Introduction
Ice cores from Greenland contain a record of climate proxies over the last
120 000 years. One of those proxies is mineral dust in the size range
0.5–100 µm. The dust has several properties that provide useful
information of the past: concentration, size distribution, morphology and
chemical and isotopic composition. These measurements have revealed that the
dust in ice cores come from central Asia during both the Holocene and the
last glacial period . The observed 100-fold decrease
in dust concentration from glacial to Holocene has constrained the aridity, windiness and insolation
forcing of glacial climate models .
Traditionally, the Coulter counter technique has been used to measure
concentration and size distribution. It works by measuring the electrical
impedance over an orifice through which a sample flows. For ice cores, this
sample is melted ice core water, with pure NaCl added to stabilize the
electrical conductivity. When a particle flows through and displaces the
conductive liquid, the impedance rises. This signal increases with the
particle volume. The Coulter counter has the disadvantage that it applies
only to discrete samples and has not been combined with continuous flow
analysis (CFA) systems.
CFA systems , on the
other hand, are a common technique for analyzing impurities in ice core
samples, offering a faster measurement speed and often higher resolution. On
the Copenhagen CFA system, 35 × 35 × 550 mm sticks
are cut from the ice core and melted upon a gold-coated melt head
. The meltwater from the outer 5 mm of
the ice core surface is discarded, while the inner uncontaminated water is
transported by a peristaltic pump to the connected instruments. One of these
instruments is the Abakus laser sensor (LDS23/25bs; Klotz GmbH, Germany) for
measuring insoluble particle concentration and size distribution.
The Abakus instrument measures the intensity of laser light through a flow
cell filled with the sample liquid. When a particle passes, the light is
attenuated. The Abakus therefore measures the optical extinction cross
section of the particle and can measure particles in the range
1–15 µm. Since it measures optical transmissivity rather than
electrical impedance, it is much less sensitive to electrical noise than the
Coulter counter. The Abakus on a CFA system can have a measurement depth
resolution of 3 mm and requires
almost no maintenance when the CFA system is running. The Coulter counter, on
the other hand, typically integrates a thicker depth interval and requires
work from the operator at all times during measurements
.
The aspect ratio of ice core dust particles was measured using the
novel single-particle extinction and scattering (SPES) instrument
.
The SPES measures both the extinction cross section, which is also
measured by the Abakus, and the optical thickness of the particles
.
The optical thickness depends on the geometrical thickness of the
particle and its refractive index.
If the refractive index is known, the aspect ratio can be derived from
the combination of extinction cross section and geometrical thickness.
The SPES is able to discern between oblate and prolate particles.
The extinction and scattering cross sections of irregularly shaped
particles can be accurately calculated with the discrete
dipole approximation (DDA) .
In the present work, we have used the Amsterdam Discrete Dipole
Approximation (ADDA) code .
The ADDA simulations were used to simulate the SPES measurements and
thereby extract the aspect ratio from the SPES data.
Furthermore, the ADDA simulations were used to show that the Mie
scattering effects on the optical extinction cross section for
spherical particles do not affect ice core dust due to its irregular
shape .
The measured samples are from the Renland Ice Cap Project
(RECAP) ice core drilled during the summer of 2015 on the Renland ice cap in
eastern Greenland only 2 km away from the old
Renland ice core .
This ice core covers the
last glacial cycle, and samples were taken from both the
Holocene and the last glacial period (the Supplement A).
As found for the central Greenlandic ice cores, the glacial RECAP dust comes from central
Asia .
The Holocene dust, similar to the old Renland core
, is dominated by a local East Greenlandic source.
The volume mode of the glacial dust is 2 µm, versus
20 µm for the Holocene dust, due to the increased
transport size fractionation for the glacial dust .
Although both instruments are typically calibrated using standard spheres of
known diameter, they produce substantially different size distribution
results when ice core samples are measured .
It has been proposed that this difference is because ice core dust is
generally nonspherical . We show
here that the nonspherical shape of the particles does quantitatively
account for the main discrepancy between the two instruments
(Fig. ). One important shape effect arises from the aspect
ratio, defined as the ratio between the length of its shortest and
longest side. We have found that Greenland ice core dust is dominated by
oblate particles of aspect ratio 0.3–0.4, which is significantly different
from the aspect ratio of 1 of the polystyrene standard spheres used for
calibration.
