AMTAtmospheric Measurement TechniquesAMTAtmos. Meas. Tech.1867-8548Copernicus PublicationsGöttingen, Germany10.5194/amt-9-5135-2016Thermodynamic correction of particle concentrations measured by underwing
probes on fast-flying aircraftWeigelRalfweigelr@uni-mainz.dehttps://orcid.org/0000-0003-1316-0292SpichtingerPeterhttps://orcid.org/0000-0003-4008-4977MahnkeChristophhttps://orcid.org/0000-0003-2606-1680KlingebielMarcusAfchineArminhttps://orcid.org/0000-0002-7669-8295PetzoldAndreashttps://orcid.org/0000-0002-2504-1680KrämerMartinahttps://orcid.org/0000-0002-2888-1722CostaAnjahttps://orcid.org/0000-0003-3097-6269MollekerSergejReutterPhilipphttps://orcid.org/0000-0001-8932-6565SzakállMiklóshttps://orcid.org/0000-0002-0261-4802PortMaxGrulichLucasJurkatTinaMinikinAndreashttps://orcid.org/0000-0003-0999-4657BorrmannStephanhttps://orcid.org/0000-0002-4774-9380Institut für Physik der Atmosphäre, Johannes Gutenberg University, Mainz, GermanyParticle Chemistry Department, Max Planck Institute for Chemistry, Mainz, GermanyInstitut für Energie- und Klimaforschung (IEK-7), Forschungszentrum Jülich, Jülich, GermanyInstitut für Energie- und Klimaforschung (IEK-8), Forschungszentrum Jülich, Jülich, GermanyInstitute of Computer Science, Johannes Gutenberg University, Mainz, GermanyInstitut für Physik der Atmosphäre, Deutsches Zentrum für Luft- und Raumfahrt (DLR), Oberpfaffenhofen, Germanynow at: Max Planck Institute for Meteorology, Hamburg, Germanynow at: Abteilung Flugexperimente (FX), Deutsches Zentrum für Luft- und Raumfahrt (DLR), Oberpfaffenhofen, GermanyRalf Weigel (weigelr@uni-mainz.de)20October2016910513551622December201518December201526September201627September2016This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://amt.copernicus.org/articles/9/5135/2016/amt-9-5135-2016.htmlThe full text article is available as a PDF file from https://amt.copernicus.org/articles/9/5135/2016/amt-9-5135-2016.pdf
Particle concentration measurements with underwing probes on aircraft are
impacted by air compression upstream of the instrument body as a function of
flight velocity. In particular, for fast-flying aircraft the necessity arises
to account for compression of the air sample volume. Hence, a correction
procedure is needed to invert measured particle number concentrations to
ambient conditions that is commonly applicable to different instruments to
gain comparable results. In the compression region where the detection of
particles occurs (i.e. under factual measurement conditions), pressure and
temperature of the air sample are increased compared to ambient (undisturbed)
conditions in certain distance away from the aircraft. Conventional
procedures for scaling the measured number densities to ambient conditions
presume that the air volume probed per time interval is determined by the
aircraft speed (true air speed, TAS). However, particle imaging instruments
equipped with pitot tubes measuring the probe air speed (PAS) of each
underwing probe reveal PAS values systematically below those of the TAS. We
conclude that the deviation between PAS and TAS is mainly caused by the
compression of the probed air sample. From measurements during two missions
in 2014 with the German Gulfstream G-550 (HALO – High
Altitude LOng range) research aircraft we develop a procedure to correct the
measured particle concentration to ambient conditions using a thermodynamic
approach. With the provided equation, the corresponding concentration
correction factor ξ is applicable to the high-frequency measurements of
the underwing probes, each of which is equipped with its own air speed sensor
(e.g. a pitot tube). ξ values of 1 to 0.85 are calculated for air speeds
(i.e. TAS) between 60 and 250 m s-1. For different instruments at
individual wing position the calculated ξ values exhibit strong
consistency, which allows for a parameterisation of ξ as a function of
TAS for the current HALO underwing probe configuration. The ability
of cloud particles to adopt changes of air speed between ambient and
measurement conditions depends on the cloud particles' inertia as a function
of particle size (diameter Dp). The suggested inertia correction
factor μ (Dp) for liquid cloud drops ranges between 1 (for
Dp < 70 µm) and 0.8 (for
100 µm < Dp < 225 µm) but
it needs to be applied carefully with respect to the particles' phase and
nature. The correction of measured concentration by both factors, ξ and
μ (Dp), yields higher ambient particle concentration by about
10–25 % compared to conventional procedures – an improvement which can
be considered as significant for many research applications. The calculated
ξ values are specifically related to the considered HALO
underwing probe arrangement and may differ for other aircraft. Moreover,
suggested corrections may not cover all impacts originating from high flight
velocities and from interferences between the instruments and e.g. the
aircraft wings and/or fuselage. Consequently, it is important that PAS (as a
function of TAS) is individually measured by each probe deployed underneath
the wings of a fast-flying aircraft.
