A new method to determine the mixing state of light absorbing carbonaceous using the measured aerosol optical properties and number size distributions

Introduction Conclusions References


Introduction
Atmospheric aerosols influence the Earth's radiative balance directly by scattering and absorbing solar radiation, and indirectly by changing the albedo, cloud amount, lifetime of clouds, and precipitations (Twomey, 1974;Albrecht, 1989;Charlson et al, 1992;Rosenfeld, 1999Rosenfeld, , 2000;;Zhao et al., 2006).The largest uncertainty in estimating the radiative forcing results from aerosols (IPCC, 2007).Light absorbing carbonaceous (LAC), as one of the most important components of aerosols, is considered as the dominant absorber of visible solar radiation in the atmosphere (Ramanathan and Carmichael, 2008), and hence has a positive radiative forcing on the climate system (Jacobson, 2001).Due to the lack of horizontal and vertical distributions of LAC, insufficient emission inventory and the rather limited knowledge on the mixing state of LAC, the quantity of positive radiative forcing caused by LAC is yet uncertain.
The LAC has been assigned various names in the literature, such as "black carbon (BC)", "elemental carbon (EC)", and "soot"."BC" is mostly used to emphasize its light-absorbing property.However, following Bond and Bergstrom (2006), "LAC" is used in the current study.
LAC is emitted into the ambient atmosphere by fossil fuel (diesel and coal) combustion, open biomass burning (associated with deforestation and crop residue burning), and N. Ma et al.: A new method to determine the mixing state of light cooking with biofuels (Ramanathan and Carmichael, 2008).The freshly emitted LAC often stays unmixed, while there are many processes that cause LAC to mix with other chemical components, such as coagulation with other particles, condensation of vapors onto the surface forming a coating layer, reactions with gases, and cloud processes.The mixing state of LAC is quite complicated and the optical properties of LAC are very sensitive to the mixing state (Khalizov et al., 2009).It is suggested that different mixing states of LAC affect its global direct radiative forcing by a factor of 2.9 (+0.27Wm −2 for an external mixture, +0.54 Wm −2 for a core-shell mixture with LAC core, and +0.78 Wm −2 for homogeneously internal mixture) (Jacobson, 2000(Jacobson, , 2001)).Winkler (1973) suggested a definition of external and internal mixture of aerosols.For an external mixture, different compounds are separated as different particles, while in an internal mixture, all particles consist of the same mixture of compounds.The external and internal mixtures are two limiting cases with all intermediate states between them to be possible.Three conceptual models are usually used to describe the mixing state of LAC and other aerosol components: external mixture, homogeneously internal mixture, and core-shell internal mixture (a LAC core surrounded by a well-mixed less absorbing shell) (Seinfeld and Pandis, 1998;Jacobson, 2001).Most of the models for estimating the direct aerosol radiative forcing, as well as aerosol optical closure studies (Wex et al., 2002b;Mallet et al., 2004;Cheng et al., 2006;Ma et al., 2011) are based on the assumption of external mixture or homogeneously internal mixture for LAC and less absorbing components.However, many studies have suggested that internally mixed LAC is usually coated with a shell of less absorbing component to form a core-shell structure rather than "well mixed".Images obtained from TEM supported that LAC particles could become coated once emitted (Katrinak et al., 1992(Katrinak et al., , 1993;;Martins et al., 1998).Volatility tandem DMA (differential mobility analyzer) measurements showed that the majority of particles are comprised of a non-volatile core and a volatile outer layer during heavily polluted days (Wehner et al., 2009).Many studies also suggested that the use of a single particle optical model assuming an absorbing spherical core surrounded by a mantle of non-absorbing material is appropriate in the estimation of the aerosol direct radiative forcing (Jacobson et al., 2000(Jacobson et al., , 2001;;Chandra et al., 2004;Bond and Sun, 2005).
Many efforts have been undertaken to investigate how LAC is mixed with other aerosol components.In general, the mixing state of LAC can be obtained through two kinds of methods: direct measurements and inferences via optical closure studies.
A transmission electron microscopy (TEM) can be used for single particle analysis.The mixing state of soot particles was observed by Katrinak et al. (1992Katrinak et al. ( , 1993) ) and Clarke et al. (2004) with the TEM.A Single-particle soot photometer can be used to distinguish the coated soot particles (Schwarz et al., 2008) by measuring the incandescence and scatter-ing at infrared wavelengths of single particles.Moffet et al. (2008Moffet et al. ( , 2009) ) used an aerosol time-of-flight mass spectrometer to yield the mixing state of soot in real-time, and a diurnal variation was found.In recent years, Tandem DMAbased techniques were widely applied in aerosol measurements.A high humidity tandem DMA (Hennig et al., 2005) can provide size-resolved fractions of externally mixed hydrophobic particles (Liu et al., 2011), while a volatility tandem DMA can be used to yield size-resolved fractions of particles with different volatility that usually indicate different mixing states of LAC (Wehner et al., 2009;Cheng et al., 2009).
Besides the direct measurements, some studies inferred the LAC mixing state via optical closure studies.Most of them were based on the Mie model and the dependence of mass absorption efficiency of LAC on its mixing state.Mallet et al. (2004) calculated the single scattering albedo (ω) from in situ aerosol data with the assumption of external and homogeneously internal mixture for LAC and other components, and compared the two calculated ω with the values of Aerosol Robotic Network (AERONET) sun-photometer measurements.They found that LAC was externally mixed in the urban area.Dey et al. (2008) did a similar optical closure study in India to infer the mixing states and made an improvement by assuming six cases of aerosol mixing state in the calculation.They found that the probable aerosol mixing state had seasonal variations.Based on in situ aerosol microphysical and chemical measurements and a two-parameter aerosol optical model, Cheng et al. (2006) developed an internally consistent algorithm to yield the ratio of externally mixed LAC to the total mass of LAC.The aerosol absorption coefficients were calculated using aerosol particle number size distributions (PNSDs) and size-resolved chemical information with a variable mass ratio of externally mixed LAC.The best estimation of the mass ratios was derived from minimizing the difference between the calculated absorption coefficients and the values measured by MAAP (multi-angle absorption photometer, Petzold et al., 2002).However, due to the low temporal resolution of the aerosol chemical composition data, only two ratio values could be retrieved for each day.
With the rapid growth of population and economy in China, emissions of anthropogenic pollutants have increased dramatically in the past several decades.The widespread consumption of coal and biomass fuels makes China a significant source region of LAC.It has been reported that the LAC amount emitted in China make up about one fourth of globally emitted anthropogenic LAC (Cooke et al., 1999;Street et al., 2001;Bond et al., 2004).Megacities in China suffer severe air pollution (Ran et al., 2009;Liu et al., 2009), meanwhile influencing the neighboring regions.One of the most polluted areas in the world is the North China Plain (NCP) region (van Donkelaar et al., 2010), where two of the most densely populated megacities in China, Beijing and Tianjin, are located (Xu et al., 2011).In such highly polluted areas with high aerosol loading and concentrations of gases pollutants, aerosol aging processes may be quite different from what has been previously recognized, thus the mixing state of LAC might be much more complicated.However, studies addressing the mixing state of LAC in this region are currently very limited (Cheng et al, 2006;Wehner et al., 2009).
In this paper, an optical closure study was performed using in situ aerosol data measured at a regional site in the NCP.The hemispheric backscattering fractions (HBFs) calculated with three assumed LAC mixing states were compared with the measured values.A new algorithm was applied to infer the mass ratio of externally mixed LAC to the total mass of LAC (r ext-LAC ), assuming the mixing state of LAC as partially externally mixed and partially core-shell mixed.
In Sect.2, the site and instruments of the campaign are introduced.The new method for inferring the r ext-LAC is described in Sect.3. Sect. 4 presents the retrieved r ext-LAC , a three-day case study, as well as the uncertainty study.The summary and conclusions are presented in Sect. 5.

