AMTAtmospheric Measurement TechniquesAMTAtmos. Meas. Tech.1867-8548Copernicus PublicationsGöttingen, Germany10.5194/amt-11-2967-2018A novel method for calculating ambient aerosol liquid water content based on
measurements of a humidified nephelometer systemA novel method for calculating ambient aerosol liquid water contentKuangYehttps://orcid.org/0000-0003-4813-9784ZhaoChun Shengzcs@pku.edu.cnZhaoGanghttps://orcid.org/0000-0001-7160-4600TaoJiang ChuanXuWanyunMaNanBianYu Xuanhttps://orcid.org/0000-0002-5846-417XInstitute for Environmental and Climate Research, Jinan University, Guangzhou, ChinaDepartment of Atmospheric and Oceanic Sciences, School of Physics, Peking University, Beijing, ChinaState Key Laboratory of Severe Weather, Chinese Academy of Meteorological Sciences, Beijing, ChinaChun Sheng Zhao (zcs@pku.edu.cn)18May20181152967298210September201727October201724April201826April2018This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/This article is available from https://amt.copernicus.org/articles/11/2967/2018/amt-11-2967-2018.htmlThe full text article is available as a PDF file from https://amt.copernicus.org/articles/11/2967/2018/amt-11-2967-2018.pdf
Water condensed on ambient aerosol particles plays significant
roles in atmospheric environment, atmospheric chemistry and climate. Before
now, no instruments were available for real-time monitoring of ambient
aerosol liquid water contents (ALWCs). In this paper, a novel method is
proposed to calculate ambient ALWC based on measurements of a
three-wavelength humidified nephelometer system, which measures aerosol light
scattering coefficients and backscattering coefficients at three wavelengths
under dry state and different relative humidity (RH) conditions, providing
measurements of light scattering enhancement factor f(RH). The proposed ALWC calculation method includes two steps: the first
step is the estimation of the dry state total volume concentration of ambient
aerosol particles, Va(dry), with a machine
learning method called random forest model based on measurements of the
“dry” nephelometer. The estimated Va(dry) agrees
well with the measured one. The second step is the estimation of the volume
growth factor Vg(RH) of ambient aerosol
particles due to water uptake, using f(RH) and the
Ångström exponent. The ALWC is calculated from the
estimated Va(dry) and Vg(RH). To validate the new method, the ambient ALWC calculated
from measurements of the humidified nephelometer system during the Gucheng
campaign was compared with ambient ALWC calculated from ISORROPIA
thermodynamic model using aerosol chemistry data. A good agreement was
achieved, with a slope and intercept of 1.14 and -8.6 µm3 cm-3 (r2= 0.92), respectively. The
advantage of this new method is that the ambient ALWC can be obtained solely
based on measurements of a three-wavelength humidified nephelometer system,
facilitating the real-time monitoring of the ambient ALWC and promoting the
study of aerosol liquid water and its role in atmospheric chemistry,
secondary aerosol formation and climate change.
Introduction
Atmospheric aerosol particles play significant roles in atmospheric
environment, climate, human health and the hydrological cycle and have
received much attention in recent decades. One of the most important
constituents of ambient atmospheric aerosol is liquid water. The content of
condensed water on ambient aerosol particles depends mostly on the aerosol
hygroscopicity and the ambient relative humidity (RH). Results of previous
studies demonstrate that liquid water contributes greatly to the total mass
of ambient aerosol particles when the ambient RH is higher than 60 %
(Bian et al., 2014). Aerosol liquid water also has
large impacts on aerosol optical properties and aerosol radiative effects
(Tao et al., 2014; Kuang et al., 2016). Liquid water condensed on aerosol
particles can also serves as a site for multiphase reactions which perturb
local chemistry and further influence the aging processes of aerosol
particles (Martin, 2000). Recent studies have shown that aerosol
liquid water serves as a reactor, which can efficiently transform sulfur
dioxide to sulfate during haze events, aggravating atmospheric environment
in the North China Plain (NCP) (Wang et al., 2016; Cheng et al., 2016).
Hence, to gain more insight into the role of aerosol liquid water in
atmospheric chemistry, aerosol aging processes and aerosol optical
properties, the real-time monitoring of ambient aerosol liquid water content
(ALWC) is of crucial importance.
Few techniques are currently available for measuring the ALWC. The
humidified tandem differential mobility analyser systems (HTDMAs) are useful
tools and widely used to measure hygroscopic growth factors of ambient
aerosol particles (Rader and McMurry, 1986; Wu et al., 2016; Meier et al.,
2009). Hygroscopicity parameters retrieved from measurements of HTDMAs can
be used to calculate the volume of liquid water. Nevertheless, HTDMAs cannot
be used to measure the total aerosol water volume, because they are not
capable of measuring the hygroscopic properties of the entire aerosol
population. With size distributions of aerosol particles in their ambient
state and dry state, the aerosol water volume can be estimated.
Engelhart et al. (2011) deployed the Dry-Ambient
Aerosol Size Spectrometer to measure the aerosol liquid water content and
volume growth factor of fine particulate matter. This system provides only
aerosol water content of aerosol particles within a certain size range (particle diameter less than 500 nm, for the setup of
Engelhart et al., 2011). In addition, in
conjunction with aerosol thermodynamic equilibrium models, ALWC can also be
estimated with detailed aerosol chemical information. However, simulations
of aerosol hygroscopicity and phase state by using thermodynamic equilibrium
models are still very complicated even under the thermodynamic equilibrium
hypothesis and these models may cause large bias when used for estimating
ALWC (Bian et al., 2014).
The idea of using the humidified nephelometer system for the study of aerosol
hygroscopicity had already been proposed early on by Covert et al. (1972).
The instrument measures aerosol light scattering coefficient
(σsp) under dry state and different RH conditions, providing
information on the aerosol light scattering enhancement factor f(RH). One
advantage of this method is that it has a fast response time and continuous
measurements can be made, facilitating the monitoring of changes in ambient
conditions. Another advantage of this method is that it provides information
on the overall aerosol hygroscopicity of the entire aerosol population (Kuang
et al., 2017). Measured σsp of aerosol particles in
dry state and f(RH) vary
strongly with parameters of particle number size distribution (PNSD), making
it difficult to directly link them with the dry state aerosol particle volume
(Va(dry)) and the volume growth factor Vg(RH) of the entire
aerosol population. So far, the ALWC could not be directly estimated based
solely on measurements of the humidified nephelometer system. Several studies
have shown that given the PNSDs at dry state, an iterative algorithm together
with the Mie theory can be used to calculate an overall aerosol hygroscopic
growth factor g(RH) based on measurements of f(RH) (Zieger et al., 2010;
Fierz-Schmidhauser et al., 2010). In such an iterative algorithm, the g(RH)
is assumed to be independent of the aerosol diameter. Thus, ALWC at different
RH levels can be calculated based on derived g(RH) and the measured PNSD.
