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**Atmospheric Measurement Techniques**
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- About
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**Research article**
12 Jul 2019

**Research article** | 12 Jul 2019

Method to retrieve cloud condensation nuclei number concentrations using lidar measurements

^{1}Department of Atmospheric and Oceanic Sciences, School of Physics, Peking University, Beijing 100871, China^{2}State Key Laboratory of Severe Weather & Key Laboratory of Atmospheric Chemistry of CMA, Chinese Academy of Meteorological Sciences, Beijing 100081, China^{3}State Key Joint Laboratory of Environmental Simulation and Pollution Control, College of Environmental Science & Engineering, Peking University, Beijing 100871, China

^{1}Department of Atmospheric and Oceanic Sciences, School of Physics, Peking University, Beijing 100871, China^{2}State Key Laboratory of Severe Weather & Key Laboratory of Atmospheric Chemistry of CMA, Chinese Academy of Meteorological Sciences, Beijing 100081, China^{3}State Key Joint Laboratory of Environmental Simulation and Pollution Control, College of Environmental Science & Engineering, Peking University, Beijing 100871, China

**Correspondence**: Chengcai Li (ccli@pku.edu.cn)

**Correspondence**: Chengcai Li (ccli@pku.edu.cn)

Abstract

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Determination of cloud condensation nuclei (CCN) number
concentrations at cloud base is important to constrain aerosol–cloud
interactions. A new method to retrieve CCN number concentrations using
backscatter and extinction profiles from multiwavelength Raman lidars is
proposed. The method implements hygroscopic enhancements of backscatter and
extinction with relative humidity to derive dry backscatter and extinction
and humidogram parameters. Humidogram parameters, Ångström
exponents, and lidar extinction-to-backscatter ratios are then linked to the
ratio of CCN number concentration to dry backscatter and extinction
coefficient (AR_{ξ}). This linkage is established based on
the datasets simulated by Mie theory and *κ*-Köhler theory with in-situ-measured particle size distributions and chemical compositions. CCN
number concentration can thus be calculated with AR_{ξ} and
dry backscatter and extinction. An independent theoretical simulated dataset
is used to validate this new method and results show that the retrieved CCN
number concentrations at supersaturations of 0.07 %, 0.10 %, and
0.20 % are in good agreement with theoretical calculated values.
Sensitivity tests indicate that retrieval error in CCN arises mostly from
uncertainties in extinction coefficients and RH profiles. The proposed
method improves CCN retrieval from lidar measurements and has great
potential in deriving scarce long-term CCN data at cloud base, which benefits
aerosol–cloud interaction studies.

How to cite

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How to cite.

Tan, W., Zhao, G., Yu, Y., Li, C., Li, J., Kang, L., Zhu, T., and Zhao, C.: Method to retrieve cloud condensation nuclei number concentrations using lidar measurements, Atmos. Meas. Tech., 12, 3825–3839, https://doi.org/10.5194/amt-12-3825-2019, 2019.

1 Introduction

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Anthropogenic activities have caused an increase in atmospheric aerosols, and some of the aerosol particles affect the climate by serving as cloud condensation nuclei (CCN). CCN in clouds can modify cloud-forming processes and cloud microphysical properties (Rosenfeld et al., 2014). Although numerous impacts of aerosol–cloud interactions on radiative forcing (McCoy et al., 2017; Zhou et al., 2017), precipitation (Xu et al., 2017; Fan et al., 2018), cloud electrification (Wang et al., 2018), and severe weather or hazards (Fu et al., 2017) have been discovered, constraining the relationships between aerosols and clouds is still a big challenge (Seinfeld et al., 2016). Lacking the knowledge of aerosol–cloud interactions limits our ability to estimate climate forcing caused by aerosols (Boucher et al., 2013).

Aerosol CCN supersaturation activation spectrum is one of the most critical parameters to quantify aerosol–cloud interactions (Schmale et al., 2018). Despite the fact that a large number of CCN number concentrations near ground have been measured worldwide (Tao et al., 2018a), ground-measured CCN may not represent CCN at cloud base that alter clouds directly. Obtaining CCN near cloud base becomes a crucial issue. Cloud base CCN can be measured in situ on aircraft platforms, but airborne measurements have the limitations of huge costs and discontinuity. Satellites have difficulty observing CCN at cloud base because clouds can obscure aerosol signals beneath them. Rosenfeld et al. (2016) have proposed an alternative approach for satellites to retrieve CCN concentrations using clouds as CCN chambers; however, employing CCN concentrations derived with this strategy limits our exploration of the relationship between CCN concentrations and cloud droplet concentrations in the natural environment. So far, CCN concentrations at cloud base are scarce for aerosol–cloud interaction studies.

Ground-based lidars can continuously provide optical properties of aerosol particles from ground up to cloud base (Mattis et al., 2016; Li et al., 2019), suggesting great potential in deriving CCN concentrations near cloud base. Ghan and Collins (2004) propose a simple method to infer CCN profiles with the combination of surface in situ CCN and aerosol optical measurements. The method is only applicable when the boundary layer is well mixed from surface to cloud base (Ghan et al., 2006). Mamouri and Ansmann (2016) investigate the potential of single-wavelength polarization lidar to retrieval CCN for three aerosol types (desert, nondesert continental, and marine). The polarization lidar can separate desert and nondesert by means of the particle linear depolarization ratio. Based on datasets from multiyear AErosol RObotic NETwork (AERONET) observations, valid relationships are found between particle extinction coefficients, and number concentrations of particles with dry radius larger than 50 nm (for nondesert and marine) and 100 nm (for desert). CCN concentrations at different supersaturations are parameterized with the particle number concentration derived from extinction profiles according to aerosol types. The consideration of the hygroscopicity of ambient particles is empirical. In addition, single-wavelength lidar also lacks sufficient information to quantify particle number concentration, which will bring large uncertainty on CCN retrieval.