The Abakus measures the extinction cross section of the
particles, while the Coulter counter measures their volume.
Both instruments convert this to an equivalent diameter,
dext and dvol, respectively.
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Materials and methods
Abakus
For the Abakus measurements, square sticks of 35×35×550 mm were cut from the center
of the RECAP ice core.
These sticks were melted on the RECAP CFA system.
This CFA system is an enlargement of the one described by
, with a higher melt rate, more analytical channels and pressure decoupling after the debubbler.
The Abakus was connected to the CFA system with a flow rate of
2 mLmin-1.
The attached tubes and the Abakus were cleaned with MQ water (Millipore Advantage, 18.2 MOhm cm-1) after
each 5.5 m of ice measured.
Occasionally the Abakus was clogged by a large particle and required
flushing with a syringe while the system was running.
The depth resolution is 5 mm due to mixing in the tubes from the
melt head to the Abakus.
For high dust concentrations, two particles may pass through the
detector at the same time and show up as one larger particle.
We found that this effect was negligible (see the Supplement B for details).
The Abakus was originally calibrated to give the correct
diameter for polystyrene beads of 2, 5 and 10 µm.
Polystyrene standard spheres of 1.5, 2, 4, 5 and 10 µm in diameter from BS-Partikel GmbH, Wiesbaden, Germany
(the Supplement C) were
measured by the Abakus.
They were diluted to concentrations between 15 000 and
90 000 particles mL-1.
To avoid coagulation, the standards were sonicated for 30 s
before measurements.
Each of the standards was measured for 6 min.
Coulter counter
The Coulter counter measured discrete samples 55 cm in length.
The measured ice consisted of an outer triangular piece 3×1 cm in cross section cut to 10 cm long pieces.
The samples were decontaminated by rinsing in three consecutive jars of MQ
water.
In each jar the outer layer of ice was melted away and removed, leaving only the cleaner
inner part to be analyzed.
This treatment reduced the sample size by 50 %.
The samples were measured in two Beckman Coulter counters, one with a 100 µm aperture and one with a
30 µm aperture. The samples were shaken prior to measurement in the 100 µm Coulter counter.
Afterwards the samples were measured by the 30 µm Coulter counter. The 30 µm aperture data
were used for particles smaller
than 4 µm and the 100 µm aperture data were used for particles larger than 4 µm.
Selected samples representative of Holocene and glacial climates
were measured by the Coulter counter for this study. For the Holocene, selected samples from 356 to 4008 years b2k (before AD 2000) were used, while for the glacial,
the whole period from 17 760 to 33 885 years b2k was measured (the Supplement A).
The same samples were used for the Abakus.
SPES
After the Coulter counter measurements, the samples were measured by
SPES (Sect. ).
The sample flows through a 200 µm flow cell and is illuminated by
a laser. The light is measured by two detectors, which in combination give
the extinction cross section and the optical thickness. There is no focusing
of the particle stream in the cell, so only a small fraction of the particles
passing through the cell is measured by the laser. Therefore the sample is
circulated through the cell several hundred to thousand times. This gives an
accurate measure of the shape distribution of the particles, but it does not
allow for concentration measurements.
The narrow cell ensures high shear, forcing the particles to attain
a preferential direction.
Oblate particles in a shear flow orient themselves with the flat side along
the flow lines and are randomly oriented in the shear direction. Prolates lie
in a plane of constant velocity and are free to rotate within it
.
Results
ADDA simulations
Using the Amsterdam Discrete Dipole Approximation software (ADDA) , we
have calculated the extinction diameter for different particles.
The extinction diameter is based on the optical extinction cross section.
The optical extinction cross section is defined for a plane light
wave interacting with a particle as the difference
between the incoming and transmitted light intensity divided by the
incoming light intensity and multiplied by the area of the plane
incoming wave.
For spherical particles much larger than the wavelength of the light, the relation between diameter and optical extinction cross section is
σext=π2d2.
For smaller particles of a size comparable to the light wavelength, the relation differs due to optical
effects (Fig. ) .
