Introduction
Aerosols, and their interaction with clouds, play a key role in
the climate of our planet. Additionally, measurements of aerosols are crucial
to a wide range of direct applications, ranging from the monitoring of clean
rooms to the impact of air quality on public health. Despite the importance
of these particles, obtaining accurate in situ measurements of their optical and
microphysical properties has remained a significant challenge.
Optical techniques of particle sizing typically capitalize on the
approximately monotonic increase in the amount of light scattered by a single
particle as a function particle size. These instruments are among the most
widespread and precise available, but the vast majority of optical particle
counter (OPC) designs require significant assumptions about the aerosol being
sampled. These simplifications result from the limited information content
present in typical OPC measurements, which frequently sample scattered light
over a single angular range, often 4 to 22∘ or
roughly 30 to 150∘ in so called wide angle OPCs. These
assumptions, generally regarding real refractive index, absorption and
particle morphology can lead to significant biases in the resulting particle
size distributions (PSDs) and generally constitute the bulk of the measurement
error . Additionally, in situ measurements of many of
these characteristics, like aerosol refractive index or particle sphericity
for example, are still virtually nonexistent, especially at altitudes far
from the surface.
A less common approach to characterizing particles is through polar
nephelometer measurements of light scattering from an ensemble of particles
over a large number of angular regions. This approach provides a large amount
of information about the sample, reducing the total number of assumptions
required and the resulting biases in the retrieved products. Unfortunately,
deploying field instruments with these capabilities can be quite challenging,
and airborne measurements of common aerosols using this technique have
previously been unavailable. Additionally, the inversion of multiangular
data is significantly more complex than the inversion of light-scattering
intensity over a single angular range.
In spite of the complexities associated with multiangle measurements and the
corresponding inversions, there have been several successful attempts over
the past four decades to retrieve particle properties from polar nephelometer
data. The first published inversion of this kind was made by Eiden in 1966,
who used multiwavelength polarization data to retrieve the complex
refractive index of an ambient aerosol, as well as match one of three
predefined aerosol PSD models . used
intensity measurements to size monodisperse, polystyrene latex (PSL) spheres,
as well as to determine their complex index of refraction. Intensity and
polarization measurements of ambient aerosols made by the Tohoku University
single wavelength polar nephelometer in Sendai, Japan have been inverted to
obtain complex refractive index and number concentrations in six log-spaced
size bins . There have also been attempts to
retrieve only the refractive index, while constraining the model's size
distribution with a traditional particle sizer .
The converse approach was reported by , who took polarized
measurements of sea spray and determined PSD by assuming a refractive index
value expected for sodium chloride particles at the ambient relative
humidity. Most recently, obtained both complex
refractive index and PSD from three-wavelength intensity measurements made
with a commercially available polar nephelometer. All of these retrieval
efforts have assumed spherical particles, and all measurements were made in
the visible spectrum, except in the case of , who used
measurements made in the near-infrared. The only polar nephelometer
retrievals to incorporate a nonspherical component in the scattering model
were performed by , who fit laboratory measurements of
desert dust.
In this work we apply a complex inversion algorithm, specifically the
Generalized Retrieval of Aerosol and Surface Properties (GRASP), to airborne
and laboratory measurements made with the Polarized Imaging Nephelometer
(PI-Neph), a multiwavelength, multiangle light-scattering instrument. The
GRASP retrieval makes no assumptions about the number of modes in the size
distribution or the complex refractive index, and it allows for both
spherical and spheroidal scatterers. This represents a significant increase
in complexity when compared to previous in situ scattering inversions. In
addition to the generality of the retrieval, this work represents the first
time that any aerosol retrieval algorithm has been applied to airborne polar
nephelometer measurements. Furthermore, the ambient airborne measurements
presented here were made in parallel to a large variety of independent
instrumentation, allowing for very robust intercomparisons of the retrieved
products.
Inversion methodology
Aerosol-scattering matrix elements are measured in situ with a polar
nephelometer and feed into a microphysical retrieval algorithm in order to
obtain aerosol size distribution, complex refractive index (m) and a
percentage of spherical particles. These measurements include a combination
of artificially suspended laboratory data as well as airborne data taken over
the continental United States during the Studies of Emissions and Atmospheric
Composition, Clouds and Climate Coupling by Regional Surveys
(SEAC4RS) field experiment in 2013. GRASP, a versatile open
source software package
(http://www.grasp-open.com) capable of
performing inversions on a wide variety of atmospheric optical measurements,
was used to obtain the retrieved microphysical parameters. A detailed
description of the GRASP retrieval algorithm and its capabilities can be
found in .
The PI-Neph instrument concept. Figure adapted from .
Polarized Imaging Nephelometer
In an effort to advance in situ characterization of atmospheric aerosols, the
Laboratory for Aerosols, Clouds and Optics (LACO) at the University of
Maryland, Baltimore County (UMBC) has developed a novel instrument concept
called the Imaging Nephelometer . The imaging nephelometer
design, first realized in the PI-Neph, uses a wide field of view charge
coupled device (CCD) camera to image the light scattered by aerosols in the
path of a high-powered continuous wave laser. This setup permits the
construction of an instrument that is compact and stable enough to be flown
on a variety of airborne platforms, while still allowing for measurements of
scattering matrix elements over an angular resolution and range that is
comparable to state of the art laboratory techniques .