This method not only requires additional measurements of PNSD, but also may
result in significant deviations of the estimated ALWC, because g(RH)
should be a function of aerosol diameter rather than a constant value.
Another method, which directly connects f(RH) to Vg(RH)
(Vg(RH) =f(RH)1.5), is also used for predicting ALWC based on
measurements of the humidified nephelometer system and mass concentrations of
dry aerosol particles (Guo et al., 2015). This method assumes that the
average scattering efficiency of aerosol particles at dry state and different
RH conditions are the same and requires additional measurements of PNSD or
mass concentrations of dry aerosol particles (Guo et al., 2015). However, the
scattering efficiency of aerosol particles varies with particle diameters,
which will change under ambient conditions due to aerosol hygroscopic growth.
In this paper, we propose a novel method to calculate the ALWC based only on
measurements of a humidified nephelometer system. The proposed method
includes two steps. The first step is calculating Va(dry) based
on measurements of the “dry” nephelometer using a machine learning method
called random forest model. With measurements of PNSD and BC, the six
parameters measured by the nephelometer can be simulated using the Mie theory
and the Va(dry) can also be calculated based on PNSD. Therefore,
the random forest model can be trained with only the regional historical
datasets of PNSD and BC. In this study, datasets of PNSD and BC measured from
multiple sites are used in the machine learning model to characterise a
regional aerosol and these datasets have covered a wide range of aerosol
loadings. The second step is calculating Vg(RH), based on the
Ångström exponent and f(RH) measured by the humidified nephelometer
system. In this step, the
influences of the variations in PNSD and aerosol hygroscopicity are both
considered to derive Vg(RH) from measured f(RH). Finally, based on
calculated Va(dry) and Vg(RH), ALWCs at different RH points can
be estimated. The used datasets are introduced in Sect. 2. Calculation method
of Va(dry) based only on measurements of the nephelometer, which
measures optical properties of aerosols in dry state, is described in
Sect. 3.2. The way of deriving Vg(RH) based on measurements of the humidified
nephelometer system is introduced and discussed in Sect. 3.3. The final
formula of calculating ambient ALWC is described in Sect. 3.4. The
verification of the Va(dry) predicted by using the machine
learning method is described in Sect. 4.1. The validation of ambient ALWC
calculated from measurements of the humidified nephelometer system is
presented in Sect. 4.2. The contribution of ambient ALWC to the total ambient
aerosol volume is discussed in Sect. 4.3.
Locations, time periods and used datasets of six field campaigns.
LocationWuqingWuqingXiangheXiangheWangduGuchengTime period7 March to 4 April 200912 July to 14 August 200922 July to 30 August 20129 July to 8 August 20134 June to 14 July 201415 October to 25 November 2016PNSDTSMPS+APSTSMPS+APSSMPS+APSTSMPS+APSTSMPS+APSSMPS+APSBCMAAPMAAPMAAPMAAPMAAPAE33σspTSI 3563TSI 3563TSI 3563TSI 3563TSI 3563Aurora 3000f(RH)Humidified nephelometer systemHumidified nephelometer systemWater-soluble ionsIGACCampaign nameF1F2F3F4F5F6Instruments and datasets
Datasets from six field campaigns were used in this paper. The six campaigns
were conducted at four different measurement sites (Wangdu, Gucheng and
Xianghe in Hebei province and Wuqing in Tianjin) of the North China Plain
(NCP), the locations of these field campaign sites are displayed in Fig. S1
in the Supplement. Time periods and datasets used from these field campaigns
are listed in Table 1. During these field campaigns, aerosol particles with
aerodynamic diameters less than 10 µm were sampled (by passing
through an impactor). The PNSDs in dry state, which range from 3 nm to
10 µm, were jointly measured by a Twin Differential Mobility
Particle Sizer (TDMPS, Leibniz-Institute for Tropospheric Research, Germany;
Birmili et al., 1999) or a scanning mobility particle size spectrometer
(SMPS) and an Aerodynamic Particle Sizer (APS, TSI Inc., Model 3321) with a
temporal resolution of 10 min. The mass concentrations of black carbon (BC)
were measured using a Multi-Angle Absorption Photometer (MAAP Model 5012,
Thermo, Inc., Waltham, MA USA) with a temporal resolution of 1 min during
field campaigns of F1 to F5 and using an aethalometer (AE33) (Drinovec et
al., 2015) during field campaign F6. The aerosol light scattering
coefficients (σsp) at three wavelengths (450, 550, and
700 nm) were measured using a TSI 3563 nephelometer (Anderson and Ogren,
1998) during field campaigns of F1 to F5, and using an Aurora 3000
nephelometer (Müller et al., 2011) during field campaign F6.
Datasets of PNSD, BC and σsp from campaigns F2, F4 and F5
are referred to as D1. Measurements of PNSD and measurements from the
humidified nephelometer system during campaign F6 (Gucheng campaign) are used
to verify the proposed method of calculating the ambient ALWC. Details about
the humidified nephelometer system during the Wangdu and Gucheng campaigns
are introduced in detail in Kuang et al. (2017). During the Gucheng campaign,
an In situ Gas and Aerosol Compositions Monitor (IGAC, Fortelice
International Co.,Taiwan) was used for monitoring water-soluble ions
(Na+, K+, Ca2+, Mg2+,
NH4+, SO42-, NO3-, Cl-) of
PM2.5 and their precursor gases: NH3, HCl, and
HNO3. The time resolution of IGAC measurements is
1 h. Ambient air was drawn into the IGAC system
through a stainless-steel pipe wrapped with thermal insulation at a flow rate
of 16.7 L min-1. The ambient RH and temperature were observed using an
automatic weather station with a time resolution of 1 min.