However, we define the extinction diameter as dext=2πσext for all particles.
We associate each particle with its volumetric diameter:
a sphere with volume V has the
diameter dvol=[3]6Vπ.
For any particle of known volume, the volumetric diameter is given
by this relation.
Specifically, we have used ellipsoids and oblate prisms with an aspect ratio
of 0.3 in the volumetric diameter range 1 to 8 µm
(Fig. ). While spheres have a unique extinction
diameter for each volumetric diameter, the extinction diameter of other
particles depends on their orientation. For each volumetric diameter, there
will therefore be several possible Abakus measurements of the extinction
diameter described by a probability density function. This is described in
more detail in Sect. , where it is called
dP(dext|dvol)dlndext.
The broadness of the probability density function for nonspherical particles
results in a smoothing of the relationship between the extinction and
volumetric diameters (Fig. ). Furthermore, the
extinction diameter oscillation maxima are not located at the same
dvol for different particle shapes. Since ice core dust has a
variable shape (the Supplement D), it is sampled from a sum of the ellipsoid,
prismatic and many more distributions. In this sum of distributions the
oscillation pattern averages out.
The average extinction diameter is larger than the volumetric diameter since
the measured dust particles are elongated (discussed further in
Sect. ). For particles larger than
1.7 µm, the average extinction diameter is approximately
proportional to the volumetric diameter. For much smaller particles, the
extinction diameter is independent of the particle shape. After calibration,
the Abakus cannot measure particles with an extinction diameter smaller than
1.8 µm, so the measured Abakus data are within the range of
proportionality: dext∝dvol
(Sect. ).
The diameter of standard
polystyrene spheres measured by the
Abakus as a function of the true diameter certified by the
manufacturer (circles and dashed line), together with three of the same standards measured
a year earlier (crosses and dotted line) and the optical extinction diameter of a sphere as a
function of diameter (solid black curve).
The grey line is where the measured and the true diameter are
equal, to which the extinction diameter converges
for large true diameters.
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ADDA simulations of particles with a refractive index of 1.586 and, except for the
spheres, an aspect ratio of 0.3.
The prisms are oblate and their cross sections are equilateral
polygons with 3, 4 and 7 sides.
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Extinction calibration using particle size standards
We have measured the diameters of five different particle size standards (the
Supplement C, Sect. ) with the Abakus
(Fig. ). The 2, 5 and 10 µm standards were measured
twice with a 1-year delay, without significantly different results. This
shows that the Abakus calibration is stable over the timescale of a typical
measurement campaign.
Since dext is proportional to dvol for ice core
dust (Sect. ) and the proportionality constant depends on
particle shape and is unknown, we would like to calibrate the Abakus such
that it gives the extinction diameter dext and not the true
diameter for the standard spheres (using the term true for the certified
diameter given by the manufacturer). Therefore we define a calibration
function such that the measured diameter divided by the calibration function
is the extinction diameter. To avoid artifacts in the calibrated
distribution, the calibration function has to be a continuous function of the
measured diameter with a continuous first derivative. Since we want the
relative error in each standard to have the same weight, the function is
fitted to the logarithm of the ratio between the measured and extinction
diameter. The function y=a(x-x0)2, where y=ln(dmeas)ln(dext) and x=ln(dmeas),
is fitted to the data as a calibration function (Fig. ).
The fit parameters found are (a,x0)=(-0.086,2.60). This particular
calibration function is chosen because it is simple, fits the data well and
satisfies the conditions described above. x0=2.60 corresponds to
dmeas=13.5 µm. As the calibration function is equal
to 1 for dmeas=13.5 µm and standards larger than
13.5 µm were not tested, no calibration is applied for diameters
larger than 13.5 µm.
The particle size standard calibration has been applied to ice core dust data
(orange curves in Fig. a, b). Since the calibration
function is less than 1 for diameters smaller than 13.5 µm, the
effect of applying the calibration function is that the small diameter data
are shifted towards larger diameters. This is most pronounced for the
smallest diameters, since the calibration values are smallest for small
diameters. The positive slope of the calibration function means that the
calibrated bin positions are squeezed more tightly together than the
uncalibrated bins. Since the probability density function is defined as the
number of counts in a bin divided by its size, the calibrated probability
density function has higher values than the uncalibrated one. This effect
decreases with diameter as the slope decreases. For further details, see the
Supplement E.