Introduction
Clouds constitute one of the most important regulators of the Earth's energy
balance. The radiation net effect of various cloud types it is not ultimately
known yet. The albedo effect and the greenhouse effect of clouds are driven
by the cloud element's microphysical properties (e.g. the particles' number,
size and shape). In a first-order estimate the cloud particle size is mostly
determined by the cloud particle number concentration, since the available
water vapour for condensation is distributed via diffusion over the number of
particles present within a cloud. Cloud particle number concentrations are
highly variable (e.g. Krämer et al., 2009), typically ranging from a few
thousandths up to hundreds of particles per cubic centimetre, since specific
mechanisms of cloud formation are determined by local dynamics (e.g.
Spichtinger and Gierens, 2009; Kärcher and Lohmann, 2002).
Airborne in situ investigations related to the microphysical properties of
cloud particles, ice crystals and hydrometeors are essential for answering
many scientific questions and therefore measurement methods by means of
underwing probes are widely used (cf. Baumgardner et al., 2011; Wendisch and
Brenguier, 2013). Airborne in situ measurements of cloud elements are
generally influenced by aerodynamic conditions at the instrument's
individual mounting position, i.e. due to specific flow fields around the
aircraft's fuselage and wings (Drummond and MacPherson, 1985; Norment, 1988).
Local fluctuations of the air density may occur in the vicinity of
measurement instruments and their sensing volumes (MacPherson and
Baumgardner, 1988), which can affect typical measurements like particle
number concentrations and subsequently derived distributions of surface
areas or volumes. Consequently, if possible, the thermodynamic conditions
during particle detection need to be considered for gaining accurate and
comparable results.
Two scientific missions were carried out in 2014 with the German Gulfstream
G-550 (HALO – High Altitude LOng range), the sister ship
of the US research aircraft HIAPER (High-Performance Instrumented
Airborne Platform for Environmental Research) (Laursen et al., 2006):
(1) ML-CIRRUS, from 24 March to 30 April with a total of ∼ 71
measurement flight hours at midlatitudes over Central Europe (Voigt et al.,
2016), and (2) ACRIDICON-CHUVA, during September, with overall ∼ 96
local mission flight hours in tropical regions, over the Amazonian basin,
Brazil. During both missions, several independent underwing probes were
deployed (e.g. the Cloud Combination Probe – CCP; the Small Ice Detector –
SID3; the Cloud, Aerosol and Precipitation Spectrometer – CAPS; the Coud and
Aerosol Spectrometer – CAS; the Precipitation Imaging Probe – PIP; and the
Particle Habit Imaging and Polar Scattering Probe – PHIPS) for studies
concerning cloud particle microphysical properties at relative high flight
velocities reached by HALO (up to Mach 0.75). Thus, the impacts on
the air flow conditions towards underwing probes, previously considered
numerically for flight velocities between 50 and 130 m s-1 (Norment
and Quealy, 1988) and empirically for up to 100 m s-1 (MacPherson and
Baumgardner, 1988), need to be reassessed for the air compression accompanied
with high flight velocities.
The diagram in Fig. 1 shows an aircraft fuselage under flight conditions when
passing a field of enhanced particle concentration, e.g. a cloud. By means
of avionic (meteorological) sensors in the air data boom (cf. Fig. 1b; also
referred to as nose boom) the ambient static air pressure (p1) and
temperature (T1) are almost undisturbedly measured. The dynamic pressure
proportion provided by the aircraft avionic sensors is transferable into the
true air speed (TAS) according to Bernoulli's law and describes the aircraft
speed relative to the current motion of air.
Illustration of the aircraft geometry, different types of probes
and their underwing position and air compression effects. (a) The moving
aircraft induces an increase of particle concentration in particular
upstream of the underwing probes (grey-shaded area). Parameters used for
deriving a thermodynamic correction are listed for ambient (undisturbed)
conditions (green box) and for measurement conditions (blue box). Note that
specified velocities refer to the moving aircraft or instrument relative to
the air or the particles. (b) The top-view diagram of the aircraft indicates
the probe's mounting position during the ML-CIRRUS and the ACRIDICON-CHUVA
field missions. Data originating from the probes indicated in red are used
for this study. (Instrument name acronyms are specified in the text.)