Comparisons between measured and calculated σsp
(Mm-1), solid red lines are 1 : 1 references lines. Dashed blue
lines are 20 % relative difference lines. R2 is square of
correlation coefficient between measured and modelled σsp.
Blue text in the upper left corners corresponds to field campaigns as listed
in Table 1.
MethodologyClosure calculations
To ensure the datasets of σsp and PNSD used are of high quality,
a closure study between measured σsp and that calculated based on
measured PNSD and BC with Mie theory (Bohren and Huffman, 2008) is first
performed. Measured σsp bears uncertainties introduced by angular
truncation errors and nonideal light source. To achieve consistency between
measured and modelled σsp, modelled σsp are calculated
according to practical angular situations of the nephelometer (Anderson
et al., 1996). During the σsp modelling process, BC was
considered to be half externally and half core–shell mixed with other aerosol
components. The mass size distribution of BC used in Ma et al. (2012), which was also observed
in the NCP, was used in this research to account for the mass distributions
of BC at different particle sizes. The applied refractive index and density
of BC were 1.80-0.54i and 1.5 g cm-3 (Kuang et al., 2015). The refractive index of non-light-absorbing aerosol components (other than BC) was set to
1.53-10-7i (Wex et al., 2002). For the
Mie theory calculation details please refer to Kuang et
al. (2015).
The closure results between modelled σsp and
σsp measured by TSI 3563 or Aurora 3000 using datasets
observed during six field campaigns (Table 1) are depicted in Fig. 1. In
general, for all six field campaigns, modelled σsp values
correlate very well with measured σsp values. Considering
the measured PNSD has an uncertainty of larger than 10 % (Wiedensohler et
al., 2012), and the measured σsp has an uncertainty of
about 9 % (Sherman et al., 2015), modelled σsp values
agree well with measured σsp values in campaigns F1, F4, F5
and F6, with all points lying near the 1 : 1 line, and most points falling
within the 20 % relative difference lines. For the closure results of
field campaign F2, the modelled σsp values are
systematically lower than measured σsp values. For the
closure results of field campaign F3, most points also lie nearby 1 : 1
line, but points are relatively more dispersed.
Calculation of Va (dry) based on measurements of the “dry” nephelometerTheoretical relationship between Va (dry) and σsp
Previous studies demonstrated that the σsp of aerosol particles
is roughly proportional to Va(dry) (Pinnick et al., 1980). Here, the quantitative relationship
between Va(dry) and σsp is analysed.
The σsp and Va(dry) can be expressed
as the following:
σsp=∫πr2Qscam,rnrdr,Va(dry)=∫43πr3nrdr,
where Qsca(m,r) is scattering efficiency for a particle with
refractive index m and particle radius r, while n(r) is the aerosol
size distribution. As presented in Eqs. (1) and (2), relating
Va(dry) with σsp involves the complex relation
between Qsca(m,r) and particle diameter, which can be simulated
using the Mie theory. According to the aerosol refractive index at visible
spectral range, aerosol chemical components can be classified into two
categories: the light absorbing component and the almost light non-absorbing
components (inorganic salts and acids, and most of the organic compounds).
Near the visible spectral range, the light absorbing component can be
referred to as BC. BC particles are either externally or internally mixed
with other aerosol components. In view of this, Qsca at 550 nm,
as a function of particle diameter for four types of aerosol particles, is
simulated using Mie theory: almost non-absorbing aerosol particle, BC
particle, BC particle core–shell mixed with non-absorbing components with
the radii of the inner BC core being 50 and 70 nm, respectively. Same with
those introduced in Sect. 2.2, the refractive indices of BC and light
non-absorbing components used here are 1.80-0.54i and 1.53-10-7i,
respectively.
(a)Qsca at 550 nm as a function of particle
diameter for four types of aerosol particles: almost non-absorbing aerosol
particle, BC particle, BC particle core–shell mixed with non-absorbing
components and the radius of inner BC core are 50 and 70 nm. The grey line
corresponds to the fitted linear line for the case of non-absorbing particle,
when particle diameter is less than 750 nm. (b) Simulated
size-resolved accumulative contribution to σsp at 550 nm
for all PNSDs measured during the Wangdu campaign, the colour scales (from
light grey to black) represent occurrences. The dashed dotted lines in
panel (b) represent the position of 800 nm and 80 %
contribution, respectively.
The simulated results are shown in Fig. 2a. Near the visible spectral range,
most of the ambient aerosol components are almost non-absorbing, and their
Qsca varies more like the blue line shown in Fig. 2a. In that
case, aerosol particles have diameters less than about 800 nm and
Qsca increases almost monotonously with particle diameter and can
be approximately estimated as a linear function of diameter. Figure 2b shows
the simulated size-resolved accumulative contribution to the scattering
coefficient at 550 nm for all PNSDs measured during the Wangdu campaign. The
results indicate that, for continental aerosol particles without influences
of dust, in most cases, all particles with diameter less than about 800 nm
contribute more than 80 % to the total σsp. Therefore,
for Eq. (1) if we express Qsca(m,r) as
Qsca(m,r)=k⋅r then Eq. (1) can be expressed as the
following:
σsp=k⋅∫πr3nrdr.
This explains why σsp(550 nm) is roughly
proportional to Va(dry). However, the value k
varies greatly with particle diameter. The ratio σsp(550 nm) /Va(dry)
(hereafter referred to as RVsp) is mostly affected by the PNSD, which
determines the weight of influence different particle diameters have on
RVsp. The discrepancy between the blue line and black line shown in
Fig. 2a indicates that the fraction of externally mixed BC particles and
their sizes has large impact on RVsp. The difference between the black
line and the red line as well as the difference between the solid red line
and the dashed red line shown in Fig. 2a indicate that the way and the amount
of BC mixed with other components also exert significant influences on
RVsp. In summary, the variation of RVsp is mainly determined by
variations in PNSD, mass size distribution and the mixing state of BC. It is
difficult to find a simple function describing the relationship between
measured σsp and Va(dry).
(a, b) Modelled σsp at 550 nm based on
PNSD and BC vs. Va(dry) of PM10 or PM2.5
calculated from measured PNSD. PNSD and BC datasets from six field campaigns
listed in Table 1 are used. The unit of Va(dry) is
µm3 cm-3 and the unit of σsp is
Mm-1. Colours of scattered points in panels (a) and
(b) represent corresponding values of the Ångström exponent.