The ratio between the diameter of spheres
measured by the Abakus in April 2017 and their extinction diameter (Fig. ) (circles and dashed line), together with three of the same standards measured a
year earlier (crosses and dotted line) and a fit to the logarithm of
the April 2017 data (solid line).
The fitted parameters are (a,x0)=(-0.086,2.60) of the
function a(x-x0)2, where x is the logarithm of the diameter in
µm.
The uncertainty on the fit (shading) is based on the
uncertainty in the data points.
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Size distributions of the dust particles in the RECAP ice
core for both the Holocene and last glacial period measured by
the Abakus and Coulter counter.
(a, b) Probability density functions of the number of particles as
a function of volumetric diameter, measured diameter or extinction
diameter for Coulter counter (black, volumetric diameter), raw Abakus
(blue, measured diameter), extinction calibrated Abakus (Sect. ) (orange,
extinction diameter), modeled Abakus data based on Coulter counter
data and the aspect ratio measured by SPES (Sect. ) (green, extinction diameter), and Abakus data fully
calibrated to Coulter counter data using both the extinction calibration and
aspect ratio (Sect. ) (red, volumetric diameter). The
uncertainty (shaded area) in the raw Abakus data is measurement uncertainty
(the Supplement H), while the remaining uncertainties are linearly propagated
from the Abakus and aspect ratio uncertainties. (c, d) Raw Abakus
data divided by Coulter counter (blue, from blue and black in a, b),
extinction calibrated Abakus data divided by modeled Abakus data (orange,
from orange and green in a, b) and fully calibrated Abakus data
divided by Coulter counter (red, from red and black in a, b).
(e, f) Probability density functions of particle volume derived from
the number density functions in (a, b) for Coulter counter (black),
raw Abakus (blue) and fully calibrated Abakus data (red).
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Glacial and Holocene samples measured by
SPES.
The brighter colors have a higher number of measured particles in a bin. The
blue lines mark the 0.25 and 0.75 quantiles of σext. The
white curves are the mean optical thickness as a function of
σext for ADDA simulations with a refractive index of 1.55.
The upper is for an aspect ratio of 0.5, the lower for 0.2.
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SPES
We have measured optical thickness (ρ) and extinction cross section
(σext) with SPES for both Holocene and glacial samples
(Fig. ) using the method of and
compared the results to ADDA simulations.
The distribution of particles in ρ,σext space can
be simulated using ADDA for a given particle shape and size distribution. We
have done this for oblate right square prisms of aspect ratios 0.2, 0.25,
0.3, 0.4 and 0.5. A total of 20 000 particles with a volumetric diameter
ranging from 100 nm to 2 µm and different refractive
indices and orientations were simulated. This size range covers the SPES
measurement range.
The refractive index, n, of atmospheric dust is on average between 1.52 and
1.55 . At
Dome C in Antarctica, the refractive index of Holocene and glacial ice core
dust is 1.53 and 1.56 . We have run the simulations
using the refractive indices 1.52 and 1.55 and found only a small effect of
the refractive index on the modeled aspect ratio.
By comparing to SPES measurements of oblate and prolate particles in
and , it was found that the
samples are dominated by oblates. Prolates have a much narrower distribution
of optical thickness than oblates, since their orientation is fixed by the
flow. The absence of a superimposed prolate distribution indicates that no
more than 15 % of the particles are prolates. The following analysis
therefore only focuses on oblates. For a similar analysis of prolates, see
the Supplement F.
To compare the simulations and the data, the average of the logarithm
of the simulated optical thickness as a function of extinction cross
section was calculated. This average was then used as a least squares
fit to the measured data, for which the aspect ratio is the variable
parameter.
For values of σext approaching the lower and upper
bound of the extinction cross section range, the SPES is not sensitive
in the full optical thickness range. To avoid bias, only
experimental data between the 0.25 and 0.75 quantile of the extinction
cross section were used in the fit.