The underwing instrument probes are contained inside Particle Measuring
Systems (PMS) standard canisters (with outer diameter of ∼ 177 mm)
which, in the HALO configuration, are pairwise mounted at an underwing pylon
such that the instrument is placed 360 mm (±30 mm) underneath the
aircraft wings. The instruments' detection volume is positioned
∼ 100 mm upstream of the wing's leading edge. This particular
underwing positioning of the cloud probes partly results from pioneer work
done in the past by comprehensive investigations concerning the impact of the
air flow in the vicinity of an aircraft's wing on cloud particle trajectories
(King, 1984; King, 1986a, b; Norment, 1988). Furthermore, detailed
computational fluid dynamics (CFD) simulations were performed to optimise the
particular underwing probe positioning on HALO, as well as for other
purposes. However, the publication of any result of these doubtlessly
valuable studies, for which detailed aircraft geometry data of the G550HALO
were used, is not permitted as a consequence of a proprietary information
agreement with the aircraft's manufacturer (K. Witte, German Aerospace
Centre, personal communications, 2016).
The instruments' probe head has a quasi-aerodynamic shape (individual probe
head designs of three different instruments are shown in Fig. 6). The
individual probe head of the respective instrument is additionally
characterised by extension arms that include the detection laser optics or
other annexes such as the CAS winglet. Although the probe heads are
generally of streamlined shape, the moving probe constitutes a flow resistance
during flight due to the instrument body's cross-sectional area perpendicular
to the direction of the air flow (cf. Fig. 1a). Thus, a compression region
forms in a distance of 0.3–0.5 m upstream of the probe head (Wendisch and
Brenguier, 2013) and the strength of compression is a function of aircraft
speed. Further flow-dynamical influences resulting from the proximity of the
instruments to the wings or the fuselage of an aircraft may contribute to the
modifications on the flow conditions (Drummond and MacPherson, 1985;
MacPherson and Baumgardner, 1988). Primarily, the air compression due to the
moving instrument body decelerates the air speed measurable at the probe, as
the probe air speed (PAS) (DMT, 2009), whereby the rate of deceleration is a
function of TAS. Furthermore, the compression of air results in the
densification of the airborne particles at the point of measurement, i.e.
well inside the compression region. This means that the particle
concentrations measured under compressed conditions need to be scaled to
ambient condition.
We aim to formulate an expression that is based on a thermodynamic
approach to provide a correction factor for inverting measured particle
number concentrations to ambient conditions. The variables contained in the
corrective expression should be available from meteorological data that are
generally measured during research flights. Further variables of the
measurement conditions should be available from the instrument itself,
provided that it is equipped with a pitot tube. The effective correction may
vary for the different instruments, the aircraft type and the position of
the probe relative to the aircraft wings and/or fuselage. However, if the
instrument is not equipped with a pitot tube, or the pitot tube is
inoperative, the air speed at the point of measurement is unknown. In such a
case the herein provided parameterisation of the compression correction
serves as a guideline for adopting the TAS from the aircraft data after
adjustments. In the following, the application of both the derived
thermodynamic correction and the unadjusted aircraft TAS on a data set of
atmospheric measurements illustrates the sensitivity of the results to the
employed procedure. Furthermore, we show that the thermodynamic correction
is relatively insensitive to the instrument position with respect to the
aircraft fuselage, and the correlations of instrument-specific correction
factors demonstrate robustness and consistency of the suggested approach.
Method
In this section, we describe a new method for determining the number
concentration of particles in a given air volume from measured quantities
and from basic thermodynamics. We will particularly emphasise the difference
between our approach and the conventionally used methods, which focus
exclusively on geometrical considerations but neglect effects of air
compression.
For the following examination some definitions need to be particularly
introduced: all velocities that are specified as air speeds (v1,
v2, TAS, PAS) and the velocities of particles (vp) refer to
the moving aircraft or instruments relative to the air as the reference
system. Measurement conditions are those under which the measurement occurs
in the detection region that is impacted by compression. Ambient
(undisturbed) conditions relate to the initial state far away from the
aircraft.
Ambient versus measured particle number densities
The measured number concentration Nmeas (in units of number per
air volume) detected with underwing probes that have a free stream detection
volume Vmeas is defined as
Nmeas=n⋅1As⋅vp⋅1Δt=nVmeas.
Here, n denotes the number of particles detected during the time interval
Δt (in seconds), and vp denotes the velocity (in m s-1) of
particles penetrating the sample area As (in square metres).
With PAS =v2 the detection volume is defined as
Vmeas=As⋅v2⋅Δt.
The ambient particle number concentration in the undisturbed ambient air is
given as
Namb=nambV1,
with the number of particles namb and the ambient air volume
V1 (in cubic metres).
Due to the compression of air upstream of the instruments, the ambient volume
V1 converts into the volume V2. Under the preliminary assumptions
that
the particle number per mass M of the air sample is not affected by
compression (i.e. remains constant and thus
nambM=nmeasM) and
the particles' inertia is negligible for given streamlines
and the ideal gas law (p⋅V=M⋅Rs⋅T; with [p] = kg m s-2, [V] = m3, [M] = kg,
[T] = K) applies, where Rs denotes the
specific gas constant (in J kg-1 K-1; while
J = kg m2 s-2),
we end up with the following equation:
nM=const.n⟹ambRs⋅T1p1⋅V1=nmeasRs⋅T2p2⋅V2.
