM_ratio (~40) exceeds that of the SCA_ratio (~3.8) by about an order of magnitude. Second, the PM_ratio is small to moderate (up to 10) for all selected locations, except the marine location (the ENA site) where the PM_ratio has the largest values (up to 40). Third, the complex relationship between the PM_ratio and SCA_ratio has a "hockey stick" shape ( Figure 2a), which is mainly attributed to different types of aerosol. Note that different types of aerosol are also responsible for an intricate association between fine-mode fraction of aerosol optical depth and its Ångström exponent (0.44-0.87 μm) (e.g., Eck et al., 2010). Thus, it is unlikely that the complex relationship between the PM_ratio and SCA_ratio can be approximated by a simple function. Note that the "hockey stick" shape represents all possible cases with small, moderate, and large values of the CMF_SCA 0.45 . The

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Note.
General information regarding the selected sites (second, third, and fourth rows) and measurements of aerosol properties (fifth and sixth rows) is included. Important details and the corresponding references are provided in the footnotes.  Figure S1 shows an example of the APS aerodynamic size distribution.
h Ultra-high-sensitivity aerosol spectrometer (UHSAS): optical size range 0.06-1 μm. The UHSAS-measured aerosol optical size distributions are converted into their aerodynamic size counterparts at the ENA site using the complex RI and density estimated from the complementary chemical composition measurements. Note that information on sea salt and dust is not provided by these measurements. Figure S1 shows an example of the UHSAS-based aerodynamic size distribution. Note that the UHSAS size spectra are not available at the ENA site during summer (Figure 1a). i TSI integrating nephelometer (TSI Inc., Model 3563): total scattering coefficient at three wavelengths (0.45, 0.55, and 0.7 μm).

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KASSIANOV ET AL. segregation of these cases by site-and season-dependent CMF_SCA 0.45 gives an opportunity to approximate this complex relationship by a group of linear regressions for a given site or season of interest ( Figure 2b).
However, it is unclear whether such simple approximation can be used to predict the PM 10,v reasonably well from the measurement-based variables (CMF_SCA 0.45 and SCA_ratio) using the introduced approach (section 2). To illustrate a benefit of this approximation in terms of the PM 10,v prediction, we consider two scenarios. The first scenario is "site-specific," which characterizes the situation when the site-and season-dependent data are available. Here, the existing seven data sets with the required size spectra and light scattering data (section 3), describing the site-and season-dependent changes of the aerosol properties, are used to generate seven groups of linear regressions. We use these seven groups and the introduced approach (section 2) to predict the PM 10,v for the corresponding locations (Figure 3, left column). The second scenario is "generic," which characterizes situation when the site-and season-dependent data are not available. To demonstrate such situation, we combine the existing seven data sets into a single data set. Then, we generate single group of linear regressions from the combined data set assuming that the site-and season-dependent data are not available. We use this single group and the introduced approach (section 2) to predict the PM 10,v at all the sites and seasons considered here (Figure 3, right column).
We begin with considering the "site-specific" scenario ( Figure 3, left column). The time series of the measured PM 10,v exhibit strong temporal and spatial changes. They are more pronounced during summer for the coastal location ( Figure 3c; the TCAP site), which defines a crossroad of distinct air-mass flow patterns (Berg et al., 2016). The opposite is true for the typical continental location during summer ( Figure 3e; the SGP site) where the temporal variability of the measured PM 10,v is fairly small. In general, there are very similar patterns of the predicted and measured PM 10,v for the selected sites and seasons. As a result, statistics describing the predicted and measured PM 10,v are comparable and the corresponding values of the correlation coefficients are quite high (about 0.66-0.97) ( Table 2). However, there are a few exceptions, which define occasional substantial differences between the predicted and measured PM 10,v especially at the urban ( Figure 3a; the CARES T0 site) and marine ( Figure 3f; the ENA site) locations. Likely, these exceptions represent events with the substantial contributions of refractory species, such as black carbon, sea salt, and dust, to the measurement-based PM 1,v (supporting information Figure S2). The current version of our approach does not take into account these contributions due to lack of information related to the refractory species. It should be emphasized that a simple screening of these events (when information about chemical composition is available) can improve substantially agreement between the predicted and measured PM 10,v . For example, the correlation coefficient increases from 0.66 (all data) to 0.83 (screened data) at the ENA site ( Figure S2). The "site-specific" scenario with the existing site-and season-dependent data (Table 1) is presumed to be applicable to locations and seasons where these data likely define a dominant type of local