A detailed schematic of the PI-Neph design is shown in Fig. . The aerosol sample inside the PI-Neph is illuminated
sequentially by a three-wavelength laser system operating at 473,
532 and 671 nm. The three beams are aligned by a system of
dichroics and mirrors before having their polarization state precisely
oriented by a Glan-Taylor linear polarizer. A liquid crystal variable
retarder (LCVR) and Fresnel rhomb are then used to actively rotate the
polarization state of laser light. After exiting the rhomb, the beam is
guided by two mirrors, through a window into a 10 L sealed chamber
containing the aerosol sample. The laser light traverses the length of the
chamber before a corner cube retroreflector redirects the beam back into a
beam trap adjacent to the entry window. The light scattered by the aerosol
and surrounding gas is then imaged twice by the CCD camera, once for each of
two roughly orthogonal linear polarization states of the laser.
If the scattering medium is assumed to be macroscopically isotropic and
symmetric, then the scattering matrix elements F13 and F14 do not
contribute to the total scattered signal and the resulting pair of image
intensities depend only on the first two scattering matrix elements. The
images can then be processed in a manner that allows for direct measurements
of both the absolute phase function F11(θ) as well as
F12(θ), with θ representing the zenith scattering angle
(azimuthal symmetry is implied by the assumption of a macroscopically
isotopic and symmetric medium). Measurements of molecular scatterers (CO2
and N2) with absolute scattering matrix elements that are well characterized
allow for the determination of unique
calibration constants for each angle. This angular-dependent absolute
calibration allows for direct measurements of absolute phase function in
known units (Mm-1 sr-1), free from any truncation error. The final
products are then reported at standard temperature and pressure, with the
Rayleigh scattering contribution from the surrounding gas subtracted.
Additionally, normalized phases functions are represented by F̃11
in this paper and are scaled such that F̃11(30∘)=1.
The angular resolution of the measurement is limited by the spatial
resolution of the CCD camera, the size of the camera's aperture and the width
of the laser beam. The resulting raw resolution typically varies as a
function of scattering angle (0.1∘<dθ<1∘) but the final results are always binned to one degree. The
angular range of the instrument is limited by stray light emanating from the
entry and exit points of the laser beam. In the PI-Neph, an angular range of
3 to 177∘ in zenith scattering angle is
frequently achieved.
Laboratory aerosol generation instrumental setup used to suspend salts and PSL spheres.
PI-Neph measurements have been validated by a variety of methods since the
instrument's completion in the summer of 2011. Measurements of monodisperse
PSL spheres have yielded results that are in excellent agreement with Mie
theory, while scattering coefficient measurements made in parallel with
commercially available integrating nephelometers have agreed to within 5 %. A
detailed summary of PI-Neph design, calibration and validation can be found
in .
Artificial aerosol generation
Ammonium sulfate ((NH4)2SO4), ammonium nitrate (NH4NO3) and sodium
chloride (NaCl) were suspended and humidified in a laboratory setting.
Figure displays a schematic diagram of the
particle generation and measurement setup. The salts were diluted with
distilled water to a concentration of 5 g L-1 before being
agitated with an ultrasonic vibrator and later suspended using a single jet
atomizer (TSI, model 9302). The generated aerosol was diluted with filtered
compressed air before being fed into a dryer and then a humidifier. In the
first stage, generated particles are dried, without heating, to a relative
humidity less than 30 % using a Perma Pure Nafion dryer. The dry particles
are later humidified to a RH > 80 % using two Perma Pure Nafion humidifiers
(Nafion1 and Nafion2). The humidifier and dryer consist of a Nafion membrane
tubing that transfers moisture to or from the surrounding medium. The drier
uses compressed air while the air passing through Nafion 1 is humidified by
flowing water and then used to humidify the sample passing though Nafion 2.
The separation of liquid water from the Nafion tube in contact with the
aerosol sample allows for subtler control of the final relative humidity
. Angular scattering measurements of the aerosol were then
made by the PI-Neph before the sample was discharged from the system.
The humidification system was set to relative humidity values above the
deliquescence points of each salt solution, typically to an RH just over
80 %. The humidity was continuously monitored throughout the measurement
using RH sensors located at the PI-Neph's inlet, measurement chamber and
outlet. The stability and reproducibility of the particle generation was
independently validated by the proper observation of deliquescence of
different salts using an integrating nephelometer (model 3563, TSI Inc., St.
Paul, MN, USA).
This setup was also used to suspend 903nm diameter monodisperse PSL
spheres (Nanosphere 3900A, ThermoFisher Scientific, Fremont, CA, USA), and
scattering measurements of these spheres were made by the PI-Neph at low
relative humidities (RH < 20 %). These measurements provide an opportunity to
test the retrieval technique on an aerosol with a monodisperse size
distribution and a refractive index that is very well characterized. The PSL
generation and measurements also allowed for a small, subdegree realignment
of the PI-Neph scattering angle calibration in the case of the salt
measurements. This correction was not applied to the data used in the PSL
retrievals to avoid biasing the result.
Flight paths of the 10 SEAC4RS flights from which data are used in this paper. Additionally,
three specific case studies are called out with diamonds. The case studies include two biomass-burning-dominated
aerosols (blue) as well as measurements made in the boundary layer of a forested region in southeastern Missouri (green).
