THE GROWTH FACTOR AND BULK HYGROSCOPICITY OF ATMOSPHERIC SOOT OF URBAN AEROSOLS

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INTRODUCTION
The microscopic solid or liquid particles suspended in the atmosphere are called aerosols, these aerosols have effect on the radiative balance of the Earth and thus, the climatic system by interacting directly with solar and terrestrial radiation or changing the formation of clouds indirectly (Lohmann and Feichter, 2005;IPCC, 2013 ;Seinfeld et al., 2016). These aerosol climatic effects are highly irregular due to of the large variability of the physical and optical properties of aerosol, which are attributed to multiplicity of sources, and their dependence on the prevailing meteorological and atmospheric conditions (Satheesh and Krishna Moorthy, 2005). The aerosol optical properties are strongly dependent on relative humidity (Tijjani and Akpootu, 2013a). The strong effect of aerosols on climate has not been given significant attention, which present significant uncertainty into climate predictions (IPCC, 2007). The Smog and Soot which are also referred to as ground-level ozone and particulate matter respectively are the two most common forms of air pollution (Meseke et al., 2022). Soot aerosols also known as black carbon (BC) are formed when incomplete combustion takes place. The major sources of soot aerosols are forest fires, diesel engines and biomass burning. Absorption properties of soot particles depend highly on the combustion temperature and other material (e.g. organic carbon) emitted during the processes of combustion (Bond and Bergstrom, 2006). Soot is made up of monodispersed spherical particles that collect into mass fractal aggregates having a broad size distribution, the primary soot particles are usually very small (Tijjani and Akpootu, 2013b). The role of soot particles in combustion is the major rationale of both experimental and theoretical investigation of soot radiative properties (Akpootu and Momoh, 2013a). The dust aerosol present in the atmosphere during the harmattan season in the northern hemisphere is a common feature of the climate of most parts of West Africa (Akande et al., 2013). The enormous amount of dust and sand particles raised and transported by the harmattan dust haze strongly decreases visibility and are estimated to reach about 6000 m above sea level (Essienimo et al., 2016a;Essienimo et al., 2016b) The hygroscopic growth and the mixing state of aerosol particles play a significant role for various atmospheric effects like the direct aerosol effect on climate, visibility degradation, and cloud formation (Sloane and Wolff, 1985;Pandis et al., 1995;McFiggans et al., 2006). Through the interaction of atmospheric particles and cloud droplets with incoming shortwave radiation, the particle hygroscopic growth is one of the major parameters influencing the terrestrial radiation budget and climate (IPCC, 2007). Some uncertainties connect to the hygroscopic growth estimation and cloud condensation nuclei (CCN) activation for the complex chemical mixtures of aerosol particles found in the atmosphere. Other uncertainties relates to how hygroscopic growth and CCN activation can be parameterized for implementation in higher scale climate models. The scattering and reflection of solar radiation by aerosols and clouds tends to cool the earth's surface, and this referred to as negative forcing while in a situation when the absorption of terrestrial radiation by greenhouse gases and clouds tends to warm it is referred to as positive forcing (Akpootu and Momoh, 2013b;Akpootu and Sharafa, 2013;Essienimo et al., 2015a). The size distribution of any particular suspended particle determines the life-span of the particle in the atmosphere and the distance it can travel (Essienimo et al., 2015a;Essienimo et al., 2015b).
Numerous studies have been carried out to investigate the effect of atmospheric aerosols. In the paper of Tijjani and Akpootu (2012), they modeled the optical depths, asymmetry parameters and single scattering albedos of urban aerosols using Optical Properties of Aerosols and Cloud (OPAC) at spectral range of 0.25 μm to 1.0 μm for eight different relative humidities (RHs). The radiative forcings (RF) and Ångström parameters was computed from the obtained data. Based on the RF, they found that as the RH increases there is a small increase in warming from 0 to 70% but as from 80 to 99% RH there is an increase in cooling from the first to the third model. Akpootu and Gana (2013) modeled the hygroscopicity properties of water soluble aerosols component based on microphysical properties of urban aerosols using OPAC to determine the effect of relative humidity on hygroscopic growth factor and bulk hygroscopicity at spectral range of 0.25-1.00 m. Akpootu and Abdul salami (2013) describes the hygroscopicity properties of water soluble aerosols component based on optical and microphysical properties of urban aerosols using simulated data obtained from OPAC to determine the density mix ratio resulting from hygroscopic growth factor and bulk hygroscopicity at spectral range of 0.25-1.00 m for eight different relative humidities (RHs). They found that the density mix ratio indicates that there is a steady increase in aerosol hygroscopic growth factor with RHs and decrease in the magnitude of bulk hygroscopicity. Other studies include Akpootu and Muhammad (2013), Akpootu and Tijjani (2014), Seinfeld et al. (2016) to mention but a few. The aim of this paper is to investigate the effect of hygroscopic growth factor and bulk hygroscopicity of soot in relation to eight different relative humidities (0,50,70,80,90,95,98 and 99%) of urban aerosols using extracted microphysical properties of number mix ratio, volume mix ratio and mass mix ratio simulated from Optical Properties of Aerosols and Clouds (OPAC).