Then we can derive the expression for determining the ambient particle
number concentration:
Namb⋅Rs⋅T1p1=Nmeas⋅Rs⋅T2p2⟹vp=v2Namb=Nmeas⋅p1p2⋅T2T1.
As will be shown later on (cf. Sect. 2.4), the assumption that the particle
mixing ratios within the flow field upstream of an underwing cloud probe
remain constant (i.e. nambM=nmeasM)
only partially reflects the reality. Essentially the particles' individual
inertia causes a modification of the measurable particle mixing ratio
compared to ambient state, which is generally of increasing importance with
increasing particle size (mass) and with the increase of the aircraft's
flight speed.
TAS-based particle number concentrations
If the air speed at the probe (v2) during measurements is unknown,
e.g. for the case that the probe is not equipped with a pitot tube or when a
present pitot tube is frozen, it is common practice to make the generalised
presumption that the particle speed (vp) equals the TAS (v1) to determine particle number concentrations (cf. Eq. 1).
Equivalent to using the TAS, the same resulting concentration is achieved
when alternatively using the velocity ratio
PASTAS (i.e. v2v1) as the
factor for multiplication with measured particle number concentration
(Nmeas, cf. Eq. 1), i.e.:
Nmeas⋅v2v1=nAs⋅t⋅v2⋅v2v1=nAs⋅t⋅v1.
If pitot tube measurements of PAS are available, the treatment of resulting
Nmeas with the factor PASTAS lacks
any physical rationale and relies only on the geometrical consideration that
V1⋅t-1= TAS ⋅As and that
V2⋅t-1= PAS ⋅As. Nevertheless,
as both procedures yield identical results with the same error level, in the
following the use of TAS for determining a particle number concentration is
treated synonymously to correcting Nmeas (as defined in Eq. 1)
by the factor PASTAS.
This approach results in significantly underestimated particle number
concentrations with respect to the ambient conditions for following reasons:
By presuming v1 as the speed of air while penetrating As
it is insinuated that a certain number of particles per Δt was
detected while probing a linearly enlarged air volume per Δt. The
compression of air causes a deceleration of the air flow upstream of an
underwing probe. Thus, if based on v1, the air volume probed per time
interval is overestimated as the volumetric compression occurring in reality
is not accounted for.
The dynamic pressure proportion gauged by means of pitot tube sensors
is the measure of the air speed towards the pitot tube. Thus, the ratio of
air speeds PASTAS solely results from the
dynamic pressure proportions, or rather the ratio thereof, obtained from two
different sensors, the data boom and the instrument's pitot probe. The
compression upstream of the instrument, however, predominantly impacts the
absolute pressure at the point of measurement in comparison to ambient
conditions. This means that the difference between the ambient state and
measurement conditions, i.e. the compressed state of air within the detection
region, is not accounted for by the ratio
PASTAS.
Indeed, it needs to be taken into account that for susceptible particles the
compression of air upstream of the probe induces changes in a particles'
motion out of the initially undisturbed ambient state, e.g. if the
particles are small enough such that they exhibit sufficient mobility. Thus,
at the point of detection the changed particle motion excludes the
non-restrictive use of v1 to describe the particle velocity through the
detection region of the instrument.
Shadow cast images of non-transparent circular spots on a spinning
disk (for calibration purposes) passing the probes' sample area As
with constant velocity (∼ 23–25 m s-1). For this illustration,
in the data acquisition program, the probe air speed (PAS) is manually varied
stepwise with the finest available resolution for triggering the timing of
imaging. Manually shifting the PAS causes a positive or a negative deviation
(ΔPAS) of the air speed relative to the constant disk rotation speed
vRot. Deformed images relative to the dashed red circles of
identical diameter (according to ΔPAS =±0 % if
vRot= PAS, marked in blue) indicate image distortion that
becomes significant for ΔPAS exceeding 10 % (red boxes). PIP
images are slightly shifted as vRot of two radially opposed
points on the edges of a 5 mm sized disk spot increases with distance from
the disk's centre.
Aspect ratios of taken images as a function of the deviation of the
probe air speed (PAS) from the penetration speed of a circular object through
the instrument's detection region. The image aspect ratio provides a measure
of the distortion strength when the PAS setting is manually shifted in the
data acquisition software compared to the constant penetration speed of a
circular object on the spinning disc used for calibrations of an optical
array probe (OAP). (a) The Cloud Combination Probe's CIPgs;
(b) the Precipitation Imaging Probe (PIP).