The field site
The HaChi (Haze in China) campaign took place in summer 2009 (12 July to 14 August, 193-226 DOY) in Wuqing, a suburban site in the Northern NCP and well representative of regional anthropogenic aerosols.The Wuqing town is situated between two megacities: Beijing (16 million inhabitants, 80 km away in the NW of Wuqing) and Tianjin (10 million inhabitants, 30 km away in the SSW of Wuqing) with about 0.8 million inhabitants.The map of the site and the area around can be found in Xu et al. (2011).During the campaign, particle number size distributions, aerosol light scattering coefficients, as well as LAC mass concentrations were continuously measured.
The measurements were conducted in a container, in which the temperature was maintained at 22 • C. Air samples were collected with a PM 10 inlet (16.67 l min −1 ) installed on the top of a stainless steel tube with a diameter of 3/4 inch (19 mm) and 7 m a.g.l.The samples were split into several flows inside the container, passing through stainless steel tubing, to different instruments.The residence time for samples in the inlet system was about 5 s.An automatic aerosol diffusion dryer (Tuch et al., 2009) was installed upstream all of the instruments to keep the relative humidity (RH) of the measured sample below 30 %.

Instrumentation
A Twin Differential Mobility Particle Sizer (TDMPS, IfT, Leipzig, Germany) (Birmili et al., 1999) and an Aerodynamic Particle Sizer (APS Model 3320, TSI, Inc., Shoreview, MN USA) were employed to measure PNSDs.Both were operated at RH < 30 %.The raw TDMPS and APS data were inverted and merged to yield the PNSDs with the range of equivalent diameter from 3 nm to 10 µm.Details can be found in Ma et al. (2011).The temporal resolution of the PNSD data was 10 min.
The scattering coefficients (σ sp ) and hemispheric backscattering coefficients (σ bsp ) for dry aerosols were measured by a total scatter/back scatter, integrating nephelometer at the wavelengths of 450, 550 and 700 nm (TSI, Inc., Shoreview, MN USA, Model 3563) (Anderson et al., 1996(Anderson et al., , 1998)), with a temporal resolution of 1 min.The nephelometer was calibrated beforehand using CO 2 (Anderson et al., 1996).Particle free air checks were performed once a day.
A multi-angle absorption photometer (MAAP Model 5012, Thermo, Inc., Waltham, MA USA) was employed to measure the absorption coefficients (σ ap ) for dry particles with a sampling frequency of 1 min.The instrument determines σ ap via simultaneous measurements of light (637 nm) passing through its filter and scattered back from particles accumulated on its surface.It operates at two detection angles to resolve the influence of light-scattering aerosol components on the angular distribution of the back-scattered radiation (Petzold and Schönlinner, 2004).The MAAP determines absorption coefficients directly and converts them to LAC mass concentrations with an assumed mass absorption efficiency (MAE) of 6.6 m 2 g −1 .This constant has been validated by the comparison between the impactor-derived elemental carbon mass and the MAAP measurements, which will be discussed in Sect.4.4.2.

Two-parameter aerosol model
A simplified aerosol model (Wex et al., 2002b;Cheng et al., 2006) was applied to aerosol optical calculations in this work.In the model, aerosol components are divided into two classes in terms of their optical properties: the lightabsorbing component (i.e.LAC) and less absorbing components (comprising inorganic salts and acids such as sulfates, nitrates, ammoniums, as well as most of the organic compounds).Although the chemical properties of numerous less absorbing compounds might be different, their refractive indices are basically the same, implying that the aerosol optical properties are not sensitive to their ratios.Therefore, the aerosol optical properties can be well represented with the two-parameter assumption in the Mie calculation (Wex, 2002a).This aerosol model is also widely used in aerosol direct radiative forcing estimations (Myhre et al., 1998;Kristjansson, 2002), but usually only LAC and sulfates were included.
The refractive indices of LAC and less absorbing components in the aerosol model were selected from related literatures (Ouimette and Flagan, 1982;Hasan and Dzubay, 1983;Sloane, 1984;Seinfeld and Pandis, 1998;Covert et al., 1990;Tang and Munkelwitz, 1994).The real part of the refractive index for LAC was chosen to be 1.80, and the imaginary part was set to be 0.54i, which was the average value for the wavelengths of 450, 550 and 700 nm (d ' Almeida et al., 1991).The refractive index of the less absorbing components was set to be 1.55-1e-7i.
For the mixing state of LAC, new evidences supporting the core-shell structure of LAC aerosols have been found in the simulation of nephelometer measurements.The nephelometer-measured HBF was simulated based on three assumed mixing states of LAC: external mixture, homogeneously internal mixture, and core-shell mixture.The HBF calculated with the assumption of core-shell mixture gives the highest results, which are about 30 % higher than those calculated with the assumption of external mixture.While the HBF calculated with the assumption of homogeneously internal mixture are the lowest, about 10 % lower than those calculated with the assumption of external mixture.The HBF given by nephelometer are always between the values calculated with the assumptions of external mixture and coreshell mixture.It definitely suggests that the sampled aerosols might be partially externally mixed and partially core-shell mixed rather than externally mixed and homogeneously internally mixed.More details will be discussed in Sect.4.1.
Consequently, aerosols are divided into two kinds in this study: the completely externally mixed LAC and a LAC core surrounded by a less absorbing component shell.To quantify the mixing state of LAC, r ext-LAC is defined as the mass fraction of externally mixed LAC (M ext-LAC ) in total LAC (M LAC ): If all LAC is externally mixed and there is no core inside the less absorbing component, r ext-LAC is 1; while r ext-LAC is 0 if all LAC is covered by less absorbing component.For atmospheric aerosols, r ext-LAC varies between 0 and 1.

