AMTAtmospheric Measurement TechniquesAMTAtmos. Meas. Tech.1867-8548Copernicus PublicationsGöttingen, Germany10.5194/amt-9-1925-2016A new method for estimating aerosol mass flux in the urban surface layer
using LAS technologyYuanRenminrmyuan@ustc.edu.cnhttps://orcid.org/0000-0002-2527-8346LuoTaoluotao@ustc.edu.cnSunJianninghttps://orcid.org/0000-0002-7683-1674LiuHaoFuYunfeiWangZhienSchool of Earth and Space Sciences, University of Science and
Technology of China, Anhui, 230026, ChinaSchool of Atmospheric Sciences, Nanjing University, Jiangsu, 210023,
ChinaDepartment of Atmospheric Science, University of Wyoming, Laramie, Wyoming, WY 82070, USARenmin Yuan (rmyuan@ustc.edu.cn) and Tao Luo (luotao@ustc.edu.cn)29April2016941925193711October201519January201610April201622April2016This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://amt.copernicus.org/articles/9/1925/2016/amt-9-1925-2016.htmlThe full text article is available as a PDF file from https://amt.copernicus.org/articles/9/1925/2016/amt-9-1925-2016.pdf
Atmospheric aerosol greatly influences human health and
the natural environment, as well as the weather and climate system.
Therefore, atmospheric aerosol has attracted significant attention from
society. Despite consistent research efforts, there are still uncertainties
in understanding its effects due to poor knowledge about aerosol vertical
transport caused by the limited measurement capabilities of aerosol mass
vertical transport flux. In this paper, a new method for measuring
atmospheric aerosol vertical transport flux is developed based on the
similarity theory of surface layer, the theory of light propagation in a
turbulent atmosphere, and the observations and studies of the atmospheric
equivalent refractive index (AERI). The results show that aerosol mass flux
can be linked to the real and imaginary parts of the atmospheric equivalent
refractive index structure parameter (AERISP) and the ratio of aerosol mass
concentration to the imaginary part of the AERI. The real and imaginary
parts of the AERISP can be measured based on the light-propagation theory.
The ratio of the aerosol mass concentration to the imaginary part of the
AERI can be measured based on the measurements of aerosol mass concentration
and visibility. The observational results show that aerosol vertical
transport flux varies diurnally and is related to the aerosol spatial
distribution. The maximum aerosol flux during the experimental period in
Hefei City was 0.017 mg m-2 s-1, and the mean value was 0.004 mg m-2 s-1. The new method offers an effective way to study aerosol
vertical transport in complex environments.
Introduction
The impacts of atmospheric aerosols on climate change have drawn significant
attention from society (IPCC, 2014). To better understand the aerosols,
there are many conventional and routine measurements, such as measuring the
concentration of aerosol particles for environmental protection (Chang
and Lee, 2007; Cruz et al., 2015), building observation networks of
ground-based and remote sensing for tropospheric aerosol properties and
radiative forcing (to measure the optical depth, concentration, and physical
and chemical properties of aerosols) s (Cruz et al., 2015; Dubovik et al.,
2002), and performing some special scientific experiments (Li et al.,
2015; Wood et al., 2013). Over the past 20 years, progress has been made to
measure the concentration, size distribution, and physical and chemical
properties of aerosols (Moosmueller et al., 2009). However,
there are still large uncertainties in quantifying the effects of
atmospheric aerosols on Earth's energy budget by scattering and absorbing
radiation and by modifying the amounts and microphysical and radiative
properties in clouds (Myhre et al., 2009; IPCC, 2007, 2014). Therefore,
more representative and accurate data are required (Chin et al., 2009; IPCC, 2014). The climatic effect of aerosol was also
extensively studied through numerical model simulations, which must also be
verified by more directly measured aerosol data, especially aerosol
emissions from the surface (Myhre et al., 2009). The forecast for urban environmental pollution must also
directly measure the aerosol source emission (Wu et al., 2012).
So far, we can provide accurate physical and chemical aerosol properties,
such as concentration, shape, size, optical properties and chemical
components, especially with in situ sampling instruments (Nakayama et
al., 2014; Wang et al., 2015). However, other key aerosol processes, such as
emission intensity and vertical transport, which are required for
simulations of large-scale atmospheric chemical transport and forecasting
local and regional air quality, are poorly measured. Studies
(Seinfeld and Pandis, 2006; Bond et al., 2004) have
shown that model simulations on the impacts of aerosols on the environment
and climate require aerosol source emission and transport data, especially
the emission of anthropogenic aerosols primarily arising from a variety of
combustion sources (Li et al., 2009).