Instead, dependent on their size (mass), the particles can be assumed to pass
the instruments' detector with a velocity (vp) that ranges between
v1 and v2 (i.e. v1≤vp≤v2),
while v2 is generally smaller (by up to 30 %) than v1. Strong
indications for the trustworthiness of recorded v2 (PAS) are given by
the imaging technique of CIP-type instruments (also referred to as OAPs –
optical array probes). This instrument type records image slices by means of
a linear diode detector for subsequent reassembling to full 2-D images of
respective particles. The scanning frequency and imaging rate of the linear
diode detector is triggered by the air speed measured by the probe's
pitot tube. Consequently, a significant deviation or falsification of this
PAS measurement would result in distorted images. Laboratory calibrations are
regularly performed by using a spinning disc of known rotation speed.
Non-transparent circular spots on the disk are moved through the instruments
sample area to simulate penetrating particles. The calibrations at relatively
low penetration speeds (∼ 23–25 m s-1) compared to airborne
measurements reveal that a deviation of the probe-measured air speed
considerably exceeding 10 % relative to the disc speed already causes a
visible deformation of taken images as illustrated in Fig. 2. The strength of
image distortion as a function of air speed deviation can be expressed by the
aspect ratio of the taken images (Fig. 3) from a circular object that
penetrates the instrument's detection region when the probe is calibrated
with the spinning disc. The relationship between the image aspect ratio and
the percentage of PAS deviation is almost linear, which appears to be
plausible as the diode array scanning frequency should be proportional to the
values of PAS. Thus the deviation between PAS and particle penetration speed
exhibits a linear relationship with the image aspect ratio. Appropriate
analyses of images taken from initially spherical particles, i.e. from
droplets, may suffice for qualitatively evaluating measured PAS compared to
the factual particle penetration speed. At higher air speeds (e.g. up to
250 m s-1 for HALO) it is expected that even smaller uncertainties of
measured PAS related to the true particle penetration speed cause severe
distortion of resulting images. Thus, for measured v2 we assume the
uncertainty to range within ∼ 10 % if recorded particle images of
droplets do not systematically exhibit a strong and, therefore, obvious
deformation.
The cloud particles' mobility
The ability of particles to adapt to changes in air speed, the
particles' mobility, depends on the particle size, mass and thus inertia and
can be expressed by the calculable relaxation time (Hinds, 1999; Kulkarni et
al., 2011, and Willeke and Baron, 1993, respectively). Cloud particles, for
example, of sizes smaller than 100 µm diameter, moving with
70 m s-1 at atmospheric pressures of 300 hPa and temperatures of
240 K, have relaxation times (at the most 9 milliseconds) on the same order of
magnitude as the compression timescales (2–4 milliseconds at flight speeds
from 125 to 250 m s-1; cf. Sect. 3.2). To assess the ability of larger
cloud particles to adapt to changes in air speed, about 400 particle images
from Cloud Imaging Probe greyscale (CIPgs) measurements over two flights “AC07” and “AC13” during the
HALO mission ACRIDICON-CHUVA (for further details see Sect. 3.4) were
analysed. The aspect ratio of images taken from presumably spherical cloud
particles was charted as a function of particle size. The images of
spheroidal objects were selected by means of an automated image analysis
algorithm after carefully filtering the particle images with respect to the
atmospheric conditions during measurement and appearance (for details cf.
Appendix B). Generally, only images were analysed with image geometries
greater than 75 µm in diameter (along both directions of the
image's main axes). Most of the analysed particle images exhibit a Poisson
spot as a result of Fresnel diffraction (Korolev, 2007). With increasing
distance (Zd) of a particle from the object plane when penetrating
the OAP detection region:
the size of resulting Poisson spot increases and
the optical aberration is amplified; i.e. the particle image exhibits
an expansion compared to the true dimension of the detected cloud element.
The cloud droplet size is reconstructed from the image dimension in relation
to the Poisson spot's size as described by Korolev (2007) – thus, reproduced
particle sizes may be smaller than the 75 µm threshold for the
image size. Particle images emanating from cloud elements which passed the
detection region in a distance that was too far away from the object plane
(Zd > 4) were discarded from further analysis. The
automated analysis is based on the Bresenham algorithm (Bresenham, 1965),
approximating an ellipse to the shape of the particle images (of
15 µm image resolution) that remain after the selection process.
The 395 selected particle images of the data set of two flights that fulfil
the criteria to be further analysed are then charted in terms of image aspect
ratio as a function of reconstructed particle size. In fact, the lengths of
the main axes of the approximated ellipse are used to determine the aspect
ratio of the individual image.