Mie code
To simulate the measurements of TSI 3563 nephelometer, a modified BHMIE code and a modified BHCOAT code (Bohren and Huffman, 1983;Cheng et al., 2009) are utilized for homogeneous spherical particles and core-shell mixed spherical particles, respectively.In the Mie theory (Mie, 1908), the scattering efficiency (Q sp ) and the hemispheric back scattering efficiency (Q bsp ) can be calculated by integrating the intensity function |S (θ,x, m)| from 0 • to 180 • and from 90 • to 180 • , respectively: where, x=πD p /λ. D p is the volume equivalent diameter of particles.λ is the wavelength of radiation.θ is the scattering angle.However, the integrating angle of TSI 3563 nephelometer is from 7 • to 170 • for scattering and from 90 • to 170 • for hemispheric backscattering, respectively.And the light source of the nephelometer is not strictly Lambertian and shows a non-ideal angular response (Anderson et al., 1996).These two effects are considered in the modified BH-MIE code and BHCOAT code.The sinθ term in Eq. ( 2) is replaced by angular sensitivity curves f(θ ) sp and f(θ ) bsp , derived from a characterization study of TSI 3563 nephelometer (Anderson et al., 1996).Then the σ sp and σ bsp could be calculated following: where N (logD p ) is the PNSD.

Retrieval algorithm
As shown in Sect.4.1, the HBF measured by the nephelometer is always between the values calculated with assumptions of external mixture and core-shell mixture of LAC.The calculated HBF is found to be sensitive to r ext-LAC .Therefore, based on the aerosol model described in Sect.3.1, it is possible to retrieve r ext-LAC by matching the measured HBF and the HBF calculated from measured PNSD and LAC mass concentration with the modified Mie model.The PNSD of externally mixed LAC particles and coreshell mixed particles, as well as the radii of the LAC core of core-shell mixed particles, are need to calculate the HBF.For a given r ext-LAC , the PNSD of externally mixed LAC particles can be calculated by where, N logD p measure is the PNSD measured by TDMPS and APS.f LAC is the volume fraction of LAC, which can be calculated by where, M LAC, measure is the LAC mass concentration measured by MAAP.ρ LAC is the density of LAC, which is reported in literature with a range from 1.00 g cm −3 to 2.00 g cm −3 (Sloane et al., 1983(Sloane et al., , 1984(Sloane et al., , 1991;;Sloane and Wolff, 1985;Ouimette and Flagan, 1982;Seinfeld and Pandis, 1998).A median value of 1.5 g cm −3 is used in this study.
Accordingly, the PNSD of core-shell mixed particles can be calculated as: Another critical parameter for calculating the optical properties of core-shell mixed particles is the size of the LAC core.Core-shell mixed particles with the same diameter might differ in the size of their cores.As a simplified optical aerosol model, the core-shell mixed particles with the same diameter are assumed to be the same in the size of the LAC core, which can be calculated as: As shown in Eqs. ( 4), ( 6) and ( 7), the input parameters of the Mie model are the functions of r ext-LAC .Therefore, the HBF calculated with the Mie model is a function of r ext-LAC .The best estimation of r ext-LAC is the one which minimizes the differences between the calculated HBF and the corresponding measured value.The deviation χ 2 is quantified by linear least squares in the form of: where i denotes the three operation wavelengths of the TSI 3563 nephelometer.HBF calc,i is the HBF calculated with Mie model, while HBF meausre,i is the HBF measured by nephelometer.The relationship between measured and calculated HBF at 700 nm is quite different from that at 450 and 550 nm.The measured HBF at 700 nm is too high, so most of them are around the calculated values of core-shell mixture.Heintzenberg et al. (2006) performed a laboratory comparison study for 12 commercial nephelometers.Compared to calculated values, a systematic deviation of about -20 % was found for σ sp,700 nm of TSI 3563 nephelometer.Such large underestimation of σ sp,700 nm would lead to a significant overestimation of HBF at 700 nm.Thus, only the HBF at 450 and 550 nm are used here to retrieve the r ext-LAC .
During the entire period of the HaChi summer campaign, 1-min-resolution data measured by nephelometer and MAAP were averaged to match the time of the 10-min-resolution PNSD records.The r ext-LAC was subsequently retrieved by minimizing the χ 2 defined in Eq. ( 8).
It should be noted that the r ext-LAC defined in Sect.3.1 is a parameter in a simplified aerosol optical model and would only be valid under some assumptions mentioned before.
The actual mixing state of aerosols in the atmosphere is far more complicated beyond the model capabilities.Thus, the retrieved r ext-LAC is an "effective parameter" and should not be used for quantitative analysis for the mixing state of LAC.However, the retrieved r ext-LAC can be considered as an indicator for the variation of LAC mixing state and used in aerosol optical calculations, which is of great value in the research of aerosol and the estimation of the direct radiative forcing.

PartMC-MOSAIC model
The PartMC-MOSAIC model (Riemer et al., 2009) was applied to simulate the diurnal variation of the mixing state of LAC.The PartMC-MOSAIC is a stochastic particle-resolved aerosol box model, capable of resolving the composition of an individual particle.A Monte Carlo approach is used in the PartMC model to simulate the coagulation process stochastically.Emissions and dilutions within the lower free tropospheric above the nocturnal boundary layer on a regional scale are also modeled in a stochastic manner.And a new aerosol chemistry model MOSAIC (Model for Simulating Aerosol interactions and Chemistry, Zaveri et al., 2008) is coupled in the PartMC to simulate the gas-and particlephase chemistry, particle phase thermodynamics, and dynamic gas-particle mass-transfer in a deterministic manner.The PartMC-MOSAIC model can predict number, mass and composition distributions of the aerosol population.