There are a few methods to provide aerosol emission data. One method is to
perform statistical analyses of the aerosol parameters and estimate the
aerosol flux based on data from sources such as the statistical yearbooks by
governments, including activities of power generation (Kondratyev et al.,
2006; Chin et al., 2009; Zhao et al., 2012). Another method is to
estimate aerosol flux using the method of estimating gas flux (Stull,
1988), such as the Bowen ratio method (Lighthart and Shaffer,
1994). However, there are still large uncertainties in estimating the upward
aerosol flux that is transported from the ground in these two methods
(Bond et al., 2004; Kanakidou et al., 2005).
In recent years, with the wide use of instruments for measuring aerosol
particle number concentrations (such as the GP-WCPC3787 particle counter
produced by TSI), it is possible to measure the vertical transport flux of
the aerosol particle number density with the eddy-covariance (EC) method.
The vertical transport flux of aerosol particle number density (Fp) is
expressed as the cross-correlation between vertical wind velocity (w′) and
aerosol particle number density (N′) (Ripamonti et al., 2013).
Fluctuations in the vertical velocity and aerosol particle number density
must be measured simultaneously at high temporal resolutions to provide an
aerosol particle number flux.
Measurements of aerosol vertical transport flux using the EC method have
been carried out recently in many cities including Stockholm
(Vogt et al., 2011b), Helsinki (Ripamonti et
al., 2013), Lecce (Samain et al., 2012), Munster
(Pauwels et al., 2008), and London (Harrison et al., 2012). The EC method
has also been used to determine the aerosol particle number concentration
flux at other sites, such as sea-salt aerosol concentration flux
measurements in Northern Europe (Brooks et al., 2009; Sproson et al., 2013).
These measurement capabilities have provided new insights about atmospheric
aerosols, such as a strong correlation between atmospheric aerosol particle
flux and traffic flow rate in urban areas (Järvi et al.,
2009), characteristics of sea-salt aerosol transportation, and the
physical-chemical properties of aerosols (Nemitz et al.,
2009). The measurements were mostly taken in cities that have key
anthropogenic sources. Urban measurements are easy to obtain with high
reliability and can be used as routine model inputs. Although an urban
aerosol particle number flux has been measured with the EC method, the
results represent an aerosol particle number flux only at a single point.
However, the underlying surface in urban areas is very complex, with a large
horizontal inhomogeneity, and single-point measurements are not very
representative. Therefore, the development of a new measurement system to
provide an aerosol flux representing a larger spatial region is important.
Furthermore, the parameter measured by the EC theory is the aerosol particle
number flux, which is often dominated by a high concentration of smaller
particles. However, for many applications, the aerosol mass flux is more
important.
The sensible heat flux measurements made by the EC method are mature and
widely used (Lee, 2004). However, the sensible heat flux can also be
measured by a general large aperture scintillometer (LAS) based on the
similarity theory and the light-propagation theory (Zeweldi et
al., 2010). This inspired us to explore the potential to measure aerosol
flux using the similarity theory and the light-propagation theory with a
LAS.
We recently measured the imaginary part of the AERISP based on the light-propagation theory (Yuan et al., 2015). The results showed
that the imaginary parts of the AERISP were related to the turbulent
transport process and the spatial distribution characteristics of aerosols.
The atmospheric equivalent refractive index (AERI) depends on scattering and
absorption of aerosol particles (Barrera et al., 2007; Calhoun et al.,
2010; van de Hulst, 1957), and should be related to the mass concentration of
aerosol particles. Therefore, similar to the fact that the temperature
structure parameter can reflect the sensible heat flux, the imaginary part
of the AERISP may reflect the aerosol mass flux. This paper will present a
new method based on this consideration and present the results from field
measurements.
Section 2 provides the theory and methods for the aerosol mass transport
flux measurement. The experiment is introduced in Sect. 3. Section 4
presents the field observational results, and a conclusion and discussion
are presented in the final section.