Aspect ratios as a function of the image's main axis dimension as
revealed from the automated reanalysis of ∼ 395 individual particle
images acquired by the CCP during two ACRIDICON-CHUVA mission flights,
“AC07” on 6 September and “AC13” on 19 September 2014, over the Amazonian
basin, Brazil. The automated procedure to identify spherical particles and to
determine their images' aspect ratio by means of the equivalent-ellipse
approximation is described in detail in Appendix B. (a) The
determined aspect ratio of the individual images of spherical particles and
(b) the statistically analysis provided as median of the aspect
ratios together with 10 %, 25 %, 75 % and 90 % percentiles.
Figure 4a depicts the result of this analysis. The scatter of the single data
points (Fig. 4a) is statistically processed by calculating the aspect ratio
median with percentiles (10, 25, 75 and 90 %) in particle diameter size
bins of 15 µm (Fig. 4b). Images of particles with diameter smaller
than 70 µm show distortions of about 13 %, which is synonymous
with a vp- PAS - deviation of less than 13 % (cf. Fig. 3).
For droplets of diameter between 70 and 100 µm the image aspect
ratios increasingly scatter, but the resulting median does not indicate that
v2 deviates from PAS by more than 20 %. The images of particles with
diameter larger than 100 µm exhibit increasing distortion as the
image aspect ratios approach values, suggesting a vp–PAS deviation
of up to 20 %. The observations indicate that the driving forces arising
in the flow field upstream of an underwing probe overcome the inertia
resistance of small cloud elements (Dp < 70 µm) but not of larger cloud elements of diameter
larger than 100 µm. This supports the suggestion that the
penetration speed of the vast majority of detected particles through an OAP's
detection region may be best described by PAS < vp < TAS. Thus, beside the correction to account for the
compression, a further correction concerning the particle inertia may be
applied to resulting particle number concentrations.
CFD simulations of the pressure field and resulting droplet trajectories in
the close vicinity of an OAP instrument (CIP, cf. Sect. 3.1) were performed
(using CFX 17.0 by ANSYS Inc.). For this investigation the aircraft's
structure as well as the particular geometry of the HALO underwing probe
configuration had to remain unconsidered (cf. Sect. 1). With respect to the
flow field boundaries a comparatively large model domain was initialised with
edge lengths of 15 times the instrument's width and 15 times the instrument's
height. The model's mesh comprised 2.17 × 106 nodes and
8.2 × 106 elements containing 15 inflation layers. The flow
field was calculated by solving the Navier–Stokes equation for a steady
state, compressible (transport of enthalpy including the kinetic energy
effects) and turbulent flow. The shear stress transport
k–ω-based turbulence model (e.g. Menter et al., 2003) was used. The
calculations were set up with a turbulence intensity of 5 %. The particle
trajectory calculations, relying on the Schiller–Naumann drag force model
(cf. Naumann and Schiller, 1935), were decoupled from the continuous fluid
simulation as for the simulations any influence of the very few particles on
the flow field was assumed to be negligible. Particles' bouncing from walls
was excluded as well as any turbulent dispersion force. The simulations were
initialised with typical conditions as encountered throughout a (HALO)
measurement flight. One set of atmospheric conditions under undisturbed
ambient conditions was used as the simulation input, for example 409 hPa
(p1) and 241 K (T1). Additionally, a typical TAS of
187 m s-1 (Mach 0.6) was taken from the recorded data set to initialise
the particle trajectory analyses. In the initial state the cloud droplets of
various diameters (5, 50, 70 and 100 µm) were assumed to move
towards the instrument with a speed equal to TAS. The simulation of the
pressure field (Fig. 5) qualitatively supports the observation that the air
is compressed in the OAP's detection region (blue circle) in comparison to
the ambient state. Moreover, the simulations qualitatively agree with the
assumption that the particles' speed is changed compared to their initial
speed when they pass the plane of the OAP's detection region. However, as
will be shown later (cf. Sect. 3.2), quantitatively the simulation exhibits
significant deviations from the in-flight measured compression strength and
thus the strengths of particle deceleration. The simulation, for example,
forecasts a pressure increase in the detection region by about 5.5 %
compared to ambient conditions. Contrarily, the comprehensive data sets of
three independent underwing cloud probes at similar flight speeds
consistently indicate a pressure increase of about 10 % (cf. Figs. 8 and
9). Furthermore, the simulated cloud droplet deceleration is not as
large (12, 3, 2 and 1 % for Dp of 5 µm, 50, 70 and
100 µm, respectively) as suggested by the grade of image
distortion. However, it needs to be noted that these simulations comprise one
particular case of atmospheric conditions with the idealising assumption that
the instrument is aligned isoaxially with the air flow. Small changes of the
aircraft's angle of attack may significantly modify the pressure field
upstream of the cloud probe compared to the CFD simulation of this particular
idealised case. Moreover, any further obstacle to the air flow (e.g. the
aircraft's wing, the neighboured underwing cloud probe or the pylon) is not
taken into consideration by this CFD simulation. Thus it is conceivable that
these simulations do not sufficiently reflect the real measurement
conditions. More comprehensive CFD analyses should doubtlessly also consider
variable atmospheric conditions, the aircraft's geometry and the variable
aircraft's attitude during flight as well as an adjacent flow obstacle. These
new CFD simulations should also account for different particle sizes of both
phases (liquid and frozen), all of which may be coverable only by a separate
study as it exceeds the scope of this publication.