Ambient measurements
In addition to the laboratory measurements, inversions were performed on
airborne data from the SEAC4RS experiment.
SEAC4RS was a large field mission, that took place
primarily over the continental United States in August and September of
2013. Over the course of the experiment three aircraft flew 54 different
instruments on a total of 57 flights in an effort to understand a broad range
of atmospheric phenomenon. A detailed description of the scientific goals,
aircraft and instrumentation, as well as the corresponding implementation can
be found in .
The PI-Neph made measurements aboard the NASA DC-8 aircraft during
SEAC4RS. Ambient air was provided to the instrument through
the NASA Langley Aerosol Research Group Experiment's (LARGE) shrouded
diffuser inlet , which sampled isokinetically. A flow
of 20 L min-1 was maintained through the PI-Neph's 10 L sample
chamber, leading to an aerosol exchange time of the order of 30 s. The
raw sampling rate of the instrument was synchronized to match this interval,
but the retrievals in this work are generally performed on time averages
taken over a period of several minutes. The sample was conditioned with a
temperature-controlled drier that heated the incoming ambient air to a
temperature of 35∘C and, in almost all cases, kept the relative
humidity of the sample below 40 %.
In addition to PI-Neph scattering measurements, the LARGE group made
comprehensive in situ measurements of aerosol properties in parallel to the
PI-Neph. These measurements, containing data on particle number density, size
distribution and optical properties, are a valuable resource for the
intercomparison of PI-Neph measurements and the corresponding retrieved
microphysical properties. In this
work, size distributions retrieved from PI-Neph data will be compared extensively
to measurements made by two dedicated optical particle size spectrometers (LAS model 3340, TSI Inc., St. Paul, MN, USA and
model UHSAS, Droplet Measurement Technologies, Boulder, CO, USA) as well as
an aerodynamic particle sizer (APS model 3321, TSI Inc., St. Paul, MN, USA).
The two optical particle spectrometers also measured at low relative
humidities during SEAC4RS, but their sample was conditioned
through a drier. This approach minimizes the evaporation of volatile
compounds but can also lead to size-dependent losses in the aerosol when the
instrument requires relatively large flow rates, as is the case for the
PI-Neph. The aerodynamic particle sizer measurements were made at ambient
humidities, but the ambient RH was determined to be less than 40 % in all
cases shown here so differences in PSD resulting from hygroscopic growth are
not expected.
Fifty separate sampling periods, occurring over the course of 10 different
flights, are highlighted in this work. The flights selected represent the 10
days with the highest quality PI-Neph data, for which data are available for
at least one of LARGE's dedicated particle sizers. The intervals containing
the highest aerosol-scattering levels during these flights were identified
and a robust averaging procedure was applied to periods
for which no detectable changes in the normalized angular scattering data
were observed. The total scattering for these averages ranged from
30 to just over 500Mm-1, with a median value of
90Mm-1. The resulting data set represents a wide range of
aerosols, including urban pollution, organics and Saharan dust, and in over a dozen
cases is dominated by biomass-burning (BB) emissions with transport ages ranging
from hours to several days.
Additionally, three individual case studies were selected
to provide detailed examples of PI-Neph measurements, the
corresponding GRASP fits and the resulting retrieved size
distributions. Two of these cases come from periods
where the scattering signal was dominated by forest fire emissions, and were
chosen to emphasize the subtle distinctions in angular scattering patterns
that can occur, even between two aerosols of similar type. The third case
consists of boundary layer (BL) measurements made over a heavily forested
region of southeastern Missouri. This case represents one of only a couple of
periods in which a significant coarse mode was observed. The sampling
locations of these three cases, as well as the flight paths for the 10
selected flights, are shown in Fig. .
Implementation of GRASP retrieval
GRASP is a versatile software package capable of retrieving a wide range of
atmospheric and surface properties from a variety of data sets. The GRASP
algorithm and corresponding software builds on the successful heritage of the
PARASOL , AERONET and laboratory
retrievals.
GRASP's base aerosol model contains very few assumptions in comparison with
traditional in situ or remote sensing retrieval algorithms. It includes all
necessary components required to simulate a diverse range of atmospheric
observations, including remote sensing (both suborbital and space-based),
optical in situ and laboratory measurements. The settings of the retrieved
characteristics can be flexibly adjusted to match the particular application.
For example, aerosol size distribution can be represented as a superposition
of several lognormal functions or as a binned continuous function with
different size resolutions (it is defined in nodal points).
As an inversion concept, GRASP implements Multi-Term Least Square fitting
. This approach allows for convenient combining of
different types of observations and multiple a priori constraints in a single
inversion. For example, following this concept the AERONET retrieval
retrieves many parameters simultaneously: aerosol size
distribution, spectral complex refractive index and fraction of spherical
particles. A priori constraints on all functions (size distribution and all
spectral dependencies) are assumed to be smooth, while a priori estimates of values
are also used for some parameters. Moreover, using the same strategy, a
statistically optimized multipixel retrieval concept was realized as an
option in GRASP . This concept uses additional a priori
knowledge about time and space variability of the retrieved parameters in the
inversion of coordinated observations (i.e., satellite observations in
different pixels).