Multiwavelength Raman lidars (MWRLs) have been increasingly used to detect aerosol
vertical distributions in recent years. The principle of MWRLs allows
independent retrieval of particle backscatter (*β*) and extinction
coefficients (*α*), which provides more information about particle
microphysical properties (Müller et al., 2016). The 3*β*+2*α* MWRL systems (backscatter coefficients at 355, 532, and 1064 nm and extinction coefficients at 355 and 532 nm) have been widely
recommended to derive particle microphysical properties (Burton et
al., 2016). Existing approaches to retrieve CCN using MWRLs are based on
microphysical inversion techniques. Lv et al. (2018) build a lookup
table based on AERONET datasets to retrieve particle number size
distributions from backscatter and extinction profiles. Then assumed
activation critical diameters according to aerosol type classification
together with the retrieved optically equivalent particle size distributions
are utilized to calculate CCN concentrations. It is worth noting that most
of the foregoing methods implement crude particle type classification to
determine particle hygroscopicity.

There are three major challenges in CCN concentration retrieval with lidars. The first is the conversion of lidar-derived optical properties into particle number concentrations. High uncertainties of retrieved particle number concentrations could be an important source of CCN retrieval error. The second one is the determination of particle hygroscopicity in order to evaluate the ability of particles to participate as CCN. Particle hygroscopicity, which is highly related to chemical composition and the aging/coating effect, is found to cause nonnegligible variations in cloud droplet activation (Hudson, 2007; Zhang et al., 2017). The last is the influence of high relative humidity (RH) near clouds. Aerosol particles are likely to be humidified in the ambient environment, and the consequent changes in optical properties make CCN retrieval more challenging. Most studies working on CCN retrieval with MWRLs mainly focus on deriving particle number concentrations, but seldom commence to solve the issue of hygroscopicity.

In recent years, several aerosol hygroscopic studies based on lidar measurements have been carried out (Fernández et al., 2018; Lv et al., 2017; Bedoya-Velásquez et al., 2018). Backscatter and extinction enhancement factors can be derived with lidar measurements and RH profiles. The enhancement factor, which is associated with both particle size and hygroscopicity (Kuang et al., 2017), is defined as

$$\begin{array}{}\text{(1)}& {f}_{\mathit{\xi}}\left(\mathrm{RH},\mathit{\lambda}\right)={\displaystyle \frac{\mathit{\xi}\left(\mathrm{RH},\mathit{\lambda}\right)}{\mathit{\xi}\left({\mathrm{RH}}_{\mathrm{ref}},\mathit{\lambda}\right)}},\end{array}$$

where *f*_{ξ} is the enhancement factor of the optical property *ξ*
(backscatter or extinction) at a specific light wavelength *λ* and RH,
and RH_{ref} is the reference RH value. Many studies
manifest that lidar-derived enhancement factors are in good agreement with
in situ measurements (Wulfmeyer and Feingold, 2000; Pahlow et al.,
2006; Fernández et al., 2015; Rosati et al., 2016). Feingold and
Morley (2003) demonstrate that the extent of backscatter and extinction
enhancements hints at the ability of particles to serve as CCN. Tao et al. (2018b) use in-situ-measured light-scattering enhancement factors to
predict *N*_{CCN} at 0.07 % supersaturation, and the result shows strong
consistency with the CCN counter.

In this paper, a new method to retrieve CCN number concentrations for
3*β*+2*α* MWRL systems is proposed. Different from the
foregoing approaches which use AERONET datasets, we use in-situ-measured
microphysical and chemical data in this study. Theoretical simulations based
on in situ measurements are carried out to seek the relationship between CCN
number concentrations and lidar-derived optical properties. The simulation
implements *κ*-Köhler theory (Petters and Kreidenweis,
2007) to describe particle hygroscopic growth and activation processes. Mie
theory (Bohren and Huffman, 2007) is utilized to calculate
particle backscatter and extinction coefficients from in-situ-measured
aerosol microphysical and chemical properties. The enhancements of
backscatter and extinction with RH are introduced to quantify particle
hygroscopicity instead of using empirical estimation according to aerosol
type classification. The new method is applicable to well-mixed aerosol
layers. We take datasets in the North China Plain (NCP) as an example of
this method. The NCP is influenced by heavy and complex pollution, which
shows strong characteristics of continental aerosols. Mineral dust and
marine particles are not considered in this study.

The paper is structured as follows. The filed campaign and in situ measurements are introduced in Sect. 2.1. Section 2.2 briefly introduces the simulations to calculate CCN number concentrations, backscatter, and extinction coefficients from in-situ-measured microphysical and chemical data. The new CCN retrieval method for MWRLs is described in Sect. 3.1 in detail. Sensitivity of the method to the systematic and random errors of backscatter, extinction, and RH is tested in Sect. 3.2. Results and discussions are given in Sect. 4. Section 5 summarizes the paper.

2 Data

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Since it is not easy to accumulate large datasets of simultaneous
measurements of lidar and aircraft, ground-measured aerosol microphysical
and chemical data are used to simulate lidar-derived backscatter and
extinction coefficients and corresponding CCN number concentrations. The
simulations are based on *κ*-Köhler theory and Mie theory. The
required datasets include particle number size distribution (PNSD), black
carbon (BC) mass concentrations (*m*_{BC}), mixing state of BC-containing particles, and size-resolved hygroscopicity. The simulation
results are used to establish and validate the new retrieval method.

In-situ-measured aerosol properties were collected from five field campaigns
at three different measurement sites in the NCP. The measurement sites are
located at Wuqing (39^{∘}23^{′} N, 117^{∘}01^{′} E, 7.4 m a.s.l.) in Tianjin, Xianghe (39^{∘}45^{′} N,
116^{∘}58^{′} E, 36 m a.s.l.), and Wangdu (38^{∘}40^{′} N, 115^{∘}08^{′} E, 51 m a.s.l.) in Hebei Province.
The specific locations, topographical information, and pollution status of
these measurement sites are shown in Fig. S1 in the Supplement. These three
sites all lie inside the polluted NCP region and are highly representative
of the polluted background (Xu et al., 2011; Bian et al., 2018; Sun et al.,
2018). Time periods, measured parameters, and corresponding instruments of the
individual campaign are listed in Table 1.

