the Creative Commons Attribution 4.0 License.

the Creative Commons Attribution 4.0 License.

# Calculating the aerosol asymmetry factor based on measurements from the humidified nephelometer system

### Gang Zhao

### Chunsheng Zhao

### Yuxuan Bian

### Jiangchuan Tao

### Chuanyang Shen

### Yingli Yu

The aerosol asymmetry factor (*g*) is one of the most important
factors for assessing direct aerosol radiative forcing. However, little
attention has been paid to the measurement and parameterization of *g*. In
this study, the characteristics of *g* are studied based on field
measurements over the North China Plain (NCP) using the Mie scattering
theory. The results show that calculated *g* values for dry aerosol can vary
over a wide range (between 0.54 and 0.67). Furthermore, when ambient relative
humidity (RH) reaches 90 %, *g* is significantly enhanced by a factor of
1.2 due to aerosol hygroscopic growth. For the first time, a novel method of
calculating *g* based on measurements from the humidified nephelometer system
is proposed. This method can constrain the uncertainty of *g* to within
2.56 % for dry aerosol populations and 4.02 % for ambient aerosols,
providing that aerosol hygroscopic growth is taken into account. Sensitivity
studies show that aerosol hygroscopicity plays a vital role in the accuracy
of predicting *g*.

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In addition to aerosol optical depth and aerosol
single-scattering albedo, the aerosol phase function is the most important
factor for assessing direct aerosol radiative forcing (DARF) (Andrews et
al., 2006; Russell et al., 1997). The Henyey–Greenstein phase function
(PF_{HG}) is a widely used method to parameterize the phase function
(Toublanc, 1996; Boucher, 1998; Pandey and Chakrabarty, 2016) because it uses
the aerosol asymmetry factor (*g*) as the only free parameter. The
PF_{HG} is expressed as

where *θ* is the angle between the incident light direction and the
scattered light direction. In this respect, the free parameter *g* can
reflect the angular aerosol scattering energy distribution. *g* is defined as follows:

where *P*(*θ*) is the normalized scattering phase function. As a result,
*g* can be a computationally efficient parameter to replace the phase
function in the study of aerosol radiative transfer properties (Toublanc,
1996; Hansen, 1969; Boucher, 1998). This replacement proves to be useful and
has been widely accepted in previous studies (Hansen, 1969; Wiscombe and
Grams, 1976; Sagan and Pollack, 1967; Andrews et al., 2006); however significant
bias may arise in *g*-related PF_{HG} when estimating
photo-dissociation rates (Toublanc, 1996) and aerosol radiative forcing
effects (Boucher, 1998). In the past, few studies have
assessed the deviation when replacing the ambient phase function with the
*g*-related PF_{HG} (Pandey and Chakrabarty, 2016; Boucher, 1998;
Wiscombe and Grams, 1976), and there are no known studies that use field measurements
of aerosol optical properties to estimate the bias. Moreover, variations in
*g* can influence the evolution of the atmospheric vertical structure by
effecting the atmospheric radiative distribution. Kudo et al. (2016)
also found that the vertical profile of the asymmetry factor plays an
important role in altering vertical variations in the solar heating rate.
Marshall et al. (1995) reported that a 10 % overestimation of *g* can
systematically reduce aerosol climatic forcing by 12 % or more. Furthermore, Andrews
et al. (2006) found that a 10 % reduction in *g* would result in a
19 % overestimation of atmosphere radiative forcing at the top of
atmosphere (TOA). Therefore, an accurate estimation of *g* has the potential to greatly improve the
assessment of the aerosol radiative effect.

There are several methods available to derive the *g* of aerosol particles
under dry and ambient conditions, respectively. Horvath et al. (2016)
measured the phase function of aerosols, calculated the *g* of aerosols, and
found that the *g*-related PF_{HG} can be used as a good
approximation of the measured phase function. Many studies have used the Mie
model (Bohren and Huffman, 2007) to calculate the phase function and have
proven its reliability (Andrews et al., 2006; Marshall et al., 1995; Bian et
al., 2017). Comprehensive attempts have been made to relate *g* to the
hemispheric backscatter fraction (*b*). The value of *b* is the ratio of
light scattered into the backward hemisphere compared to total light
scattered in all directions (Wiscombe and Grams, 1976; Andrews et al., 2006;
Horvath et al., 2016), and is defined as follows:

The main advantage of the backscatter ratio is that it can be measured with an integrating nephelometer equipped with a backscatter shutter (Charlson et al., 1974).

The free parameter *g* varies significantly for different aerosol types and
different seasons. In previous studies, the *g* values have mainly been
examined using the Mie scattering theory and the measured aerosol particle numbers
size distribution (PNSD). D'Almeida et al. (1991) suggested that *g*
ranges from 0.64 to 0.83 at a wavelength of 500 nm depending on the aerosol type
and the season; their study also found a mean *g* value of 0.67 at an ambient relative humidity (RH).
Furthermore, Hartley and Hobbs (2001) reported
a median *g* value of 0.7 for aerosols along the east coast of the United
States. Formenti et al. (2000) measured Saharan dust aerosol and found that
the aerosol *g* values ranged from 0.72 to 0.73. Biomass burning aerosols in
Brazil were found to have a low *g* value of 0.54 (Ross et al., 1998).