The flexibility built into the design of GRASP allows the user to select the
assumptions that best match the information content of a particular data set.
Moreover, while all of the above features have never been used in one single
application, they often provide important potential for evolution of each
application, for example via implementing synergy retrievals using a
combination of different observations. The GRASP algorithm has previously
been successfully applied to both satellite and ground-based upward-looking
sky radiance measurements , while this
paper represents the first application of GRASP to polar nephelometer data.
In this work GRASP size distributions were modeled with 16 logarithmically
spaced size bins, generally ranging from 50 nm to 2.94µm in
radius. The lower end of this range corresponds to the sensitivity limit of
ensemble-type light-scattering measurements, given realistic particle size
distributions. The upper bound was chosen to include the vast majority of
coarse-mode particles capable of passing through the LARGE inlet, which has a
50 % passing efficiency at an aerodynamic radius of 1.8µm
. This size range was reduced to radii between
425 and 476 nm in the case of the PSL spheres, in order to
better capture the fine structure of their very narrow size distribution. In
all retrievals the shape of the size distribution is only constrained by a
smoothness parameter and no assumptions about the number of modes are made.
PI-Neph measurements at 532 nm (points) with 2σ instrumental error (gray fill) and the GRASP
retrieval best fit (solid line) for ammonium sulfate measurements made in the laboratory.
(a) shows absolute F11 (Mm-1 sr-1) data plotted on a log scale, while (b) shows -F12/F11 data on a linear scale.
(c) shows the F11 differences according to the log transformation described in Eq. (),
while the conventional residuals in -F12/F11, as given by Eq. (), are plotted in (d).
The search space for the real part of the refractive index (n) is
semi-continuous between 1.33 and 1.68, while the imaginary part (k) can range
from 0 to 10-1. The refractive index is held constant with respect to
size but is allowed to vary as a function of wavelength. GRASP assumes the
aerosol is made up of a mixture of spheres and spheroids. The spheroid component
has an axis ratio distribution that is fixed and is derived from feldspar measurements made by
. It can be shown that small deviations in the spheroid
component's axis ratio distribution produces negligible changes in the
angular dependence of the scattered light . It is
therefore believed that this fixed shape distribution is capable of
accurately modeling a wide range of nonspherical aerosols. The spheroid
component was omitted from the PSL retrievals due to the computational demands
associated with generating the required precomputed kernels for the finer
size parameter grid spacing.
Normalized scattering matrix elements (circles) measured by the PI-Neph at 532 nm and the
corresponding GRASP fits (solid lines) for the three highlighted SEAC4RS aerosol samples.
Retrieval results and discussion
Measured data and retrieval fit
In both the 50 selected SEAC4RS cases and in the laboratory
measurements, the residuals between the GRASP fits and the PI-Neph measured
values are generally within the PI-Neph instrumental error. Figure shows the measured and fit F11 and -F12/F11
for the ammonium sulfate case, and is typical of the bulk of the retrievals
performed in this work. The residuals are also plotted to clearly emphasize
the differences between the measurement and fit relative to the instrument's
2σ error. In the case of the F11 data the distances between the
fit and measured values are reported as
RESF11=Log10(F11MEAS)-Log10(F11FIT),
with the PI-Neph error transformed accordingly. This transformation provides
a measure of relative (as opposed to absolute) error, and provides a
consistently sized metric across the 2 orders of magnitude covered by
F11. The separation in -F12/F11 data is represented simply as
the difference between the measured and fit values.
RESF12/F11=F12F11FIT-F12F11MEAS
Figure shows the normalized scattering matrix elements at
532 nm for the three selected SEAC4RS case studies. A
strong forward peak can be seen in the forest boundary layer measurements,
which is in accordance with the significant coarse mode observed by the
aerodynamic and optical particle sizers. The two biomass-burning cases
display very similar F11 values, with the only significant difference
being slightly enhanced forward and backward scattering in BB plume #2.
These subtle differences are likely to be driven by the slightly larger fraction of
coarse-mode particles present in the latter case. In contrast to F11,
-F12/F11 shows significant differences between the two biomass
burning cases. The reduced magnitude of -F12/F11 in BB plume #1 is
likely driven primarily by differences in real refractive index between the
two samples. This hypothesis is supported by simulations with a Mie code
which demonstrated that, in the relevant size regime,
changes in the refractive index of the order of 0.03 had little effect on
F11 but could easily change the ratio of F12 to F11 by 20 % or
more. It is this effect, in combination with the small median size of the
fine mode, that produces the highest degree of linear polarization of the
three samples in the forested boundary layer case.
The spectral dependence of F11 and -F12/F11 for the biomass
burning case study sampled on 19 August is shown in
Fig. . The absolute phase function values are shown here
to emphasize the additional information present in the spectral dependence of
the scattering intensities. It should be noted that there is also significant
spectral dependence in the shape of the scattering matrix elements,
particularly in -F12/F11. These difference are driven primarily by
changes in size parameter, but also result in some part from a nonzero
spectral dependence of the complex refractive index. The same variables are
plotted for the forested boundary layer case in Fig. to show the spectral dependence of the measured
scattering matrix elements and the corresponding fits when a significant
coarse mode is present. In this last case, low aerosol concentrations and
greater than average stray light levels inside the instrument resulted in a
gap in the 473 nm F12 measurements between 80 and
142∘ in scattering angle.