During these field campaigns, except measurement for size-resolved chemical
compositions, ambient particles were drawn in through a PM_{10} inlet (16.67 L min^{−1}), passed through a silica gel diffusion drier, and then were split
into different instruments. All instruments were operated at RH less than
30 %.

The particle number size distributions (PNSDs) were measured with the combination of a twin differential mobility particle sizer (TDMPS, IfT, Leipzig, Germany) or a scanning mobility particle size spectrometer (SMPS) and an aerodynamic particle sizer (APS, TSI, Inc., Shoreview, MN USA, model 3320 or model 3321). The statistical information about the measured PNSDs is shown in Fig. 1a. The peaks of the PNSDs are at about 100 nm (diameter in log scale), which shows strong characteristics of continental aerosols.

The black carbon (BC) mass concentrations (*m*_{BC}) were measured
by a multi-angle absorption photometer (MAAP, Thermo, Inc., Waltham, MA USA,
model 5012). As for mixing states of BC, BC and other non-absorbing
compositions were found to be both externally mixed and core–shell mixed
during the campaigns (Ma et al., 2012). The mass
fraction of externally mixed BC (*r*_{ext}) is defined to quantify
the mixing states of BC:

$$\begin{array}{}\text{(2)}& {r}_{\mathrm{ext}}={\displaystyle \frac{{m}_{\mathrm{ext}\mathrm{\_}\mathrm{BC}}}{{m}_{\mathrm{BC}}}},\end{array}$$

where *m*_{ext_BC} is the mass concentration of
externally mixed BC. According to Ma et al. (2012), *r*_{ext} can be retrieved from hemispheric
backscattering fractions (HBFs) measured by an integrating nephelometer
(TSI, Inc., Shoreview, MN USA, model 3563).

Size-resolved chemical compositions all come from campaign C2. The
size-resolved aerosol sampling was carried out with a 10-stage Berner low-pressure impactor (BLPI). Chemical species including inorganic ions
(${\mathrm{NH}}_{\mathrm{4}}^{+}$, Na^{+}, K^{+}, Mg^{2+}, Ca^{2+}, ${\mathrm{NO}}_{\mathrm{3}}^{-}$,
${\mathrm{SO}}_{\mathrm{4}}^{\mathrm{2}-}$, Cl^{−}), elemental carbon, organic carbon, water-soluble
organic carbon, and some other species such as dicarboxylic acids were
analyzed from sample substrates. After transforming the ambient wet
aerodynamic diameters into dry volume-equivalent diameters, size-resolved
*κ* distributions were derived from measured size-resolved chemical
compositions. The chemical compositions are found to be size dependent
during campaign C2, especially the mass fraction of organic matter
(Liu et al., 2014). A total of 25 typical size-resolved
*κ* distributions in the NCP are given in Fig. 1b. The measured
size-resolved *κ* distributions vary a lot and cover a wide range of
aerosol hygroscopicity (Kuang et al., 2018). More details about the
measurements can be found in Liu et al. (2014).

In-situ-measured aerosol properties mentioned above are utilized to
calculate CCN number concentrations and particle backscatter and extinction
coefficients based on *κ*-Köhler theory and Mie theory. For each
simultaneously measured PNSD, *m*_{BC}, and *r*_{ext}
(16 183 sets of data), simulations are carried out with every one of the
25 size-resolved *κ* distributions.

CCN number concentrations can be calculated with PNSD and size-resolved
*κ* distributions based on the *κ*-Köhler equation.
Petters and Kreidenweis (2007) introduce the *κ*-Köhler
equation to describe the relationship between particle or droplet diameter
*D* and critical supersaturation ratio (SS) or RH with a single hygroscopic
parameter *κ*:

$$\begin{array}{}\text{(3)}& \begin{array}{rl}\mathrm{RH}\left(D\right)& =\mathrm{1}+\mathrm{SS}\left(D\right)={\displaystyle \frac{{D}^{\mathrm{3}}-{D}_{\mathrm{dry}}^{\mathrm{3}}}{{D}^{\mathrm{3}}-{D}_{\mathrm{dry}}^{\mathrm{3}}\left(\mathrm{1}-\mathit{\kappa}\right)}}\\ & \mathrm{exp}\left({\displaystyle \frac{\mathrm{4}{\mathit{\sigma}}_{\mathrm{s}/\mathrm{a}}{M}_{\mathrm{w}}}{RT{\mathit{\rho}}_{\mathrm{w}}D}}\right),\end{array}\end{array}$$

where *D*_{dry} is particle dry diameter, *σ*_{s∕a} is the surface tension of the solution–air interface,
*M*_{w} is the molecular weight of water, *R* is the universal gas
constant, *T* is temperature, and *ρ*_{w} is the density of water.
For a specific supersaturation, critical activation diameter can be derived
with the *κ*-Köhler equation using size-resolved *κ*
distributions. CCN number concentrations can thereby be calculated by
integrating number concentrations of particles larger than the critical
diameter. CCN number concentrations at the supersaturations of 0.07 %,
0.10 %, 0.20 %, 0.40 %, and 0.80 % are accordingly simulated. The
selected supersaturation ratios are widely used in CCN measurements.