Some studies have examined the impacts of aerosol hygroscopic growth on the
parameter *g* (Hartley and Hobbs, 2001; Kuang et al., 2015; Andrews et
al., 2006) and found that variations in *g* with RH can have significant
influences on aerosol radiative effects (Kuang et al., 2015, 2016; Andrews et
al., 2006). Therefore, a parameterization scheme of *g*, which takes RH and aerosol
hygroscopic growth into account, is necessary.

When exposed to the ambient atmosphere, aerosols can grow by taking up water,
which causes their corresponding optical properties to change considerably.
The *κ*-Köhler theory (Petters and Kreidenweis, 2007) is widely used
to describe the hygroscopic growth of aerosol particles using a single
aerosol hygroscopic growth parameter (*κ*) and the *κ*-Köhler
equation, which is described as follows:

where *D*_{d} is the dry particle diameter; *g**f*(RH) is the
aerosol growth factor, defined as the ratio of the aerosol diameter at a
given RH to the dry aerosol diameter (*D*_{RH}∕*D*_{d}); *T* is
the temperature; *σ*_{s∕a} is the surface tension of the
solution; *M*_{water} is the molecular weight of water; *R* is the
universal gas constant; and *ρ*_{w} is the density of water. The
aerosol hygroscopic growth parameter *κ* can be further used to
investigate the influence of aerosol hygroscopic growth on aerosol optical
properties (Tao et al., 2014; Kuang et al., 2015; Zhao et al., 2017) and
aerosol liquid water contents (Bian et al., 2014).

According to the Mie theory, *g* is associated with aerosol particle number
size distribution, the particle complex refractive index, the aerosol mixing
state and ambient RH. At the same time, the aerosol morphology has a
significant influence on *g*. Datasets from the humidified nephelometer
system can partially account for all of these factors. The humidified
nephelometer system consists of two parallel nephelometers, one of which
measures dry aerosol scattering properties whilst the other measures aerosol
scattering properties under well-controlled RH conditions. This system can
give the light scattering enhancement factor (*f*_{RH}), which is
defined as ${f}_{\mathrm{RH}}\left(\mathit{\lambda}\right)={\mathit{\sigma}}_{\mathrm{sca}\left(\mathit{\lambda}\right)}/{\mathit{\sigma}}_{\mathrm{sca}\left(\mathit{\lambda}\right)}$, or the ratio
of the aerosol scattering coefficient under given RH conditions to that under
dry conditions. Each nephelometer can provide a scattering coefficient
(*σ*_{sca}) and a back-scattering coefficient
(*β*_{sca}) at three wavelengths (450, 525, and 635 nm).
*σ*_{sca} can be used to calculate the aerosol scattering
Ångstrom index, which reflects the aerosol PNSD to some extent. In
general, a larger value for the Ångstrom index always corresponds to a
smaller predominant aerosol size. Variations in *β*_{sca} and
*σ*_{sca} can be used to deduce the aerosol black carbon (BC) mixing state (Ma
et al., 2012). At the same time, datasets from the humidified nephelometer
system can also be used alone to measure the aerosol hygroscopicity and
provide an overall hygroscopic parameter *κ* (Kuang et al., 2017). In
conclusion, measurements from the humidified nephelometer system might be
used for estimating *g* under given RH conditions. However, there is no
clear relationship between the measured datasets from the humidified
nephelometer and *g*. Furthermore, the nonlinear influence of the above listed factors on
*g* also makes it difficult to parameterize the *g*.

The random forest machine learning model is a powerful technique that can be used
for classification and nonlinear regression (Huttunen et al., 2016; Breiman,
2001; Hu et al., 2017). This model is a widely used nonparametric machine
learning algorithm that has several strengths. First, it involves fewer
assumptions regarding the dependence between observations and outcomes when
compared with traditional parametric regression models. Second, strict
relationships among variables are not needed before implementing the model. Third, this learning model requires far less computing
resources than deep learning. Finally, this model has very low risk of over
fitting by averaging over an ensemble of decision trees. Thus, the random
forest machine learning model is used in this work to study the calculation
of *g* based on the datasets of the humidified nephelometer system.

In this study, the Mie scattering theory and field measurements over the
North China Plain (NCP) are used to study the characteristics of *g*.
Section 2 describes the related datasets used in this study. Details of the
study on the characteristics of *g* and the impacts of aerosol hygroscopic growth
on *g* are shown in Sect. 3.1. A new method, which is based on a random
forest machine learning model, is introduced to calculate *g* in Sect. 3.2.
We also discuss the impacts of *g* variations on the uncertainties of DARF in
Sect. 3.3, and the corresponding results are presented in Sect. 4.3.
Section 4.1 gives the calculated characteristics of *g* and Sect. 4.2 proves
the feasibility of using the machine learning model to calculate *g*. At the
same time, this method is validated by the ambient aerosol phase function
measured with a charge-coupled device–laser aerosol detective system
(CCD–LADS). Conclusions are given in Sect. 5.