Calculated HBF based on the limiting mixing states of LAC: a closure study
During the HaChi summer campaign, the PNSDs, LAC mass concentrations, scattering and hemispheric backscattering coefficients for dried aerosols were continuously measured on-line.An optical closure study on aerosol scattering and absorption coefficients has been conducted by Ma et al. (2011), which showed that the data are of high quality.
The time series of aerosol volume concentrations, effective radii, LAC mass concentrations, as well as the LAC volume fractions for the whole period of the campaign are shown in Fig. 1a and b.It can be seen that all of these parameters vary greatly with time, mainly in response to synoptic weather systems.Diurnal cycles are also present during some periods.The average aerosol volume concentration for the diameter range from 3 nm to 10 µm is 59.74 µm 3 cm −3 , with a 5th percentage value of 15.92 µm 3 cm −3 and a 95th percentage value of 137.49µm 3 cm −3 .The average aerosol effective radius, defined as r eff = 1.59 µg m −3 and a 95th percentage value of 15.87 µg m −3 .Futher details on aerosol optical properties for the HaChi summer campaign can be found in Ma et al. (2011).
To simulate the measurements of nephelometer, the HBF was calculated with the Mie model and the aerosol model introduced in Sect. 3 based on the measured PNSDs and LAC mass concentrations.The mixing state of LAC and less absorbing component was also needed in the simulation.Since there was no information on the mixing state of ambient aerosols available, the HBF was calculated for three limiting mixing states of LAC: external mixture, homogeneously internal mixture and core-shell mixture.Figure 1c shows the calculation results at the wavelength of 550 nm, as well as the HBFs yielded from nephelometer measurements.Figure 1d presents the frequency of each time series of HBFs in Fig. 1c.
It can be seen that the three calculated HBFs vary with time, which is caused by the variations of PNSDs and LAC mass concentrations.The relative standard deviations of calculated HBFs at 550 nm are respectively 5.2 %, 6.3 % and 5.1 % for the three assumptions of LAC mixing state mentioned above.However, it should be noted that the differences between the three time series of calculated HBF are more significant than the variations of each time series.The mean values of the three calculated HBF are shown in Ta-ble 1.For 550 nm, the calculated HBF under the external mixture assumption (HBF calc,external ) is 11.4 % higher than that under the homogeneously internal mixture assumption (HBF calc, internal ).The calculated HBF under the core-shell mixture assumption (HBF calc,core-shell ) is even 41.0 % higher than that under the homogeneously internal mixture assumption.These differences are much higher than the variations of each time series caused by the variations of PNSDs and LAC mass concentrations.Therefore, the calculated HBF is more sensitive to the mixing state of LAC rather than the variations of PNSDs and LAC mass concentrations.This sensitivity of HBF provides an approach to retrieve the mixing state of LAC, as described in Sect.3.
In Fig. 1c, the purple dots denote the HBF yielded from the nephelometer measurements (HBF neph ), i.e. the ratio of measured hemispheric backscattering coefficients to measured scattering coefficients.If the widely-used assumption that the atmospheric aerosol is a partial mixture of externally mixed and homogeneously internally mixed particles is appropriate, the HBF neph values should fall between the HBF calc,external and the HBF calc, internal .However, for 550 nm, almost all of the HBF neph are higher than the HBF calc,external and HBF calc, internal , and distributed between the HBF calc,external and the HBF calc,core-shell .Table 1 shows the averages of HBF calc,external , HBF calc, internal , HBF calc,core-shell and HBF neph at the three operation wavelengths of the TSI 3563 nephelometer.It can be seen that the relationship of the calculated and measured HBF is HBF calc,core-shell >HBF neph >HBF calc,external >HBF calc,internal .
The HBF neph at 700 nm is higher than all of the calculated ones.This might be caused by the underestimation of the TSI 3563 nephelometer on σ sp,700 nm , as mentioned in Sect.3.3.
The mixing state of atmospheric aerosols is considered as an intermediate state between external and internal (Winkler, 1973).The internal mixture are usually treated as a homogeneously internal mixture in aerosol optical calculations (Wex et al., 2002b;Mallet et al., 2004;Cheng et al., 2006).In that case, external mixture and homogeneously internal mixture are two limiting cases of mixing state.The aerosol optical properties calculated with the assumptions of external mixture and homogeneously internal mixture should be the boundaries of the measured values.However, as presented in this study, the HBF neph is significantly higher than both the HBF calc,external and HBF calc, internal , and is close to the HBF calc,core-shell .This means that the former assumptions of LAC mixing state, which have been widely used in aerosol optical calculations, are generally not appropriate.In the NCP, the ambient aerosols seem to be more similar to coreshell mixtures, rather than to homogeneously internal mixtures.The aerosols can be considered as a partial mixture of externally and core-shell mixed particles.

Retrieved mixing state of LAC
The r ext-LAC was retrieved with the new method introduced in Sect. 3 for the whole period of the HaChi summer campaign.The time series of r ext-LAC is presented in Fig. 2b.The corresponding wind direction and wind speed measured by an automatic weather station are illustrated in Fig. 2a.
For the whole period, r ext-LAC varied between 0 and 1, with an average of 0.51 ± 0.21, indicating that the mixing state of LAC is a combination of external and core-shell mixture.Pronounced variation can be found in the time series of r ext-LAC , reflecting the large variation of LAC mixing state with time.Moreover, significant diurnal cycles of r ext-LAC can be discerned during some periods.The time-scale of the measured variability can be also revealed by autocorrelation analysis (Cheng et al., 2008).Figure 2d depicts the result of the autocorrelation analysis for the entire time series of r ext-LAC .When t = 24 h, The autocorrelation coefficient of r ext-LAC shows a peak with a value of about 0.3, indicating the existence of pronounced diurnal cycles in the variation of r ext-LAC .
The average diurnal variation of r ext-LAC is illustrated in Fig. 2c, with error bar of one standard deviation.Consistent with the result of the autocorrelation analysis, a pronounced diurnal pattern can be found.Around midnight, the average r ext-LAC is around 0.58 and increases from 04:00 LT.A