Particle backscatter and extinction can be calculated with PNSD,
*m*_{BC}, and *r*_{ext} using Mie models. Mie theory can
solve light-scattering problems of homogeneous and coated spherical
particles. Without the consideration of mineral dust, using the Mie model is
quite reasonable because particles are likely to be spherical near clouds
where the RH could be relatively high. When simulating particle backscatter
and coefficients, PNSD, *m*_{BC}, *r*_{ext}, and the complex
refractive index are needed. PNSD at different RHs can be calculated with the
*κ*-Köhler equation as well. The refractive indices of BC,
the non-absorbing component, and pure water are set to be 1.8+0.54*i*
(Ma et al., 2012), $\mathrm{1.53}+{\mathrm{10}}^{-\mathrm{7}}i$ (Wex
et al., 2002), and $\mathrm{1.33}+{\mathrm{10}}^{-\mathrm{7}}i$, respectively. Backscatter coefficients
(355, 532, and 1064 nm) and extinction coefficients (355 and 532 nm) at dry
conditions and RH from 60 % to 90 % are simulated with an interval of 1 %.

The simulations are introduced in detail in Sect. S3 in the Supplement. The new method and all the analyses in this paper are based on the Mie-model-simulated datasets, and all the simulations mentioned above are implemented.

3 Methodology

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An optically related CCN activation ratio, AR_{ξ}, is
introduced to bridge the gap between CCN and lidar-derived optical
properties. AR_{ξ} is the ratio between CCN number
concentration and backscatter or extinction coefficient, which can be
expressed as

$$\begin{array}{}\text{(4)}& {\mathrm{AR}}_{\mathit{\xi}}\left(\mathrm{SS},\mathit{\lambda}\right)={\displaystyle \frac{{N}_{\mathrm{CCN}}\left(\mathrm{SS}\right)}{{\mathit{\xi}}_{\mathrm{dry}}\left(\mathit{\lambda}\right)}}={\displaystyle \frac{{N}_{\mathrm{CCN}}\left(\mathrm{SS}\right)}{{N}_{\mathrm{aerosol}}}}\cdot {\displaystyle \frac{{N}_{\mathrm{aerosol}}}{{\mathit{\xi}}_{\mathrm{dry}}\left(\mathit{\lambda}\right)}},\end{array}$$

where *N*_{CCN} is the CCN number concentration, and
*N*_{aerosol} is the total number concentration of aerosol
particles. AR_{ξ} can be divided into two parts: one is the
ratio of CCN to the total particles, which is the origin definition of CCN
activation ratio; the other is the ratio of total number concentration to
backscatter or extinction at dry conditions. Bulk CCN activation ratio is
related to particle size distribution and hygroscopicity, and the
relationship between particle number concentration and optical properties is
mainly controlled by size distribution. Therefore, AR_{ξ}
could be quantified with size and hygroscopicity information. The key point
of our method is to seek parameters that can indicate size and
hygroscopicity of particles from lidar measurement and use these parameters
to estimate AR_{ξ}. In addition, deriving backscatter and
extinction coefficients at dry conditions is also important.

A schematic diagram of the method to retrieve CCN number concentration is shown in Fig. 2.

Firstly, enhancement of backscatter and extinction coefficients with RH
(also called humidogram) is derived from lidar measurements and additional
ancillary data (i.e. pressure, temperature, RH profiles). Humidogram
parameter which can indicate particle hygroscopicity can be fitted from
humidograms with parameterization equation. Particle dry backscatter and
extinction can also be inferred from the humidograms. This step is applied
to all the 3*β*+2*α* parameters. The approaches to select
appropriate hygroscopic layers and fit humidogram parameters, dry
backscatter, and dry extinction are described in Sect. 3.1.2.

Then, Ångström exponent (*å*) and lidar
extinction-to-backscatter ratio (lidar ratio, *s*_{a}) are calculated from
inferred dry backscatter and extinction coefficients. Extinction-related
Ångström exponent (*å*_{α}) is the most commonly used
parameter to reveal information about the predominant size of aerosols.
Generally speaking, a smaller *å*_{α} represents more
large particles. Similarly, backscatter-related Ångström exponent
(*å*_{β}) is often employed in lidar analysis
(Fernández et al., 2015), and particle
backscatter coefficients of different wavelengths have also been proven to
have a valid Ångström exponent relationship
(Komppula et al., 2012). Ångström
exponent of dry backscatter and extinction coefficients (*å*_{ξ})
between two wavelengths can be derived using Eq. (5):

$$\begin{array}{}\text{(5)}& {\mathit{\xe5}}_{\mathit{\xi}}\left({\mathit{\lambda}}_{\mathrm{1}},{\mathit{\lambda}}_{\mathrm{2}}\right)=-{\displaystyle \frac{\mathrm{log}\left({\mathit{\xi}}_{\mathrm{1}}/{\mathit{\xi}}_{\mathrm{2}}\right)}{\mathrm{log}\left({\mathit{\lambda}}_{\mathrm{1}}/{\mathit{\lambda}}_{\mathrm{2}}\right)}},\end{array}$$

where the subscripts 1 and 2 represent different wavelengths. Another widely
used parameter to express aerosol characteristics in lidar studies is the
particle lidar extinction-to-backscatter ratio (lidar ratio, *s*_{a}), which
is defined as the ratio of extinction coefficient to backscatter coefficient
at a specific light wavelength:

$$\begin{array}{}\text{(6)}& {s}_{a}\left(\mathit{\lambda}\right)={\displaystyle \frac{\mathit{\alpha}\left(\mathit{\lambda}\right)}{\mathit{\beta}\left(\mathit{\lambda}\right)}}={\displaystyle \frac{\mathrm{4}\mathit{\pi}}{P\left(\mathit{\pi}\right)\cdot \mathit{\omega}}}.\end{array}$$

As is shown in Eq. (6), lidar ratio is determined by the scattering phase
function at 180^{∘} *P*(π) and the single-scattering
albedo *ω*. *P*(π) is mainly influenced by particle
size and *ω* indicates the content and mixing state of light-absorbing
components. Lidar ratio is often utilized in aerosol type classification and
is proven to be very sensitive to particle sizes (Zhao et al., 2017).
The lidar ratio can provide information on particle type and also serve as a
proxy for particle hygroscopicity. Therefore, lidar ratio of dry particles
could be a reliable parameter to estimate AR_{ξ}.