Theory and methodTheory of aerosol mass flux measurement
Experiments showed that small aerosol particles followed the same laws of
turbulent motion as air molecules, that is, the fluctuation of the particle
concentration followed the “-5/3” power law under unstable atmospheric
stratification, and the concentration-velocity co-spectra for particle number
flux followed the “-4/3” power law (Mårtensson et al., 2006; Vogt et
al., 2011a; Kaimal et al., 1972). Therefore, the distribution of small particles
can be regarded as a passive conservative quantity, just like the
temperature field. Then, at the separation (r) of the order of inertial
subrange scales, the aerosol mass concentration (denoted as Ma)
structure function (DM(r)) in a locally isotropic
field follows the “2/3 law” (Wyngaard, 2010) and can be expressed as
DM(r)=[Ma(x)-Ma(x+r)]2‾=CM2r2/3,
where r is the separation vector, x is
the position vector, CM2 is the aerosol mass concentration
structure parameter, and the overbar in Eq. () indicates the spatial
average. Based on field experiments (Mårtensson et al., 2006; Vogt et al.,
2011a), the mass concentration in the surface layer will follow the
similarity theory (Obukhov, 1971; Wyngaard et al.,
1971):
CM2z2/3M∗2=η(zL),
where z is the effective height above the reference plane (Evans and De
Bruin, 2011; Hartogensis et al., 2003), L is the Monin-Obukhov (M-O) length
and is defined as L=T¯u∗2κgT∗=-T¯u∗3κgθ′w′‾ (Stull, 1988), T¯ is the average temperature, u∗ is the friction velocity, T∗ is the surface-layer
temperature scale, κ is the Karman constant, which is 0.4, g is
gravity acceleration, and w′θ′‾ is the
cross-correlation between the vertical turbulent velocity and temperature
fluctuation. M∗ can be regarded as the atmospheric aerosol mass
concentration scale in the surface layer, which is similar to the
surface-layer temperature scale. The stability function (η(zL)) can be expressed as in the following form depending on the
stability condition (DeBruin et al., 1995):
η(zL)=4.9(1+9zL)-2/3
for unstable conditions (z/L < 0), and
η(zL)=4.9(1+2.75zL)
for stable conditions (z/L > = 0) (Wyngaard
et al., 1971).
Equation () has the same form as the similarity theory
(Obukhov, 1971; Wyngaard et al., 1971) for the
temperature structure parameter (CT2) with the condition of free
convection in the surface layer:
CT2z2/3T∗2=η(zL).
Similar to the expression of heat flux (Q=θ′w′‾=-u∗T∗) (Stull, 1988), the aerosol mass flux can be
expressed as Fa=-u∗M∗, which is used to obtain
aerosol flux from measurements. From Eqs. () and (), we have
Fa=-(CM2CT2)1/2u∗T∗.
When the free convection approximation (-zL≫1) is assumed,
based on the similarity theory (Wyngaard et al., 1971)
and the definition of M-O length, we can obtain
Fa=a(gT¯)1/2(CM2)1/2(CT2)1/4z,
where the coefficient a can be set as 0.567 (DeBruin et al., 1995; Lagouarde
et al., 2006). Equations ()–() are the theoretical basis for the aerosol
mass flux measurements.
Measurement methods
The variables CT2 and CM2 in Eqs. ()–() can be derived from
the real and imaginary parts of the AERISP as Cn,Re2 and
Cn,Im2, respectively (Yuan et al., 2015).
The real part of the AERI (nRe) for a visible optical wave is
(Hill, 1978):
nRe=77.6×10-6×(1+7.52×10-3λ2)P¯T¯,
where P¯ is the atmospheric pressure (hPa) and λ is the
work wave length (µm). Then, we have
CT2=RTN2Cn,Re2,
where the coefficient RTN=1.29×104×(1+7.52×10-3λ2)-1T¯2P¯.
The gases and aerosol particles in the atmosphere as a whole can be regarded
as an equivalent medium, and its equivalent refractive index is called the
atmospheric equivalent refractive index (AERI). The AERI consists of the
real part (nRe) and the imaginary part (nIm). For the atmosphere
transparent band, nRe mainly depends on atmospheric temperature, and
nIm depends on aerosol extinction (details are given in the Appendix A).
For a given wavelength (λ) (usually constant in an experiment),
nIm is related to the chemical composition, concentration and size
distribution of aerosol particles. From the results of the numerical
calculation (Jennings et al., 1978, 1979), even if the
concentration of the aerosols is constant, the aerosol extinction changes
with the refractive index and size distribution of the aerosols. Therefore,
we can conclude that the AERI changes with the refractive index and size
distribution of aerosols even if the concentration of aerosols is constant.
In other words, a simple relationship, or a one-to-one corresponding
relationship, does not exist between nIm and the mass concentration of
aerosols (Ma). However, experimental results (Cachorro and Tanre,
1997) showed that nIm (or βe, the aerosol extinction
coefficient) and Ma have a good linear relationship (see Sect. 4.2).
We can define a parameter as the ratio of the aerosol mass concentration
Ma to the imaginary part of the AERI (nIm):
RMN=ManIm.
Theoretical analysis has shown that RMN is related to the aerosol
particle refractive index, mass density of the aerosol particles, and
particle size distribution. For near-surface aerosols at a given location,
we can treat RMN as a constant because of the relatively small
variations in particle size and aerosol refractive index
(Dubovik et al., 2002). Then, there is a simple
linear relationship between CM2 and Cn,Im2. Based on Eq. (), the relationship is
CM2=RMN2Cn,Im2.
To obtain RMN, measurements must be taken for Ma and nIm.