Diurnal variation of LAC mixing state: a case study
To better understand the diurnal pattern of the r ext-LAC retrieved with this method, a period of 3 days (219-221 DOY) was selected for a case study.During this period, the synoptic conditions were relatively stable, dominated by easterly winds with speeds lower than 3 ms −1 .The weather was cloud-free with no precipitation event occurred.Therefore, the aerosols in the boundary layer were mostly from local and regional emissions sources.With no obvious pollutant transport under this meteorological situation, this period was appropriate for investigating the diurnal variation of LAC mixing state caused by the evolution of boundary layer, emissions and corresponding chemical processes.The time series of retrieved r ext-LAC during this period is presented in Fig. 3b.A similar diurnal pattern, with high r ext-LAC during night and low r ext-LAC during daytime, can be found in all of the three days.
During the whole period of the campaign, a high humidity tandem differential mobility analyser (HHTDMA, Hennig et al., 2005) was used to measure the hygroscopic growth factor (GF) at relative humidities of 90 %, 95 % and 98.5 % for particles with dry diameters of 50 nm, 100 nm, 200 nm and 250 nm, respectively.More details on the HHTDMA measurement can be found in Liu et al. (2011).The probability distributions of GF usually showed a distinct bimodal pattern, consisting of a dominant more-hygroscopic (MH) mode and a smaller nearly-hydrophobic (NH) mode.During the whole period, a strong diurnal pattern of the number fraction of these two modes was found, indicating the diurnal variation of the aerosol mixing state.For all of the four measured sizes, the number fraction of NH particles remains at a high level during the night and begins to decrease at 06:00 LT.During the daytime, the number fraction of NH stays at low level.And a rapid rise occurs around 18:00 LT.The high number fraction of NH particles during the night indicates that the freshly emitted hydrophobic particles have accumulated in the surface layer, apparently externally mixed with the hygroscopic particles.During the daytime, the low fraction of NH mode indicates that aged aerosol was dominant in the atmosphere near the surface (Liu et al., 2011).This result yielded from HHTDMA is well consistent with the diurnal variation of retrieved r ext-LAC .
In Liu's (2011) work, a stochastic, particle-resolved aerosol model PartMC-MOSAIC was applied to simulate the aerosol hygroscopicity for the same period as in this study.A good agreement between the model results and the measurements indicates that the model can be well representative of the hygroscopicity of ambient aerosols.To investigate how the chemical and meteorological processes affect the diurnal variation of the mixing state of LAC, the same model was applied in this study.The simulated scenario represented a Lagrangian air parcel over a large megacity region.The model was initialized 12 h before the simulation period for model adjustment.The mixing layer height was set according to the boundary layer height simulated by the Weather Research and Forecasting (WRF) model.The temperature and water vapour mixing ratio were set based on the measurement.The initial gas phase concentrations and emission rates were set according to Riemer et al. (2009).Based on the PNSDs measured by TDMPS and APS, a tri-modal distribution was used as the initial PNSD.The initial aerosols were assumed to consist of (NH 4 ) 2 SO 4 , primary organic aerosol and LAC, with mass fractions of 60 %, 35 % and 5 %, respectively.The aerosol emission pattern and chemical composition was set according to Riemer et al. (2009), while some modification was made to better represent the pollution in the North China Plain.More details about the parameter settings of the model can be found in Liu et al. (2011).
The model results are shown in Fig. 3c.The mass of the modelled externally mixed LAC is compared to the total mass of the modelled LAC to yield the r ext-LAC,model .It can be seen that the simulated r ext-LAC,model for all the size ranges match well with the retrieved r ext-LAC , indicating that the variation of the modelled result is well consistent with that of retrieved r ext-LAC .This means the diurnal pattern of retrieved r ext-LAC can be explained by the mechanisms included in the model, such as emissions, aging processes and the entrainment by the increase of the mixing layer height.During the night, the freshly emitted LAC aerosols accumulate in the shallow nocturnal boundary layer and the aging processes are relatively weak.Under such a condition, the fraction of the externally mixed LAC to the total LAC mass is relatively high.As illustrated in Fig. 3c, more than 80 % of LAC mass is externally mixed for the particles smaller than 125 nm.In the morning during 07:00 LT to 12:00 LT, the development of the mixing layer causes a downward entrainment of aged aerosol from aloft, resulting in a decrease of the fraction of externally mixed LAC.The aging processes may also make contributions.Only less than 40 % of LAC is externally mixed at noon.The fraction of externally mixed LAC remains low until the evening.The collapse of the mixing layer and the high emission rate due to rush hours cause a rapid increase in the fraction of externally mixed LAC, and the fraction remains high in the stable shallow nocturnal boundary layer.A sensitivity study of the modelled aerosol mixing state to the chemical and meteorological processes was performed by Liu et al. (2011).The results suggested that the diurnal evolution of the mixing layer was decisive in explaining the diurnal cycle of aerosol mixing state.Other processes such as condensation, photochemical aging and coagulation processes also made contributions but were not as effective as the evolution of the mixing layer.A similar boundary layer mechanism was also suggested by Rissler et al. (2006).
In Fig. 3c, the r ext-LAC,model for large particles are much lower than that for small ones.In the model, the initial aerosol for all size range is assumed to consist of LAC as 5 % in mass, and the freshly emitted LAC particles are assumed to be distributed as a log-normal distribution with geometric average diameter of 50 nm.Therefore, during the daytime as well as during the nighttime, the fraction of externally mixed LAC decreases with increasing particle size.

Sensitivity study
The input parameters of the new method include in situ measured data (PNSDs, LAC mass concentrations, aerosol scattering and hemispheric backscattering coefficients) and some constants assumed beforehand (the refractive indices of LAC and less absorbing component, the density of LAC and the mass absorption efficiency (MAE)).The retrieved r ext-LAC would no doubt be influenced by the uncertainties of these variables.Also, some assumptions included in the model, such as spherical particles and constant fraction of LAC mass for all size, would introduce uncertainties to the retrieved r ext-LAC .In order to quantify the influences of the uncertainties of these input parameters and assumptions on the retrieved r ext-LAC , a sensitivity study was performed.The potential uncertainties introduced by the assumptions in the model are discussed first.The sensitivity of the r ext-LAC to the input parameters was determined by varying them individually and evaluating the changing of the retrieved r ext-LAC .The overall uncertainty of the retrieved r ext-LAC was estimated by a Monte Carlo approach.