Datasets used in this study come from three field campaigns, which were
conducted at three different sites in the NCP. These three field measurements
were conducted at Gucheng in Hebei Province (Gucheng, 39^{∘}09^{′} N,
115^{∘}44^{′} E) from 15 October to 25 November in 2016, at the AERONET
Beijing PKU station in Beijing (PKU, 39^{∘}59^{′} N,
116^{∘}18^{′} E) from 21 March to 10 April in 2017, and at the Yanqi
Campus of the University of Chinese Academy of Sciences (UCAS,
40^{∘}24^{′} N, 116^{∘}40^{′} E) in the Huairou district in Beijing
from 3 January to 27 January in 2016. Details of these locations are shown in
Fig. S1 in the Supplement. The PKU station is located in the northwest of
Beijing, between the 4th and 5th ring road. It is 11 km from the center of
the megacity of Beijing, which is adjacent to Hebei Province and the megacity
of Tianjin. In the abovementioned three areas,
industrial manufacturing has led to heavy air pollution. Datasets for the PKU
station are representative of urban aerosols in the NCP. Gucheng is located
between two megacities (120 km from Beijing and 190 km from Shijiazhuang)
in the NCP; therefore, the pollution conditions of Gucheng are a good
representation of the continental background in the NCP. Details regarding
the Gucheng station can be found in a study by Kuang et al. (2017). The UCAS
station is 60 km away from the center of Beijing and is at the edge of the
NCP, which makes it suitable for measuring the regional pollution properties
of the NCP (Ma et al., 2016). More details about the measurement sites are
available in Sect. S1 of the Supplement.

Table 1 lists the information for the field campaigns and the datasets used
in this study. During the campaigns, sampled aerosols that had an aerodynamic
diameter of less than 10µm are selected by an impactor (Mesa Labs,
Model SSI2.5) at the inlet. These aerosols are then dried to below 30 %
RH with a Nafion drying tube and lead to each instrument. Aerosol PNSDs
ranging from 3 nm to 10 µm are measured using a scanning
mobility particle sizer spectrometer (SMPS, TSI Inc., model 3936) and an
aerodynamic particle sizer spectrometer (APS, TSI Inc., model 3321) with a temporal
resolution of 5 min. Black carbon (BC) mass concentrations are measured by a
multi-angle absorption photometer (MAAP model 5012, Thermo, Inc., Waltham, MA
USA) at UCAS and by an Aethalometer (AE33)(Hansen et al., 1984; Drinovec et
al., 2015) at PKU and Gucheng. The aerosol *σ*_{sca} is measured at
wavelengths of 450, 525, and 635 nm by an Aurora 3000 nephelometer and the
corresponding values are recorded every minute
(Müller et al., 2011).

The *f*_{RH} is measured by a self-constructed humidified nephelometer
system. In this system, a humidifier is used to control the RH of the sample
aerosol and *σ*_{sca} is measured for each of the controlled RH
levels. The sample aerosol is humidified through a Gore-Tex tube, which is
surrounded by a circulating water layer in a stainless steel tube. The RH is
changed by changing the temperature of the circulating water, which is
controlled by a water bath and software. For each cycle, the RH points are
set to range from about 50 to about 90 % over 45 min. For most of the
cases, the aerosol PNSDs are consistent over the cycle. These cycles of
*f*_{RH} values are abandoned when either the measured maximum or the
minimum *σ*_{sca} values are beyond the range of 1.4 and
0.6 times the mean measured scattering coefficient of each cycle. The humidified
nephelometer is described in detail by Kuang et al. (2017).

An ambient aerosol phase function with a time resolution of 5 min is measured
at UCAS using a CCD–LADS. This system consists of a continuous laser, two
charge-coupled device cameras, and corresponding fish eye lenses. The
wavelength of the laser is 532 nm and a quarter-wave plate was mounted in
front of the laser emitter to change the polarization state of the laser from
linear to circular. The CCD–LADS can measure the ambient aerosol phase
function at a wide angular range of 10–170^{∘} with a high resolution
of 0.1^{∘}. More details of the measurement system can be found in Bian
et al. (2017).

## 3.1 Calculating characteristics of *g* based on the Mie scattering theory (*g*_{Mie})

The Mie model (Bohren and Huffman, 2007) is applied to calculate the
characteristics of *g*_{Mie}. When running the Mie model, aerosol
PNSD, aerosol complex refractive index, BC mixing state, and BC mass
concentration are essential. Its results include the aerosol phase function, and
*g*_{Mie} can be calculated using Equation 2.