In the case of the polydisperse samples, the oscillations occasionally
present in the data over angular scales of roughly 10 degrees are likely
nonphysical, and are artifacts of insufficient sampling statistics in the coarse
mode. The extended length of the imaging nephelometer sample volume makes it
especially susceptible to sampling statistic artifacts that are produced by
the largest particles. These particles make up a very small fraction of the
total number concentration while simultaneously accounting for a
disproportionately large portion of the total scattered light. This is
especially apparent in the measurements of -F12/F11 as these values
are closely related to the differences between sequential measurements at
different polarizations. A large particle that is present at a given location
in one image, but not present in the corresponding adjacent image will
produce a significant artifact. The effect is also evident at low scattering
angles, where larger particles tend to represent a larger portion of total
scattering.
Scattering matrix elements at 473 nm (blue), 532 nm (green) and 671 nm (red)
measured in BB plume #1 on 19 August along with the corresponding GRASP fits (solid lines).
The monodisperse PSL measurements and corresponding GRASP fits (shown in
Fig. ) agree well in the case of F11. Overall
there is also good agreement in the -F12/F11 data, but some
significant deviations do occur. The GRASP size distribution retrieval for
this case had a full width, 67 percentile (FW67) of 17 nm, which is
more than twice the width specified by the manufacturer (FW67 = 8.2 nm).
However, a narrower size distribution corresponding to the manufacturer's
specification was found to reproduce some features of the measurement
significantly better than GRASP's original retrieval. This improvement was
most apparent in the 473 and 532 nm -F12/F11 data,
particularly at scattering angles between 20 and
60∘ where Mie theory predicts -F12/F11 to have high
sensitivity to the distribution's width. Further studies indicated that GRASP
was able to reproduce -F12/F11 corresponding to this narrower PSD
with high accuracy when noise-free synthetic data were used as input.
Additionally, running retrievals on the measured data using increasingly
finer size resolution kernels did not improve the retrieval's ability to fit
these features. The deviations in the fit were thus determined to be the
result of GRASP's sensitivity to certain characteristics of the noise in the
measured data, not insufficient size resolution in the fine-resolution
kernels used in the PSL case.
Predicted and retrieved real refractive indices, median radii in volume and spherical fractions for the
three artificially generated aerosols. Also shown are the deliquescence relative humidities (DRH), κ values,
and dry real refractive indices taken from the literature. All refractive indices are at 532 nm.
Compound
DRH
Measured RH
κ
r50GRASP
Sphere
ndry
nwetGRASP
nwetκKöhler
(%)
(%)
(nm)
(%)
NaCl
80
83.7±2
0.91–1.33
144
100
1.544
1.395
1.353–1.372
(NH4)2SO4
75
82.6±2
0.33–0.72
120
100
1.530
1.383
1.370–1.414
NH4NO3
62
83.5±2
0.58–0.75
129
54
1.554
1.392
1.371–1.393
Scattering matrix elements at 473 nm (blue), 532 nm (green) and 671 nm (red)
measured over a forested region of southeastern Missouri along with the corresponding GRASP fits (solid lines).
Refractive index retrievals
Crystalline particles do not take on water until reaching relative humidities
above their deliquescence point, generally around 80 % in the case of salts.
A range of methods are available for calculating the size of a given salt
droplet after the transformation to an aqueous state has been made. In this
work we choose the parameterization proposed by for its
simplicity and because the required κ parameters are well known for
the salts in question. This method states that gfvol, the volume growth
factor of a particle, can be estimated as
gfvolRH=1+κRH1-RH,
where RH is the relative humidity of the air surrounding the droplet and
κ is a constant that is determined by the composition of the particle
in question.
The dry (crystalline) refractive indices of all three salts studied in this
work are well known and the resulting wet refractive index
can be calculated from the volume mixing rule:
nwetRH=gfvol-1nH2O+ndrygfvol,
where nH2O is the refractive index of water, ndry is the
refractive index of the dry salt and nwet is the refractive index of the
solution . Alternative methods for estimating the
refractive index of hygroscopic particles exist, but their deviation from the
volume mixing rule is less than 1 % for solutions that are made up of more
than 50 % water .
Scattering matrix elements at 473 nm (blue), 532 nm (green) and 671 nm (red) for
903 nm diameter PSL sample along with the corresponding GRASP fits (solid lines).
The refractive indices predicted from Eqs. () and ()
are compared with the corresponding GRASP retrievals in Table . The ranges of κ values given for sodium chloride and
ammonium sulfate are taken from Table 3 of and were
derived from hygroscopic growth factors in the subsaturated domain. The
κ range used for ammonium nitrate are derived from measurements of
cloud condensation nuclei (CCN) at supersaturations less than 1 %, and
originate from , with the spread representing an
uncertainty of 1 standard deviation. Growth-factor-derived κ values
were not available for ammonium nitrate but the difference between growth
factor and CCN-derived κ values is generally small compared to the
uncertainty in κ resulting from measurement errors
. The range in the final predicted wet refractive indices
results from the bounds on the κ values, as well as a 2 % uncertainty
in the RH measurement made inside the PI-Neph.
The retrieved refractive index values are in good agreement with the range
predicted by κ-Köhler theory and the existing literature.