Potential uncertainties introduced by the assumptions in the model
The most important assumption in the Mie theory is that all particles are spherical.This assumption simplifies the mathematical treatment.However, atmospheric aerosols are sometimes non-spherical.Soot aggregates and mineral dust particles are typical and often observed as non-spherical aerosols (Katrinak et al., 1993;Okada et al., 2001;Kaaden et al., 2009).The shape of the particles may influence their optical properties.If the responses of the σ sp and σ bsp to the particle shape are different, a large uncertainty will be introduced in the retrieved r ext-LAC .Unfortunately, no literature mentioning the dependence of σ bsp on particle shape was found.Therefore, it is difficult to quantify the influence of non-spherical particles on the retrieved r ext-LAC .However, there is some indirect evidence from which we may estimate the influence.Figure 4 shows the cumulative contributions of aerosols with different size to the optical properties (i.e.σ sp , σ bsp and σ ap ), which were derived with the Mie model, average PNSD and LAC mass concentration, and three assumed mixing states.It can be seen that at the wavelengths of 450 and 550 nm, the scattering and hemispheric backscattering are dominated by the particles with the size range from 100 to 600 nm in diameter, which are also the main part of the accumulation mode (Hussein et al., 2005).Freshly generated soot exists in the form of chainlike aggregates.However, during aging processing, a marked change in morphology of soot particles occurs.It was found that a transformation of the soot aggregates to spherical particles occurs as sulphuric acid and water condense onto fresh soot.Also, the soot core was restructured to more compact form (Zhang et al., 2008;Pagels et al., 2009).Therefore, the optical properties are thus considered to be mainly dominated by spherical particles.
For larger sizes, mineral dust particles with non-spherical shape exist.However, due to the huge concentrations of the fine particles in the NCP, the relative optical contribution is less than 20 % for particles larger than 600 nm, and is only about 5 % for super-micron particles.There was no strong dust event observed during the HaChi summer campaign.The influence of the non-spherical mineral dust particles is thus ignored.It should be noted that LAC is usually observed to be non-spherical and in the form of aggregate structures (Katrinak et al., 1993).However, there is not enough information available to evaluate the influence of these agglomerates on the retrieved r ext-LAC .
In the algorithm, only two kinds of particle morphology are assumed: externally mixed LAC and a LAC core surrounded by a less absorbing shell.In the atmosphere, externally mixed less absorbing particles should also exist.There   2009) used a volatility tandem DMA to determine the aerosol volatility based on the changes in particle diameter between 25 • C and 300 • C.They found that most of the particles had a low to moderate volatile fraction, corresponding to the externally mixed LAC and core-shell mixed LAC.Around 40 % of the particles with diameters smaller than 300 nm were found to have a large volatile fraction with over 55 % decrease in diameter after heating.If the non-volatile core in the high volatile particles is very small, it might not consist of LAC but of low-volatile organic material (Kalberer et al., 2004), since freshly emitted LAC particles are usually at least 50 nm in diameter (e.g., Harris and Maricq, 2001).Therefore, there are some externally mixed less absorbing particles included in the high volatile group, with a number fraction lower than 40 %.To estimate the influence on the r ext-LAC , the r ext-LAC was retrieved with the assumption that the externally mixed less absorbing particles exist with assumed number fractions.It was found that the retrieved r ext-LAC decrease with the increase of the fraction of externally mixed less absorbing particles.The r ext-LAC is about 6 % lower than the original value (with no less absorbing component externally mixed) if 20 % of the less absorbing component is externally mixed.And the decrease in percentage goes up to 25 % if 40 % of the less absorbing component is externally mixed.Another assumption included in the retrieving model is that the volume fraction of LAC is independent of particle size.This is no doubt the simplest description for LAC volume size distribution.The real situation in the atmosphere is much more complicated.Freshly emitted LAC particles are usually concentrated at around 100 nm in diameter (Moffet and Prather, 2009).During coagulations and condensation processes, the LAC mass will be transferred to larger particles.In order to evaluate the influence of this assumption on the retrieved r ext-LAC , the average EC volume fractions obtained from the Berner impactor measurements were used, which are shown in Fig. 5.The size-dependent volume fractions of LAC were assumed to be the same as that of EC.The r ext-LAC was retrieved from the size-independent LAC volume fractions and the average measured size-dependent LAC volume fractions, respectively.The calculations were carried out for three cases: average condition (using the average values for the whole period as the inputs of the model), high r ext-LAC case (using the average values for the period from DOY 220 to DOY 220.25 as the inputs), and low r ext-LAC case (using the average values for the period from DOY 220.5 to DOY 220.75 as the inputs).The results are presented in Table 2.
The values retrieved with the measured size-dependent fractions are always higher than those retrieved with the sizeindependent fractions.The sensitivity of retrieved r ext-LAC to the assumption of LAC volume fraction distribution is also found to be insignificant.For the average case, the difference between the two retrieved r ext-LAC is 0.032.The difference for the high r ext-LAC case is only 0.02.But for the low r ext-LAC case, the difference reaches up to 0.081, which is relatively high.It seems that the lower the r ext-LAC is, the more sensitive it becomes.
The assumption of the size-independent LAC volume fraction distribution used in the model does cause an overestimation in the retrieved r ext-LAC , but the influence is relatively small.The reason for choosing a size-independent LAC volume fraction is to make the method be able to provide information on the LAC mixing state solely from aerosol physical properties.Mobility size spectrometers have been widely used for measuring the PNSD.Nephelometers and MAAPs are also commonly used to provide aerosol optical properties.All of these instruments can measure the aerosol properties online with high time resolutions.However, the volume fraction distribution of LAC is usually obtained from aerosol chemical composition measurements, which is normally based on impactor sampling and offline analyzing.This kind of measurement is usually with low time resolution and not as common as the measurements of aerosol physical properties.Therefore, a method based on the aerosol physical property measurements is more valuable than that based on aerosol chemical data.

