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C O P Y R I G H T © 2 0 0 9 D R O P L E T M E A S U R E M E N T T E C H N O L O G I E S ,
I N C .
Data Analysis
User’s Guide
Chapter I:
Single Particle
Light Scattering
DOC-0222, Rev A
2545 Central Avenue
Boulder, CO 80301-5727 USA
Data Analysis User’s Guide – Chapter I: Single Particle Light Scattering
Copyright © 2009 Droplet Measurement Technologies, Inc.
2545 CENTRAL AVENUE
BOULDER, COLORADO, USA 80301-5727
TEL: +1 (303) 440-5576
FAX: +1 (303) 440-1965
WWW.DROPLETMEASUREMENT.COM
All rights reserved. No part of this document shall be reproduced, stored in a retrieval system, or
transmitted by any means, electronic, mechanical, photocopying, recording, or otherwise, without
written permission from Droplet Measurement Technologies, Inc. Although every precaution has
been taken in the preparation of this document, Droplet Measurement Technologies, Inc. assumes
no responsibility for errors or omissions. Neither is any liability assumed for damages resulting from
the use of the information contained herein.
Information in this document is subject to change without prior notice in order to improve accuracy,
design, and function and does not represent a commitment on the part of the manufacturer.
Information furnished in this manual is believed to be accurate and reliable. However, no
responsibility is assumed for its use, or any infringements of patents or other rights of third parties,
which may result from its use.
Trademark Information
All Droplet Measurement Technologies, Inc. product names and the Droplet Measurement
Technologies, Inc. logo are trademarks of Droplet Measurement Technologies, Inc.
All other brands and product names are trademarks or registered trademarks of their respective
owners.
Data Analysis User’s Guide – Chapter I: Single Particle Light Scattering
C O N T E N T S
Foreword ........................................................................................ 4
1.0 Single Particle Light Scattering ................................................... 5
1.1 Theory ........................................................................................ 5
1.1.1 Particle Size Determination .......................................................... 5
1.1.2 Sample Volume Determination ...................................................... 11
1.2 Uncertainties and Limitations ........................................................... 13
1.2.1 Sizing Errors ............................................................................ 14
1.2.2 Counting and Concentration Errors ................................................. 16
1.2.3 Contamination from Drop and Crystal Shattering ................................ 17
1.3 Data Analysis ............................................................................... 21
1.3.1 Size Distributions ...................................................................... 21
1.3.2 Derivation of Bulk Parameters ...................................................... 29
1.3.2.1 Total Number Concentration ................................................. 31
1.3.2.2 Extinction Coefficient and Visibility ........................................ 31
1.3.2.3 Liquid Water Content ......................................................... 32
1.3.2.4 Mean, Median Volume and Effective Diameter ............................ 33
1.3.3 Derivation of Refractive Index ...................................................... 34
1.3.4 Derivation of Asphericity ............................................................ 37
1.3.5 Evaluation of Cloud Microstructure ................................................ 40
1.4 Further Reading on Single Particle Scattering ......................................... 42
L i s t o f T a b l e s
Table 1.1: CAS Setup Table (Forward Scattering Only) ......................................... 23
Table 1.2: CAS Setup Table with and without Combined Channels ........................... 24
Table 1.3: Cloud Properties, Hydrometeor Characteristics, and Environmental Impact .. 29
Table 1.4: Hydrometeor Properties ............................................................... 30
Table 1.5: Sample Table of Forward and Backward Scattering Cross Sections .............. 36
Table 1.6: Sample Table of Aspect Ratios vs. Forward to Backscatter ....................... 38
Data Analysis User’s Guide – Chapter I: Single Particle Light Scattering
Form DOC-0222 4 © 2009 DROPLET MEASUREMENT TECHNOLOGIES, INC.
Foreword
The analysis of cloud particle measurements requires a certain degree of understanding
of the basic principles of operation of the sensors and, perhaps more importantly, an
appreciation of the limitations and uncertainties that are associated with the
measurement techniques. This user‟s guide is designed to introduce the reader to the
fundamental concepts that Droplet Measurement Technologies (DMT) employs to measure
cloud particles, the inherent uncertainties and limitations associated with these
measurement techniques and suggestions on how the measurement results can be
evaluated and analyzed within these constraints.
This manual is not a substitute for the many publications that have been written on the
subject of particle measurements and methodologies for data analysis. Throughout this
guide we will extract from many of such publications with extensive, up-to-date
reference lists at the end of each chapter. As newer publications become available this
guide will be updated accordingly with addendums that describe new analysis techniques,
correction algorithms or new technology that decreases the uncertainties or improves
resolution or response.
This guide is separated into three general chapters related to the technology that is
employed in the DMT instruments: 1) single particle light scattering, 2) single particle
imaging and 3) thermal analysis of liquid water. Each chapter contains a simplified
description of the measurement theory, a discussion of the uncertainties and limitations
inherent in the technique, derivation of the most commonly used atmospheric
parameters and some examples of typical applications. At the end of each chapter is a
list of references and suggested reading.
Most of the graphs throughout the manual were generated by the DMT analysis program,
“PAPI”, that runs on the Wavemetrics Inc. software package IGOR. PAPI is an open source
set of routines for ingesting data files written by DMT‟s Particle Acquisition and Display
System (PADS). In various parts of the chapters, examples will be given to show how PAPI
can help users analyze and display data. There is a separate User‟s Guide for PAPI, but
the examples contained in this manual do not require an extensive knowledge of IGOR or
PAPI to run on the user‟s own data set.
Data Analysis User’s Guide – Chapter I: Single Particle Light Scattering
Form DOC-0222 5 © 2009 DROPLET MEASUREMENT TECHNOLOGIES, INC.
1.0 Single Particle Light Scattering
1.1 Theory
1.1.1 Particle Size Determination
The operating principle of instruments that detect particle by light scattering is based on
the concept that the intensity of scattered light is proportional to the particle size and
can be predicted theoretically if the shape and refractive index of the particle is known
as well as the wavelength of the incident light. As illustrated in Fig. 1.1, scattering is the
result of the interaction of the electromagnetic wave of incident light with the molecular
structure of a particle that subsequently produces electromagnetic emissions with
components of reflection, refraction and diffraction.
Figure 1.1
The composite of these three components is a field of scattered light whose intensity
varies as a function of angle around the particle. If the particle is spherical and of
homogeneous composition, the scattered intensity is symmetric around the axis parallel
with the incident wave but varies in intensity from 0 to 180º, where 0º is the most
forward scattering and 180º is directly backward. Figure 1.2 shows an example of the
angular pattern of scattering. This angular dependency of the scattering around a
Reflection, Q1
Refraction, Q2
Diffraction, Q3
Q2
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Form DOC-0222 6 © 2009 DROPLET MEASUREMENT TECHNOLOGIES, INC.
spherical particle can be calculated using the equations that were developed by Mie
(1908) for a specific diameter, refractive index and incident wavelength.
This theory is applied in optical particle counters (OPCs) by collecting scattered light
from particles that pass through a light beam of controlled intensity and wavelength and
converting the photons to an electrical signal whose amplitude can be subsequently
related back to the size of the particle.
Figure 1.2
The property of a particle to interact with light is usually described by its scattering cross
section, σ. This is the product of the scattering efficiency, θ, and cross sectional area,
(π/4)D2, where D is the particle diameter. Figure 1.3 shows the scattering cross section
as a function of angle for particles with three different diameters and an incident
wavelength of 680 nm. In order to determine the amount of light scattered in any
direction, it is only necessary to multiply the scattering cross section by the intensity of
the incident light. Alternatively, if we have an optical system that collects light over a
range of angles and we measure the intensity of scattered light collected from a particle,
we can determine the particle size from the information shown in Figure 1.3 by
integrating the scattering function over the range of angles used in the instrument.
The collection angles used in the DMT single particle scattering instrument, i.e. the cloud
and aerosol spectrometer (CAS), the cloud droplet probe (CDP) and the fog monitor, are
from 3.5º to 12º, as shown on Fig. 1.3 (the backscattering angles used in the CAS are also
shown). The near forward angles are used because, as can be seen in Fig. 1.3, the largest
percentage of light scattered from a particle is in the forward direction. This is generally
true when the size of the particle is large with respect to the incident wavelength.
Data Analysis User’s Guide – Chapter I: Single Particle Light Scattering
Form DOC-0222 7 © 2009 DROPLET MEASUREMENT TECHNOLOGIES, INC.
Figure 1.3
The DMT light scattering spectrometers use an optical configuration similar to the block
diagram shown in Fig. 1.4 that is the conceptual design for the CAS with polarization
option (discussed in section 1.3). A diode laser is used as the source for coherent,
monochromatic light that is focused and transmitted across the airstream that carries the
particles. The beam falls on a light absorbing circular „dump‟ spot that blocks the beam
from the detectors. The forward scattered light is collected by the optics and focused
onto two detectors via a beam splitter (the purpose of this arrangement is discussed
below in Section 1.1.2). The acceptance angles are determined by the diameter of dump
spot and the aperture of the primary collection lens.