Sensitivity studies, performed on ensembles of synthetic data perturbed with
modeled PI-Neph noise, suggest uncertainties of 1 standard deviation in
retrieved real refractive indices of around 0.02 for nonabsorbing particles
in the size range of these humidified salts. These studies also showed a
general trend of increasing accuracy in the retrieved real part of the
refractive index as the median radius of the particles increased. The
converse was true for absorption, where more absorbing particles tended to
produce more error in the real refractive index inversion. The agreement
between the retrieved and predicted refractive index values is consistent
with this error analysis.
The retrieved imaginary parts of the refractive index (not shown) of the
ammonium nitrate and ammonium sulfate solutions were both found to be of the order of 10-3. These values are indicative of moderate absorption but
are larger than more established values found in the existing literature,
which suggests very little absorption (k<10-7) for all three of the
solutions measured . An even higher
imaginary part of the refractive index (k=0.026) was retrieved in the case
of the sodium chloride sample. The magnitude of this value may be, at least
in part, related to an unrealistically high retrieved real refractive index.
This hypothesis is supported by the fact that constraining the retrieved real
refractive index to the range predicted by the sample RH and
κ-Köhler theory resulted in significantly lower retrieved values
of sodium chloride absorption. A comparison was also made between the
retrieved single-scattering albedo (SSA) and the SSA derived from Particle
Soot/Absorption Photometer (PSAP, Radiance Research, Seattle, WA, USA) and
integrated scattering measurements (Integrating Nephelometer 3563, TSI Inc.,
St. Paul, MN, USA) in SEAC4RS. A statistically significant
correlation between the two data sets was determined to exist, but the
retrieved SSA was also found to systemically overestimate the measured
absorption. Notice that the retrieval was based only on scattering
measurements (no absorption or extinction data were included) and therefore is
expected to show limited sensitivity to these variables. A detailed analysis
of the sensitivity of the GRASP/PI-Neph retrieval to absorption is beyond the
scope of this work.
Retrieved real part of the refractive index for PSL spheres, alongside three previous, modern measurements of
polystyrene refractive indices .
The subplot shows the retrieved size distribution (blue) along side the manufacturer's specified central radius
(red dashes) and FW67 (red dots).
After passing their deliquescence point, crystalline salt particles should
transform into saline droplets and become spherical in shape. The
GRASP/PI-Neph inversion was able to accurately reproduce this spherical
morphology in the sodium chloride and ammonium sulfate case, but a spherical
fraction of only 54 % was retrieved for the ammonium nitrate sample. This
deviation from expectation is likely driven by a combination of random error
in the PI-Neph measurement and the fact that the scattering of nonspherical
particles tends to deviate less from that of spherical particles as particle
size decreases. This notion is confirmed in the sensitivity studies
previously described, where it was found that there was very little
sensitivity to sphericity in the case of small particles (r< 200 nm).
Retrievals of the monodisperse PSL spheres produced real refractive index
values that were within the range of existing measurements available in the
literature at all three wavelengths . The spectral dependence of the retrieved values,
as well as the three most recently reported Cauchy's equation parameterizations
of PSL refractive index can be found in Fig. . The
retrieved imaginary part of the refractive index for these spheres was of the order of 10-3 for all three wavelengths, slightly higher than the values
of around 4×10-4 that have been reported by more sensitive
techniques .
Truncation-corrected total scattering (βsca) from the integrating nephelometer as well as the GRASP retrieval of real
refractive index, sphere fraction and SSA for the three highlighted case studies. Additionally, the SSA derived from PSAP and integrating
nephelometer measurements is shown for comparison. All spectrally dependent parameters are listed at 532 nm.
Aerosol case
Date
Time (UTC)
βsca
mGRASP
SphereGRASP
SSAGRASP
SSAPSAP
BB plume #1
19 August
19:06–19:13
489 Mm-1
1.594
64.5 %
0.976
0.964
BB plume #2
27 August
21:42–21:48
95.9 Mm-1
1.565
91.0 %
0.962
0.959
Forested BL
30 August
20:55–21:12
41.9 Mm-1
1.566
53.9 %
0.908
0.930
Retrieved refractive index at all three PI-Neph wavelengths for the 50 selected SEAC4RS samples.
Box and whisker plots show the data distribution by quartile while the connected black squares show the spectral dependence
of the mean. The gray bounds at 532 nm denote the minimum and maximum values measured by
in SEAC4RS while the gray square denotes the corresponding mean.
Figure shows the spectrally dependent distribution of
the retrieved dry refractive indices for the 50 chosen
SEAC4RS cases. The mean retrieved real part of the
refractive index at 532 nm for the 50 cases, composed primarily of
biomass-burning and urban-biogenic mixtures, was found to be 1.53. This
figure is in line with the existing measurements made under similar
conditions , but unfortunately very few airborne,
in situ measurements of refractive index are available. Remote sensing
retrievals of biomass-burning aerosol generally range from 1.47 to 1.55
, while remote
retrievals of urban pollution have generally yielded somewhat lower values,
ranging from 1.39 to 1.46 . These lower
values observed in the urban-pollution remote sensing retrievals are likely
driven in large part by particle hygroscopicity. The PI-Neph/GRASP retrievals
of real refractive index are expected to be significantly higher in analogous
cases as the PI-Neph measurements were made at very low relative humidities,
where hygroscopic growth is virtually nonexistent. In spite of these
differences in measurement conditions, as well as in the sample regions in
question, the values are remarkably similar, especially in the case of
biomass-burning emissions, where hygroscopic influences are expected to be
much more limited. Additionally, the spectral dependence is in line with
expectation and closely matches measurements of common natural aerosol
constituents made by .