MATERIALS AND METHODS
The models extracted from OPAC are given in table 1. The urban aerosols data used in this study are derived from the Optical Properties of Aerosols and Clouds (OPAC) data set (Hess et al., 1998). A mixture of three components was used to describe Urban aerosols: a water soluble (WASO) components consist of scattering aerosols that are hygroscopic in nature, such as sulphates and nitrates present in anthropogenic pollution, water insoluble (INSO) and Soot. The particle number densities of soot were varied as 110,000 120,000 and 130,000 cm -3 while the water soluble and insoluble components were kept constant.
The key parameter used to characterize the hygroscopicity of the aerosol particles is the aerosol hygroscopic growth factor gf(RH), which indicates the relative increase in mobility diameter of particles due to water absorption at a certain RH and has been defined as the ratio of the particle diameter at any RH to the particle diameter at RH = 0, the RH is taken for seven values 50%, 70%, 80%, 90%, 95%, 98% and 99% (Swietlicki et al. , 2008;Randles, et al., 2004;Akpootu and Gana, 2013): The gf(RH) are subdivided into different classes with respect to hygroscopicity. One classification is based on diameter growth factor by Liu et al. (2011) and Swietlicki et al. (2008) as barely Hygroscopic (gf(RH) = 1.0 -1.11), less Hygroscopic (gf(RH) = 1.11-1.33), more Hygroscopic (gf(RH) = 1.33-1.85) and most hygroscopic growth (gf(RH) >1.85).
Most of the atmospheric aerosols are externally mixed with respect to hygroscopicity, and consist of more and less hygroscopic sub-fractions (Swietlicki et al., 2008). The ratio between these fractions as well as their content of soluble material determines the hygroscopic growth of the overall aerosol. Particle hygroscopicity may change as a function of time, place, and particle size (McMurry and Stolzenburg, 1989;Swietlicki et al., 2008). Estimation of hygroscopic growth factors with Köhler theory requires detailed knowledge of particle composition as well as a thermodynamic model, which describes the concentration dependence of the water activity for such a mixture. The hygroscopic growth factor of a mixture, gfmix(RH), can be calculated from the growth factors of the individual components of the aerosol and their respective volume fractions, , by employing the Zdanovskii-Stokes-Robinson relation (ZSR relation) (Stokes and Robinson, 1966;Meyer et al., 2009;Sjogren et al., 2007;Stock et al., 2011;Akpootu and Gana, 2013): (2) where the summation was performed over all compounds present in the particles. Solute-solute interactions are neglected in this model while the volume additivity was assumed. The model assumes spherical particles, ideal mixing (i.e. no volume change upon mixing) and independent water uptake of the organic and inorganic components. This was also calculated using the corresponding number fractions nk as (Meier et al., 2009;Duplissy et al., 2011;Akpootu and Gana, 2013).
(3) where nk is the number fraction of particles having the growth factor gfk . The gfmix(RH) as a function of mass mix ratio has been proposed by Tijjani and Uba (2013) as reported by Akpootu and Abdul salami (2013) to be (4) The subscript k in the above equations represents the different substances. The RH dependence of gfmix(RH) was parameterized in a good approximation by a one-parameter equation (Petters and Kreidenweis, 2007;Akpootu and Abdul salami, 2013): Here, aw is the water activity, which can be replaced by the relative humidity RH at equilibrium (Seinfeld and Pandis, Humidograms of the ambient aerosols obtained in different atmospheric conditions revealed that gfmix(RH) could as well be fitted well with a γ-law (Swietlicki et al., 2000;Putaud, 2012;Akpootu and Abdul salami, 2013) as

THE GROWTH FACTOR AND BULK…
Particle hygroscopicity is a measure that scales the volume of water associated with a unit volume of dry particle (Petters and Kreidenweis, 2007) and depends on the molar volume and the activity coefficients of the dissolved compounds (Christensen and Petters, 2012). The bulk hygroscopicity factor under subsaturation RH conditions was determined using the following relation (Akpootu and Abdul salami, 2013): where aw is the water activity that is replaced by the relative humidity as previously explained from equation (5).  Table 2 shows that there is an overall increase in aerosol hygroscopic growth factor for number mix ratio model with increase in relative humidity from 50-99% RHs in each model. The bulk hygroscopicity decreases with increase in RH from 50 -99% RHs for all the three models used. More so, it was observed that the growth factor decreases with RHs from 50-99% RHs when the models were compared from model 1 to model 3. Similarly, the bulk hygroscopicity decreases with RHs from model 1 to model 3. The aerosol growth factor revealed that the mixture is barely hygroscopic from 50 -80% RHs, less hygroscopic from 90 -95% RHs and more hygroscopic from 98 -99% RHs for the number mix ratio. The bulk hygroscopicity ranges between 0.02316 to 0.09456 for model 1, 0.02152 to 0.08792 for model 2 and 0.02007 to 0.08201 for model 3. The bulk hygroscopicity decreases with increase in RHs as displayed in figure 2 for the three models.   