Mixing states of the BC come from field measurements. In the work by Ma et
al. (2012), the mixing states of BC in the NCP are presented as both
core-shell mixed and externally mixed. Ma et al. (2012) also provides the ratio of
BC mass concentrations under an externally mixed state,
*M*_{ext_BC}, to total BC mass concentration, *M*_{BC} as
follows:

The mean value of *r*_{ext_BC}=0.51 (Ma et al., 2012) is used in
this study. The size-resolved distribution of the BC mass concentration is
the same as that used by Ma et al. (2012). The *κ*-Köhler theory and
the Mie scattering model are employed to calculate *g*_{Mie} under
different RH conditions. When the aerosol grows by taking up water, the BC is
treated as a non-hygroscopic and insoluble core. The real time value
*κ*, which is derived from the measurement of *f*_{RH}, is used
to account for aerosol hygroscopic growth. For each RH value, the growth
factor can be calculated based on Equation 4. The corresponding ambient
aerosol PNSD at a given RH can also be determined by applying the *κ*
and Equation 4. The refractive index ($\stackrel{\mathrm{\u0303}}{m}$), which accounts for water
content in the particle, is derived as a volume mixture between the dry
aerosol and water (Wex et al., 2002):

where *f*_{v, dry} is the ratio of the dry aerosol volume to the
total aerosol volume under a given RH condition;
${\stackrel{\mathrm{\u0303}}{m}}_{\mathrm{aero},\phantom{\rule{0.125em}{0ex}}\mathrm{dry}}$ is the refractive index for dry ambient
aerosols; and ${\stackrel{\mathrm{\u0303}}{m}}_{\mathrm{water}}$ is the refractive index of water.

The refractive indices of BC, non-light-absorbing aerosols, and water, which
are used in this study, are 1.8+0.54*i* (Kuang et al., 2015), $\mathrm{1.53}+{\mathrm{10}}^{-\mathrm{7}}i$ (Wex et al., 2002), and $\mathrm{1.33}+{\mathrm{10}}^{-\mathrm{7}}i$, respectively. Then, the
corresponding *g* values under the given RH and PNSD can also be calculated.
More details on using the Mie model to calculate the aerosol phase function
for different RH conditions can be found in Zhao et al. (2017).

## 3.2 Calculating *g* using the random forest machine learning model (*g*_{ML})

In this study, the random forest machine learning model from the scikit-learn
machine learning library (Hu et al., 2017; Pedregosa et al., 2011) was used
to calculate *g*. The random forest model has two parameters: the number of
input variables (*n*_{pre}) and the number of trees grown
(*n*_{tree}). In this study, the *n*_{pre} and
*n*_{tree} are determined by minimizing the relative difference of the
*g*_{ML} and *g*_{Mie}. Details of choosing the values of
*n*_{pre} and *n*_{tree} are shown in Sect. S2. The
*n*_{pre} and *n*_{tree} are set as eight and thirty-two in
this study, respectively. The eight input parameters include the three dry
scattering coefficients, the three dry backscattering coefficients, the RH,
and *κ*.

The measured datasets are divided into two parts: the training data
for the random forest model and the testing data. All training
datasets come from field measurements at Gucheng station, whereas the
datasets from PKU are employed to test the accuracy of the model. With split
datasets from different sites, the feasibility of the random forest model in
the NCP can be guaranteed. Before calculating *g*_{Mie}, we compare
the measured *σ*_{sca} from the dry nephelometer and calculate
*σ*_{sca} from the Mie scattering model. These data, where the
relative difference between the measured and calculated *σ*_{sca}
is within 30 %, are used for the following analyses; therefore, instrument measurement
inaccuracy can be avoided to some extent. More details regarding the data used is shown in Sect. S3.

To further avoid measurement uncertainties when training the
random forest machine learning model, both the required input parameters and
the predictors (*g* values) come from the calculations of the Mie scattering
model. The Mie scattering model used aerosol PNSD and BC measurements from the field
campaign in Gucheng. For each measured PSND and BC, the corresponding
*σ*_{sca} and *β*_{sca} under dry conditions at
450, 525, and 635 nm are modeled based on the Mie theory. With
the concurrently measured *κ* values from the humidified nephelometer,
the *g*_{Mie} values under different RH can also be determined. Then
the modeled *σ*_{sca}, *β*_{sca} under dry condition,
the *κ* values, and the RH are used as the input data for the model and
the corresponding *g*_{Mie} values are used as the prediction data.

## 3.3 Aerosol DARF estimations

Earth–atmosphere systems can be significantly influenced by aerosols
through the scattering and absorption of energy. In this study, the Santa
Barbara DISORT (discrete ordinates radiative transfer) Atmospheric Radiative
Transfer (SBDART) model (Ricchiazzi et al., 1998) is employed to estimate the
DARF. The characteristics of DARF relating to variations in *g* are studied.

The instantaneous DARF is calculated at the TOA for cloud-free conditions. DARF is defined as the difference between radiative flux at the TOA under present aerosol conditions and aerosol-free conditions:

where $\left({f}_{\mathrm{a}}\downarrow -{f}_{\mathrm{a}}\uparrow \right)$ is the downward radiative irradiance flux with given aerosol distributions and $\left({f}_{\mathrm{m}}\downarrow -{f}_{\mathrm{m}}\uparrow \right)$ is the radiative irradiance flux under aerosol-free conditions. The DARF at 50 km is calculated because almost all of the aerosols are distributed within the height of 50 km in the parameterization scheme (Liu et al., 2009). Wavelengths in the range of 0.25 to 4 µm are calculated for irradiance in this study.