R2 is the square of correlation coefficient. Panel
(c) represents the probability distribution of the modelled ratio
between σsp at 550 nm and Va(dry) of
PM10 or PM2.5.
Based on PNSD and BC datasets of field campaigns F1 to F6, the relationship
between σsp at 550 nm and Va(dry) of
PM10 or PM2.5 are simulated using the Mie theory. The results are
shown in Fig. 3. The results demonstrate that the σsp at 550 nm is
highly correlated with the Va(dry) of PM10
and PM2.5. The square of the correlation coefficient (r2) between
σsp at 550 nm and Va(dry) of PM10
or PM2.5 are 0.94 and 0.99, respectively. A roughly proportional
relationship exists between Va(dry) and σsp(550 nm), especially for Va(dry) of PM2.5. However, both RVsp of PM10 and PM2.5
vary significantly. RVsp of PM10 mainly ranges from 2 to 6 cm3 (µm3 Mm)-1, with an
average of 4.2 cm3 (µm3 Mm)-1. RVsp of PM2.5 mainly ranges from 3 to 6.5 cm3 (µm3 Mm)-1, with an average of
5.1 cm3 (µm3 Mm)-1. Simulated size-resolved accumulative contributions to
σsp at 550 nm for all PNSDs measured during campaigns F1 to F6
and corresponding size-resolved accumulative contributions to Va(dry) of PM10 are shown in Fig. S2. The results indicate
that particles with diameter larger than 2.5 µm usually contribute
negligibly to σsp at 550 nm but contribute about 20 % of the
total PM10 volume. Hence σsp at 550 nm is insensitive to
changes in particles mass of diameters between 2.5 and 10 µm. This may
partially explain why Va(dry) of PM2.5
correlates better with σsp at 550 nm than Va(dry) of PM10.
Machine learning
Based on analyses in Sect. 3.2.1, RVsp varies a lot with PNSD being the
most dominant influencing factor. The “dry” nephelometer provides not only
one single σsp at 550 nm, it measures six parameters including
σsp and back scattering coefficients (σbsp) at three
wavelengths (for TSI 3563: 450, 550 and 700 nm). The
Ångström exponent calculated from spectral
dependence of σsp provides information on the mean predominant
aerosol size and is associated mostly with PNSD. The variation of the
hemispheric backscattering fraction (HBF), which is the ratio between
σbsp and σsp, is also essentially related to the PNSD.
HBFs at three wavelengths (450, 550 and 700 nm) and the
Ångström exponents calculated from σsp
at different wavelengths (450–550, 550–700 and 450–700 nm) for typical
non-absorbing aerosol particles with their diameters ranging from 100 nm to
3 µm are simulated using the Mie theory. The results are shown
in Fig. 4a and b. HBF values at three different wavelengths and their
differences are more sensitive to changes in PNSD of particle diameters less
than about 400 nm. Ångström exponents calculated
from σsp at different wavelengths almost decrease monotonously
with particle diameter when particle diameter is less than about 1 µm; however, they differ distinctly when particle diameter is
larger than 300 nm. These results indicate that HBFs at three wavelengths
and Ångström exponents calculated from σsp at different wavelengths are sensitive to different diameter ranges
of PNSD.
Thus, all six parameters measured by the “dry” nephelometer together can
provide valuable information about variations in RVsp. However, no
explicit formula exists between these six parameters and Va(dry). How to use these six optical parameters is a
problem;
machine learning methods that can handle many input parameters are capable
of learning from historical datasets and then make predictions, and strict
relationships among variables are not required. Machine learning methods are
powerful tools for tackling highly nonlinear problems and are widely used in
different areas. In the light of this, predicting Va(dry) based on six optical parameters measured by the “dry”
nephelometer might be accomplished by using a machine learning method. In
this study, random forest is chosen for this purpose.
(a) Simulated HBF at three wavelengths as a function of
particle diameter. (b) Simulated Ångström exponent values as
a function of particle diameter.
Random forest is a machine learning technique that is widely used for
classification and non-linear regression problems (Breiman, 2001). For
non-linear regression cases, random forest model consists of an ensemble of
binary regression decision tress. Each tree has a randomised training scheme,
and an average over the whole ensemble of regression tree predictions is used
for final prediction. In this study, the function RandomForestRegressor from
the Python Scikit-Learn machine learning library
(http://scikit-learn.org/stable/index.html, last access: 16 May 2018)
is used. This model has several strengths. First, through averaging over an
ensemble of decision trees there is a significantly lower risk of
overfitting. Second, it involves fewer assumptions about the dependence
between inputs and outputs when compared with traditional parametric
regression models. The random forest model has two parameters: the number of
input variables (Nin) and the number of trees grown
(Ntree). In this study, Nin and Ntree are
six and eight, respectively. The six input parameterises the three scattering
coefficients, three backscattering coefficients.
The quality of input datasets is critical to the prediction accuracy of the
machine learning method. As discussed in Sect. 3.1, modelled
σsp during some field campaigns are not completely
consistent with measured σsp, large bias might exist between
them due to the measurement uncertainties of PNSD and σsp.
To avoid the uncertainties in measurements of PNSD, aerosol optical properties are propagated in the training processes of the random forest model. In this study, both the
required datasets of six optical parameters which corresponding to
measurements of TSI 3563 and Va(dry) for training the random
forest model are calculated or simulated based on measurements of PNSD and BC
from field campaigns F1 to F4 and F6. Datasets of PNSD and six optical
parameters measured by the nephelometer during campaign F5 are used to verify
the prediction ability of the trained random forest model. The performance of
this random forest model on predicting both Va(dry) of
PM10 and PM2.5 are investigated. A schematic diagram of
this method is shown in Fig. 5.