154 Tables 3, 4 and 5 shows the data estimated for the number mix ratio using equations (5) and (6). The results of the modeling using equations (12) and (13) are shown in table 6 The fitted curve can be represented by any of the empirical parameters in the form of either equation (5) or (6) However, it was observed that equation (6) gives a higher coefficient of determination, 2 as compared to equation (5) for the three models indicating that the growth factor is well fitted with the -law as compared to the parameterization by oneparameter equation.  Table 7 shows that there is a general increase in aerosol hygroscopic growth factor for the volume mix ratio model with increase in RHs from 50-99% RHs in each model. However, the bulk hygroscopicity decreases with increase in RH from 50 -99% RHs for all the three adopted models. It was observed that both the aerosol growth factor and bulk hygroscopicity decreases when compared from model 1 to model 3. The growth factor revealed that the mixture is less hygroscopic from 50 -80% RHs, more hygroscopic from 90 -95% RHs and most hygroscopic from 98 -99% RHs for the volume mix ratio. The bulk hygroscopicity ranges between 0.13658 to 0.32956 for model 1, 0.13628 to 0.32587 for model 2 and 0.13596 to 0.32224 for model 3.  figure 4 for the three models.    Tables 8, 9 and 10 shows the data obtained for the volume mix ratio using equations (5) and (6). The results of the modeling using equations (5) and (6)   The fitted curve can be represented by any of the empirical parameters in the form of either equation (5) or (6) However, it was observed that equation (6) gives a higher coefficient of determination, 2 as compared to equation (5) for the three models indicating that the growth factor is well fitted with the -law as compared to the parameterization by oneparameter equation.  Table 12 shows that there is a general increase in aerosol hygroscopic growth factor for the mass mix ratio model with increase in RHs from 50-99% RHs in each model. However, the bulk hygroscopicity decreases with increase in RH from 50 -99% RH for all the three models. It was observed that both the aerosol growth factor and bulk hygroscopicity decreases when compared from model 1 to model 3. The growth factor revealed that the mixture is less hygroscopic from 50 -80% RHs, more hygroscopic from 90 -95% RHs and most hygroscopic from 98 -99% RHs for the mass mix ratio. The bulk hygroscopicity ranges between 0.12884 to 0.29925 for model 1, 0.12857 to 0.29706 for model 2 and 0.12831 to 0.29487 for model 3.  Figure 5 depicts a non-linear increase in aerosol hygroscopic growth factor with RHs, however, the rate of increase appears to be almost constant. The growth factor rises up steadily with increasing RH, this may be attributed to the fact that higher RH implies more atmospheric moisture content which makes the aerosol particles to absorb more water vapour on particle surface. The range of values estimated for the gfmix shown in table 12 the mixture as depicted in figure 5 are described as less hygroscopic, more hygroscopic and most hygroscopic growth in accordance with the description for the range of values by Swietlick et al. (2008), Liu et al. (2011). The bulk hygroscopicity decreases with increase in RHs as displayed in figure 6 with almost constant rate for the three models under study.   158 Tables 13, 14 and 15 shows the data obtained for the mass mix ratio using equations (5) and (6). The results of the modeling using equations (5) and (6)   The fitted curve can be represented by any of the empirical parameters in the form of either equations (5) or (6) However, it was observed that equation (6) gives a higher coefficient of determination, 2 as compared to equation (5) for the three models indicating that the growth factor is well fitted with the -law as compared to the parameterization by oneparameter equation.

CONCLUSION
The analysis in this study shows that the aerosol hygroscopic growth factor gfmix increases with increase in RH while the bulk hygroscopicity factor decreases with increase in RH. The growth factor indicates that the mixture is barely hygroscopic, less hygroscopic, more hygroscopic for the number mix ratio and it's less hygroscopic, more hygroscopic and most hygroscopic for the volume and mass mix ratios. The bulk hygroscopicity ranges between 0.02007 to 0.09456 for the number mix ratio from model 1 to model 3, the bulk hygroscopicity ranges between 0.13596 to 0.32956 for the volume mix ratio from model 1 to model 3 while the bulk hygroscopicity ranges between 0.12831 to 0.29925 for the mass mix ratio from model 1 to model 3. The growth factor is well fitted with the -law as compared to the parameterization by oneparameter equation based on the coefficient of determination. The number mix, volume mix and mass mix ratios shows an increase in particle diameter with increase in RH with a steep curve of deliquescence found from 95-99% RHs. However, the volume mix ratio shows more increase in gfmix with RHs and gives higher coefficient of determination when compared to the number mix ratio and mass mix ratio. The results showed that the coefficient of determination, 2 > 96% for all the three models used in this study.