For n=1.52 the Holocene aspect ratio is 0.42±0.03 and the glacial is
0.38±0.02, while for n=1.55 the Holocene is 0.36±0.01
and the glacial is 0.29±0.01.
This is independent of the volumetric diameter size distribution used
in the simulation.
The average in the refractive index range of ice core dust is
therefore 0.39±0.03 for the Holocene and 0.33±0.04 for the
glacial.
Aspect ratio effect
Spheres have the lowest geometrical cross section to
volume of all particles when averaged over all rotation angles of the
particles .
We define the geometric cross section diameter of a particle as
dgeom=2πσgeom, where
σgeom is the geometric cross section of the
particle.
However, since ice core dust is nonspherical (Sect. ),
dgeom>dvol and
dext=dgeom (Sect. ).
We can therefore calculate the distribution of dext
based on the aspect ratio
c and the distribution of dvol. The distribution of
dvol, dP(dvol)dlndvol, can be determined by the Coulter counter.
Since oblates dominate the measured samples, we will focus our model on those
instead of also considering prolates (Sect. ). As
previously mentioned (Sect. ), oblate particles in a
shear flow orient themselves with the flat side along the flow lines, while
they are randomly oriented in the shear direction .
Since they are free to rotate along an axis orthogonal to the light beam
direction, we can model them as rectangles embedded in two dimensions for
which all orientation angles are equally likely (the Supplement G). The light
and detector also lie in the plane. In this 2-D model, dvol is
the square root of the area of the rectangle, and dext is the
cross section of the rectangle.
Denoting the length of the short side b, the length the long side
a and the aspect ratio c=b/a, the probability of dext given a certain
dvol is
dP(dext|dvol)dlndext=0for dext<bzfor b<dext<a2zfor a<dext<a2+b2,
for
z=2π1a2+b2dext2-1.
The distribution of dext for all
dvol can then be found as
dP(dext)dlndext=∫dP(dext|dvol)dlndextdP(dvol)dlndvoldlndvol.
In Sect. we calibrated the Abakus such that
dmeas=dext. Therefore
dP(dext)dlndext
calculated here simulates Abakus measurements.
This can be used to find the aspect ratio of the particles just from the
Coulter counter–Abakus discrepancy. To do this, the sum of the square of the
logarithm of the ratio between
dP(dext)dlndext as calculated from the Coulter counter data and the
Abakus data was minimized with respect to the aspect ratio. This gives the
aspect ratio in which dP(dext)dlndext is most consistent with the Abakus data, which is
the most likely aspect ratio given the data.
For the Holocene data this gave c=0.41±0.09, while for the
glacial c=0.31±0.04.
The errors are propagated from the total errors on the calibrated Abakus
data.
There is, however, a large correlation between the errors in the
Holocene and glacial data, so the error in the difference is only
around 0.02, confirming a significant difference in aspect ratio between glacial and Holocene dust particles.
Calibration of Abakus
Equation () gives the extinction diameter size distribution
(Abakus) given a measured volumetric size distribution (Coulter counter) and
a known aspect ratio. However, often a measurement of the volumetric size
distribution is desired, while only Abakus measurements are available. This
requires the inversion of Eq. (), which cannot be done
analytically. However, multiplying the extinction calibrated Abakus bins by
the cubic root of the aspect ratio is a good approximation. This gives the
fully calibrated Abakus data of Fig. . For the glacial
volumetric distributions, the modes of the Coulter counter, the uncalibrated
Abakus and the fully calibrated Abakus data are 2.3, 5.0 and 2.7 µm, respectively. Further details on the calibration are found in the
Supplement E.
Discussion
Fig. 1a demonstrated that the data produced by the
Coulter counter and Abakus are proportional over 4 orders of magnitude, even
if the absolute concentration results do not agree. This is partly because
the instruments have different detection limits (see the Supplement I) and
partly because they measure two different properties of the particles:
volumetric and extinction cross section.
When the Abakus is calibrated using the true diameter of polystyrene spheres,
it gives up to 10 times as many counts as the Coulter counter for some
particle sizes when ice core samples are measured
(Fig. ). It is not possible in general to calibrate the
Abakus such that it yields the same distribution as the Coulter counter for
all ice core samples. However, by combining Coulter counter and Abakus data,
additional information is gained about the aspect ratio that was not
available from the two instruments individually.