0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180
Angle
1E -010
1E -009
1E -008
1E -007
1E -006
Sc
att
erin
g C
ro
ss
Se
cti
on
(c
m-2
)
5 um
15 um
25 um
CA
S a
nd
CD
P F
orw
ard CA
S B
ack
Data Analysis User’s Guide – Chapter I: Single Particle Light Scattering
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Figure 1.4
The detectors convert the collected photons into an electrical current that is
subsequently conditioned and digitized into a signal whose peak amplitude is proportional
to the scattered light of the particle as it passes through the beam. To derive the size of
the particle, two steps are needed: 1) the amplitude of the digitized signal must be
converted into a light scattering cross section and 2) the light scattering cross section
must be linked to the diameter of the particle that produced it.
The first step is executed through the calibration of the system using particles of known
scattering cross section. Polystyrene Latex Spheres (PSL) with a refractive index of 1.58
and crown glass beads with refractive index of 1.51 (at the wavelength of 680 nm used in
DMT instruments) are used for this purpose. These particles are commercially available
and come in a range of sizes. Each set of beads is also relatively monodispersed with
standard deviations about the mean size of only a few percent.
In order to obtain the scale factor between digitized volts and scattering cross section,
the calibration particles are passed through the system and an average, peak voltage, V0,
is measured. The scale factor is S = I0/V0, where I0 is the scattering cross section for a
calibration particle with diameter, D, and refractive index, m, for an optical detection
system with an incident wavelength of λ, and collection angles of θ0-θ1. This scattering
cross section is calculated using Mie theory and can be computed with programs such as
described by Bohren and Huffman (1983).
Figure 1.5 shows the scattering cross section as a function of diameter and the optical
configuration of the CAS and CDP. The dashed line is the scattering cross section for
crown glass beads and the solid line is the equivalent was water droplets.
Sizing Detector
Backward Scatter
Detector (S-pol)
Laser Diode
(polarized)
Qualifying
Detector
Backward Scatter
Detector (No-pol)
Polarized Filter
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Form DOC-0222 9 © 2009 DROPLET MEASUREMENT TECHNOLOGIES, INC.
Figure 1.5
With this scale factor, the signal measured from each particle is converted to a diameter
by multiplying the peak voltage by the scale factor to obtain the scattering cross section
and then going to a chart like Figure 1.5, or a lookup table stored in the data acquisition
system, to find the diameter of the particle that has the calculated scattering cross
section.
A pause here is needed to emphasize a very important point: single particle optical
scattering spectrometers do not measure particle size; they measure optical
scattering cross section. Hence, in order to determine particle size, the refractive
index of the particle that scattered the light must be known or assumed and it must
also be assumed that the particle was spherical.
From Figure 1.5 it is seen that particles with the same size but different refractive
indices may have substantially different scattering cross sections. Put a different way,
0 5 10 15 20 25 30 35 40 45 50
Particle Diameter ( m)
0.00E+000
2.50E-007
5.00E-007
7.50E-007
1.00E-006
1.25E-006
1.50E-006
1.75E-006
2.00E-006
2.25E-006
2.50E-006
2.75E-006
3.00E-006
3.25E-006
3.50E-006
3.75E-006
4.00E-006S
catt
eri
ng
Cro
ss S
ecti
on
(cm
2) Water
Glass
Data Analysis User’s Guide – Chapter I: Single Particle Light Scattering
Form DOC-0222 1 0 © 2009 DROPLET MEASUREMENT TECHNOLOGIES, INC.
depending on the assumed refractive index, the scattering cross section derived from the
measurement will lead to different particle diameters. For example, in Fig. 1.5, a 25 μm
water droplet and 30 μm glass calibration particle have the same scattering cross section.
To further complicate the issue of sizing, for the same refractive index, two particles
with different sizes can sometimes have nearly identical cross sections. For example, as
seen in Fig. 1.6, 5 and 7 μm water droplets have almost the same cross section. This
measurement limitation is elaborated further in section 1.2.1.
Figure 1.6
The conversion from signal voltage to particle size is further complicated in the CAS, the
OPC that covers the size range from 0.5 to 50 μm. The scattering cross sections of water
droplets in this size range cover almost six orders of magnitude. The linear amplifiers
used in the CAS, and their associated A/D converters, can only measure over two orders
of magnitude. Hence, the CAS uses three sets of electronics, each with different
amplification, to measures this range of diameters. This requires that the calibration is
done with particles whose sizes will fall in each of the gain stages and three scale factors
are derived to relate the digitized volts to scattering cross section.
The DMT spectrometers can transmit two types of information: digitized counts from
individual particles, also known as particle-by-particle (PBP) and frequency distributions
of particle sizes. In the PBP case, the counts range from 0 to 3072 for the CAS and 0-4095
for the CDP. These can be subsequently scaled to scattering cross sections and converted
0 1 2 3 4 5 6 7 8 9 10 11 12
Particle Diameter ( m)
0.00E+000
5.00E-008
1.00E-007
1.50E-007
2.00E-007
2.50E-007
3.00E-007
Scatt
eri
ng
Cro
ss S
ecti
on
(cm
2) Water
Glass
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Form DOC-0222 1 1 © 2009 DROPLET MEASUREMENT TECHNOLOGIES, INC.
to a size as discussed previously. Section 1.3 describes in greater detail the utility of PBP
and how additional information about particle properties can be obtained from these
data.
The frequency distribution information comes in the form of a table of values that is
generated by the spectrometer and transmitted at fixed intervals (usually once per
second) to the data acquisition system. The table consists of a preselected number of
channels (bins), usually 30, where each bin represents a voltage range given as A/D
counts. The scattering intensity of each particle that is measured within the sample
period is digitized and represents a single event that is added to the bin whose A/D
counts (scattering intensity interval) encompasses that of the measured particle.
The method for selecting the channel intensity thresholds is described in Section 1.3.
Suffice to say at this point that these are typically set to represent evenly spaced size
intervals of particles with predetermined refractive index, such as water droplets. Since
these thresholds are scattering cross sections, not particle diameters, they can be
derived for whatever refractive index is assumed, i.e. if aerosols like ammonium
sulfate are being measured, the size thresholds will be different than if measuring
water but the scattering cross sections remain the same.
1.1.2 Sample Volume Determination
In addition to deriving the size from the scattered light, the particles counted and sized
in a selected time period must be converted to a number concentration, i.e. number of
particles per unit volume or mass of air. This requires a definition of the sample volume.
The sample volume is the amount of air that passes through the sensitive area of the
laser beam during the sample period. This is defined as:
Sample Volume = (Sample Area)(airspeed)(sample time) (1.1)
In the open-flow CAS, CDP and Fog monitor, particles pass randomly through various
sections of the beam. Given that the laser beam does not have uniform intensity across
its cross section, and because it is focused so that it is most intense in the center of the
sample tube or between the arms of these instruments, a technique is implemented to
only accept and convert to a size those particles that pass through the most intense
section of the laser.
The sensitive area of the laser beam is defined with a combination of optical and
electronic techniques that selects a depth-of field (DOF) that is a certain length along the
beam, and an effective beam diameter (EBD) that is a portion of the beam width. This is
accomplished using two detectors as is shown above in Fig. 1.4. The scattered signal is
divided with a beam splitter into two components that are measured independently by
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Form DOC-0222 1 2 © 2009 DROPLET MEASUREMENT TECHNOLOGIES, INC.
sizing and qualifier detectors. The qualifier detector has an optical mask that is in the
shape of a rectangle. As shown in Figure 1.7, this mask allows a full image of a particle
that is in the beam to appear at the detector only when the particle passes within a
certain distance of the center chord through the beam. When the particle passes through
the center of focus, the image is distinct and represents the true size of the particle. As
the particle moves away from the center of focus, the image seen at the detector
becomes larger and fuzzier and the complete image will no longer be within the edges of
the optical mask.
As a result, as compared with the detector that has no optical mask, the measured signal
will be smaller. This is illustrated in Figure 1.8 by the dashed line that represents the
voltage signal from the qualifying detector and the solid curve is the signal from the
sizer. The qualifier signal is larger than the sizing signal when a particle is in focus
because the beam splitter divides the scattered light in such a way that the qualifier
receives more light than the sizer, typically 67% for the qualifier, 33% for the sizer (the
CDP uses a 50:50 split in signal), when a particle is in focus. This is done in order to keep
the gains of the two detection systems the same while providing a good discrimination
between the qualifier and signal when particles are in and out of focus.
Figure 1.7
Out of focus
Depth of Field
Beam
Diameter
In focus
Center of Focus
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Form DOC-0222 1 3 © 2009 DROPLET MEASUREMENT TECHNOLOGIES, INC.
Figure 1.8
As shown in Fig. 1.7, the shape of the sample area is not actually rectangular but is more
like an oblate spheroid due to the inherent nature of the optical definition of the depth
of field. The sample area is mapped at DMT using a droplet stream moved with a micro-
positioner.