Input data for the SBDART are as follows: vertical profiles of the aerosol
optical properties, which include the aerosol extinction coefficient
(*σ*_{ext}), aerosol single scattering albedo (SSA), and *g*. All data
have a vertical resolution of 50 m and come from the results of the Mie
scattering model and the parameterized aerosol vertical distributions. Methods for
parameterization and calculation of the aerosol optical profiles can be found
in Sect. S4 or in Kuang et al. (2016) and Zhao et al. (2017).
Atmospheric meteorological parameter profiles come from the results of the
intensive radiosonde observations at the Meteorological Bureau of Beijing
(39^{∘}48^{′} N, 116^{∘}28^{′} E) at 13:30 LT from
July to September in 2008. Kuang et al. (2016) studied these measured
profiles and found that the vertical distributions of these parameters, which
include profiles for water vapor, pressure, and temperature, can be used as a
good representation of the meteorological parameter profiles in the NCP
during summer. The corresponding measured mean results during field
measurement are used in this study and the details of these profiles are
shown in Sect. S4. Surface albedo values are obtained from the Moderate
Resolution Imaging Spectroradiometer (MODIS) V005 Climate Modeling Grid (CMG)
Albedo Product (MCD43C3). The mean results of the surface albedo of Beijing
from July to September in 2008 are used. The remaining input data for the
SBDART are set to their default values (Ricchiazzi et al., 1998).

## 4.1 Characteristics of *g*_{Mie}

### 4.1.1 Characteristics of *g*_{Mie} at different sites

Figure 1 gives the statistical results for the calculated *g* properties at
Gucheng, PKU, and UCAS. The RH values at the three sites show almost the same
diurnal variation pattern (Fig. 1a, b, and c). The RH reaches a peak in the
morning at approximately 06:00 LT , and then reaches its lowest value at
approximately 16:00 LT in the afternoon. However, the mean values of RH are
77.7 % ± 20.9 % at Gucheng, 47.8 % ± 20.8 % at
PKU, and 33.49 % ± 15.22 % at UCAS. The *g*_{Mie} values
under dry conditions that are calculated by the measured PNSD have almost no
diurnal patterns. The *g*_{Mie} values at PKU (0.614 ± 0.025)
are slightly lower than those at Gucheng (0.601 ± 0.021) and UCAS
(0.595 ± 0.023) (Fig. 1d, e, and f). The difference in the
*g*_{Mie} values results from different aerosol properties at these
sites. From Fig. S6, it can be noted that the peak diameter of the mean and median PNSD at
Gucheng is located around 150 nm. However, the peak diameter of the mean and median
PNSD at PKU is located at around 100 nm. The peak values of the mean and median
diameter of the aerosol PNSD at UCAS is located at around 60 nm. At the same
time, there are large partitions of small particles that are lower than
60 nm at PKU and UCAS. However, these particles, which are lower than
100 nm, do not really contribute to the total aerosol scattering. The aerosol PNSD
at PKU is more dispersed than that at the Gucheng and UCAS sites, which corresponds
to a larger variation in the *g* values. From Fig. S6g, h, and i, the size
distribution of the aerosol scatter coefficient at around 500 nm contributes
less to the scatter coefficient at PKU than to the scatter coefficients at Gucheng and UCAS.
Thus these particles with a diameter larger than 500 nm contribute more to
the aerosol scattering coefficient. As *g*_{Mie} increases with the
aerosol diameter, the aerosol *g*_{Mie} under dry conditions at PKU
tends to be larger than that at Gucheng and UCAS.

However, ambient *g*_{Mie} values have different patterns at different
sites, as shown in Fig. 1g, h and i. The *g*_{Mie} values have an
RH-related diurnal pattern at Gucheng, with a mean value of
0.668 ± 0.073; although *g*_{Mie} values show no diurnal variation at PKU and UCAS, where the
mean values of *g*_{Mie} are 0.639 ± 0.049 and
0.618 ± 0.033, respectively. The variations in ambient *g*_{Mie}
values mainly result from the variation in the aerosol hygroscopic
growth under ambient conditions, which is highly related to the ambient
RH. The *g*_{Mie} value is significantly influenced by RH when the RH
is higher than 80 %, which is be detailed in Sect. 4.1.2. Ambient
*g*_{Mie} values at Gucheng, PKU, and UCAS can vary from 0.57 to 0.8,
0.55 to 0.76, and 0.56 to 0.72, respectively; this makes them comparable to *g*_{Mie} values from Andrews et
al. (2006), which range from 0.59 to 0.72.