Next, *å*_{ξ}, *s*_{a}, and humidogram parameters are utilized to
estimate AR_{ξ}. AR_{ξ} of all the 3*β*+2*α* parameters is calculated. Statistical relationships among
humidogram parameters *å*_{ξ}, *s*_{a}, and AR_{ξ}
are used in our new method. The estimation of AR_{ξ} is
introduced in Sect. 3.1.3 in detail. The implementation of *å*_{ξ} and
*s*_{a} is quite similar to the microphysical inversion process for particle
size distribution retrieval. Microphysical inversion is a physics-based
approach but will bring large uncertainties in retrieving particle number
concentrations. Constraining AR_{ξ} directly with a
statistical relationship is a much more simple and straightforward way.

Finally, after AR_{ξ} values of backscatter and extinction at
different wavelengths are derived, CCN number concentration can be
calculated by multiplying AR_{ξ} by the corresponding *ξ*_{dry}. The average value of CCN concentrations calculated by
different *ξ*_{dry} is the final retrieval result.

A constraint needs to be satisfied when quantifying the enhancements of backscatter and extinction coefficients with lidar measurements. The selected vertical layers must be well-mixed, so we can guarantee that the variations in particle backscatter and extinction coefficients are caused by different RH and not by various aerosol types or loads. Atmospheric vertical homogeneity is fulfilled if the layer has little variability of virtual potential temperature profile and water vapor mixing ratio profile (Lv et al., 2017). Additional analyses can also be considered to evaluate vertical mixing of air masses, such as backward trajectory, horizontal wind velocities at different altitude, or the third moment of the frequency distribution of vertical wind velocities (Bedoya-Velásquez et al., 2018).

Once vertical homogeneity is ensured, physical and chemical properties at dry conditions can be assumed to be uniform in the selected layer, and the number concentrations are proportional to air molecule number density. Accordingly, the relative variations in particle backscatter and extinction coefficients against different RHs can be achieved after normalizing the backscatter and extinction coefficients with air molecule number density.

Humidogram parameterization is needed to find a representative parameter for
the relationship between enhancement factor and RH. Unlike in-situ-controlled RH measurements, there is no such generic reference RH for dry
conditions for lidar measurements to derive enhancement factor. Inferring
backscatter and extinction coefficients at dry conditions (*ξ*_{dry}) is also an important issue in CCN retrieval. Therefore,
humidogram parameterization of lidar-derived optical properties should
combine *ξ*_{dry} and *f*_{ξ}(RH,*λ*) together.

Many equations to parameterize enhancement factors have been proposed by
previous studies (Titos et al., 2016). Two one-parameter equations are
selected to test their performance on estimating *ξ*_{dry} and
representing particle hygroscopic growth characteristics. The first equation
is the most commonly used one initially introduced by Kasten (1969):

$$\begin{array}{}\text{(7)}& \begin{array}{rl}\mathit{\xi}\left(\mathrm{RH},\mathit{\lambda}\right)& ={\mathit{\xi}}_{\mathrm{dry}}\left(\mathit{\lambda}\right)\cdot {f}_{\mathit{\xi}}\left(\mathrm{RH},\mathit{\lambda}\right)={\mathit{\xi}}_{\mathrm{dry}}\left(\mathit{\lambda}\right)\\ & \cdot {\left(\mathrm{1}-\mathrm{RH}\right)}^{-{\mathit{\gamma}}_{\mathit{\xi}}\left(\mathit{\lambda}\right)},\end{array}\end{array}$$

where the exponent *γ*_{ξ} is the fitting parameter and describes
the hygroscopic behavior of the particles; the other equation is proposed
based on physical understanding by Brock et al. (2016), which has been reported to have better performance in describing
light-scattering enhancement factor than Eq. (7) (Yu et al., 2018):

$$\begin{array}{}\text{(8)}& \begin{array}{rl}\mathit{\xi}\left(\mathrm{RH},\mathit{\lambda}\right)& ={\mathit{\xi}}_{\mathrm{dry}}\left(\mathit{\lambda}\right)\cdot {f}_{\mathit{\xi}}\left(\mathrm{RH},\mathit{\lambda}\right)={\mathit{\xi}}_{\mathrm{dry}}\left(\mathit{\lambda}\right)\\ & \cdot \left[\mathrm{1}+{\mathit{\kappa}}_{\mathit{\xi}}\left(\mathit{\lambda}\right){\displaystyle \frac{\mathrm{RH}}{\mathrm{1}-\mathrm{RH}}}\right],\end{array}\end{array}$$

where *κ*_{ξ} is the fitting parameter and shows significant
correlation with bulk hygroscopic parameter *κ* (Kuang et al.,
2017). Here, Eqs. (7) and (8) are denoted as the *γ* equation and
*κ* equation, respectively. With given backscatter and extinction at
different RHs, *ξ*_{dry} and *γ*_{ξ} or *κ*_{ξ}
can be fitted simultaneously by means of least squares.

Comparisons between the performances of the *γ* equation and *κ* equation on inferring backscatter and extinction at dry conditions are
carried out to select a better parameterization. Four RH ranges
(60 %–90 %, 60 %–70 %, 70 %–80 %, and 80 %–90 %) are
selected. The fitted *ξ*_{dry} values are compared with the *ξ*_{dry} calculated by the Mie model. The slopes of linear regressions,
determination coefficients (*R*^{2}), and relative errors are listed in
Table 2. Apparently, the *κ* equation has a better performance than the
*γ* equation for all RH ranges. Inferring *ξ*_{dry} with the
*γ* equation will underestimate by about 10 %–30 %. It is consistent
with the finding of Haarig et al. (2017) that the *γ* equation does
not hold for RH lower than 40 %. The bias of backscatter is found to be
larger than the bias of extinction.