1.2 Uncertainties and Limitations
The uncertainties and limitations of the light scattering probes are associated with the
derivation of size from light scattering, with the determination of the sample volume,
with issues of counting statistics and coincidence and with contamination from particles
produced from shattering of water drops and ice crystals on the inlet (CAS) or arms (CDP)
of the sensors.
The errors in counting and sizing propagate into parameters that are derived from these
measurements, i.e. number, area and mass concentrations and size parameters like the
median volume diameter and effective radius. The limitations and the associated
uncertainties are described in the following sections and the estimated uncertainties in
derived parameters are elucidated in section 1.3.
Sizing Signal
Qualifier Signal
Out of Focus
Qualifier Signal
In Focus
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Form DOC-0222 1 4 © 2009 DROPLET MEASUREMENT TECHNOLOGIES, INC.
1.2.1 Sizing Errors
The sizing accuracy is affected by several factors. The lasers used in the probes have a
Gaussian intensity distribution, i.e. the center of the beam is the most intense with
exponentially decreasing intensity towards the edge of the beam. The optical mask on
the qualifying detector has a dimension such that only particles that pass through the
beam where the intensity is within 15% of the maximum intensity will be accepted. This
means that for a given particle size, the measured scattering intensity has an uncertainty
of approximately ±5%, assuming that on average, particles pass through the portion of the
beam with approximately 90% of the maximum intensity and that the system is calibrated
under that assumption. The uncertainty in the sizing, however, may be more or less than
±5% depending on where on the scattering cross section curve the size is being derived. In
general, the uncertainty is larger at larger sizes where the slope of the scattering cross
section as a function of size is less steep than at smaller sizes. Mis-sizing will also occur
as a result of particles coincident in the beam which will be detected as a single particle
but sized somewhat larger. This type of sizing error will usually be negligible and, at
present, no attempt is made to correct the data for this event.
The multi-valued nature of the scattering function, and its sensitivity to refractive index
and shape, discussed in section 1.1.1, presents the largest uncertainty in deriving particle
size. As shown in Fig. 1.9, the actual, atmospheric size distribution may have a smooth,
Gaussian-like shape (solid, blue curve) but because of the multi-valued scattering
function, the measured size distribution will have anomalous dips as shown by the solid
black curve.
By having multiple bins in the regions of ambiguity, the spectra can be sensibly smoothed
by combining the counts in channels that adjoin the delinquent sections, i.e. where
fluctuations in the spectra are counter to our understanding of physical processes. For
example, in clouds, although bi-modal size distributions are frequently found and we
understand this process as a result of entrainment and mixing, we do not expect to have
abrupt, anomalous dips in the size spectrum as seen in Fig. 1.9. In this figure, channels
have been combined to produce an adjusted size spectrum with smoother shape, albeit
with less resolution.
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Form DOC-0222 1 5 © 2009 DROPLET MEASUREMENT TECHNOLOGIES, INC.
Figure 1.9
Another sizing uncertainty implied in the principles of operation is that these probes
cannot discriminate between water and ice particles. Ice particles pass through the
sample volume of these probes in random orientation and the measured sizes will depend
upon the orientation and the shape of the crystals. Ice particles outside the nominal
sample area of these probes will sometimes be sized and counted if they fall partially
within the sample volume. In general, aspherical particles will be undersized; however, if
assumptions are made about the shape, corrections can be applied (Borrmann et al.,
2000).
2 4 6 8 10 12 14 16 18 20
Particle Diameter (um)
0
50
100
150
200
Co
nc
en
tra
tio
n
Measurements with Original Bins
Measurements after grouping bins
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The uncertainty in deriving particle diameter depends, in part, on the diameter of the
particle, its shape (if aspherical) and its refractive index (if different than what is
assumed when relating its scattering cross section to a size). On average, the estimated
error in diameter is ±20%. This error can be much larger in certain size ranges and if the
particle shape differs greatly from spherical.
1.2.2 Counting and Concentration Errors
Counting errors will occur when there are high concentrations and two or more particles
are coincident in the beam volume. Within the nominal depth of field of 1.5 mm,
qualifier width of 0.10 mm and beam diameter of 2.0 mm, the volume within which two
or more particles could be coincident and counted as only one is approximately 0.3 mm3.
Assuming that particles in the atmosphere are uniformly, randomly distributed, with their
spacing described by Poisson statistics, the probability of more than one particle in the
beam volume is less than 1% until particle concentrations exceed 1000 cm-3.
The determination of number, surface (extinction), or mass (water content)
concentrations is sensitive not only to the counting accuracy but to the uncertainty in
defining the volume of air within which particles are counted. As previously described in
section 1.1.2, the sample volume is the product of the effective beam diameter, depth of
field, air speed and sample period. The spectrometers have been designed to allow air to
pass isokinetically through the laser beam so that the air is neither accelerated nor
decelerated with respect to environmental air. This does not account for mounting
location, however, where the aircraft fuselage or wings may cause airflow distortion (for
additional information see further reading, Appendix I).
The cross-sectional area of the beam that sweeps out the sample volume is the product
of the effective beam diameter and depth of field, both determined by the optical
magnification of the collection optics and the geometry of the optical mask that is placed
in front of the qualifying detector (Fig. 1.7). The form of this cross-sectional area is not a
precise rectangle but has its maximum dimension in the center of focus, then tapers
slightly towards the edges of the DOF, each side of the center of focus. This produces a
shape that is like a prolate spheroid and presents a challenge for a precise measurement.
As previously stated, the sample area has been mapped using a droplet stream moved
with a micro-positioner. The area measured this way has been validated by producing
monodispersed particles, e.g. PSL or glass beads, in very clean air, free of any
background particles, and measuring the concentration of these particles with a
condensation nucleus (CN) counter sampling air after it has passed through the CAS and
CDP. The CN counter is a high precision particle counter with a well-defined sample
volume. The sample area of the DMT spectrometers was estimated by comparing with the
CN measurements and the uncertainty is approximately ±20%.
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1.2.3 Contamination from Drop and Crystal Shattering
It has been recognized since 1985 (Gardiner and Hallett, 1985) that the inlets and arms
on particle probes were a potential obstruction to the airflow and provided surfaces
where water droplet and ice crystals can impact and produce secondary fragments, some
of which arrive in the measurement sample volume.
More recent studies (McFarquhar et al. 2007; Heymsfield, 2007) have shown correlations
between anomalously high concentrations of small particles (< 20 μm), measured with
light scattering probes, and the ice water content in ice crystals larger than 100 μm. This
is indirect evidence that large ice crystals are shattering and producing fragments in the
measurement volume of the instrument. Figure 1.10 is another way to look at the
problem whereby comparisons are made of the measurements with the CAS and CIP
(cloud imaging probe). The CIP is also susceptible to crystal shattering on its arms but the
measurements shown in this figure have been corrected for this problem (see section
2.2.3). The CIP in this example is the gray-scale imaging probe with 15 μm resolution so
that it has an overlap in sizes with the CAS from 15-45 μm. What is shown in Fig. 1.10 is
that when the ice crystals are small and in low concentrations, there is a good agreement
between the CAS and CIP measurements in the overlapping size range. As the ice crystals
become larger and in higher concentration, the discrepancy increases, indicating that the
CAS measures what are presumably false particles, i.e. those being produced through
fragmentation.
This generation of false particles is a major source of error in the CAS measurements.
This problem is under investigation and solutions are being assessed to resolve this
problem. Flow simulations have been conducted to assess the magnitude of the problem
and to develop algorithms that correct those measurements that have already been
made.
As shown in Fig. 1.11, flow field analyses with the commercial software, Fluent, are used
to compute the three dimensional pressure, temperature and velocity fields around the
DMT instruments, in this case the CAS. These flow fields, dependent on ambient pressure
and temperature, are then used as the boundary conditions for trajectory analysis of
particles embedded in these fields. Figure 1.12 shows an example of particle trajectories
computed from the flow fields. What is important to note is that there is a very small
subset of particle trajectories that eventually result in a particle measured in the CAS
sample volume. The analysis shows that only those particles whose trajectories result in a
reverse course after breaking or bouncing will produce a path that eventually arrives in
the probe sample volume.
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Figure 1.10
Figure 1.11
T = 200 K
P = 100 mb
AOA = 0o
Elasticity = 0.2-1.0
Exit Angles = All possible
Fragment diameters = 5-50 μm
Fragment density = 0.2 to 0.9 g cm-3
Flow modeling with FLUENT
Unknowns
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Form DOC-0222 1 9 © 2009 DROPLET MEASUREMENT TECHNOLOGIES, INC.