Connecting f(RH) to Vg(RH)κ-Köhler theory
κ-Köhler theory is used to describe the hygroscopic
growth of aerosol particles with different sizes, and the formula expression
of κ-Köhler theory can be written as follows (Petters and Kreidenweis, 2007):
RH=D3-Dd3D3-Dd3(1-κ)⋅exp4σs/a⋅MwaterR⋅T⋅Dp⋅g⋅ρw,
where D is the diameter of the droplet, Dd is the dry diameter, σs/a is the surface tension of solution/air interface, T is the temperature,
Mwater is the molecular weight of water, R is the universal gas
constant, ρw is the density of water, and κ is the
hygroscopicity parameter. By combining the Mie theory and the
κ-Köhler theory, both f(RH) and Vg(RH) can be simulated. In
the processes of calculations for modelling f(RH)
and Vg(RH), the treatment of BC is same
with those introduced in Sect. 2.2. As aerosol particle grows due to aerosol
water uptake, the refractive index will change. In the Mie calculation,
impacts of aerosol liquid water on the refractive index are considered based
on volume mixing rule. The used refractive index of liquid water is
1.33-10-7i (Seinfeld and Pandis, 2006).
Schematic diagram of training the random forest (RF) model and
verifying the performance of trained RF predictor. The trained datasets of
PNSD and BC are from field campaigns F1 to F4 and F6, the test datasets of
PNSD and optical parameters are from campaign F5 and σbsp is
the backscattering coefficient.
Parameterization schemes for f(RH) and Vg(RH)
The f(RH) is defined as f(RH) =σsp(RH,550 nm) /σsp(dry,550 nm), where σsp(RH,550 nm) and σsp(dry,550 nm) represents σsp at wavelength 550 nm under certain RH and dry
conditions. Additionally, Vg(RH) is defined
as Vg(RH) =Va(RH) /Va(dry), where
Va(RH) represents total volume of aerosol particles under
certain RH conditions.
A physically based single-parameter representation is proposed by Brock et al. (2016) to describe f(RH). The parameterization
scheme is written as follows:
fRH=1+κscaRH100-RH,
where κsca is the parameter which fits f(RH) best. Here, a
brief introduction is given about the physical understanding of this
parameterization scheme. For aerosol particles whose diameters larger than
100 nm, regardless of the Kelvin effect, the hygroscopic growth factor for
an aerosol particle can be approximately expressed as
g(RH) ≅1+κRH100-RH13 (Brock et al.,
2016). Enhancement factor in volume can be expressed as the cube of g(RH).
Aerosol particles larger than 100 nm contribute the most to
σsp and Va(dry) (as shown in Fig. S2). If a
constant κ which represents the overall aerosol hygroscopicity of
ambient aerosol particles is used as the κ of different particle
sizes, then Vg(RH) can be approximately expressed as Vg(RH) =1+κRH100-RH. In addition, σsp is
usually proportional to Va(dry), which indicates that the
relative change in σsp due to aerosol water uptake is
roughly proportional to relative change in aerosol volume. Therefore, f(RH)
might also be well described by using the formula form of Eq. (5). Previous
studies have shown that this parameterization scheme can describe f(RH)
well (Brock et al., 2016; Kuang et al., 2017).
During processes of measuring f(RH), the sample RH
in the “dry” nephelometer (RH0) is not zero. According to Eq. (5), the measured f(RH)measure=f(RH)f(RH0) should be fitted using the
following formula:
fRHmeasure=1+κscaRH100-RH/1+κscaRH0100-RH0.
Based on this equation, κsca can be calculated from measured
f(RH) directly. The typical value of RH0
measured in the “dry” nephelometer during the Wangdu campaign is about 20 %.
The importance of the RH0 correction changes under different aerosol
hygroscopicity and RH0 conditions. The parameter κsca is
fitted with and without consideration of RH0 for f(RH) measurements during the Wangdu campaign, and the results
are shown in Fig. S3. The results demonstrate that, overall, the κsca will be underestimated if the influence of
RH0 is not considered, and the larger the κsca, the more that the κsca will be underestimated.
In addition, based on discussions about the physical understanding of
Eq. (5), the Vg(RH) should be well
described by the following equation:
VgRH=1+κVfRH100-RH,
where κVf is the parameter which fits Vg(RH) best. To
validate this conclusion, a simulative experiment is conducted. In the
simulative experiment, average PNSD in dry state and mass concentration of BC
during the Haze in China (HaChi) campaign (Kuang et al., 2015) are used.
During HaChi campaign, size-resolved κ distributions are derived from
measured size-segregated chemical compositions (Liu et al., 2014) and their
average is used in this experiment to account the size dependence of aerosol
hygroscopicity. Modelled results of f(RH) and Vg(RH) are shown in
Fig. S4. Results demonstrate that modelled f(RH)
and Vg(RH) can be well parameterized using the formula form of Eqs. (5) and
(7). Fitted values of κsca and κVf are
0.227 and 0.285, respectively. This result indicates that if linkage between
κsca and κVf is established, measurements
of f(RH) can be directly related to Vg(RH).
(a) Colours represent RVf values and the
colour bar is shown on the top of this figure, x axis represents
the Ångström exponent and y axis represents κsca.
(b) Meanings of x axis and y axis are same as those in
panel (a). However, colour represents the percentile value of the
standard deviation of RVf values within each grid divided by
their average.
Bridge the gap between f(RH) and Vg(RH)
Many factors have significant influences on the relationships between f(RH)
and Vg(RH), including PNSD, BC mixing state and the size-resolved aerosol
hygroscopicity. To gain insights into the relationships between
κsca and κVf, a simulative experiment
using Mie theory and κ-Köhler theory is designed. In this
experiment, all PNSDs at dry state along with mass concentrations of BC from
D1 are used, characteristics of these
PNSDs can be found in Kuang et al. (2017). As to size-resolved aerosol
hygroscopicity, a number of size-resolved κ distributions were
derived from measured size-segregated chemical compositions during HaChi
campaign (Liu et al., 2014). Results from other research also show similar
size dependence of aerosol hygroscopicity (Meng et al., 2014). In view of
this, the shape of the average size-resolved κ distribution during
HaChi campaign (black line shown in Fig. S5) is used in the designed
experiment. Other than the shape of size-resolved κ distribution, the
overall aerosol hygroscopicity, which determines the magnitude of f(RH),
also has a large impact on the relationship between κsca and
κVf. In view of this, ratios ranging from 0.05 to 2, with an
interval of 0.05, are multiplied with the average size-resolved κ
distribution (the black line shown in Fig. S5) to produce a number of
size-resolved κ distributions which represent aerosol particles from
nearly hydrophobic to highly hygroscopic. During simulating processes, each
PNSD is modelled with all produced size-resolved κ distributions. In
the following, the ratio κVf/κsca, termed as
RVf, is used to indicate the relationship between
κsca and κVf.