### 4.1.2 Influence of RH on *g*

To assess the influence of RH on *g*, the *g*_{Mie} values are
calculated under different RH conditions for each aerosol PNSD. The
statistical results of *g*_{Mie} versus RH are shown in Fig. 2. The
*g*_{Mie} value has a wide variation, ranging between 0.54 and 0.67 with
the mean value located at 0.61, under dry conditions. However, the mean
*g*_{Mie} value can change from 0.65 to 0.8 when the RH reaches
90 %. The *g*_{Mie} enhancement factor, which is defined as the
ratio of *g*_{Mie} at a given RH and *g*_{Mie} under dry
conditions, can reach a mean value of 1.2 at an RH of 90 %, which means
that the *g*_{Mie} value under wet conditions is approximately
20 % higher than that under the dry conditions. This finding is
consistent with that of Hartley and Hobbs (2001), who found that *g* is
highly related to RH.

Contrary to RH, the aerosol complex refractive index has little influence on
*g* and the uncertainties for *g* are less than 0.004 based on the Monte
Carlo simulation of the *g* at different complex refractive index values.
More details regarding the influence of the aerosol complex refractive index
on *g* can be found in Sect. S6.

## 4.2 Calculating *g*_{ML} using the machine learning model

### 4.2.1 Feasibility of using the random forest model

We establish two independent random forest machine learning models to predict
*g*_{ML} values under dry conditions and under ambient RH conditions,
respectively.

When the random forest machine learning model is run for *g* values under dry
conditions, *σ*_{sca} and *β*_{sca} are used as the
input for independent variables at three different wavelengths. The other two
input parameters, RH and *κ*, are set to zero. The predictor *g* values
come from the results of the Mie scattering model. Figure 3a shows the
calculated and the predicted *g*_{ML} values from the random forest
machine learning model under dry conditions at the PKU site. The results show
that the *g*_{Mie} values and *g*_{ML} values have good
consistency, with an *R*^{2} value of 0.98. Therefore, in 95 % of the
cases, the relative difference between *g*_{Mie} and *g*_{ML}
is within 2.56 %.

Figure 3b shows the comparison of the predicted *g*_{ML} values under
different RH conditions and *g*_{Mie} values calculated by the Mie
scattering model. The correlation coefficient between *g*_{Mie} and
*g*_{ML} reaches 0.93, and 95 % of the relative differences are
within 4.02 %. The random forest model has the potential to be a good method to predict
*g* values under different RH conditions with high accuracy; the
uncertainties of predicting *g* values using the random forest machine
learning model is estimated to be 4.02 %.

The fill colors of the dots in Fig. 3 represent the concurrently measured
*σ*_{sca}. It is shown that *g* values tend to be larger with an increase in
*σ*_{sca}, which is in accordance
with the particle scattering properties. When a particle has a larger
diameter the *σ*_{sca} of the particle is higher, and there
tends to be a larger partition of forward scattering light.

The reliability of the previous parameterization of the *g* using *b* is tested here.
Wiscombe and Grams (1976) studied the relationship between *b* and *g* and
gave the expression between them as follows:

This equation is widely used to calculate *g* from *b* (Andrews et al., 2006;
Horvath et al., 2016; Kassianov et al., 2007). We use the field measurement
results to test its reliability. The comparison results between calculated
*g* values from the Mie scattering model and parameterized *g* values from
Eq. (6) are shown in Fig. S9. From Fig. S9, we can see that the parameterized
*g* values are prevalently larger than the calculated *g* values by
approximately 10 %. When the *σ*_{sca} is smaller, the
deviations become larger. Some other empirical relationships between *b* and
*g* (Moosmüller and Ogren, 2017) are also tested. This parameterization
scheme almost has the same result as Wiscombe and Grams (1976), which means that
the previously established parameterization scheme is not
applicable in the NCP

### 4.2.2 Sensitivity of the random forest model

Sensitivity studies are carried out to assess the influence of each input
variable on *g*_{ML}. Based on the work of Müller et al. (2011),
the uncertainties in total scattering are 4 % (450 nm), 2 %
(525 nm), and 5 % (635 nm) for experiments with ambient air and laboratory
generated white particles. For backscattering, the differences are higher and
amount to 7 % (450 nm), 3 % (525 nm), and 11 % (635 nm). The
uncertainty of the RH measured by the RH sensors is 1.7 % for RH ranges
from 0 to 90 % (Kuang et al., 2017) and the uncertainty of the derived
*κ* values is 6 % (Kuang et al., 2017). Monte Carlo simulations
are conducted to study the sensitivity of the *g*_{ML} to the input
parameters in three steps. First, the mean results of the measured dry
*σ*_{sca}, dry *β*_{sca}, RH, and *κ* values are
used to predict the *g* value. Second, the dry *σ*_{sca} at
450 nm is randomly changed with a mean value of 0 and standard deviation of
4 % and the other inputs remain unchanged. The
corresponding standard deviation of the predicted *g* value is used as the
sensitivity of the *g*_{ML} to the *σ*_{sca} at 450 nm.
Lastly, the sensitivity is determined for each input parameter and
the uncertainties of the *g*_{ML} values to the input
parameters are estimated. The total uncertainties of predicting *g* RH are
derived when all of the input parameters are randomly changed with their
corresponding uncertainties. For each test, the Monte Carlo simulations are
carried out 20 000 times.