Computational fluid dynamic (CFD) simulations of the pressure field
upstream of a CIP-type instrument head for one initial state at
p1= 409 hPa, T1= 241 K and TAS =vp= 187.29 m s-1. Background colour contours indicate the change
of absolute pressure upstream of the probe. The plane of detection region is
signified by a single bluish circle. Cloud particle trajectories were
simulated for different droplet sizes: (a)Dp= 5 µm, (b)Dp= 50 µm,
(c)Dp= 70 µm and (d)Dp= 100 µm, illustrated by their trace through the detection
region. The change of the particles' speed towards the instrument is colour-coded along the trace correspondingly to the generally decreasing cloud
droplet velocity.
Hence, we conclude that
there are strong indications that the compression of air
causes a densification of small airborne particles (Dp < 70 µm) in the detection region of the considered
instrument;
for these small particles (Dp < 70 µm)
the compression is reflected by systematically lower values of v2 (PAS)
compared to v1 (TAS), exhibiting a discrepancy that is too large to be
covered by a 10 % uncertainty of measured PAS;
for these small particles (Dp < 70 µm)
the particles' velocity vp while passing the instrument sample
area is best approximated with v2, rather than with v1, whilst for
larger particles (Dp > 100 µm) the inertia
forces lead to a particle velocity of PAS < vp < TAS;
the conventionally applied practice of treating Nmeas with
the factor PASTAS (geometric approach) is
invalid for correcting measured number concentration to ambient conditions as
the air volume probed per time interval differs under compressed conditions
from the air volume under ambient conditions;
a method is needed to reasonably correct Nmeas by accounting
for the air compression, particularly at high flight velocities, to determine
Namb;
an additional correction is needed that accounts for the inhibited
mobility of larger cloud droplets (Dp > 100 µm) resulting in a penetration speed through
the OAP detector, which ranges from PAS < vp < TAS, whereas the assumption vp≈ PAS is
invalid for droplets of this size.
Correction of Nmeas based on thermodynamic considerations
The expression that accounts for the described compression effect is
formulated in its general form with Eq. (5). The unknown parameter in this
expression is the probe air temperature T2 that is increased in
comparison to ambient air temperature T1 as a consequence of the
compression. The temperature increase is obtainable by using Bernoulli's law
together with the ideal gas law and, furthermore, by presuming adiabatic
conditions, i.e. the conservation of energy. The derivation emanates from
following different conditions which are illustrated in Fig. 1 for the air velocity v, the air pressure p, the specific
enthalpy h of an uniform system and the gravitational potential ϕ: based on Bernoulli's law for compressible gases the specific enthalpy is
transduced into an expression that includes the air's specific heat capacity
cp (presumed as nearly constant under most of the flight
conditions; cf. Appendix A) and the temperatures states in the ambient
environment and under measurement conditions of the OAP detection region.
Solving the equation for the probe air temperature T2 finally allows for
converting Eq. (5) into the aspired expression:
Namb=Nmeas⋅p1p2⋅1+12008Jkg-1K-1⋅T1v12-v22=Nmeas⋅ξ.
For the detailed steps taken to derive Eq. (7) refer to Appendix A.
Correction for the particle inertia
Apart from the compression correction one further correction needs to be
considered that results from the inertia of probed cloud elements. As
illustrated in Sect. 2.2, small cloud particles (Dp < 70 µm) exhibit enough mobility to adapt a movement
into flight direction that causes the particles to penetrate the OAP
detection region with vp≈ PAS. The same investigation
shows that all detected presumably liquid spheroids with diameter
100 µm < Dp < 225 µm
penetrate the detection region with vp that is about 20 %
faster than the PAS but still about 10 % slower than the measured TAS.
Hence, the assumption of vp≈ PAS seems to lack further
validity for particles with Dp > 100 µm,
whereas more likely a penetration speed of PAS < vp < TAS is to be presumed for particles of this size. As an
example, this means that compact cloud elements of size
100 µm < Dp < 225 µm for
which systematically distorted images are recorded (with aspect ratio of
∼ 0.8; cf. Fig. 4) penetrate the OAP detection region faster (by
∼ 17–20 %, cf. Fig. 3) than the surrounding air at the point of
measurement. In other words, due to the particles' individual inertia, the
large and compact cloud elements (Dp > 100 µm) are over-represented in the detection
region compared to ambient conditions. Thus, for larger cloud droplets the
particles' size (inertia) needs to be considered with the additional
correction μ as a function of Dp such that Eq. (7) in
generalised form reads as
Namb=Nmeas⋅ξ⋅μDp.