Considering that values of the Ångström exponent contain information
about PNSD (Kuang et al., 2017) and values of κsca represent
overall hygroscopicity of ambient aerosol particles, and that both of these
parameters can be directly calculated from measurements of a three-wavelength
humidified nephelometer system (Kuang et al., 2017), simulated
RVf values are spread into a two-dimensional gridded plot. The
first dimension is the Ångström exponent with an interval of 0.02 and
the second dimension is κsca with an interval of 0.01.
Average RVf value within each grid is represented by colour and
shown in Fig. 6a. Values of the Ångström exponent corresponding to
used PNSDs are calculated from simultaneously measured σsp
values at 450 and 550 nm from the TSI 3563 nephelometer. Results shown in
Fig. 6a exhibit that both PNSD and overall aerosol hygroscopicity have
significant influences on RVf. Simulated values of
RVf range from 0.8 to 1.7, with an average of 1.2. Overall, the
RVf value is lower when the value of the Ångström
exponent is larger. The percentile value of standard deviation of
RVf values within each grid, divided by its average, is shown in
Fig. 6b. In most cases, these percentile values are less than 10 % (about
90 %) which demonstrates that RVf varies little within each
grid shown in Fig. 6a. Figure 6 shows the influence of aerosol size and
chemistry on RVf. For an Ångström exponent less than
∼ 1.1, RVf varies strongly with κsca.
However, for an Ångström exponent values greater than ∼ 1.1,
the RVf relative standard deviation exhibits a higher variability
with the Ångström exponent, thus showing the sensitivity of
RVf to changes in aerosol size for small particles. In general,
results shown in Fig. 6 imply that results of Fig. 6a can serve as a lookup
table to estimate RVf and thereby κVf, such that
these values can be directly predicted from measurements of a
three-wavelength humidified nephelometer system.
(a) All size-resolved κ distributions, which are
derived from measured size-segregated chemical compositions during HaChi
campaign, colours represent corresponding values of average
σsp at 550 nm (Mm-1), the black solid line is the
average size-resolved κ distribution and error bars are standard
deviations; (b) the grey colours represent the distribution of
relative differences between modelled and estimated RVf values,
darker grids have higher frequency and dashed lines with the same colour mean
that corresponding percentile of points locate between the two lines.
For the lookup table shown in Fig. 6a, a fixed size-resolved κ
distribution is used, which might not be able to capture variations of
RVf induced by different types of size-resolved κ
distributions under different PNSD conditions. A simulative experiment is
conducted to investigate the performance of this lookup table. In this
experiment, the following datasets are used: PNSDs and mass concentrations of
BC from D1 (the number of used PNSD is 11996), and size-resolved κ
distributions from HaChi campaign (Liu et al., 2014), which are presented in
Fig. 7a (the number is 23). Results shown in Fig. 7a imply that the shape of
size-resolved κ distribution is highly variable, yet has no apparent
correlation with aerosol loading. During the simulating processes for each
PNSD, it is used to simulate RVf values corresponding to all used
size-resolved κ distributions; therefore, 275 908 RVf
values are modelled. Also, modelled values of κsca and
corresponding values of the modelled Ångström exponent are used
together to estimate RVf values using the lookup table shown in
Fig. 7a. Results of relative differences between estimated and modelled
RVf, values under different pollution conditions are shown in
Fig. 7b. Overall, 88 % of points have absolute relative differences less
than 15 % and 68 % of points have absolute relative differences less
than 10 %. This lookup table performs better when the air is relatively
polluted.
Calculation of ambient ALWC
According to the equation
Vg(RH) =1+κVfRH100-RH,
ALWC refers to volume concentrations of aerosol liquid water at different RH points and can be expressed as the following:
ALWC=Vadry×(VgRH-1)=Vadry⋅κsca⋅RVf⋅RH100-RH.
According to discussions of Sect. 3.2, Va(dry) can
be predicted based only on measurements from the “dry” nephelometer by
using a random forest model. The training of the random forest model
requires only regional historical datasets of simultaneously measured PNSD
and BC. The κsca is directly fitted from f(RH) measurements. The RVf can be estimated using the lookup table
introduced in Sect. 3.3. Thus, based only on measurements from a
three-wavelength humidified nephelometer system, ALWCs of ambient aerosol
particles at different RH points can be estimated. If both measurements from
the humidified nephelometer system and ambient RH are available, ambient
ALWC can be calculated. The flowchart of calculating ambient ALWC based on
measurements of the humidified nephelometer system is shown in Fig. 8. The
nephelometer used, corresponding to this flowchart, should be TSI 3563. If
nephelometer of the used humidified nephelometer system is Aurora 3000,
wavelengths in this flowchart will change but other steps are totally the
same.
Results and discussionValidation of the random forest model for predicting
Va(dry) based on measurements of the “dry” nephelometer
The machine learning method, random forest model, is proposed to predict
Va(dry) based only on σsp and σbsp at three wavelengths measured by the “dry” nephelometer.
Datasets of PNSD and BC from field campaigns F1 to F4 and F6 are used to
train the random forest model. Datasets of PNSD and optical parameters
measured by the “dry” nephelometer from field campaign F5 are used to
verify the trained random forest model. The schematic diagram of this method
is shown in Fig. 5. The comparison results between calculated and predicted
Va(dry) of PM10 and PM2.5 are shown in
Fig. 9. The square of correlation coefficient between predicted and
calculated Va(dry) of PM10 is 0.96, and almost all
points lie between or near 20 % relative difference lines. The square of
correlation coefficient between predicted and calculated Va(dry)
of PM2.5 is 0.997, and almost all points lie between or near
10 % relative difference lines. The standard deviations of relative
differences between predicted and calculated Va(dry) of
PM10 and PM2.5 are 10 and 4 %, respectively. These
results indicate that Va(dry) of PM2.5 can be well
predicted by using the machine learning method. While Va(dry) of
PM10 predicted by using the machine learning method has a
relatively larger bias.
The flowchart of calculating ambient aerosol liquid water contents
based on measurements of a three-wavelength humidified nephelometer system.
The comparison between Va(dry)
(µm3 cm-3) of PM10 or PM2.5,
calculated from measured PNSD and Va(dry) of PM10 or
PM2.5, which are predicted based on six optical parameters measured
by the “dry” nephelometer, by using the random forest model. R2 is the
square of correlation coefficient. The solid red line is the 1 : 1 line, dashed
red lines and dashed blue lines represent 20 and 10 % relative difference
lines.