Figure 1.12
On average, this is less than 1% of the particles that strike any segment of the inlet. On
the other hand, because of the surface area of the inlet, approximately 5 cm2 for the
original CAS (the new design uses a much thinner inlet), each second the CAS sweeps out
a volume of 1000 cm2 at an airspeed of 200 m-1, the velocity of the NASA WB57F. If we
assume that ice crystals break into evenly sized spheres of 15 μm when they strike the
inlet, we can calculate the potential number of fragments that would be measured by the
CAS. Figure. 1.13 shows the relationship between concentration of particles produced
from fragmentation and ice crystal volume, using measurements from three projects
when the CAS was flown on the WB57F. The individual points are the actual
measurements from the CAS and CIP and the solid lines are predictions based upon the
flow model predictions for the fraction of 15 μm particles that would be produced and
arrive in the sample volume. The inlet of the CAS also has a shroud whose purpose is to
reduce sensitivity to changes in flow angle due to aircraft attitude. As seen in Figure
1.13, (black curves), this shroud introduces an additional surface where particles will
shatter. What is clear from the figure is that the slope of the measurements is very
Particle Diameter
10 m, =0.9
30 m, =0.9
45 m, =0.9
10 m, =0.5
30 m, =0.5
45 m, =0.5
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similar to the predicted slope and that the shroud is an additional source of crystal
fragments.
The fragments are embedded in the field of real particles and represent a bias that needs
to be removed. During the CRAVE experiment, the shroud was removed and the inlet
made much thinner. This clearly decreased the number of fragments, as seen by the
comparison with predicted concentrations (top panel, Fig. 1.13), but at higher ice crystal
concentrations there remains a clear fragmentation signature.
Figure 1.13
Corrections algorithms are under development and will be implemented to remove
some fraction of the erroneous particles in the CAS measurements from previous
projects. The technique uses the CIP measurements as a benchmark against which to
compare those from the CAS and estimate the number of fragments being produced as a
function of size.
1.0E+002 1.0E+003 1.0E+004 1.0E+005 1.0E+006 1.0E+007 1.0E+008
volume ( m3 cm-3)
1E-002
1E-001
1E+000
1E+001
1E+002
1E+003
1E+004
1E+005
Nu
mb
er
co
nc
(l-1
)
Measurements - 15 m
Inlet Breakup - 15 m
Inlet + shroud Breakup - 15 m
CRYSTAL/FACE
1E-002
1E-001
1E+000
1E+001
1E+002
1E+003
1E+004
1E+005
Nu
mb
er
co
nc
(l-1
)
MidCix
volume ( m3 cm-3)1E-002
1E-001
1E+000
1E+001
1E+002
1E+003
1E+004
1E+005
Nu
mb
er
co
nc
(l-1
) CRAVE
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The CAS inlet is also being redesigned to further limit the problem of crystal
fragmentation and contamination of the measurements. This manual will be revised at a
later date when the correction algorithms have been validated and a methodology
developed that can be implemented by users to correct measurements prior to the date
when a new CAS inlet is implemented.
1.3 Data Analysis
1.3.1 Size Distributions
The most commonly used analysis technique for evaluating particle measurements is the
display of particle concentration as a function of size. The concentrations can be
number, water content, surface area or any other extrinsic property derived with respect
to the volume or mass of air. Prior to constructing such size histograms, however, the
concentrations must be binned according to size. It may be recalled that the scattering
probes transmit a frequency histogram with a predefined number of bins and the
thresholds of the bins are predefined in terms of the A/D counts that are related to the
scattering intensity. It then remains to associate these counts to an optical diameter
(NOTE: the term optical diameter is used here instead of geometric diameter because
of the method being used to determine the size).
The channels thresholds are typically determined prior to a measurement campaign and
reflect calibrations with particles of known size, as discussed in Section 1.1.1, and are
adjusted for the expected particle composition, e.g. water or haze droplets. It is highly
recommendable, however, to recalculate the sizes associated with the A/D counts after
post-project calibrations. It is also sometimes of interest to see how the shape of the size
distribution might change if the particles measured were some refractive index other
than the one assumed when the channels were defined.
As a demonstration of how this is done, we take a CAS as the target instrument since it is
the more complicated to set up, due to the three gain stages. The CAS used in this
example has been set up to measure nominally between 0.3 and 20 μm.
Step I
The scale factors for the three gain stages are computed from the measurements with
calibration particles. In this example, 0.65 μm PSL particles were used to calibrate the
high gain (channels 1-10), 2 μm PSL particles calibrated the mid-gain (channels 11-20)
and 15 μm glass beads calibrated the low gain. These three calibrations set the scale
factors, Shigh, Smid and Slow. Caution! Although the counts in the CAS are listed in the
setup tables ranging from 0 to 3072 over the 30 channels, each gain stage is actually
represented by A/D counts from 0-1023. If the 0.65 μm particles peak in channel 8
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with A/D counts of 600, then the scale factor for this stage is Ihigh/600, where Ihigh is
the scattering cross section for a 0.65 μm PSL particle. If the 2 μm particles peak in
channel 16, with A/D counts of 1400 as the channel threshold, the scale factor, Smid
for this stage is Imid/(1400-1023), where Imid is the scattering cross section for 2 μm
PSL. Likewise, the low gain average A/D count must have 2047 subtracted before
calculating the scale factor.
Step II – 1st option
The A/D counts are converted to scattering cross sections using the scale factor. In this
case, the counts have already been set and the goal is to associate a diameter with the
counts. The counts are converted to a scattering cross section by multiplying the
threshold counts of each channel for the scale factor associated with the appropriate
gain stage. Caution! As in the case of calculating the scale factors, the mid gain counts
must have 1023 subtracted and the low gain counts must have 2047 subtracted
before applying the scale factor.
Step II – 2nd option
In this case, the goal is to determine the threshold counts for the channels based upon
preselected sizes and refractive index for the particles. Here, we go to the table of
scattering cross sections as a function of size and refractive index, select the 30 sizes
that we wish to associated with the 30 channels, and extract the scattering cross sections
for each of the sizes. These values are converted to counts by dividing by the scale
factor (recall that the scale factor has units of cm2/counts). The subsequent counts will
all range between 0 and 1023, so the user must decide whether to add 1023 or 2047
based upon the range of sizes and which gain stage will contain each size range.
Step III – 1st option
Each of the scattering cross sections must be associated with a size by using the table of
scattering cross sections as a function of size and refractive index. For a given refractive
index, several sizes may have similar scattering cross sections. This requires that an
average is calculated of all the possible sizes and used to associate the counts with a
size.
Step III – 2nd option
There is no third step for the option of preselecting sizes and channel counts.
Table 1.1 shows how the 30 channels were set up and the sizes associated with the A/D
counts, assuming refractive indices of 1.33 (water) and 1.44 (sulfuric acid). The effect of
changing the composition of the particles is to slightly increase the range of sizes from
0.41 to 36 μm to 0.37 to 40 μm. In general, increasing the refractive index will increase
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the range of sizes because the slope of the scattering cross section, for this range of
collection angles and incident wavelength, decreases as refractive index increases.
Adding a light absorbing component via the imaginary part of the refractive index has a
similar impact.
Table 1.1: CAS Setup Table (Forward Scattering Only)
CH# Forward
Counts
Forward
Intensity
Forward Size
(water, m=1.33)
Forward Size
(m = 1.48)
1 60 6.357E-011 0.41 0.37
2 90 9.536E-011 0.44 0.4
3 131 1.388E-010 0.47 0.43
4 186 1.971E-010 0.5 0.46
5 259 2.744E-010 0.53 0.49
6 352 3.73E-010 0.56 0.51
7 470 4.98E-010 0.59 0.54
8 618 6.548E-010 0.62 0.56
9 800 8.477E-010 0.65 0.59
10 1024 1.085E-009 0.68 0.62
11 1084 3.018E-009 0.83 0.78
12 1124 5.03E-009 0.93 0.88
13 1159 6.791E-009 0.99 0.97
14 1224 1.006E-008 1.11 1.31
15 1309 1.434E-008 1.21 1.91
16 1414 1.962E-008 1.81 2.01
17 1549 2.641E-008 2.51 2.11
18 1684 3.32E-008 2.61 2.15
19 1849 4.15E-008 2.72 2.21
20 2024 5.03E-008 2.8 2.31
21 2109 1.156E-007 5.6 5.71
22 2136 1.668E-007 8 8.91
23 2183 2.559E-007 10.2 11.51
24 2268 4.17E-007 15 17.21
25 2373 6.16E-007 18 20.81
26 2438 7.392E-007 20.5 23.61
27 2538 9.287E-007 23.5 25.91
28 2693 1.223E-006 26.8 30.91
29 2848 1.516E-006 31.4 34.01
30 3072 1.941E-006 35.8 40.21
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Once the size thresholds are determined, the concentrations can be displayed in
graphical form by creating a plot of the concentrations as a function of particle size.
Figures 1.14 and 1.15 illustrate a size histogram of number concentration as a function of
particle diameter, displayed in a number of ways. Table 1.2 lists the channel definitions
assuming water droplets and for the original 30 channels. Also shown in this table is a
new size definition where channels have been combined to encompass those regions
where there are multiple values of size that have the same scattering cross sections. In
Fig. 1.14 the same information has been displayed but using the original and a
redistribution of the information in the size channels and by normalizing by the
logarithm, base 10, of the width of each size bin (also listed in Table 1.2).