It has previously been suggested that it is impossible to calibrate the
Abakus using polystyrene beads due to the strong Mie oscillations
p. 20. It was argued that since for spheres
the measured extinction cross section is a non-monotonous function of the
true diameter, it cannot be inverted. However, this is based on the criterion
that dmeas of the Abakus should be identical to
dtrue when measuring spheres. Since spheres have strong Mie
oscillations but ice core dust does not, this criterion is invalid. Therefore
the Abakus should be calibrated such that dmeas is equal to
dext instead of dtrue
(Sect. ).
With the SPES instrument we found that the average aspect ratio of our ice
core dust samples is 0.39±0.03 for the Holocene and 0.33±0.04 for
the glacial, so the particles are significantly elongated
(Sect. ). Using our simple model for the relation
between dmeas and dvol, we have calculated the
aspect ratio independently from the Abakus and Coulter counter data. This
gave an aspect ratio of 0.41±0.09 for the Holocene and 0.31±0.04
for the glacial in accordance with SPES. The SPES aspect ratio was calculated
for particles less than 2 µm in volumetric diameter and the Abakus
for particles between 1.2 and 9 µm, so the measurements are not
directly comparable. However, as we only investigate the leading order effect
of the aspect ratio and atmospheric studies find no size dependence of the
aspect ratio p. 28, it is assumed that any
possible size dependence of the aspect ratio is not large enough to
significantly change the results. In addition to giving the same aspect ratio
as SPES, the model also gives a consistent size distribution within the
Abakus uncertainties (Fig. ).
In the Dome C ice core from the East Antarctic plateau the aspect ratios of
oblate and prolate particles have been determined to be 0.2±0.1 and 3.5±1.3, respectively . The ranges refer to the
variability in the aspect ratio among different particles and not the
uncertainty of the mean. In the RECAP ice core studied here, we found a
similar but slightly less extreme aspect ratio in both the Holocene and
the glacial ice. For the RECAP core, we speculate that the Holocene dust
originates from local eastern Greenlandic sources, while the glacial dust is
from central Asia . Measurements of dust particles in dust
storms generally show an aspect ratio above 0.5. However, during transport,
the dust fractionates towards more extreme aspect ratios
pp. 28–30. Since large ice sheets are
located far from typical dust sources, the dust extracted from ice cores
would be subject to more fractionation. Therefore we do expect more extreme
aspect ratios to be found in ice core dust than in the atmospheric dust storm
measurements. The greater aspect ratio of the local Greenlandic Holocene dust
compared to the Asian glacial dust agrees well with the aspect ratio
fractionation observed in the atmosphere.
Conclusions
The Abakus laser sensor and the Coulter counter give different size
distributions when measuring the same ice core dust sample. This is because
ice core dust particles are not spherical, so the particle volume
measurements of the Coulter counter are different from the cross section
measurements of the Abakus. When spherical particles are measured by the
Abakus, the measured extinction diameter oscillates strongly as a function of
particle size due to Mie scattering oscillations. The extinction diameter of
ice core dust does not show this oscillation pattern, but is proportional to
the volumetric diameter. When the Abakus is calibrated using spherical
particles, it should therefore be calibrated to the extinction diameter and
not to the true diameter.
We derived a model for extracting the aspect ratio of the dust particles
from the differences between Abakus and Coulter counter measurements of
the same ice core dust samples.
This process suggests an aspect ratio of 0.41±0.01 for Holocene and 0.32±0.01 for glacial dust samples from the RECAP ice core, which is consistent
with direct aspect ratio measurements from a single-particle
extinction and scattering instrument.
This shows that not only is the discrepancy between the two
instruments explained by the nonspherical shape of the particles, but it
can also be used to obtain the aspect ratio.
As the Holocene dust has Greenlandic origin, while the glacial dust is
Asian, the aspect ratio could potentially aid in provenance
determination and in understanding atmospheric transport processes.
Moreover, by determining the aspect ratio, a better size distribution can
be obtained from the Abakus data.