Machine learning methods do not explicitly express relationships between
many variables; however, they learn and implicitly construct complex
relationships among variables from historical datasets. Many different and
comprehensive machine learning methods are developed for diverse
applications and can be directly used as a tool for solving a lot of
nonlinear problems which may not be mathematically well understood. We
suggest using a machine learning method for estimating Va(dry) based on measurements of the “dry” nephelometer. The
way of estimating Va(dry) with machine learning
method might be applicable for different regions around the world if used
estimators are trained with corresponding regional historical datasets.
The comparison between ALWC calculated from ISORROPIA thermodynamic
model (ALWCISORROPIA) and ALWC calculated from measurements of
the humidified nephelometer system (ALWCHneph). The black solid
line is the 1 : 1 line and the two dashed black lines are 30 % relative
difference lines. R2 is the square of correlation coefficient. Colours of
scatter points represent ambient RH. (a) ALWCHneph is
calculated using the method proposed in this research.
(b) ALWCHneph is calculated by assuming
Vg(RH) =f(RH)1.5 (Guo et al., 2015).
Comparison between ambient ALWC calculated from ISORROPIA and measurements
of the humidified nephelometer system
So far, widely used tools for prediction of ambient ALWC are thermodynamic
models. ISORROPIA-II thermodynamic model
(http://nenes.eas.gatech.edu/ISORROPIA/index_old.html, last access:
16 May 2018) is a famous one and is widely used in research for predicting pH
and ALWC of ambient aerosol particles (Guo et al., 2015; Cheng et al., 2016;
Liu et al., 2017; Fountoukis and Nenes, 2007). Water-soluble ions and gaseous
precursors are required as inputs of thermodynamic model. During the Gucheng
campaign, measurements from both the humidified nephelometer system and IGAC
are available. Thus, the ambient ALWC can be calculated through two
independent methods: thermodynamic model based on IGAC measurements and the
method proposed in Sect. 3.4, which is based on measurements of the
humidified nephelometer system. In this study, the forward mode in
ISORROPIA-II is used and water-soluble ions in PM2.5 and gaseous
precursors (NH3, HNO3, HCl) measured by the IGAC
instrument along with simultaneously measured RH and T are used as inputs.
The aerosol water associated with organic matter is not considered in the
method of ISORROPIA model, due to the lack of measurements of organic aerosol
mass. However, results from previous studies indicate that organic matter
induced particle water only account for about 5 % of total ALWC (Liu et
al., 2017). For the ALWC calculated from the humidified nephelometer system,
the needed Va(dry) of PM2.5 in Eq. (7) is calculated
from simultaneously measured PNSD.
The comparison results between ambient ALWC calculated from these two
independent methods are shown in Fig. 10a. The square of correlation
coefficient between them is 0.92, most of the points lie within or nearby
30 % relative difference lines. The slope is 1.14, and the intercept is
-8.6 µm3 cm-3. When ambient RH is higher than 80 %,
the ambient ALWCs calculated from measurements of the humidified
nephelometer system are higher relative to those calculated based on
ISORROPIA-II. When ambient RH is lower than 60 %, the ambient ALWCs
calculated from measurements of the humidified nephelometer system are
lower relative to those calculated based on ISORROPIA-II. Overall, a
good agreement is achieved between ambient ALWC calculated from measurements
of the humidified nephelometer system and ISORROPIA thermodynamic model.
Volume fractions of water in total volume of ambient aerosols during
the
Wangdu (WD) and Gucheng (GC) campaigns. X axis represents measured ambient
RH. The y axis represents volume fractions of water. Colours of scatter points
represent corresponding κVf. Black solid lines in
panels (a) and (b) show the average volume fractions of
water under different ambient RH conditions.
Guo et al. (2015) conducted the
comparison between ambient ALWC calculated from ISORROPIA model and ambient
ALWC calculated from measurements of the humidified nephelometer system by
assuming Vg(RH) =f(RH)1.5. Thus, the comparison results between ambient ALWC
calculated based on ISORROPIA and ambient ALWC calculated by assuming
Vg(RH) =f(RH)1.5 are also shown in Fig. 10b. The square of the correlation
coefficient between them is also 0.92. However, the slope and intercept are
1.7 and -21 µm3 cm-3, respectively. When the ambient
RH is higher than about 80 %, calculated ambient ALWC will be
significantly overestimated if it is assumed that Vg(RH) =f(RH)1.5. This method assumes
that average scattering efficiency of aerosol particles at dry state and
different RH conditions are the same. When ambient RH is high, the particle
diameters changes a lot. As the results shown in Fig. S6, for non-absorbing
particle, when diameter of aerosol particle in dry state is less than 500
nm, the aerosol scattering efficiency increase almost monotonously with
increasing RH especially when RH is higher than 80 %. Therefore, it is not
suitable to assume that average scattering efficiency of aerosol particles
at dry state and different RH conditions are the same.
Volume fractions of ALWC in total ambient aerosol volume
During the Wangdu campaign, κsca ranged from 0.05 to 0.3 with an
average of 0.19. Estimated values of RVf ranges from 0.86 to 1.47, with
an average of 1.15. Estimated values of κVf ranges from 0.05 to
0.35, with an average of 0.22. The calculated volume fractions of water in
total volume of ambient aerosols during the Wangdu campaign are shown in
Fig. 11a. The results indicate that during the Wangdu campaign, when ambient RH
is higher than 70 %, the κVf values are relatively higher. The
volume fractions of water are always higher than 50 % when ambient RH is
higher than 80 %.
During the Gucheng campaign, κsca ranges from 0.008 to 0.22 with an
average of 0.1, κVf ranges from 0.01 to 0.21 with an average of
0.12. The aerosol hygroscopicity during the Gucheng campaign is much lower than
aerosol hygroscopicity during the Wangdu campaign. The calculated volume
fractions of water in total volume of ambient aerosols during the Gucheng
campaign are shown in Fig. 11b. During the Gucheng campaign, the maximum volume
fraction of water in ambient aerosol is 42 % when ambient RH is at
80 %. On average, when ambient RH is higher than 90 %, the volume
fraction of water in ambient aerosols reaches higher than 50 %.