Table 1.2: CAS Setup Table with and without Combined Channels
Channel Original
Size
Log10
Width
New Size Log10 Width
1 0.60 0.08 0.5 - 5.0 1.00
2 0.70 0.07 5.0 -10.0 0.30
3 0.75 0.03 10.0 - 15.0 0.18
4 0.80 0.03 15.0 - 20.0 0.12
5 0.90 0.05 20.0 - 25.0 0.10
6 0.95 0.02 25.0 - 30.0 0.08
7 1.0 0.02 30.0 - 35.0 0.07
8 1.1 0.04 35.0 - 40.0 0.06
9 1.2 0.04 35.0 - 45.0 0.05
10 1.25 0.02 45.0 - 50.0 0.05
11 1.5 0.08
12 2.0 0.12
13 2.5 0.10
14 3.0 0.08
15 3.5 0.07
16 4.0 0.06
17 5.0 0.10
18 6.5 0.11
19 7.0 0.03
20 8.0 0.06
21 10.0 0.10
22 12.5 0.10
23 15.0 0.08
24 20.0 0.12
25 25.0 0.10
26 30.0 0.08
27 35.0 0.07
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28 40.0 0.06
29 45.0 0.05
30 50.0 0.05
The black, solid line is the average number concentration, as a function of the 30 sizes
defined in Table 1.2, for all cirrus clouds measured on May 2, 2004 by the CAS on the
NASA WB57F during the MidCix project. The roughness or irregularities are a result of the
multi-valued nature of the scattering cross sections. The irregularities are also a result of
non-uniform intervals in the sizes, i.e. in the small sizes some of the intervals are 0.05
μm wide, whereas others are 0.1 or 0.5. Normalization by the width of an interval, i.e.
dividing the concentration by the width of the size intervals decreases the irregularity, as
shown by the black, dashed line in Fig. 1.14. In this case the base 10 logarithm of the size
interval has been used (log10(di+1/di) for the reason that is discussed below.
Combining those channels whose size thresholds encompass regions where the Mie
scattering function is multi-valued (illustrated in Fig. 1.6) further removes the
irregularities in the size distribution as shown by the solid red line in Fig. 1.14. Some of
the detail in the size distribution, of course, is also removed by combining the channels.
As Table 1.2 shows, the newly defined size thresholds also are not uniform in their
intervals so that the concentrations need to be normalized by the width of each size
channel. In addition, in order to compare size distributions, be they from different
instruments with different size definitions or from the same instrument with different
size intervals, normalization is mandatory. Figure 1.14 shows such a comparison and
illustrates how the subsequent shape of the distributions can look quite different
dependent on how the information is presented.
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Figure 1.14
The size distributions in Fig. 1.14 are displayed on a log-log plot in order to show the
details of size distribution. It is often better, however, to display the concentrations on a
linear-log plot, as seen in Fig. 1.15. The reason is that from the graphical perspective,
when the concentrations are normalized by the base 10 logarithm of the size interval and
when the abscissa is plotted as a base 10 logarithmic scale, the area under the curve
between two diameters, di and di+1, is directly proportional to the total concentration of
particles within this size range. This allows by quick inspection an estimate of where the
majority of particles are found, e.g., in this case, between 5 and 20 μm.
Likewise, by computing the extinction and water mass as a function of size (described in
Section 1.3.2), the graphical representation of these size distributions represents the
measurements so that we can see which size of particles contribute the most to these
two derived parameters that are important for assessing impacts on climate and on
precipitation or hydrological impacts, respectively. This is illustrated in Figs. 1.16 and
1.17.
0.01
0.1
1
10
100
Nu
mb
er
Co
nce
ntr
ati
on
5 6 7 8 9
12 3 4 5 6 7 8 9
102 3 4 5
Diameter ( m)
All channels All channels normalized Combined channels Combined channels normalized
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Figure 1.15
100
80
60
40
20
0
Nu
mb
er
Co
nce
ntr
ati
on
5 6 7 8 9
12 3 4 5 6 7 8 9
102 3 4 5
Diameter ( m)
All channels normalized Combined channels normalized
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Figure 1.16
Figure 1.17
40
30
20
10
0
Exti
ncti
on
(m
-1m
-1)
5 6 7 8 9
12 3 4 5 6 7 8 9
102 3 4 5
Diameter ( m)
All channels Combined channels
0.16
0.14
0.12
0.10
0.08
0.06
0.04
0.02
0.00
Liq
uid
Wate
r C
on
ten
t (g
m-3
m-1
)
5 6 7 8 9
12 3 4 5 6 7 8 9
102 3 4 5
Diameter ( m)
All channels Combined channels
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1.3.2 Derivation of Bulk Parameters
The particle distributions measured by the particle spectrometers can provide estimates
of many parameters that are relevant to atmospheric processes. Tables 1.3 and 1.4
summarize these parameters and the equations that relate the parameters to the size
distributions. Some of the more commonly derived parameters are described in sections
1.3.2.1 – 1.3.2.5.
The uncertainties that are estimated in the following sections use error propagation
whereas the error in a derived parameter is estimated from the errors in counting, sizing
and sample volume discussed in section 1.2. In general, the uncertainty, σ2, in a derived
parameter, P, is equal to
σP2 = σx1
2 + σx22 + …. + σxn
2 (1.2)
where x1 … xn are the n independent variables and σx12 + σx2
2 + …. + σxn2 are the
estimated uncertainties in these variables. This methodology is often referred to as the
„root sum squared‟ approach to estimating uncertainties from propagated errors.
Table 1.3: Cloud Properties, Hydrometeor Characteristics, and Environmental Impact
Cloud Property Hydrometeor
Characteristic
Environmental Impact
Albedo Number and Surface Area
Phase function and
Extinction
Effective Radius
Climate
Lifetime Number and mass
Fall Velocity
Climate, Weather, and
Hydrological Cycles
Spatial Distribution Number, surface area and
mass
Fall Velocity
Climate, Weather, and
Hydrological Cycles
Precipitation Efficiency
and Rain rate
Number and mass
Fall Velocity
Climate, Weather, and
Hydrological Cycles
Chemical Processing
Efficiency
Number, Surface Area and
Mass Concentration
Fall Velocity
Climate and Hydrological
Cycles
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Table 1.4: Hydrometeor Properties
Number concentration (cm-3) N =
m
i
ic
1
Surface area concentration ( m2cm-3) S =
2
1
i
m
i
iidcs
Mass concentration (g m-3) M =
3
1
6 i
m
i
iiidcs
Fall Velocity (cm s-1) Vt = f(di, g, a, CD)
Phase Function P , = drrcrrF
r
r
)(),,,(2
2
1
Extinction (m-1) Be = drrcrrQ
r
r
e)(),,(
2
2
1
Effective Radius ( m)
Re = m
i
ii
m
i
ii
dc
dc
1
2
1
3
4
3
m = number of size categories
ci = number concentration of hydrometeors in size category, i.
di = average diameter of size category, i.
ri = average radius of size category, i.
si = shape factor of the hydrometeor of size category, i, to account for asphericity
(this factor depends upon the intrinsic property being defined)
i = density of the hydrometeor in size category, i.
a = air density
g = gravitational acceleration
CD = drag coefficient
F = Angular scattering intensity efficiency
Qe = Extinction efficiency
= hydrometeor refractive index
= wavelength of incident light
= Angle of light scattered from the hydrometeor
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1.3.2.1 Total Number Concentration
Particle number concentration is defined as the number of particles per unit volume and
is also the 0th moment of the size distribution. In the case of the light scattering probes
with size ranges from 0.1 to 50, the conventional units are in the number of particles per
cubic centimeter. The method of calculating the total concentration is
SV
n
C
m
i
i
T
1 (1.3)
where
CT = total concentration units = # cm-3
ni = number of particles accumulated in channel i
m = total number of size channels
SV = sample volume as defined in equation 1.1
The estimated uncertainty in number concentration, ignoring coincidence, is ±20%, due
to the uncertainties in sample volume determination.
1.3.2.2 Extinction Coefficient and Visibility
The extinction coefficient is proportional to the geometric cross section of particles and
for spherical particles over the size range from r1 to r2 is defined as
m
i
iieedcdQB
1
2),,(
4 (1.4)
where
Qe = Extinction efficiency
= hydrometeor refractive index
= wavelength of incident light
ci = number concentration of hydrometeors in size category, i.
di = average diameter of size category, i.
For cloud droplets and visible wavelengths, Qe is approximately 2 and the extinction
coefficient is just twice the optical cross section. In equation 2.3 the units of σe are in
inverse length. The extinction coefficient is normally expressed in inverse meters,
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kilometers or mega-meters, depending on whether it is being computed for aerosols or
clouds.
Visibility is inversely proportional to the extinction and is calculated via the Koschmeider
equation, 3.91/σe.
The uncertainty in extinction is:
σe = (σθ2 + σc
2 + 2σd2)1/2 = ((20%)2 + (20%)2 + 2(20%)2)1/2 = ±40% (1.5)
where
σθ = uncertainty in the extinction efficiency
σc = uncertainty in the number concentration
σd = uncertainty in the diameter
Here we multiply the uncertainty in the diameter by two because the diameter is squared
in equation 1.4.