The RH range of humidogram equations also influences the fitting results.
Table 2 shows the fitted *ξ*_{dry} values have larger bias when the
value of RH increases. The fitted humidogram parameters *γ*_{ξ} and
*κ*_{ξ} from different RH ranges are compared to each other, and
the results are displayed in Table 3. Parameterization equations are not
always perfect for the whole RH range, so humidogram parameters fitted with
various RH ranges can be different. If *γ*_{ξ} and *κ*_{ξ}
are used to represent hygroscopic behavior of particles, more careful
attention should be paid to the RH ranges.

Based on the comparisons above, Eq. (8) (*κ* equation) is selected as
our humidogram equation to derive *ξ*_{dry} and *κ*_{ξ}. The RH range for parameter fitting used is fixed to 60 %–90 % in the
following method.

Ångström exponents, lidar ratios, and optical humidogram parameters
*κ*_{ξ} are used to estimate the optically related activation ratio
AR_{ξ}. Concerning that the Ångström exponents and lidar
ratios are not independent of each other (any parameter can be calculated
from other parameters), we reduce the number of parameters to a sufficient
number to represent all the information. The selected nine parameters are
listed in Table 4. One possible way to seek the relationship between the
nine parameters and AR_{ξ} is to build a lookup table, but
too many input parameters would make the lookup table too large to build and
operate.

In the past few decades, machine learning has been a field that has
developed rapidly, which experiences a very wide range of applications
(Grange et al., 2018). Compared to traditional statistical methods,
many machine learning techniques are nonparametric and do not need to
fulfill many assumptions required for statistical methods (Immitzer
et al., 2012). Random forest (RF) is an ensemble decision tree machine
learning method that can be used for regression. (Breiman, 2001; Tong et
al., 2003). In addition to the free restraints on input parameters and assumptions,
RF also has the advantage of being able to explain and investigate the
learning process (Kotsiantis, 2013). The Python module
RandomForestRegressor from the Python Scikit-Learn library
(http://scikit-learn.org/stable/modules/generated/sklearn.ensemble.RandomForestRegressor.html,
last access: 18 December 2018) is utilized as the RF model. The nine
parameters in Table 4 are the input parameters for the RF model, and the
AR_{ξ} values of 3*β*+2*α* are the output
parameters.

Some tuning parameters required by the RF model need to be specified by users. Experiments are made to determine the optimal values of the tuning parameters. Experiment results are showed in Fig. S7 in the Supplement and the detailed settings of the RF model are listed in Table S2 in the Supplement. In this case, the results are rather insensitive to the tuning parameters. Data simulated with datasets measured from campaigns C1–C4 are utilized as the training data, and those from C5 are used as test data.

Both systematic and random errors exist in lidar-retrieved backscatter and extinction coefficients (Mattis et al., 2016). Systematic errors in backscatter and extinction can come from instrumentation setup, data processing method, and retrieval algorithm. Sensitivity test is carried out to test the impact of systematic errors of backscatter and extinction on CCN retrieval. Errors in backscatter or extinction influence the value of Ångström exponents and lidar ratios. The errors of individual backscatter or extinction are considered to be independent, though systematic errors of different parameters are related. The systematic errors are given in the range of −20 % to 20 % with an interval of 2 %. In each test, the error is only applied to one parameter, and other parameters are error-free.

RH is another crucial factor in this new method to retrieve CCN. Profiles of
RH derived by remote-sensing techniques are also influenced by errors. At
present, RH profiles are usually obtained with the combination of
temperature from microwave radiometer and water vapor mixing ratio from
MWRL. Both measurements can cause systematic and random errors in RH
(Bedoya-Velásquez et al., 2018). Errors in RH will influence the
values of *ξ*_{dry} and *κ*_{ξ}, which in turn
influence all the nine input parameters. Systematic errors ranging from
−10 % to 10 % in intervals of 1 % are considered for RH.

Random errors in observations can be reduced by temporal averaging but cannot be eliminated. The influence of random errors in backscatter, extinction, and RH on CCN retrieval are investigated with the Monte Carlo method. Three sets of sensitivity tests for random errors are conducted. Errors obeying Gaussian distribution are generated randomly with the mean value of zero. The standard deviation of Gaussian distribution is fixed at 10 % for backscatter and extinction, and the standard deviation of RH is set to be 5 %, 10 %, and 20 % for each test. The procedure is repeated 2000 times. All the 80 575 sets of data from campaign C5 are used for sensitivity test.

4 Results and discussions

Back to toptop
CCN number concentrations are related to supersaturations. Critical
diameters of each supersaturations calculated with 25 size-resolved
*κ* distributions are shown in Fig. 3a. Most of the critical diameters
at a supersaturation of 0.07 % are larger than 200 nm, while critical
diameters at a supersaturation of 0.80 % are around 50 nm. Suitable
supersaturations for lidar CCN retrieval depend on the ability of lidar
optical properties to provide information about number and hygroscopicity of
CCN-related sizes.

Size cumulative contributions of particle number of all measured particle size distribution and corresponding calculated backscatter and extinction at dry conditions are also displayed in Fig. 3a. As the cumulative contributions of particle number suggest, particles with diameter less than 100 nm dominate particle number concentrations (over 65 %). However, most backscatter and extinction come from particles larger than 200 nm (around 90 %) and almost 100 % come from particles larger than 100 nm. If critical diameter is small, dry backscatter and extinction are insensitive to particle diameters that contribute to most CCN concentrations.

Size-resolved enhancement contributions of backscatter and extinction are calculated to discuss hygroscopicity-sensitive size of optical enhancement factor measurement. The enhancement contribution is defined as the difference between optical cross sections of RH at 90 % and 60 %, and represents the proportion of each size to the enhancement in backscatter or extinction. As is shown in Fig. 3b, the contributions of the extinction enhancements are concentrated in the diameters within 200 to 700 nm, and extinction enhancement at 355 nm is related to smaller particles than that at 532 nm. Similar to particle number, particles with diameters smaller than 100 nm contribute little to the enhancements of both backscatter and extinction.