Uncertainties of input parameters
All of the input parameters for the retrieving algorithm are listed in Table 3.The possible values of each parameter are assumed to be normally distributed with standard deviations presented in Table 3.The uncertainty of the measured PNSD originates from the uncertainties of the TDMPS and APS measurements.From a comparison test reported by Wiedensohler et al. (2011), the maximum uncertainty of the particle size measured by mobility size spectrometers reaches 3.5 %, and the maximum uncertainty of the number concentration is 30 %, 10 % and 25 % for the size range of 3-20 nm, 20-200 nm and 200-700 nm, respectively.These values are used as the uncertainties of the TDMPS measurement.For the size and number concentration measured by APS, the uncertainty is respectively estimated as 9 % and 10 % (Wex et al., 2002b).The uncertainty of σ ap measured by MAAP is reported as about 12 % (Petzold et al., 2004).To convert σ ap to LAC mass concentration, a MAE of 6.6 m 2 g −1 is used in the MAAP.In order to estimate the uncertainty of this value, the Berner impactor-derived EC mass concentrations were compared with the MAAP-measured σ ap , as shown in Fig. 6.It should be noted that LAC and EC are two different definitions and have slightly different thermal, optical and chemical behaviour.However, they share a similar fraction of the carbonaceous aerosol and are supposed to be comparable (Lavanchy et al., 1999).Thus, the LAC mass concentration is assumed to be the same as the Berner impactor-derived EC mass concentration.It can be seen that all data points locate around the line of MAE = 6.6 m 2 g −1 , with determination coefficient R 2 of 0.837.The coefficient of linear regression is 7.20 m 2 g −1 , which is close to the MAE value used in MAAP.Since there is no direct way to evaluate the uncertainty of MAE, the difference between the recommended value and the value yielded from the regression is taken as one standard deviation of the MAE, which is 9.1 %.This value is an empirical estimation and only valid in this study.
The corresponding uncertainty of the MAE (3σ ) is also illustrated in Fig. 6 as dash lines.In literature (Sloane et al., 1983(Sloane et al., , 1984(Sloane et al., , 1991;;Sloane and Wolff, 1985;Ouimette and Flagan, 1982;Seinfeld and Pandis, 1998), ρ EC is reported as a range from 1.00 g cm −3 to 2.00 g cm −3 .Accordingly, the uncertainty of ρ EC is set to be 33 % to cover the above mentioned range.The uncertainties for the refractive indices of LAC and less absorbing component are chosen according to Cheng et al. (2006).Their estimated uncertainties for the real part of refractive index of the less absorbing component, the real part and imaginary part of refractive index of LAC are 1.5 %, 12 % and 20 %, respectively.The uncertainty of the HBF derived from the nephelometer measurements is estimated as 20 % (Anderson et al., 1996).

Sensitivities of retrieved r ext-LAC to the uncertainties of input parameters
The sensitivities of the retrieved r ext-LAC to the uncertainty of each input parameter were investigated for three cases: average condition (using the average values for the whole period as the inputs of the model), high r ext-LAC case (using the average values for the period from DOY 220 to DOY 220.25 as the inputs), and low r ext-LAC case (using the average values for the period from DOY 220.5 to DOY 220.75 as the inputs).The r ext-LAC was retrieved with one parameter varying from its original value to the original plus one σ , while keeping other parameters fixed.The difference between the new r ext-LAC and the original value, defined as =r ext-LAC, newr ext-LAC,original , represents the influence of the uncertainty of the varying input parameter on r ext-LAC .In other words, the influences of the uncertainties of input parameters on the retrieved r ext-LAC were determined independently.Table 4 presents the r ext-LAC retrieved with the varying of each parameter, as well as the difference ( ).It can be noted from .20 m 2 g −1 , R 2 = 0.837).The black line corresponds with MAE = 6.6 m 2 g −1 .The error bar of each data point denotes the standard deviation of the σ ap averaged to yield the data, since the time resolution of σ ap is much higher than that of the impactor-derived EC mass concentrations.
Table 3 that, among all of the input parameters, the largest influence on retrieved r ext-LAC stems from the uncertainty of HBF.A shift of 6.6 % in HBF leads to a shift of more than 0.1 in r ext-LAC for the average case.However, it should be noted that there is no reference in the literature to the uncertainties of σ bsp or HBF measured by the TSI 3563 nephelometer.Only one reference (Anderson et al., 1996) mentioned that the uncertainty of HBF derived by the TSI 3563 nephelometer is within 20 %.Therefore, the influence of the uncertainty of measured HBF should be reconsidered after getting a better estimation of the uncertainty of the measurement.
The second largest influence on retrieved r ext-LAC comes from the uncertainty of LAC density.Due to the large range of LAC density reported in the literature, the standard deviation of LAC density is estimated as 11 %, which is the highest among all of the input parameters.This high standard deviation of LAC density induces a shift of 0.047 in r ext-LAC for the average case.
Following the LAC density, the uncertainty of measured LAC mass concentration also makes a great contribution.The uncertainty of LAC mass concentration is separated into two parts, the uncertainty of the measured σ ap and the uncertainty of the MAE, and treated separately.For the average case, a shift of 4 % in measured σ ap leads to a shift of 0.017 in r ext-LAC , while a shift of 9.1 % in MAE leads to a shift of 0.039 in r ext-LAC for the average case.
The influences of the uncertainties in the refractive indices on r ext-LAC are of the same magnitude.A shift of one σ in each of the three assumed refractive indices respectively causes a shift of around 0.024 in r ext-LAC for the average case.
For the PNSD, a shift of one σ in the size and number concentration of TDMPS measurement leads to a shift of 0.021 and 0.042 in r ext-LAC for the average case, respectively.However, it can be seen that the influence of the uncertainties in the APS data on r ext-LAC is weak.Since an averaged PNSD was used in this sensitivity study, the contribution of particles in the size range of the APS measurements to the overall aerosol optical properties is relatively small.During certain heavy pollution periods, the contribution of coarse particles to the overall aerosol optical properties might be significant.In those cases, the influence of the uncertainties in the APS measurement to r ext-LAC might become higher.
It should be noted that the influences of the uncertainties of model inputs on r ext-LAC also depend on the levels of r ext-LAC .The lower the r ext-LAC is, the more significant the influence would be.It means that the r ext-LAC with low values have more uncertainty than those with high values.This also can be seen in Fig. 3b, r ext-LAC with lower values show much larger variability than those with higher values.
Overall, the retrieved r ext-LAC shows the highest sensitivity to the HBF yielded from the nephelometer measurements, followed by the assumed LAC density.The uncertainty in the LAC mass concentration also makes great contribution.The uncertainties in the refractive indices of less absorbing component and LAC cause similar responses in r ext-LAC .And the influence of the uncertainties in measured PNSD on r ext-LAC is relatively low among the input parameters.Therefore, under current method, an accurate measurement of σ sp and σ bsp is most important to retrieve r ext-LAC .A better estimation of the uncertainties in measured σ bsp or HBF is urgently needed.Furthermore, more accurate estimations of the LAC density and the refractive indices are required to reduce the uncertainty of retrieved r ext-LAC .