Table 2 gives the error to two standard deviations of the *g*_{ML}
values corresponding to the uncertainties of the input
parameters. From Table 2, it can be noted that the uncertainty of the measured
*σ*_{sca} has little influence on the *g*_{ML} with *g*
value uncertainties of 0.487, 0.492, and 0.486 % for 450, 525, and
635 nm, respectively. However, the measurement of the three
*β*_{sca} have larger uncertainties and lead to greater influence
on predicting *g*_{ML} with uncertainties of 0.651, 0.486, and
0.710 %. The uncertainty of the RH (0.487 %) has little influence on
predicting *g*_{ML}. However, the uncertainty of the derived *κ*
values (6 %) influence the *g* values the most with a *g* value
uncertainty of 1.92 %. The total uncertainty of predicting *g* due to
uncertainties in the measurement parameters is 1.95 %. All in all, the
total uncertainty of predicting the *g*_{ML} is estimated to be
4.47 %, considering the 4.02 % uncertainty of the random forest
machine learning model from Sect. 4.2.1.

### 4.2.3 Validation of the random forest machine learning model

Datasets of the UCAS campaign are also used to validate the random forest
machine learning model. On one hand, the *g*_{ML} values are
calculated by using the random forest machine learning model with the
measurements of the humidified nephelometer. On the other hand, ambient
*g* values are calculated by using the measured phase function from the
CCD–LADS *g*_{CCD} according to the definition shown in Equation 2.
The *g* values are then calculated, and the two methods are compared.

The results of the comparison of these two kinds of *g* values are shown in
Fig. 4. As seen in Fig. 4, the values of *g*_{ML} and *g*_{CCD}
show good consistency. In 95 % of cases the relative differences between
the *g*_{ML} and *g*_{CCD} are within an acceptable range of
6.5 %, which is a little higher than the relative difference of the *g*
values (4.02 %) between the machine learning method and the Mie
scattering method. During the study period, the *σ*_{sca} ranged from
30 to 260 Mm^{−1}, which led to cleaner conditions in UCAS than in Gucheng
and PKU. Correspondingly, most of the *g*_{Mie} values are small and
located in the 0.54 to 0.62 range, which is obviously lower than the range of
values from other campaigns. At the same time, the surrounding conditions at
UCAS during winter are relative dry, which results in small *g* values. These
conditions may partially explain the higher difference between the
*g*_{ML} and *g*_{CCD}. With this validation, we conclude that
the random forest machine learning model can give a reasonable *g* value
based on the measurements of the humidified nephelometer system.

## 4.3 Estimating the impacts of *g* on DARF

### 4.3.1 Uncertainties of replacing the calculated phase function with the PF_{HG}

When the PF_{HG} is used to parameterize the calculated phase
function using the Mie theory (PF_{Mie}), there are some
deviations and the influence of these deviations should be estimated. The
relative difference between the DARF from the PF_{Mie} and from the
PF_{HG} is used to estimate uncertainties when using the
PF_{HG}. First, the PF_{Mie} profiles are used as inputs to
estimate DARFs. The PF_{Mie} is then replaced with the *g*-related
PF_{HG}, which is parameterized by *g*_{Mie} from the
PF_{Mie}, and the DARFs are calculated again. These relative
differences between the DARFs from the above two steps are recorded and
compared. The relative differences at different zenith angle conditions are
calculated to comprehensively estimate the influence of the PF_{HG}.

Figure 5 shows the estimated DARFs at different zenith angles. In Fig. 5a,
DARF at the TOA can vary from −2.55 to
−4.8 W m^{−2}. When the
PF_{Mie} is replaced by the PF_{HG}, the calculated DARF
ranges from −2.6 to −5.1 W m^{−2}. The relative difference of the
DARFs between the two methods ranges from 1.3 to 7.1 %, as shown in
Fig. 5b. It is concluded that using the *g*-related PF_{HG} to
replace the PF_{Mie} to estimate aerosol radiative effects is
applicable in the NCP, with a deviation of less than 7 %.

### 4.3.2 Impacts of *g* variations on DARF estimation

Variations in *g* can lead to significant changes in the estimated DARF
(Kuang et al., 2016; Andrews et al., 2006; Mccomiskey et al., 2008). In this
study, the uncertainty of the *g* value due to the uncertainty of the input parameters is
estimated to be 1.95 % and the total variation in running the random
forest machine learning model is estimated to be 4.47 %. At the same
time, the *g* can vary about 10 % for different aerosol PNSD and can be
enhanced by 20 % by an increase of the RH from 30 to 90 %. It is very
important to know the extent of the variation in DARF corresponding to the
uncertainties from *g*.

The variation in DARF from the uncertainties of *g* is calculated by
increasing or decreasing *g* by 1.95, 4.47, and 10 % of the original *g*
values, and then comparing the corresponding DARFs with the original values. To
study the influence of RH on *g* and DARF, the DARF with the *g* values
calculated from the dry parameterized aerosol population profile, is
estimated.