Ma is easily available from regular particle air quality measurements
with several standard instruments (Gebicki and Szymanska, 2012; Wang et
al., 2012), such as the beta ray attenuation method. Based on the definition
of the aerosol extinction coefficient (βe) (Liou,
2002; van de Hulst, 1957), nIm can be obtained from the relationship
between nIm and the aerosol extinction coefficient (βe)
(seen in the Appendix A):
nIm=λβe4π,
where βe can be obtained from the visibility measurements
(Qiu et al., 2004):
βe=3.912LV(0.55×10-6λ)α,
where α is the Angstrom exponent and is usually set to 1, λ
is the work wave length (µm) for the visibility measurements.
Based on the relationship between βe and nIm in Eqs. ()–(), we obtain
nIm=0.55e-64π⋅3.912LV,
where the unit of visibility (LV) is m. Thus, we can obtain
nIm from visibility measurements.
Cn,Re2 and Cn,Im2 can be measured by a specially made LAS
(Yuan et al., 2015). After a spherical wave propagates over
a distance in a turbulent atmosphere, the light intensity on the receiving
end will fluctuate. When the attenuation caused by scattering and absorption
along the propagation path is very weak, light intensity fluctuation depends
on the fluctuation of the real part of the AERI along the propagation path.
When the attenuation caused by scattering and absorption along the
propagation path is relatively strong, the light intensity fluctuation is
also related to the fluctuation of the imaginary part of the AERI along the
propagation path. With the spectral analysis method, the LAS light intensity
fluctuations can be separated into the contributions of the real and
imaginary parts of the AERI. The contribution of the real part of the AERI
corresponds to the high frequencies, whereas the contribution of the
imaginary part of the AERI corresponds to the low frequencies, suggesting
that the variances resulting from the real and imaginary parts are
independent. Therefore, the light intensity variances induced by the real
and imaginary parts can be detected separately at high frequencies and low
frequencies from the LAS measurements (Yuan et al., 2015). The real part of
the AERISP (Cn,Re2) can be calculated from the variance of the
high-frequency part, and the imaginary part of the AERISP (Cn,Im2)
can be calculated from the variance of the low-frequency part. According to
the relationship between the temperature and the real part of the AERI,
CT2 can be obtained from the real part of the AERISP (Cn,Re2).
Similarly, CM2 can be obtained from the imaginary part of the
AERISP (Cn,Im2). Although the LAS was widely used to measure the
sensible heat flux along the propagation path, only the high-frequency part
of the light intensity fluctuation could be provided, and the low-frequency
light intensity was often discarded (Solignac et al.,
2012). Thus, a specially designed LAS (see details in Sect. 3) was needed
(Yuan et al., 2015).
To apply Eq. () to obtain the aerosol mass flux, the friction velocity
(u∗) and the surface-layer temperature scale (T∗) in Eq. () were needed, which can be determined from the wind speed (U(z))
and CT2 measurements. Based on the surface similarity theory for
wind speed, the friction velocity (u∗) can be expressed as
u∗=κU(z)lnzz0-3ln(1+1+3.6z/L2/31+1+3.6z0/L2/3)
for unstable conditions (z/L < 0) (Wilson, 2001), where z0 is
the roughness length, and
u∗=κU(z)ln(zz0)+4.7(zL)
for stable conditions (z/L > 0) (Stull, 1988).
The variables u∗ and T∗ can be calculated iteratively
using Eqs. (), (), (), (), and () from CT2 and wind velocity
(U(z)) at an effective height (z) (Samain et al., 2012). The
variables u∗ and T∗ can also be calculated as u∗2=(u′w′‾)2+(v′w′‾)2 and
T∗=-θ′w′‾/u∗ (Stull, 1988). The
cross-correlations between the turbulent velocity components (u′w′‾,v′w′‾and u′v′‾) or between
the turbulent velocity components and the temperature fluctuation
(u′T′‾,v′T′‾and w′T′‾)
can be calculated from the data collected from a 3-D sonic anemometer
(u′,v′,w′andT′). Then, the Monin-Obukhov (M-O) length (L) can
be calculated based on the definition of M-O length (Stull,
1988; Wyngaard, 2010).
Although u∗ and T∗ can be obtained for the aerosol mass
flux from measurements, Eq. () is more attractive because fewer variables
are needed if a large error is not introduced by the free convection
approximation. According to Kohsiek (1982), Eq. () can be applied down
to -z/L > 0.02. In Eq. (), Fa is proportional to the product
of the square root of Cn,Im2 and one-quarter of the power of
CT2. That is, the aerosol mass flux is related to both the spatial
distribution of the aerosol and the turbulence strength. It can also be seen
from Eq. () that the aerosol mass flux is related to RMN, which is
related to the aerosol type and size distribution. Based on the surface
similarity theory, Cn,Im2 and CT2 are both
proportional to the four-thirds power of the effective height (z), so the
aerosol mass flux does not vary with height, but the effective height (z)
must still be carefully estimated. The method to estimate the effective
height (z) is the same as the method for estimating the sensible heat flux
with a LAS (Evans and De Bruin, 2011).