1.3.2.3 Liquid Water Content
The liquid water content, W, is the summation of the individual particle masses per unit
sample volume,
m
i
ii
wdcW
1
3
6 (1.6)
where ρw = density of water.
Note, given that W is usually expressed in g m-3, the value of ρw is 1.0e6 g m-3 and ci
and di are converted to units of # m-3 and meters, respectively.
The uncertainty in W is:
σw = (σc2 + 3σd
2)1/2 = ((20%)2 + 3(20%)2)1/2 = ±40% (1.7)
where
σc = uncertainty in the number concentration
σd = uncertainty in the diameter
Here we multiply the uncertainty in the diameter by three because the diameter is
squared in equation 1.6. Note: this uncertainty can be much larger if the particles are
aspherical and the density is different than that of water.
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1.3.2.4 Mean, Median Volume and Effective Diameter
The mean diameter is the arithmetric average of all the particle sizes, also known as the
1st moment of the size distribution, and is calculated by
T
m
i
ii
C
dc
D1 (1.8)
The uncertainty in the mean diameter is approximately the same as the uncertainty in
diameter, ±20%, even though in (1.8) there is the concentration parameter also in the
equation. Given that concentration appears in the numerator and denominator of (1.8),
on average the uncertainty in this variable cancels and it is only the uncertainty in
determining the size that dominates.
The median volume diameter is the size of droplet, below which 50% of the total water
volume resides. This is computed as follows.
Step 1: Compute the liquid water content (2.4)
Step 2: Beginning at the first size channel and calculate the accumulated mass, Sn= w1+
w2 + ... wn, where w1 is the mass of water in channel 1 and wn is the channel where the
accumulated mass > 0.5w, i.e. greater than or equal to 50% of the total LWC.
Step 3: Compute the median volume diameter, Dmvd, by interpolating linearly between
the channels that bracket where the accumulated mass exceeded the total LWC
Dmvd = Dn-1 + (0.5 – Sn-1/Sn)*(Dn-Dn-1) (1.9)
where
Sn = the sum of water masses in channels 1 to n, up until S> 0.5w
Sn-1 = the sum of water masses in channels 1 to n-1
w = total liquid water content
Dn = the diameter of the size channel when S = Sn
Dn-1 = the diameter of the size channel when S = Sn-1
The effective radius is a parameter used by climate modelers to describe the optical
properties of cloud hydrometeors and also in retrievals of cloud properties from satellite
measurements. It is not so much a physical dimension of the particle population as a way
to parameterize the optical properties of this population as a function of the liquid water
content and the optical cross section of the particles. It has been expressed many ways
but is commonly seen in the literature (McFarquhar and Heymsfield, 1998) as
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Form DOC-0222 3 4 © 2009 DROPLET MEASUREMENT TECHNOLOGIES, INC.
m
i
iw
e
r
wr
1
24
3 (1.10)
As discussed by McFarquhar and Heymsfield (1998), this definition is only meaningful for
water clouds. The definition becomes more complicated in ice clouds and the
denominator of 2.7 should be replaced with a cross sectional area that represents the
average population of non-spherical particles.
Given that operationally the effective radius is also defined as the ratio of the water
content to the extinction, although there is some correlation between the uncertainties
in these two parameters, a conservative estimate of the uncertainty in effective radius is
σRE = (σw2 + σe
2)1/2 = ((40%)2 + (40%)2)1/2 = ±57% (1.11)
1.3.3 Derivation of Refractive Index
The refractive index is derived using a look-up table that has the theoretical values for
the forward and backward scattering cross sections as a function of refractive index. As
shown for three refractive indices, in Fig. 1.18, there are various pairs of forward and
backscattering cross sections that are unique to specific refractive indices. Table 1.5 also
lists these pairs as a function of particle diameter and refractive index. In the PBP file for
the forward and non-polarized scattering data, the information is listed as counts. These
data must be converted to equivalent scattering cross section values as discussed above
in section 1.3.1.
To derive the refractive index of a particle, the measured forward and backscattering
counts must be converted to the corresponding scattering cross sections using the
calibration scale factors discussed in section 1.1.1 and 1.3.1. The second step is to search
the table for all occurrences of the forward scattering value. Since an exact match will
not necessarily be found, a range of values around the measured value can be prescribed
that is plus and minus some percentage of the measured value. For each of the forward
scattering values found in the table, compare the corresponding backscatter values with
the one measured. Again, a plus or minus range should be prescribed prior to the search.
When a pair of forward and backward scattering cross sections is found that match those
that were measured within the specified error for acceptance, this will indicate the most
probable refractive index for that particle.
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In many cases there may not be a unique answer, i.e., as seen in Figure 1.18, there are
overlapping regions in the graph where particles with different refractive indices will
have similar forward to backward relationships. In those cases where more than one
match is found, the investigator can choose to discard the information or keep all the
matches but in a separate analysis category that indicates the possibility of more than a
single refractive index. If the particle population is assumed to be composed of
approximately the same composition, then for an ensemble of particles of many sizes,
those sizes that have a unique forward to backward relationship will help decide the
correct refractive index for those particles whose size is associated with more than one
forward to backward scattering pair.
Note that the refractive index can be derived only if the particles are assumed spherical.
In addition, the sample shown in Table 1.5 does not take into account any light
absorption by the particles, i.e. the complex refractive indices only include the real
component. Tables can also be calculated to include imaginary components but this
increases the complexity of the analysis as well as the resulting uncertainty.
Figure 1.18
1E-009 1E-008 1E-007 1E-006
Forward Scattering Cross Section (cm2)
1E-011
1E-010
1E-009
1E-008
1E-007
Bac
k S
ca
tteri
ng
Cro
ss S
ec
tio
n (
cm
2)
= 1.33
= 1.44
= 1.60
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Table 1.5: Sample Table of Forward and Backward Scattering Cross Sections
Size
fwdrf1.3
3
bckrf1.3
3
fwdrf1.4
0
bckrf1.4
0
fwdrf1.4
4
bckrf1.4
4
fwdrf1.4
8
bckrf1.4
8
1 7.00E-09 3.01E-11 7.49E-09 2.85E-11 7.29E-09 4.12E-11 6.96E-09 8.79E-11
1.01 7.25E-09 2.65E-11 7.72E-09 2.79E-11 7.56E-09 4.86E-11 7.33E-09 1.10E-10
1.11 1.07E-08 3.05E-11 1.11E-08 8.72E-11 9.86E-09 1.10E-10 8.06E-09 1.27E-10
1.21 1.41E-08 4.33E-11 1.27E-08 5.51E-11 1.15E-08 9.86E-11 9.48E-09 1.87E-10
1.31 1.87E-08 2.27E-11 1.44E-08 9.12E-11 1.04E-08 1.62E-10 7.05E-09 2.96E-10
1.41 2.09E-08 5.33E-11 1.55E-08 8.62E-11 1.11E-08 1.03E-10 6.41E-09 1.64E-10
1.51 2.47E-08 2.43E-11 1.29E-08 1.10E-10 7.84E-09 3.14E-10 5.93E-09 4.89E-10
1.61 2.45E-08 6.28E-11 1.27E-08 1.01E-10 6.54E-09 1.23E-10 4.43E-09 2.63E-10
1.71 2.47E-08 6.51E-11 8.85E-09 2.05E-10 6.75E-09 3.48E-10 7.94E-09 3.60E-10
1.81 2.30E-08 1.08E-10 7.33E-09 1.87E-10 6.74E-09 3.21E-10 1.41E-08 5.82E-10
1.91 1.85E-08 1.57E-10 8.27E-09 3.06E-10 1.20E-08 3.07E-10 2.05E-08 5.19E-10
2.01 1.65E-08 2.24E-10 9.11E-09 4.02E-10 2.07E-08 5.52E-10 3.22E-08 4.43E-10
2.11 1.11E-08 3.16E-10 1.56E-08 4.52E-10 2.87E-08 4.76E-10 4.36E-08 1.16E-09
2.21 1.01E-08 3.99E-10 2.61E-08 7.42E-10 4.13E-08 6.48E-10 4.93E-08 6.27E-10
2.31 1.05E-08 5.53E-10 3.44E-08 7.04E-10 5.36E-08 1.13E-09 5.26E-08 7.46E-10
2.41 1.23E-08 6.25E-10 4.90E-08 7.33E-10 5.88E-08 9.74E-10 5.46E-08 1.77E-09
2.51 2.05E-08 7.02E-10 5.91E-08 1.29E-09 6.28E-08 7.01E-10 4.65E-08 1.03E-09
2.61 2.82E-08 9.77E-10 6.87E-08 1.04E-09 6.16E-08 1.63E-09 3.68E-08 9.28E-10
2.71 4.13E-08 8.41E-10 7.40E-08 1.06E-09 5.53E-08 1.43E-09 3.01E-08 2.56E-09
2.81 5.51E-08 1.31E-09 7.28E-08 1.19E-09 4.54E-08 8.47E-10 2.19E-08 1.75E-09
2.91 6.68E-08 1.05E-09 6.88E-08 1.72E-09 3.56E-08 1.59E-09 1.88E-08 8.69E-10
3.01 8.07E-08 1.22E-09 6.16E-08 1.67E-09 2.79E-08 2.45E-09 2.57E-08 4.24E-09