Figure 3b also shows that different *κ*_{ξ} values are sensitive to the
hygroscopicity of different size. Size-dependent hygroscopicity is important
to estimate CCN rather than bulk hygroscopicity information, especially
for different supersaturation conditions. One humidogram may indicate the
bulk hygroscopicity, but it is the hygroscopicity of small particles that
influences CCN number concentrations most. Using *κ*_{ξ} of all the
3*β*+2*α* values can provide some information about the hygroscopicity
of small particles.

Comparing sensitive size of optical properties and critical diameters at
different supersaturations, 3*β*+2*α* MWRL systems have
potential to retrieve CCN number concentrations at supersaturations smaller
than 0.20 %. It is not recommended to estimate CCN concentrations using
lidar data at supersaturations larger than 0.40 %.

With error-free data as input, the model-predicted extinction-related
activation ratio at 532 nm (AR_{α532}) and the retrieved
CCN number concentrations at supersaturations of 0.07 %, 0.10 %, and
0.20 % are compared to the theoretical calculated values. A total of 80 575
pairs of data calculated from campaign C5 are used for verification. The
retrieval results are displayed in Fig. 4. The values AR_{α532} at a specific supersaturation are distributed in a wide range and can
span over an order of magnitude, indicating that the relationship between
CCN and optical parameters is very complex. According to Fig. 4, all data
points are distributed almost evenly on both sides of the 1:1 line and the
relative errors of most points are within 20 %. The determination
coefficients (*R*^{2}) of CCN concentrations are all larger than 0.97, and
the results do not show obvious systematic deviations. The retrieval errors
are found to grow with supersaturation. Retrieval results for higher
supersaturations (i.e. 0.40 % and 0.80 %) are displayed in Fig. S8 in the
Supplement. There are larger errors for supersaturations of 0.40 % and
0.80 %. Only 47.76 % of the retrieved CCN number concentrations at a
supersaturation of 0.80 % have relative errors less than 20 %. The
results demonstrate again that lidars may not be sufficient enough to
retrieve CCN number concentrations at supersaturations lager than 0.40 %.

RF models can evaluate the importance of features (input parameters) by
calculating the mean decrease impurity (MDI) for each feature among all the
trees in the forest. The MDIs and corresponding standard deviations of each
parameter at different supersaturations are shown in Fig. 5. Importance of
the nine input parameters varies with supersaturations. For 0.07 % and
0.10 %, *κ*_{α355} and *κ*_{β1064} are the two most
important parameters, showing the impact of hygroscopicity on the
relationship between CCN and optical properties. For 0.20 %,
*å*_{α355&532} becomes much more important. Among the nine input
parameters, *κ*_{ξ} values are denoted as hygroscopicity-related
parameters, and *å*_{ξ} values are denoted as size-related parameters.
In particular, *s*_{a} can be regarded as a parameter related to both size and
hygroscopicity. As is shown in Fig. 5,
hygroscopicity-related parameters, especially *κ*_{α355},
*κ*_{β1064}, and *s*_{a532}, play crucial roles in retrieving
CCN. Size-related parameters have already been proven to be vital in
retrieving CCN; however, humidogram parameters *κ*_{ξ} have not
been implemented in previous methods. CCN concentrations retrieved with and
without *κ*_{ξ} are compared to show the importance of *κ*_{ξ}. When retrieving CCN without *κ*_{ξ}, the RF model is also
trained with datasets from campaigns C1–C4, but the input data only contain
Ångström exponents and lidar ratios. The retrieved CCN
concentrations are all compared with datasets from campaign C5, and the
results are listed in Table 5. *R*^{2} of retrieved CCN decreases from 0.991
to 0.887 for supersaturations of 0.07 %, from 0.992 to 0.857 for 0.10 %,
and from 0.973 to 0.785 for 0.20 %. Retrieval errors also increase
overwhelmingly, and there are significant positive systematic biases.
Parameters which are derived from backscatter and extinction enhancements,
*κ*_{ξ}, are indispensable parameters in CCN retrieval.

Figure 6 shows the relative errors of CCN retrieved with systematic errors
in backscatter and extinction. Errors of retrieved CCN increase as errors of
backscatter and extinction increase, and higher supersaturations are more
affected by errors of optical parameters. Errors in extinction coefficients
at 355 nm (*α*_{355}) influence the retrieval results most. On
average, a positive relative error of 20 % in *α*_{355} will cause
about a 20 % overestimate in CCN number concentrations for supersaturation
of 0.07 %, about a 40 % overestimate for 0.10 %, and about a 60 %
overestimate for 0.20 %. A negative error of 20 % in *α*_{355}
will underestimate CCN concentrations, and the degree of impact is slightly
smaller than the positive error. Errors in extinction coefficient at 532 nm
(*α*_{532}) and at 355 nm have the opposite effect on retrieval error.
Errors in *α*_{532} do not show a significant impact at supersaturations
of 0.07 % and 0.10 %, but an overwhelming effect is found at
supersaturations of 0.20 %. It is interesting to note that the errors in
backscatter coefficients do not affect the results much. However, in
practical applications of MWRLs, the errors in extinction are always much
larger than the errors of backscatter. If the error of retrieved CCN
concentrations needs to be limited to 20 % at a supersaturation of 0.20 %,
the errors of retrieved extinction coefficients should to be controlled
within 5 %.

The test result of systematic error in RH is shown in Fig. 7. When RH has a negative systematic error, CCN concentrations are overestimated, and the extent of overestimation increases as the error increases. A negative error of 10 % in RH will overestimate CCN at supersaturations at 0.20 % by about 60 % on average, and the standard deviation is over 60 %. Effects of positive errors in RH are much smaller than negative errors but more complex. The standard deviations of retrieval relative error increase with RH error, and the extreme value of the mean retrieval error appears at the RH error of 5 %. Underestimating RH will cause much more errors than overestimation. Great care should be paid to RH profiles if enhancements of backscatter and extinction with RH are utilized.