Measurement and data processing
Experiments were conducted at two sites, shown as the shadow part and point
P in the southern part of Hefei City in Fig. 1a. The shadow part in Fig. 1a is the campus of USTC (the University of Science and Technology of
China), which was the location for the light-propagation experiments, and
point P represents the location for determining the aerosol mass
concentration (Ma) and visibility (LV).
Figure 1b displays the measurement site on the USTC campus corresponding
to the shadow part in Fig. 1a. The measurement site is a typical urban
surface in the area. The roads near the campus often have heavy traffic. One
road to the west of campus is a viaduct, and one road to the north of campus
has eight lanes. The two roads are two arterial highways in Hefei City.
There are trees and four-story buildings across most areas of the campus,
and the mean height is approximately 1 m; therefore, a plane at a height of
15 m can be the reference plane. The roughness (z0) is derived from
Chen's method (Chen et al., 1993). Eventually, average values
of z0= 0.96 m were used for the measurement site.
The LAS measurements were performed between one building with a height of 55 m
(symbol A in Fig. 1b) and another with a height of 62 m (symbol B in
Fig. 1b) The distance between the two buildings was 960 m. The transmitter
of the LAS was placed at building A, and the receiver was placed at building
B. The propagation path was along the south-north direction. The experiments
were conducted on the 10th floor of the two buildings, 18 m above the
reference plane. For a typical LAS measurement, the measurement height is a
very important physical quantity and should be carefully measured and
calibrated (Evans and De Bruin, 2011; Hartogensis et al., 2003). For our
measurement of aerosol mass flux, the effective height is also a very
important parameter and can be calculated as 18.0 m. The signal measured by
the LAS to retrieve the heat flux had a relatively large weight in the
middle of the propagating path (Wang et al., 1978). The
sonic anemometer measurements showed that the turbulence characteristics
over the campus did not exhibit significant inhomogeneity. The measurement
height of 18 m above the reference plane was high enough to meet the
isotropy assumption (Mårtensson et al., 2006).
The LAS was built at USTC based on an instrument concept initially developed
by Wang et al. (1978), and the light wavelength was 0.625 µm. Our LAS was very similar to the LAS used to measure the
surface-layer sensible heat flux (Moene et al., 2009; Kleissl et al.,
2008). The LAS for measuring surface-layer sensible heat flux often discards
the electronic component with a frequency lower than 0.2 Hz (Kipp and
Zonen, 2007). The bandwidth of the amplifier for our LAS receiver ranged
from 0.001 to 250 Hz, and the output signal was sampled at a frequency of
500 Hz. The unprocessed raw data files were saved in 20 min intervals. The
diameters of transmitting and receiving apertures of our LAS were both 0.18 m. The emitted light converged on a transmit lens so as to reduce the
divergence angle and then propagated over 960 m to the receiver. A
photodetector was placed at the focus of the receiving lens, which transfers
light intensities to electrical signals. The electrical signals were
demodulated and amplified by an amplifier. More details about our LAS can be
found in the previous paper of Yuan et al. (2015).
A meteorology tower was installed on the roof of a building (symbol C in
Fig. 1b). The tower was close to the light path, and the top was 18 m
above the reference plane. A Campbell CSAT3 anemometer (manufactured in
Utah, USA) was mounted to the top of the tower at the same height as the
light path. Three-dimensional velocities and temperature fluctuations were
sampled and recorded at 10 Hz and can be processed to provide the sensible
heat flux, momentum flux, and stability near the surface every 30 min. The
measurement data were used to obtain the dimensionless parameter z/L in the
surface layer. Sensors for wind speed, wind direction, temperature and
humidity were mounted at three levels on the tower, the uppermost level of
which was at the top of the tower. The meteorological data were sampled
every minute, averaged and saved every 20 min.
At site P in Fig. 1a, approximately 3 km from the USTC experimental site,
the mass concentrations and visibility data were measured at a height of 6 m
above ground. The aerosol mass concentrations were recorded for Ma in
Eq. () every hour. The visibility data were recorded every 10 min and
averaged hourly.
The measurement period was from 20 to December 29 2014, a
total of 10 days. The weather remained sunny during the experiment, and the
typical properties of aerosol mass vertical transport were easy to
determine.
Experimental results
To estimate the urban aerosol vertical transport flux, we measured the
meteorological conditions, aerosol mass concentration, visibility, and real
and imaginary parts of the AERISP. Finally, we calculated the aerosol mass
flux.