Table shows details of the retrievals performed on the
three cases studies. The retrieved real refractive index of the 19 August
biomass-burning plume is slightly higher than the
values reported in the literature, and represents the upper end of the values
retrieved in the 50 selected samples. The other two cases also returned
higher than average values, although they were more in line with the other
samples and typical values reported in the existing literature. The biomass
burning particles were also found to be less absorbing than that of typical
smoke, but the values produced by GRASP are in good agreement with direct SSA
measurements aboard the DC-8 derived from PSAP and integrating nephelometer
measurements . A significant percentage of particles
were determined to be nonspherical in these cases, especially the 19 August
biomass-burning plume and 30 August
forested boundary layer aerosols. The cases on 19
and 27 August are dominated by
small particles, and in turn there are large uncertainties in the sphericity
product. The low spherical percentage retrieved for the 30 August
case is potentially realistic given the significance
of the coarse mode, but additional independent measurements of sphericity are
limited.
Direct comparisons of size distributions retrieved using GRASP with dedicated particles sizers that
sampled in parallel to the PI-Neph. The three cases selected show measurements from the (a) 19 August
and (b) 27 August biomass-burning cases, as well as (c) boundary layer
measurements made above a forested region of southeastern Missouri on 30 August.
Scatter plot comparisons of retrieved size distributions with particle sizers sampling in parallel to the PI-Neph.
In order from left to right the panels show total fine mode (a) volume concentration, (b) volume median radius and
(c) span =r90-r10r50.
The value retrieved from PI-Neph measurements is plotted on the horizontal axis while the value measured by the
corresponding dedicated aerosol spectrometer is plotted along the vertical axis.
The comparisons are made against LAS measurements (purple pluses), UHSAS ammonium-sulfate equivalent optical
diameters (blue crosses) and UHSAS PSL equivalent optical diameters (red circles).
Size distribution retrievals
The size distribution retrieved for the PSL spheres is shown in the subpanel
of Fig. and agrees well with the manufacturer's
specifications. The median diameter of the retrieved distribution was found
to be 902.7 nm which shows excellent agreement with the manufacturer's
NIST traceable specification of 903 nm ± 12. It is the authors'
experience, based on PI-Neph measurement inversions on a range of PSL
products from the same manufacturer, that the uncertainty listed often
significantly overestimates the true uncertainty in the central diameter of
the size distribution. As discussed in Sect. , the
retrieval returned a distribution width that was approximately twice the
value specified by the manufacturer but features in the -F12/F11
measurement indicate that the true width is more likely inline with the
manufacturer's specification FW67 of 8.2 nm. Similarly accurate results
sizing PSL spheres with PI-Neph data are demonstrated in
through the use of a Mie theory lookup table.
The retrieved size distributions for all three SEAC4RS case
studies are plotted alongside measurements made by dedicated particle sizers
in Fig. . The APS data were converted from aerodynamic
to geometric size using an assumed density of 1.3 g cm-3 and a
shape factor of unity. Uncertainties in these assumptions can generate
significant changes in the resulting geometric PSD, but the presence of APS
data can still be used as an optically independent, qualitative confirmation
regarding the presence of significant coarse mode. The UHSAS (Ultra-High Sensitivity Aerosol Spectrometer) data are shown
for two different calibration aerosols, PSL spheres and ammonium sulfate,
which have real refractive indices of 1.61 and 1.53
respectively. The LAS (Laser Aerosol Spectrometer) data shown correspond to calibration
with PSL spheres.
In all three of these cases the peak of the fine mode generally occurs around
a radius of 150 nm. These values are typical of the majority of the 50
selected periods, all of which have fine mode median radii (in volume)
between 100 and 200 nm. The PI-Neph/GRASP PSD retrievals
fall between the two different UHSAS calibrations in each of the three cases,
which again is typical of almost all 50 samples.
Among the 50 selected periods for which size distribution comparisons were
made, only two cases had coarse modes with volume concentrations that made up
a significant portion of the total particle volume. The first of these cases,
a sample dominated by transported Saharan dust, had very low aerosol loading
and the bulk of the scattering matrix data at scattering angles above
40∘ was below the PI-Neph's limit of detection. The second of
these cases, the forested boundary layer measurements taken on 30 August, was therefore chosen as one of the three highlighted
case studies. In both cases the size distributions agree remarkably well in
the coarse mode, suggesting significant sensitivity to larger particles in
the retrieved product. This sensitivity likely resulted primarily from the
PI-Neph's ability to measure down to scattering angles as low as
3∘ during SEAC4RS.
was also able to show sensitivity to supermicron particles given a minimum scattering angle of around 2∘.
On the other hand, determined that single-scattering
measurements over a scattering angle range of 10 to
90∘ were insufficient to provide significant information
about the coarse mode. All of these conclusions are in agreement with
theoretical sensitivity studies indicating that measurements at very low
scattering angles are required if the coarse mode is to be accurately
recovered .