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We continue with considering the "generic" scenario ( Figure 3, right column). Mainly, there are coherent patterns of the predicted and measured PM 10,v values for the selected sites and seasons. The "generic" patterns have several noticeable differences in comparison with those obtained for the "site-specific" scenario. These differences include rougher and smoother variations in the predicted PM 10,v for the urban (Figure 3g; the CARES T0 site) and marine ( Figure 3l; the ENA site) location, respectively. Thus, the corresponding values of root-mean-square error (RMSE) are larger (the CARES T0 site) and smaller (the ENA site), while Figure 3. Hourly time series of the measured (blue and cyan) and estimated (red and magenta) PM 10 volumes for the "site-specific" (left column) and "generic" scenarios (right column). The comparison is performed for five locations and two seasons (Table 1): (a, g) the T0 (blue and red) and T1 (cyan and magenta) sites during the CARES, (b, h) the SPL during the STORMVEX, (c, i) the TCAP site, (d, j) the SGP site (winter), (e, k) the SGP site (summer), and (f, l) the ENA site.  Table 2). The differences ( Figure 3 and Table 2) suggest that the "generic" scenario with the existing aerosol data (Table 1) can offer overall information on the temporal changes of the predicted PM 10,v for a given location and season, such as its general pattern and periods with large and small values, but the range of these changes can be underestimated or overestimated substantially especially at fine scales (e.g., 1-hr averages). Likely, the "generic" scenario with the existing aerosol data (Table 1) would be more beneficial for predicting the PM 10,v changes at coarser temporal resolution (e.g., daily averages) rather than those at finer scales (e.g., 1-hr averages). Note that daily averages typically describe the temporal changes of pollutants (e.g., Vahlsing & Smith, 2012).

Conclusions
We introduce a new method for predicting total aerosol volume PM 10,v (particulate matter with aerodynamic particle diameter below 10 μm). The PM 10,v prediction involves both (1) fine aerosol volume PM 1,v (particulate matter with aerodynamic particle diameter below 1 μm) calculated from measured size spectra of submicron particles and (2) measured wavelength and size dependence of aerosol total scattering coefficient. The wavelength dependence is described by a ratio of total scattering coefficients measured at two wavelengths (0.45 and 0.7 μm) and for 10-μm size cutoff (aerodynamic particle diameter). The size dependence is described by coarse-mode fraction of the aerosol total scattering coefficient calculated at single wavelength (0.45 μm) using two scattering coefficients measured with 1-and 10-μm size cutoffs (aerodynamic particle diameters).
To illustrate the performance of this method, we use aerosol size distributions and total scattering coefficients measured at five sites with continental, alpine, coastal, and marine environments. Distinct environmental conditions and aerosol types observed at these sites are responsible for strong temporal and spatial changes of the total aerosol volume. Despite of these strong changes, we demonstrate that the introduced method is able to predict PM 10,v reasonably well. For example, the correlation coefficient between the measured and predicted PM 10,v volumes is relatively high (0.65-0.97) and the RMSEs are typically smaller than the corresponding mean values of the measured PM 10,v . The ARM user facility (e.g., Mather & Voyles, 2013;Miller et al., 2016) and Global Atmosphere Watch (GAW) stations (e.g., Andrews et al., 2019) offer important measurements of the aerosol properties required for potential PM 10,v prediction around the world. The introduced approach, if proven accurate, could be applied to the existing and future ARM and GAW data with worldwide coverage, and the expected PM 10,v predictions would provide useful, but previously missed, pieces of the climate puzzle.

Data Availability Statement
Here is a list of websites with description of the selected field campaigns as well as the SGP site (Table 1)