Temporal variations in the (a) wind speed, (b) wind direction,
(c) air temperature, (d) relative humidity (RH) and (e) dimensionless parameter
(z/L) observed during 20–29 December 2014. The dashed line in (c) denotes RH
80 %, and the dotted line in (c) denotes RH 60 %. The dotted line in
(e) denotes z/L= 0. Details can be found in the text.
Meteorological conditions
To better analyse the characteristics of aerosol vertical transport flux, we
provided meteorological conditions during the experiment in Figs. 2a–e,
including temperature, humidity, wind speed, wind direction and the
dimensionless parameter z/L. Figure 2a shows that 90 % of the wind speed
was less than 3 m s-1, and the maximum wind speed was 5.7 m s-1. As
shown in Fig. 2b, all wind directions were detected, with easterly and
westerly wind dominating. The statistical characteristics of wind speed and
wind direction were near the annual mean distributions and are
representative of the region. Figure 2c provides the temperature variation
with time, showing clear diurnal variations. The highest air temperature was
14.9 ∘C, and the lowest air temperature was 0.76 ∘C.
During the experimental period, it was warm compared to the local
temperature climatology, while industrial production and other daily
activities were normal. Figure 2d shows the temporal variations in
relative humidity. As we know, relative humidity is an important factor that
controls aerosol particle growth (Flores et al., 2012; Winkler, 1973).
Therefore, to study the transport flux of dry aerosol mass from different
surface aerosol sources, only measurements with a relative humidity less
than 60 % were used in the analysis to minimize the influence of the water
content in the aerosols. As shown in Fig. 2d, the relative humidity was
less than 60 % during most of the experiment and was less than 80 %
throughout the entire experiment. Figure 2e provides the dimensionless
parameter z/L, which shows that the atmosphere was experiencing unstable
stratification during the day and was stable during night. The turbulence
during the unstable conditions in the surface layer significantly
contributed to the vertical transport of heat, mass, and water vapour
(Stull, 1988).
Ratio of aerosol mass concentration to the imaginary part of the AERI
RMN in Eq. () is the ratio of the aerosol mass concentration to the
imaginary part of the AERI. Theoretical analysis showed that RMNis
related to the refractive index, mass density of the aerosol particles, and
aerosol particle size distribution. Figure 3 presents the temporal
variations of mass concentration (Ma) and visibility (LV) in the
surface layer. The maximum Ma was 712 µg m-3, and the mean
Ma was 67 µg m-3. The maximum visibility(LV) was 31 km, and
the mean was 13 km. The imaginary part of the AERI can be calculated from
the visibility using Eq. () and is presented in Fig. 4 for measurements
with a relative humidity less than 60 %. The scatter diagram of the
imaginary part of the AERI (nIm) and Ma given in Fig. 4 shows that
there is a good correlation between them, with a linear correlation
coefficient of 0.94. The linear fit given in Fig. 4 has a slope of 6216 kg m-3. Therefore, RMN was set to 6216 kg m-3 in this study to
estimate the aerosol vertical transportation flux.
Temporal variations in the aerosol mass concentration Ma(a) and
visibility Lv(b) observed during 20–29 December 2014.
Scatterplots of aerosol mass concentration Ma vs. the imaginary
part of AERI calculated from Fig. 3b by Eq. ().
Temporal variations in the real part of the AERISP (a), and
imaginary part of the AERISP (b) observed during 20–29 December 2014.
Temporal variations in the mass flux of aerosol observed during
20–29 December 2014.
Comparison of aerosol mass fluxed based on the basis of similarity
theory (ST) and the free convection (FC) approximation under three different
stability conditions (z/L < -0.15, -0.15 < z/L < 0 and
z/L > 0).
Temperature structure parameter and the imaginary part of the AERISP
To calculate the aerosol mass flux from Eq. (), the temperature structure
parameter and the imaginary part of the AERISP must be measured. The
temperature structure parameter can be obtained by measuring the real part
of the AERISP. Figure 5 shows the temporal variations of Cn,Re2 and Cn,Im2.
Cn,Re2 in Fig. 5a exhibits a
general diurnal variation (Stull, 1988), indicating that
turbulence was strong during the day and weak during the night.
Cn,Im2 did not show the typical diurnal variation. The
previous study showed that Cn,Im2 is related to both the turbulence
strength and the pollution distribution (Yuan et al.,
2015).
Aerosol mass flux
With the above-measured parameters, the aerosol mass flux can be calculated
based on Eq. () and is presented in Fig. . The aerosol mass flux
exhibited an obvious diurnal variation. The strong aerosol mass upward
transport occurred at noon, while the weak transport occurred during the
night. The aerosol upward transport was also strong during the local traffic
rush hours every day (06:00–9:00 and 17:00–19:00), especially in the mornings
of 22 and 29 December 2014, suggesting an increased number of vehicles on
Monday mornings. During the experimental period, the mean value was 0.004 mg m-2 s-1 with a maximum aerosol mass flux of 0.017 mg m-2 s-1.