The relative error of retrieved CCN with random errors is presented in
Table 6. The retrieval error does not change significantly as the random
error of RH increases. For all the conditions that are tested, the mean
values of relative error are below or near zero, and the standard deviations
are within 18 %–28 %. The impact of random errors on the nine input
parameters is also evaluated and is shown in Fig. 8. Random errors will
underestimate *κ*_{ξ} by 30 %–35 % on average for 5 % RH
error, 80 %–85 % for 10 % RH error, and 90 %–95 % for 20 % RH error.
*s*_{a355} , *s*_{a532}, and *å*_{β532&1064} are likely to be
overestimated. As the random error of RH grows, the absolute relative error
of input parameters will become larger.

5 Summary

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CCN number concentration at cloud base is a crucial and scarce parameter to
constrain the relationship between aerosols and clouds. A new method to
retrieve CCN number concentrations using backscatter and extinction
coefficients from MWRL measurements is proposed. Enhancements of backscatter
and extinction coefficients with RH are implemented to derive dry
backscatter and extinction *ξ*_{dry} and humidogram parameter
*κ*_{ξ}. The ratio of CCN number concentration to dry backscatter
or extinction coefficient AR_{ξ}, which is estimated by
*κ*_{ξ}, Ångström exponents, and lidar ratios, is
introduced to retrieve CCN number concentrations.

The method is established and verified by theoretical simulations using Mie
theory and *κ*-Köhler theory with in-situ-measured particle size
distributions, mixing states, and chemical compositions. The values of
AR_{ξ} are found to have large variations due to different
size distributions and hygroscopicity. Theoretical analyses show that
optical properties provided by current 3*β*+2*α* MWRL systems
basically contain size distribution and hygroscopicity information of
particles with diameters larger than 100 nm, which only fits the critical
diameters for supersaturations lower than 0.20 %. Accordingly, CCN number
concentrations at supersaturations of 0.07 %, 0.10 %, and 0.20 % are
retrieved. The performance of the new method is evaluated with error-free
data, and CCN number concentrations at all three supersaturations are in
good agreement with theoretical calculated values.

Sensitivity tests are carried out to show the influence of systematic and
random errors of lidar-derived optical properties and auxiliary RH profiles
on CCN retrieval. Systematic errors in extinction coefficients and RH are
found to have a large impact on error in retrieved CCN. Parameters fitted from
backscatter and extinction enhancements (i.e. *ξ*_{dry} and
*κ*_{ξ}) are significantly influenced by RH. The uncertainty of RH
profiles derived by remote-sensing techniques is a major problem in CCN
retrieval. Optical properties near cloud base from lidar measurements are always
influenced by high RH. Thus, transforming backscatter and extinction
coefficients at ambient RH to dry conditions is a must for CCN retrieval,
and accurate RH profiles are in high demand.

The importance of humidogram parameters *κ*_{ξ} is demonstrated by
comparing the error of CCN concentration retrieved with and without *κ*_{ξ}. Neglecting hygroscopicity information contained in backscatter and
extinction enhancements will bring huge errors to CCN retrieval by lidars.
The performance of two parameterization schemes for backscatter and
extinction humidograms is evaluated. The *κ* equation shows better
performance on inferring dry backscatter and extinction than the *γ* equation. The *κ* equation, therefore, is recommended to describe
the hygroscopic behaviors of the backscatter and extinction coefficients
from lidar measurements. The fitted hygroscopic parameters are found to be
sensitive to fitting RH range when the RH range is limited and relatively
high (between 60 % and 90 %). This is an extreme essential problem for
current research for aerosol hygroscopicity with lidar measurements. Great
care should be paid to the RH range when evaluating the hygroscopic growth
of the lidar-related optical properties.

It should be noted that the theoretical analyses in this paper are based on datasets of continental aerosols, and the implementation of Mie theory also limits the scope of the results. The results can be applied in the North China Plain but are not fit for sea salt and mineral dust. Studies with datasets of other aerosol types should be carried out in the future. Although the applicability of this new method is limited by large uncertainties in RH profiles, comparison between real measured MWRL data and airborne in situ measurement should also be conducted.

This work furthers our understanding of the relationship between CCN and aerosol optical properties and providing an optional way to retrieve CCN number concentration profiles from lidar measurements. The newly proposed method has the potential to provide long-term CCN at cloud base for aerosol–cloud interaction studies.

Data availability

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Data availability.

All of the datasets from field measurement and the corresponding simulated datasets can be obtained from the repository with the doi https://doi.org/10.5281/zenodo.3255086 (Tan et al., 2019).

Supplement

Back to toptop
Supplement.

The supplement related to this article is available online at: https://doi.org/10.5194/amt-12-3825-2019-supplement.

Author contributions

Back to toptop
Author contributions.

CZ and CL determined the main goal of this study. WT and GZ designed the methods. WT carried them out and prepared the paper with contributions from all co-authors.

Competing interests

Back to toptop
Competing interests.

The authors declare that they have no conflict of interest.

Financial support

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Financial support.

This research has been supported by the National Key R&D Program of China (grant nos. 2016YFC0202004 and 2017YFC0209904) and the National Natural Science Foundation of China (grant nos. 41375008, 41590872, 9154400001, and 41527807).

Review statement

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Review statement.

This paper was edited by Ulla Wandinger and reviewed by two anonymous referees.

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Short summary

A new method to retrieve CCN number concentrations using multiwavelength Raman lidars is proposed. The method implements hygroscopic enhancements of backscatter and extinction with relative humidity to represent particle hygroscopicity. The retrieved CCN number concentrations are in good agreement with theoretical calculated values. Sensitivity tests indicate that retrieval error in CCN arises mostly from uncertainties in extinction coefficients and RH profiles.

A new method to retrieve CCN number concentrations using multiwavelength Raman lidars is...

Atmospheric Measurement Techniques

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