Monte Carlo variations
A Monte Carlo simulation was applied to investigate the overall influence of input parameters on the retrieved r ext-LAC for the three cases mentioned in Sect.4.4.3.The retrieving algorithm was repeated using a randomly varying set of input parameters.The random values of the input parameters were generated independently.The values of each input parameter were normally distributed, with the original value used in Sect.4.4.3 as the mean value, and the standard deviation listed in Table 3. 2000 runs were carried out to yield a stable distribution of the retrieved r ext-LAC .The retrieved r ext-LAC shows a quasi-lognormal distribution with standard deviations of 0.202, 0.130 and 0.241 for the average case, high r ext-LAC case, and low r ext-LAC case, respectively.Such large uncertainty in the retrieved r ext-LAC is induced by all input parameters.However, all the uncertainties of input parameters discussed in Sect.4.4.2 are the worst case estimations, thus the standard deviation of r ext-LAC might be lower.

Summary and conclusions
In this paper, a new method was proposed to retrieve information on the mixing state of LAC from measured PNSDs, LAC mass concentrations and HBFs.
Based on a two-parameter optical aerosol model, an aerosol optical closure was conducted using independent in situ measured data.The HBFs yielded from the nephelometer were compared with the values calculated from the PNSDs and LAC mass concentrations with a modified Mie model.Three limiting mixing states of LAC were assumed in the calculation: external mixture, homogeneously internal mixture and core-shell mixture.It was found that the HBF is more sensitive to the assumption of LAC mixing state, rather than to the variations of the PNSDs or the LAC mass concentrations.The HBFs calculated based on core-shell mixture are much higher than those based on external mixture or homogeneously internal mixture.Moreover, almost all of the HBFs yielded from the nephelometer locate between the values calculated based on core-shell mixture and external mixture, but are much higher than the values calculated under the homogeneously internal mixture assumption.This finding indicates that the assumption of LAC mixing state which has been widely applied in aerosol optical calculations cannot be used properly in the NCP.In this area, the internally mixed aerosols are rather core-shell mixed than homogeneously mixed.Thus, an assumption of a system consisting of externally mixed LAC and core-shell mixed LAC and less absorbing component is more appropriate in aerosol optical calculations.
With the new method, a high-resolution time series of the mass fraction of the externally mixed LAC was retrieved from in situ measurements of PNSDs and LAC mass concentrations.A pronounced diurnal cycle was found.During the night, the average r ext-LAC is around 0.58, and reaches its maximum around 06:00 LT, indicating the accumulation of the freshly emitted LAC in the nocturnal boundary layer.During the daytime, r ext-LAC remains at a relatively low level, reflecting the dominance of aged aerosol in the boundary layer.This diurnal variation of r ext-LAC is mainly caused by the diurnal evolution of the mixing layer.Other processes, such as condensation, coagulation and photochemical aging, also make contributions.As a case study, a three-day period with constant synoptic situation was selected.A stochastic, particle-resolved aerosol model PartMC-MOSAIC was applied to yield the information of LAC mixing state during this period.The retrieved r ext-LAC and the model results showed a very similar variation patterns.This good agreement further proves our explanations for the diurnal pattern of the retrieved r ext-LAC .
A sensitivity study was carried out to investigate the sensitivities of the retrieved r ext-LAC to the input parameters of the algorithm.The retrieved r ext-LAC shows the highest sensitivity to the HBF yielded from the nephelometer measurements, followed by the assumption of the LAC density.The uncertainties in the LAC mass concentrations and the refractive indices also cause great influences on r ext-LAC .It was found that r ext-LAC with low values have more uncertainty than those with high values.The overall uncertainty of the retrieved r ext-LAC was derived via the Monte Carlo approach.Considering the uncertainties of all input parameters of the algorithm, the standard deviation of the retrieved r ext-LAC was found to be 0.20 for average case.

Fig. 1 .
Fig. 1.Time series of selected parameters during the HaChi summer campaign: (A) aerosol volume concentration, effective radius, (B) LAC mass concentration, LAC volume fraction, (C) HBF measured by nephelometer and HBF calculated with three limiting mixing states of LAC at the wavelength of 550 nm.(D) frequency distributions of measured and calculated HBF.All the data have been averaged corresponding to the time of TDMPS measurement with time resolution of 10 min.
Fig. 2. (A) Time series of wind speed and wind direction (denoted by the colour of dots).(B) Time series of retrieved r ext-LAC .(C) Average diurnal pattern of r ext-LAC .(D) Result of autocorrelation analysis of r ext-LAC .The dash-line box denotes the period selected as a case study.

Fig. 3 .
Fig. 3. Time series of parameters for the selected period: (A) wind speed and wind direction (denoted by the colour of dots), (B) the retrieved r ext-LAC , (C) the fraction of externally mixed LAC at different size ranges yielded from the PartMC-MOSAIC model.

Fig. 4 .
Fig. 4. The cumulative contributions of aerosols with different size to the optical properties: σ sp , σ bsp and σ ap .The results is based on the Mie model, average PNSD and LAC mass concentration, and three assumed mixing states.

Fig. 5 .
Fig. 5.The average distribution of EC mass concentration and EC volume fraction yielded from Berner impactor measurements.

Fig. 6 .
Fig. 6.Comparison of the σ ap measured by MAAP and the Berner impactor-derived EC mass concentrations.The result of linear regression is shown as red line (b = 7.20 m 2 g −1 , R 2= 0.837).The black line corresponds with MAE = 6.6 m 2 g −1 .The error bar of each data point denotes the standard deviation of the σ ap averaged to yield the data, since the time resolution of σ ap is much higher than that of the impactor-derived EC mass concentrations.

Table 1 .
The average of calculated HBF under the assumptions of externally, homogeneously internally and core-shell mixture, as well as the averaged HBF measured by nephelometer.(nm)HBFcalc,externalHBF calc, internal HBF calc,core-shell HBF neph And then r ext-LAC decreases rapidly after 08:00 LT with the minimum appearing in the afternoon.During the night, the average r ext-LAC increases again.This distinct diurnal pattern of average r ext-LAC reflects the diurnal variation of the mixing state of LAC and less absorbing component.During the night, the high level of r ext-LAC indicates that the freshly emitted LAC, which is considered to be externally mixed with aged particles, accumulates in the nocturnal boundary layer.The low value of r ext-LAC during daytime reflects the dominance of core-shell mixed particles in the boundary layer.Similar diurnal pattern of aerosol mixing state was reported byMoffet  and Prather (2009)andLiu et al. (2011). λ

Table 2 .
r ext-LAC retrieved from assumed LAC volume fractions and measured LAC volume fractions.

Table 3 .
Uncertainties of the input parameters for the retrieving algorithm, giving in terms of one standard deviation.

Table 4 .
r ext-LAC retrieved with each input parameter varying from its original value to the original value plus σ , as well as the differences ( ) between each new r ext-LAC and original value.