3.11 8.75E-08 1.47E-09 4.73E-08 1.40E-09 2.31E-08 9.66E-10 3.53E-08 2.02E-09
3.21 9.44E-08 1.42E-09 3.95E-08 1.07E-09 2.33E-08 1.57E-09 4.88E-08 1.80E-09
3.31 9.47E-08 1.73E-09 3.12E-08 2.39E-09 3.02E-08 2.44E-09 6.41E-08 5.41E-09
3.41 9.16E-08 1.36E-09 2.69E-08 2.08E-09 4.46E-08 8.69E-10 7.66E-08 3.06E-09
3.51 8.68E-08 1.63E-09 2.88E-08 7.22E-10 5.61E-08 2.31E-09 8.48E-08 1.83E-09
3.61 7.76E-08 1.79E-09 3.27E-08 1.91E-09 6.97E-08 1.36E-09 8.53E-08 2.71E-09
3.71 6.84E-08 1.78E-09 4.62E-08 3.60E-09 8.35E-08 1.43E-09 8.08E-08 3.21E-09
3.81 6.05E-08 2.10E-09 5.94E-08 8.53E-10 8.88E-08 2.37E-09 7.02E-08 2.63E-09
3.91 5.08E-08 1.11E-09 6.87E-08 1.71E-09 9.06E-08 1.66E-09 6.36E-08 3.01E-09
4.01 5.03E-08 2.16E-09 8.06E-08 1.48E-09 8.81E-08 1.93E-09 5.11E-08 3.40E-09
4.11 4.46E-08 1.91E-09 8.84E-08 1.55E-09 8.08E-08 2.41E-09 4.81E-08 3.00E-09
4.21 5.25E-08 1.61E-09 9.40E-08 1.57E-09 7.37E-08 2.16E-09 5.13E-08 3.84E-09
4.31 5.28E-08 1.23E-09 9.44E-08 1.84E-09 7.04E-08 2.51E-09 4.99E-08 3.73E-09
4.41 5.85E-08 9.05E-10 9.28E-08 3.62E-09 5.97E-08 2.87E-09 6.02E-08 3.10E-09
4.51 6.27E-08 2.10E-09 8.71E-08 2.13E-09 6.41E-08 2.40E-09 6.49E-08 4.80E-09
4.61 6.62E-08 2.12E-09 8.89E-08 2.17E-09 6.01E-08 3.25E-09 7.43E-08 3.13E-09
4.71 8.03E-08 1.08E-09 8.18E-08 2.43E-09 6.36E-08 2.71E-09 7.73E-08 3.64E-09
4.81 8.16E-08 9.20E-10 7.99E-08 2.64E-09 7.05E-08 3.00E-09 8.02E-08 4.60E-09
4.91 8.87E-08 9.73E-10 8.29E-08 2.69E-09 6.79E-08 3.18E-09 8.46E-08 4.19E-09
5.01 8.51E-08 2.83E-09 7.56E-08 2.66E-09 7.54E-08 3.39E-09 7.86E-08 5.63E-09
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1.3.4 Derivation of Asphericity
The particle shape is evaluated on a particle by particle basis using the same approach as
deriving refractive index, except in this case the refractive index is assumed constant and
the relationship between the forward to backscatter cross sections changes as a result of
shape deviation, i.e. asphericity. There are two approaches. Both approaches require
converting the counts to their respective scattering cross sections. Similar to the tables
for refractive index, a similar table has been constructed for the relationship between
the forward and backscattering as a function of the aspect ratio, where an aspect ratio of
unity designates a sphere, an aspect ratio smaller than one is an oblate spheroid (disk
shaped) and greater than one is a prolate spheroid (football shaped). Table 1.6I shows
the ratio of forward to backscattering for particles with radius between 1 – 10 μm with
the refractive index of ice (1.31) and a range of aspect ratios.
A slightly different methodology is used than with the estimation of refractive index.
First, the particle effective diameter is calculated from the forward scattering cross
section, where the effective diameter is found by assuming the refractive index of the
particle then finding the size in the Mie lookup table that corresponds to the measured
forward scattering signal. Then the ratio is calculated between the measured forward
and backscattering cross sections, after converting the A/D counts to scattering. The
aspect ratio is found from the look up table by going to the column that represents the
size closest to the derived size and finding the ratio closest to the calculated ratio from
the measurements. The value in the first column that is associated with that row will be
the estimated aspect ratio.
An alternative approach is to search the entire table for the forward to back scattering
ratios that most closely match the ratio calculated from the measurements. As seen in
the examples in Table 1.6, there are multiple values that depend on the various pairs of
size versus aspect ratio. From all the matches, the one associated with the particle radius
that most closely matches the size derived from the forward scattering will be used to
estimate the aspect ratio.
An empirical approach can also be taken that takes advantage of all three signals, the
forward scattering, non-polarized and polarized backscattering (only in the CAS-POL). For
every particle, three ratios are calculated: 1) forward to non-polarized backscatter
(F2Bnon), 2) forward to polarized backscatter (F2Bpol) and 3) nonpolarized to polarized
backscatter ratio (noPOL2POL). Figure 1.19 shows averages of these three ratios, along
with their standard deviations (vertical bars), as a function of the average forward
scattering value for water droplets, quartz and dust particles. From these comparisons,
we can see that there are some particle sizes, represented by the forward scattering
value, where there is a much greater difference between the ratios for the three types of
particles than for other sizes. This figure also shows that the forward scattering values
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where the greatest separation is seen as a function of particle type is not the same for
each of the three ratios. This means that the three ratios can be used, in different
combinations with respect to the forward scattering values to differentiate between
different shapes.
Table 1.6: Sample Table of Aspect Ratios vs. Forward to Backscatter
Particle Radius
Aspect
Ratio 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0
0.5 307 850 290 506 390 0 0 0 0 0
0.6 338 602 221 462 286 314 352 308 265 204
0.7 310 265 153 303 214 319 256 245 180 164
0.8 216 186 108 163 150 273 164 156 127 116
0.9 164 215 74 118 105 173 98 80 75 73
1 151 248 64 73 68 165 57 82 61 95
1.1 159 201 72 90 117 139 87 76 68 57
1.2 180 165 83 103 98 169 101 97 79 74
1.3 207 176 87 115 108 165 146 116 100 95
1.4 238 215 91 122 117 152 209 158 134 123
1.5 271 269 101 136 150 154 226 171 146 134
1.6 310 344 120 165 183 134 180 184 196 139
1.7 354 439 149 190 214 135 164 185 193 199
1.8 404 538 202 227 256 147 150 166 143 159
1.9 455 635 282 278 292 153 0 0 0 0
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Figure 1.19
800 1000 1200 1400 1600 1800
Forward Scattering Counts
12
16
20
Fo
rwa
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o N
on
-Po
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Quartz
Dust
2
4
6
8
10
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10
20
30
40
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1.3.5 Evaluation of Cloud Microstructure
Measurements of the fine-scale structure of clouds can give us useful information about
the physical processes that underlie cloud evolution. Although the fundamental processes
of nucleation, condensation and coalescence are well understood conceptually, when
taken in the context of real clouds in the atmosphere, their relative interactions are
much more complex. For example, entrainment and mixing, turbulence, and
inhomogeneities in supersaturation will produce changes in the cloud‟s microstructure
that will lead to changes in the rate at which the new droplets are formed, and others
are removed or grow more rapidly than conventional theory predicts.
The light scattering probes offer the opportunity to evaluate the cloud microstructure
because they analyze individual particles. This feature has been exploited since the mid-
1980‟s to examine how droplets are spatially distributed in cloud (Baumgardner, 1986;
Paluch and Baumgardner, 1989; Baker, 1992; Baumgardner et al., 1993; Malinowski et
al., 1994). All of these studies investigated the inhomogeneity of cloud droplet
distributions by analyzing the particle-by-particle measurements from light scattering
instruments.
The basic premise is that droplets should be distributed uniformly and randomly in a well-
mixed cloud. This means that when the spatial distribution is measured, i.e. the distance
between individual droplets, their spacing can be described with a Poisson probability
distribution, as shown in Fig. 1.20. In this figure, at the top is illustrated that the for the
CAS, used in this example, the time between particles are recorded, the interarrival
times. These are used to generate a frequency distribution as shown in the graph of
frequency of events versus arrival time. The frequency has been normalized here by the
total number of events. In this way of representing the data, for a large number of
events, a frequency distribution is an approximation to a probability distribution.
The probability that an arrival time, Δt, will be longer than some time, t, is given by
P(Δt > t) = e-nt 1.12
where n is the particle rate,
n = (Concentration)(Sample Area)(Air Velocity) 1.13
and the sample area is that of the CAS. Hence, we can predict the probability distribution
from the concentration measurements, derived from equation (1.3).