Figure 6 shows the estimated DARFs with different variations in *g* and the
corresponding variations in the estimated DARF. The results show that when
*g* varies by 1.95 %, the DARF can vary by 4 %. However, variations of
4.47 and 10 % in *g* values can lead to variations of 9.4 and 21 % in the estimated DARF, respectively.

The estimated DARF using the parameterized aerosol profile, which considers
the aerosol hygroscopic growth, is smaller than the DARF using the *g*
profiles from the dry aerosol population. The *g* values under dry conditions
are smaller than those under wet ambient conditions. Thus, there is larger partition of
energy that is scattered forward which leads to less outgoing backscattering
energy and a larger value of the estimated DARF.

When the DARF are estimated ignoring the impacts of aerosol hygroscopic
growth on *g*, the relative difference can be as high as 20 % for all of
the zenith angles. Thus, it is necessary to consider the aerosol hygroscopic
growth when calculating the *g* values.

The characteristics of *g* in the NCP are studied based on the
Mie scattering theory and field measurements from the Gucheng and PKU study sites.
The results show that *g*_{Mie} values are 0.604 ± 0.025 at
Gucheng and 0.615 ± 0.021 at PKU. The ambient *g*_{Mie} values
at Gucheng show obvious diurnal variations due to variations in RH. When the
ambient RH reaches 90 %, *g*_{Mie} can be enhanced by 20 % and
the *g* values from different aerosol population can vary by 10 %.
Comparison of the calculated *g*_{Mie} values from the Mie scattering
model and the parameterized *g* values from the Wiscombe and Grams (1976)
method shows that the parameterized *g* is overestimated by approximately
10 % and that the deviations become larger when the measured
*σ*_{sca} is below 200 Mm^{−1}.

The random forest machine learning model and datasets from the humidified
nephelometer are employed to calculate *g*_{ML} values. The input data
of the random forest model contain measured *σ*_{sca} and
*β*_{sca} at three wavelengths, RH, and the hygroscopic parameter
*κ*. Except for RH, all input data came from measurements from the
humidified nephelometer system (Kuang et al., 2017). The random forest model
can significantly improve the accuracy of *g*_{ML} prediction. The
uncertainties of the predicted *g*_{ML} values are constrained within
2.56 % under dry conditions and 4.02 % under ambient conditions and
the uncertainties from the measurement of the humidified nephelometer can
lead to a variation of 1.95 % in g, which mainly results from the
inaccuracy of the derived *κ*. The total uncertainty of the *g* calculation
using the random forest machine learning model is 4.47 %. This is the
first time that a machine learning model and datasets from the humidified
nephelometer system have been combined to study *g*. Additionally, this method
can account for the influence of aerosol hygroscopic growth on *g*.

This new method for calculating *g* is validated by comparing the
*g*_{ML} values from the random forest machine learning model and the
*g*_{CCD} values from the measured phase function by using the
CCD–LADS. The *g* values from these two methods show good consistency, with
95 % of the data within a relative difference of 6.5 %.

The SBDART model is used to study the impacts of *g* on DARF. We first
studied the relative differences between the estimated DARFs using the
PF_{HG} and the calculated phase function using the Mie theory, the
measured mean aerosol PNSD, and BC mass concentration at the Gucheng and PKU
study sites. The results show that the relative differences in DARF can be
contained within 7.1 % of the mean when replacing the
PF_{Mie} with the *g*-related PF_{HG}. The PF_{HG}
has the potential to be a feasible parameterization scheme to study DARF in
the NCP.

The sensitivity study shows that the maximum uncertainties of DARF are 4,
9.4, and 21 %, which correspond to the uncertainties of the *g* from
instrument measurements, the machine learning model, and the variation of
aerosol PNSD. However, when the DARF are estimated ignoring the effects of
aerosol hygroscopic growth on *g*, the relative differences of the DARF are
as large as 20 % for all zenith angles. It is necessary to parameterize
the *g* accounting for the effect of aerosol hygroscopic growth.

This work furthers our understanding of the role of *g* in influencing
aerosol radiative effects and can help reduce uncertainties in estimating
DARF.

The measurement data involved in this study are available upon request to the authors.

The supplement related to this article is available online at: https://doi.org/10.5194/acp-18-9049-2018-supplement.

The authors declare that they have no conflict of interest.

This work is supported by the National Natural Science Foundation of China
(41590872) and the National Key R&D Program of China
(2016YFC020000: task 5).

Edited by: Armin Sorooshian

Reviewed by: two anonymous referees

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*g*) is one of the most important factors for assessing direct aerosol radiative forcing (DARF) and remote sensing. So far, few studies have focused on the measurements and parameterization of

*g*. Our study shows that relative humidity has significant impacts on

*g*and DARF due to aerosol hygroscopic growth. For the first time, a novel method based on measurements from the humidified nephelometer system is proposed to calculate

*g*accurately with high time resolution.

*g*) is one of the most important factors for assessing direct...