Discussions about the applicability of the proposed method
The method proposed in this research is based on datasets of PNSD, σsp and size-resolved κ distribution, which are measured on the
NCP without influences of dust events and sea salt. Caution should be
exercised if using the proposed method to estimate the ALWC when the air
mass is significantly influenced by sea salt or dust. The way of estimating
Va(dry) with machine learning method might be
applicable for different regions around the world. However, the used
predictor from machine learning should be trained with corresponding
regional historical datasets of PNSD and BC. The way of connecting f(RH) to Vg(RH) might also
be applicable for other continental regions. Still, we suggest that the used
lookup table is simulated from regional historical datasets.
Note that the humidified nephelometer usually operates with RH less than
95 %. However, aerosol water increase dramatically with increasing RH
when RH is greater than 95 %. Such high RH conditions can occur during
the haze events. This may limit the usage of the proposed method when ambient
RH is extremely high. As discussed in Sect. 3.3, the proposed way of
connecting f(RH) and Vg(RH) is based on the κ-Köhler theory. If
κ does not change with RH, the proposed method should be applicable
when RH is higher than 95 %, even if the measurements of humidified
nephelometer system are conducted when RH is less than 95 %. Many studies
have done research about the change of κ with the changing RH (Rastak
et al., 2017; Renbaum-Wolff et al., 2016), their results demonstrate that the
κ changes with increasing RH. However, few studies have investigated
the variation of κ of ambient aerosol particles with changing RH when
RH is less than 100 %. Liu et al. (2011) have measured κ of
ambient aerosol particles at different RHs (90, 95 and 98.5 %) on the
NCP. Their results demonstrated that κ at different RHs differs
little for ambient aerosol particles with different diameters. Results of
Kuang et al. (2017) indicated that κ values retrieved from f(RH)
measurements agree well with κ values at RH of 98 % of aerosol
particles with diameter of 250 nm. In this respect, the proposed method
might be applicable even when ambient RH is extremely high for ambient
aerosol particles on the NCP. Moreover, for calculating the ambient ALWC, the
measured ambient RH is required. If the ambient RH is higher than 95 %,
the measured ambient RH with current techniques is highly uncertain. Given
this, cautions should be exercised if the ambient ALWC is calculated when the
ambient RH is higher than 95 %.
Conclusions
In this paper, a novel method is proposed to calculate ALWC based on
measurements of a three-wavelength humidified nephelometer system. Two
critical relationships are required in this method. One is the relationship
between Va(dry) and measurements of the “dry”
nephelometer. Another one is the relationship between Vg(RH) and f(RH). The ALWC can be
calculated from the estimated Va(dry) and
Vg(RH).
Previous studies have shown that an approximate proportional relationship
exists between Va(dry) and corresponding σsp,
especially for fine particles (particle diameter less than 1 µm).
However, PNSD and other factors still have significant influences on this
proportional relationship. It is difficult to directly estimate
Va(dry) from measured σsp. In this paper, a
random forest predictor from machine learning procedure is used to estimate
Va(dry) based on measurements of a three-wavelength nephelometer.
This random forest predictor is trained based on historical datasets of PNSD
and BC from several field campaigns conducted on the NCP. This method is then
validated using measurements from the Wangdu
campaign. The square of correlation coefficient between measured and
estimated Va(dry) of PM10 and PM2.5 are 0.96
and 0.997, respectively.
The relationship between Vg(RH) and
f(RH) is investigated in Sect. 3 by conducting a
simulative experiment. It is found that the complicated relationship between
Vg(RH) and f(RH)
can be disentangled by using a lookup table, and parameters required in the
lookup table can be directly calculated from measurements of a
three-wavelength humidified nephelometer system. Given that the Va(dry) can be estimated from a three-wavelength “dry”
nephelometer, the ambient ALWC can be estimated from measurements of a
three-wavelength humidified nephelometer system in conjunction with measured
ambient RH. We have conducted the comparison between ambient ALWC calculated
from ISORROPIA and ambient ALWC calculated from measurements of the
humidified nephelometer system. The square of correlation coefficient
between them is 0.92, and most of the points lie within or nearby 30 %
relative difference lines. The slope and intercept are 1.14 and -8.6 µm3 cm-3, respectively. Overall, a good
agreement is achieved between ambient ALWC calculated from measurements of
the humidified nephelometer system and ISORROPIA thermodynamic model.
Results introduced in this research have bridged the gap between f(RH) and Vg(RH). The
advantage of using measurements of a humidified nephelometer system to
estimate ALWC is that this technique has a fast response time and can
provide continuous measurements of the changing ambient conditions. The new
method proposed in this research will facilitate the real-time monitoring of
the ambient ALWC and further our understanding of roles of ALWC in
atmospheric chemistry, secondary aerosol formation and climate change.
The data used in this study are available from the
corresponding author upon request (zcs@pku.edu.cn).
Abbreviations
RHrelative humidityPM2.5particulate matter with aerodynamic diameter of less than 2.5 µmPM10particulate matter with aerodynamic diameter of less than 10 µmf(RH)aerosol light scattering enhancement factor at 550 nmALWCaerosol liquid water content: volume concentrations of water in ambient aerosolsVa(dry)total volume of ambient aerosol particles in dry stateVg(RH)aerosol volume enhancement factor due to water uptakeNCPNorth China PlainHTDMAhumidified tandem differential mobility analyser systemPNSDparticle number size distributionBCblack carbong(RH)hygroscopic growth factorAPSAerodynamic Particle SizerSMPSscanning mobility particle size spectrometerσspaerosol light scattering coefficientσbspaerosol back scattering coefficientσextaerosol extinction coefficientRVspσsp(550 nm) /Va(dry)F1 to F6referred as to five field campaigns listed in Table 1D1PNSD, BC and nephelometer measurements from F2, F4 and F5
The supplement related to this article is available online at: https://doi.org/10.5194/amt-11-2967-2018-supplement.
The authors declare that they have no conflict of
interest.
Acknowledgements
This work is supported by the National Natural Science Foundation of China
(41590872 and 41505107), the National Key R&D Program of China
(2016YFC020000: Task 5) and the National Research Program for Key Issues in
Air Pollution Control (DQGG0103).
Edited by: Mingjin Tang
Reviewed by: three anonymous referees
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