In order to simplify the comparison of the retrieved size distributions with
those measured by the dedicated aerosol spectrometers, the fine mode of each
PSD was parameterized according to three metrics: total volume concentration,
median radius and the span of the distribution. When determining these
metrics, the values of the volume distributions corresponding to radii less
than 50 nm were first removed, as this lower bound corresponds to the
bottom of the PI-Neph/GRASP retrieval range. The upper end of the remaining
size distribution was then further truncated to include only fine-mode
particles. The division between the fine and coarse modes was defined as the
minimum value of the LAS volume distribution, closest to r=300 nm. A
visual inspection of all cases confirmed that this metric was sufficient to
reasonably isolate the fine mode when two modes were present. The volume
concentration, median (r50) and span ((r90-r10)/r50) were
then calculated using theses final truncated volume distributions. Linear
interpolation was used when the 10th,
50th or 90th percentile values, as well
as the bounds of the truncated distributions, fell between the midpoints of
two size bins. Scatter plots showing the results of these parameterizations
for the three OPC measurements vs. the corresponding PI-Neph retrieval are
shown in Fig. .
The retrieved volume concentrations and median radii generally fall
somewhere between the two different UHSAS calibrations, with the best
agreement generally tending towards the ammonium sulfate calibration. This is
consistent with the average retrieved refractive index for the 50 cases
(n= 1.53) which is in very close agreement to the dry refractive index of
ammonium sulfate found in the literature. The LAS consistently measured
smaller and fewer particles than all the other sizing techniques, but still showed significant correlation with the GRASP retrievals of PI-Neph measurements. There was
weaker agreement regarding the width of the distribution among the four
techniques. The retrieved spans generally best matched the corresponding PSL-calibrated UHSAS values, but the values covered a larger range of spans than
the values measured by the OPCs. The spans retrieved from PI-Neph measurements fell between
0.55 and 1.03 in 95 % of the cases. In contrast, the LAS showed the least
variability in span, with 95 % of the values falling between 0.65 and 0.85.
The differences in span between PI-Neph retrievals and the OPCs was likely
driven in large part by their different sampling techniques (ensemble vs. single particle measurements).
The large differences between UHSAS measurements under different
calibrations, with disparate refractive indices, demonstrates the
significance of the refractive index assumptions required. The results of
this work, as well as others , suggest that the
real refractive indices of natural aerosol can frequently reach values as low
as 1.48 at 532 nm. This is substantially lower than the refractive
index of ammonium sulfate (n= 1.53), which has the lowest value of the
aerosols that are commonly used to calibrate optical particle sizers, and
further emphasizes the significance of the basis resulting from uncertainty
in refractive indices.
In order to further asses the retrieval variability, resulting from changes
in refractive index and sphericity, the 50 SEAC4RS cases
were inverted a second time with assumptions corresponding to PSL spheres. In
this analysis the complex refractive index was forced match measurements of
PSL and nonspherical particles were excluded from GRASP's aerosol model.
This configuration produced significantly better agreement with the PSL
calibrated UHSAS measurements in volume concentration, median radius and
span, when compared to the unconstrained retrievals. This result further
demonstrates that differences in fundamental assumptions about the optical
and morphological properties of the particles are driving a significant
portion of the differences between the retrieved and measured values.
Conclusions
This work represents the first time that aerosol optical and microphysical
properties were retrieved from airborne, polar nephelometer data.
Additionally, the PI-Neph/GRASP inversion makes fewer assumptions regarding
the shape of the recovered size distribution and particle sphericity than
previous in situ light-scattering retrievals. The resulting products are in
good agreement with the expectations, and compare well with existing measurement
techniques. Furthermore, the GRASP fit to PI-Neph data is consistent with the
PI-Neph's level of error, indicating that the assumptions made in the
retrieval are sufficient to faithfully reproduce the light scattering of
realistic, ambient aerosols.
The real refractive index of humidified salts retrieved with this method
agree well with the predictions made by κ-Köhler theory and existing
dry measurements. The PI-Neph retrieval of PSL refractive index agrees with
other contemporary techniques to within the deviation present in those
reported values. Furthermore, inversions of airborne
SEAC4RS data produced refractive indices that were in good
agreement with the existing literature.
There is significant spread in the aerosol size distribution measurements
made by the OPCs, but the corresponding PI-Neph/GRASP retrievals generally
fall within the range of the existing measurements. A major part of the
differences in the measured size distributions stem from the need to assume a
refractive index during the calibration process. The PI-Neph/GRASP retrieval
has sufficient sensitivity to constrain the refractive index with enough
accuracy to potentially reduce these biases. The fact that the PSD retrievals
fell between the two UHSAS calibrations, in a manner consistent with the
retrieved refractive index, supports this conclusion.
The PI-Neph inversions have also shown moderate sensitivity to absorption but
a detailed assessment of the accuracy of this retrieved parameter is beyond
the scope of this paper and will have to remain the subject of future study.
Additionally, promising results were obtained regarding the retrieval of
sphericity in the case of the humidified salts as well as in sensitivity
studies, but as a result of the limited morphological information available
in the SEAC4RS data set, a robust evaluation of this product
is limited at this time.