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Form DOC-0222 4 1 © 2009 DROPLET MEASUREMENT TECHNOLOGIES, INC.
Figure 1.20
The dashed line shown in Fig. 1.20 shows the predicted distribution based on the number
concentration for an example of measurements in a wave cloud. The solid line shows the
distribution of arrival times that was actually measured. The differences between the
predicted and measured provide information about the underlying processes that are
changing the spatial distribution from one that is well-mixed to that where the droplets
are organized in a different arrangement than predicted from Poisson statistics.
It is beyond the scope of this document to describe the possible mechanisms by which
droplet ensembles do not behave a expected, but some of the possible processes could
be entrainment that mixes cloud-free air with the cloud, small scale turbulence,
electrification and droplet charging, or activation of new droplets or coalescence.
0.14
0.12
0.10
0.08
0.06
0.04
0.02
0.00
Arr
iva
l F
req
uen
cy
600500400300200100
Interarrival Time ( s)
Upwind Measured Upwind Predicted
Δt1 Δt2 Δt3 Δt4 Δt5 Δt6
Predicted for randomly uniform distribution
and measured averageconcentration, Cm
Steeper measured
slopes signifies cluster
of particles with higher
concentration.
Cm = Σn/(Volume)
Cderived Frequency
distribution
slope
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1.4 Further Reading on Single Particle Scattering
Baker, B., 1992: Turbulent entrainment and mixing in clouds: A new observational
approach, J. Atmos. Sci., 49, 387-404.
Baumgardner, D., 1983: An analysis and comparison of five water droplet measuring
instruments. J. Appl. Meteor., 22, 891-910.
Baumgardner, D., J.W. Strapp, and J.E. Dye, 1985: Evaluation of the forward scattering
spectrometer probe Part II: Corrections for coincidence and dead-time losses.,
J.Atmos. and Oceanic Tech., 2, 626-632.
Baumgardner, D., 1986: A new technique for the study of cloud microstructure. J.
Oceanic and Atmos. Tech., 3, 340-343.
Baumgardner, D., W.A. Cooper, and J.E. Dye, 1990: Optical and electronic limitations of
the forward scattering spectrometer probe. Liquid particle Size Measurement
Techniques: 2nd Volume, ASTM STP 1083, E. Dan Hirleman, W.D. Bachalo, and Philip
G. Felton, Eds. American Society for Testing and Materials, Philadelphia, 1990,
115-127.
Baumgardner, D., J.E. Dye, and B.W. Gandrud, 1989: Calibration of the forward
scattering spectrometer probe used on the ER-2 during the airborne Antarctic
ozone experiment. J. Geophys. Res., 94, 16,475-16,480.
Baumgardner, D. and M. Spowart, 1990: Evaluation of the forward scattering
spectrometer probe. Part III: Time response and laser inhomogeneity limitations. J.
Atmos. Oceanic Tech., 7, 666-672.
Baumgardner, D., J.E. Dye, R.G. Knollenberg, and B.W. Gandrud,1992: Interpretation of
measurements made by the FSSP-300X during the Airborne Arctic Stratospheric
Expedition, J. Geophys. Res., 97, 8035-8046.
Baumgardner, D., B. Baker, and K. Weaver 1993: A technique for the measurement of
cloud structure on centimeter scales, J. Atmos. Oceanic Tech., 10, 557-565.
Baumgardner, D., J.E. Dye, B. Gandrud, K. Barr, K. Kelly, K.R. Chan, 1996: Refractive
indices of aerosols in the upper troposphere and lower stratosphere, Geophys. Res.
Lett, 23, 749-752.
Baumgardner, D., H. Jonsson, W. Dawson, D. O‟Connor and R. Newton, 2001: The cloud,
aerosol and precipitation spectrometer (CAPS): A new instrument for cloud
investigations, Atmos. Res., 59-60, 251-264.
Baumgardner, D., J.F. Gayet, H. Gerber, A. Korolev, and C. Twohy, 2002: Clouds:
Measurement Techniques In-Situ, in the Encyclopaedia of Atmospheric Science,
Eds. J, Curry, J. Holton and J. Pyle, Academic Press, U.K., ISBN: 0-12-227090-8
Baumgardner, D., H. Chepfer, G.B. Raga, G.L. Kok, 2005: The Shapes of Very Small Cirrus
Particles Derived from In Situ Measurements, Geophys. Res. Lett.,32, L01806,
doi:10.1029/2004GL021300, 2005.
Bohren, C. F. and Huffman, D. R.: Absorption and Scattering of Light by Small Particles,
John Wiley, Hoboken, N.J., 1983.
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Borrmann, S., Beiping Luot and Michael Mishchenko, 2000: Application of the T-matrix
method to the measurement of aspherical (ellipsoidal) particles with forward
scattering optical particle counters, ,J. Aerosol Sci. 31, 789-799.
Brenguier, J.L. and L. Amodei , 1989: Coincidence and Dead-Time Corrections for Particle
Counters. Part I: A General Mathematical Formalism, Journal of Atmospheric and
Oceanic Technology, 6,575–584.
Brenguier, J.L., 1989: Coincidence and Dead-Time Corrections for Particles Counters.
Part II: High Concentration Measurements with an FSSP, Journal of Atmospheric
and Oceanic Technology, 6, 585–598.
Brenguier, J.L., A.R. Rodi, G. Gordon, and P. Wechsler, 1993: Real-Time Detection of
Performance Degradation of the Forward-scattering Spectrometer Probe, Journal
of Atmospheric and Oceanic Technology, 10, 27–33.
Brenguier, J.L., D. Baumgardner, B. Baker, 1994: A review and discussion of processing
algorithms for FSSP concentration measurements, J. Atmos. Ocean. Tech.,11,
1409-1414.
Brooks, S.D., Toon, O.B., Tolbert, M.A., Baumgardner, D., Gandrud, B.E., Browell, E.,
Flentje, H., Wilson, J., 2004: Polar Stratospheric Clouds during SOLVE/THESEO:
Comparison of Lidar Observations with In-Situ Measurements, J. Geophys. Res.109,
D02212,doi: 10.1029/2003JD003463.
Chepfer, H., V. Noel, P. Minnis, D. Baumgardner, L. Nguyen, G. Raga, M.J. McGill, P.
Yang, 2005: Particle Habit In Tropical Ice Clouds During CRYSTAL-FACE:
Comparison of Two Remote Sensing Techniques With In Situ Observations, J.
Geophys. Res., VOL. 110, D16204, doi:10.1029/2004JD005455.
Cooper, W.A., 1988: Effects of coincidence on measurements with a forward scattering
spectrometer probe, Journal of Atmospheric and Oceanic Technology, 5, 823–832.
Dye, J.E. and D. Baumgardner, 1984: Evaluation of the forward scattering spectrometer
probe: I. Electronic and optical studies. J. Atmos. Ocean. Tech., 1, 329-344.
Field, P. R., R. Wood, P. R. A. Brown, P. H. Kaye, E. Hirst, R. Greenaway, and J. A.
Smith, 2003: Ice Particle Interarrival Times Measured with a Fast FSSP, Journal of
Atmospheric and Oceanic Technology, 20, 249–261.
Gardiner, B. A., and J. Hallett, 1985: Degradation of in-cloud forward scattering
spectrometer probe measurements in the presence of ice particles, J. Atmos.
Oceanic Technol., 2, 171– 180.
Heymsfield, A.J., 2007: On Measurements of Small Ice Particles in Clouds, Geophys. Res.
Lettr, 34, doi:10.1029/2007GL030951, 6 pp.
Knollenberg, R.G., 1981: Techniques for probe in cloud microstructure. Clouds, Their
Formation, Optical Properties, and Effects, P.V. Hobbs and A. Deepak, Eds.,
Academic Press, 495 pp.
McFarquhar, G. M. J. Um, Matt Freer, D. Baumgardner, G. L. Kok, and G. Mace, 2007:
Importance of small ice crystals to cirrus properties: Observations from the
Tropical Warm Pool International Cloud Experiment (TWP-ICE), Geophys. Res.
Lettr., 34, L13803, doi:10.1029/2007GL029865.
McFarquhar, G. M. and A.J. Heymsfield, 1998: The Definition and Significance of an
Effective Radius for Ice Clouds,J. Atmos. Sci.,55 , 2039-2052.
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Malinowski, S.P., M.Y. Leclerc and D. Baumgardner, 1994: Fractal analysis of high
resolution cloud droplet measurements, J. Atmos. Sci., 51, 397-413.
Mie, G. (1908) Beitrage zur optik trüber medien speziell kolloidaler metallösungen. Ann.
Phys., 25, 377-445.
Paluch, I. and D. Baumgardner, 1989: Entrainment and fine scale mixing in a continental
convective cloud. J. Atmos. Sci., 46, 261-278.
Pontikis, C., E. Hicks, A. Rigaud, and D. Baumgardner, 1991: A method for validating FSSP
measurements using observational data, J. Atmos. Oceanic Tech.,8, 802-811.