A comparison between Fa calculated by using the surface similarity
theory (ST) with Eq. () and by using free convection approximation
(abbreviated as FC) with Eq. () is shown in Fig. 7. According to Lagouarde
et al. (2006), stability can be classified as z/L < -0.15, -0.15 < z/L < 0 and z/L > 0 for
unstable, weakly unstable and stable conditions, respectively. The
comparison shows that scattering was a little large under stable and weakly
unstable conditions, and the relative errors were 31 and 21 %,
respectively. A good agreement was shown under unstable conditions with the
relative error about 5 %. All of the data together gave a relative error
of approximately 8 % with a coefficient of determination (or R2) of
0.92. The overall small error indicates that Eq. () for FC approximation is
very attractive from a practical point of view because it allows one to
compute the flux without needing any extra meteorological measurements. For
the LAS for heat flux, the sign for the heat flux should be determined
(Samain et al., 2012), but for our LAS measurements, the aerosol
mass flux was always upward because the aerosol source was at the surface.
Although there are no direct measurements for aerosol mass flux for
comparison, the aerosol mass flux measurements can be compared to the
aerosol particle number flux using the EC method with a few assumptions.
Järvi et al. (2009) measured the aerosol particle number
flux from July 2007 to July 2008 near a road in Helsinki, Finland. The main
pollution source in Helsinki is vehicle emissions. According to Fig. 5 in
their paper, the maximum aerosol particle number flux was approximately
663 × 106 m-2 s-1 and occurred at noon in the urban
areas during the winter season as well. It is reasonable to assume that
urban aerosol is mainly composed of fine particles, and the aerosol particle
volume distribution can be described by lognormal distributions with a
median diameter of 0.3 µm and geometric standard deviation of 1.7 (Dubovik et al., 2002). Furthermore, assuming that
the mass density of aerosol particles is 1.46 × 103 kg m-3 (Yin et al., 2015), Järvi et al. (2009) observed a
maximum aerosol particle number flux that corresponded to a maximum aerosol
mass flux of approximately 0.0092 mg m-2 s-1. Although this was
approximately half the maximum mass flux observed in Hefei City, the two
measurements are comparable considering that Hefei City is much more
polluted than Helsinki most of the time. Although this was not a
side-by-side comparison, it indicated that the new method presented here was
reasonable.
Conclusion and discussion
Based on the similarity theory and the light-propagation theory, a new
method was developed to quantitatively estimate the aerosol mass flux in the
urban surface layer. The similarity theory and light-propagation theory can
be applied to aerosol transport in the surface layer, which required the
aerosol particles to be small enough to follow the movement of air and the
size distribution of the aerosol particles to remain unchanged. For aerosols
with a residence life in the boundary layer longer than 1 hour, this
requirement was well satisfied. Although there are coarse particles in the
source regions (Dubovik et al., 2002), they
typically fall out quickly.
The estimations for the aerosol mass flux by the proposed method require
experimental measurements of the following parameters: the temperature
structure parameter, the imaginary part of the AERISP and the ratio of the
aerosol mass concentration to the imaginary part of the AERI. According to
the 10-day measurements, the aerosol mass vertical transport flux showed the
typical diurnal variation. During the experimental period, it was mainly
sunny. Thus, the convective turbulence greatly contributed to the aerosol
mass flux and resulted in a large aerosol mass flux during the day.
Moreover, the aerosol mass flux was higher during local traffic rush hours.
The measurement site was in Hefei City. The city has a population of
approximately 3 500 000 and more than 600 000 vehicles. Thus, vehicle
emissions provide one of the main pollution sources. Our results indicated
that the vertical transport flux of aerosol mass was controlled by both the
turbulence transport and aerosol emissions, which was physically expected.
Although there were no other direct measurements available for comparison,
the measurements were indirectly compared to the aerosol particle number
flux measured by the EC method at another location, which revealed a
comparable maximum mass flux. In the near future, we will explore
side-by-side comparisons. Compared to the EC method, measuring aerosol mass
flux with the light-propagation method had some advantages, such as no need
to build a high tower and offering a large spatial coverage.
The error in the aerosol mass flux measurements resulted from theory and the
instruments. Similar to the LAS for measuring sensible heat flux at the
surface layer, instrument measurement error may be attributed to electronic
or optical problems, which include a poor focal alignment of the receiver
detector and the transmitter diode, calibration of electronics, and the
effective diameter of the LAS transmitter and receiver (Moene et al.,
2009; Kleissl et al., 2008, 2009). These errors can be
minimized through careful experiment setup and data quality control.
Theoretical error sources come from the invalidity of the surface-layer
similarity theory under certain conditions, the occurrence of significant
large aerosol particles, and the variations of between nIm and
Ma relationship. Under neutral and stable conditions, the sensible heat
flux is difficult to assess with a LAS (Pauwels et al., 2008; Samain et
al., 2012). Unlike the sensible heat flux, the aerosol source is often at
the surface, and the aerosol vertical transport flux under the stable
condition was very weak. Measurement results were in accordance with fact.
Thus, lacking accurate aerosol vertical transport flux under the stable
condition did not introduce significant error in overall aerosol mass flux
estimations. The ratio of the aerosol mass concentration to the imaginary
part of the AERI was assumed to be constant, which is a reasonably good
assumption for a given location with a dominant aerosol type, such as urban
aerosols. However, the variations in the ratio RMN will introduce
errors into the aerosol mass flux measurements. The ratio RMN depends
on the refractive index and size distribution of aerosol particles.
Therefore, the ratio can be determined locally when the approach is applied
to different locations. Of course, if there are some variations in the
aerosol particle refractive index and particle size distribution, RMN
can be obtained by simultaneously measuring Ma and the imaginary part
of the AERI, so that real-time RMN can be obtained. The large
aerosol particles cannot follow the movement of air well
(Seinfeld and Pandis, 2006; Vogt et al., 2011a),
which is one of the error sources for aerosol mass flux measurements.
However, these large aerosols fall out very quickly and have a small impact
on estimated aerosols, which can stay in the atmosphere for a day. All of
these error estimations should be discussed quantitatively in the future.
Atmospheric equivalent refractive index (AERI) and aerosol mass
concentration
When the gases and aerosol particles in the atmosphere are considered as a
whole, the AERI neff can be written as follows (van de Hulst,
1957; Barrera et al., 2007; Calhoun et al., 2010):
neff=nm+ik2π(nmk)2∫0∞S(0)dNdDdD.
Equation (A1) includes two parts. The first is the contribution of air
molecules, where nm is the air refractive index. The second
represents the scattering and absorption of aerosol particles, where k is the
light wave number (k= 2π/λ, where λ is the work
wavelength) and i is an imaginary number. S(0) is the aerosol forward
scattering function (0 in the parentheses represents the scattering angle of
zero), which can be calculated from the Mie scattering theory. N is the
number of aerosol particles per unit volume, D is the aerosol diameter, and
dN/dD is the size distribution function of the aerosol particles.
For the atmosphere transparent band, the absorption of gases can be ignored
because the extinction caused by molecular scattering is relatively small
compared with that caused by atmospheric aerosols in the urban area.
Therefore, there is only the real part of the refractive index of air in Eq. (A1).
The real and imaginary parts of the AERI (nRe and nIm, neff=nRe+i⋅nIm) can then be derived as
nRe=nm-1k2π(nmk)2∫0∞Im[S(0)]dNdDdDnIm=1k2π(nmk)2∫0∞Re[S(0)]dNdDdD.
As shown in Eqs. (A2)–(A3), nRe is determined by the refractive index
of air, the imaginary part of the forward scattering function of aerosol
particles, and the distribution ofthe aerosol particles. nIm is
determined by the real part of the forward scattering function of aerosol
particles and the distribution of the aerosol particles. According to the
magnitude comparisons and the variation ranges of the two terms in Eq. (A2),
nRe is mainly determined by the refractive index of air (Liou,
2002; Tatarskii, 1961). Thus, the second term on the right-hand side of Eq. (A2) can be ignored.
According to the theory of small particle scattering (Liou, 2002), the
extinction cross section of one particle is given by (Eq. (5.2.92) in Page
189 in Liou's book),
σe=4πk2Re[S(0)].
So, for aerosols with a size distribution of dN/dD, the total extinction
coefficient is
βe=4πk2∫0∞Re[S(0)]dNdDdD.
A comparison between Eqs. (A3) and (A5) shows that there is a
relationship between nIm and the aerosol extinction coefficient
(βe), i.e. nIm=λβe/4π (Liou,
2002). Thus, the variable nIm in Eq. () corresponds to the extinction,
which is the sum of the contributions of scattering and absorption.
The aim of analysing the imaginary parts of the AERI (nIm) is to
obtain information about the aerosol mass concentration. The mass
concentration of aerosols, Ma, can be expressed as
Ma=ρ16π∫0∞D3dNdDdD,
where ρ is the mass density of the aerosol particles.
Acknowledgements
This study was funded by the National Natural Science Foundation of China
(41475012) and partially by the Jiangsu Provincial Collaborative Innovation
Centre of Climate Change. We also thank two anonymous reviewers for their
constructive and helpful comments.
Edited by: P. Xie
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