Accepting that for small cloud elements (Dp < 70 µm) the inertia is negligible due to the
particles' mobility, a general correction with μ= 1 in most cases may
suffice such that Namb is determined as suggested by Eq. (7).
The previous investigation concerning the grade of distortion of recorded
particle images (Sect. 2.2) suggests that in this particular case for larger
cloud droplets (100 µm < Dp < 225 µm) an inertia correction with μ= 0.8
is appropriate.
Thus, in summary, an inertia correction with μ may be applied by
following particle-size-dependent first-order approach:
μDp=1forcloudparticlesofdiameterDp<70µm0.8forcompactparticles,with100µm<Dp< 225µm.
As corresponding data sets are lacking for larger-sized cloud and
precipitation droplets (225 µm < Dp < 6 mm) the results of available data sets could be
extrapolated towards larger particle sizes. With increasing size of liquid
droplets, i.e. in the millimetre size range, any unbiased image aspect ratio
analysis is impeded as these precipitating droplets are increasingly impacted
to deviate from spherical shapes (Thurai et al., 2009). However, it remains
only to surmise that an inertia correction between 0.8 and 0.7 is to be
applied to liquid cloud elements and precipitating droplets of diameter
225 µm < Dp < 6 mm.
For spherical ice particles further differentiation is required concerning
the definition of particle diameter. In the liquid phase the geometrical
diameter (equivalent to the herein used Dp) and the aerodynamic
diameter (Da) of a particle are almost identical (Dp≈Da with Da= 0.99 ⋅Dp, for atmospheric air pressures of
1000–200 hPa) (Kulkarni et al., 2011; Willeke and Baron, 1993). The
Da of a frozen spheroid, however, significantly differs from
corresponding geometrical diameter (Da= 0.95 ⋅Dp, with negligible uncertainty over the
range of 1000–200 hPa). This means that frozen spheres of any geometrical
size Dp exhibit the aerodynamic behaviour, i.e. the mobility, of a
less inert particle of smaller size, which is expressed by Da.
Thus, for particles of geometrical sizes
70 µm < Dp < 100 µm an
inertia correction of general validity is difficult to specify. For this
particular size range, the value of μ may be closer to 1 in cases when
the particles are frozen as their aerodynamic diameters correspond to smaller
equivalent sizes (e.g. 66.5 µm < Da < 95 µm, at 200 hPa; Kulkarni et al., 2011; Willeke
and Baron, 1993). Frozen cloud elements exhibit reduced material density
(mass) and thus reduced compactness (if ice particles exhibit extremities)
compared to a compact (liquid) cloud droplet of the same geometrical
diameter. As a consequence, grown ice particles (e.g. needles, plates,
dendrites, bullets or higher-grade combinations) may exhibit lower inertia,
yielding μ values above 0.8. Moreover, the mobility of larger ice
particles, i.e. with Dp > 100 µm, may
improve due to a diminishing inertia effect when these particles form
extremities resulting in μ values well between 0.8 and 1.
Furthermore, in the progressed state of ice formation certain disturbances
of the local flow field in the vicinity of underwing probes can cause an
almost uniform population of ice particles (either predominantly columnar or
planar) to pass the OAP detection region with a preferential orientation
(cf. Wendisch and Brenguier, 2013; Sect. 6.4.1.2 therein). Such a
preferential orientation would be visible in recorded 2-D images of these
particles, exhibiting shapes that are systematically aligned. This effect is
indicative of an impact of the local flow field on the ice particles'
airborne state while passing through the detection region.
In essence, any inertia correction turns out to be individually applicable
after careful investigations with respect to the particles' phase and nature
(i.e. density, compactness, shape) during the flight. For data obtained
exclusively from iced clouds, e.g. from measurements in cirrus clouds or in
the outflow anvil of a convective cloud system, it appears suitable to
generally assume an inertia correction with μ values above 0.8.
Corrections of measured cloud particle number concentrations accounting for
the particles' inertia need to be applied carefully. In contrast, the air's
compressibility is generally a feature to be considered which is of
increasing importance with the aircraft's flight velocity. Compared to the
undisturbed ambient state, the compression of the probed air volume upstream
of a flow obstacle exhibits a varying but continuous impact on the particle
number concentrations to be measured. Therefore, for any underwing probe
measurement aiming at cloud element number concentrations under ambient
conditions, the compression of the probed air volume compared to the ambient
state needs a non-restrictive correction as a function of flight velocity.
Applying the compression correction to airborne measurements
The magnitude of compression increases with air speed, i.e. with flight
velocity. Thus, the derived thermodynamic correction should have the largest
effect on data acquired during flights with fast aircraft, for example with
the Learjet-35A, the Gulfstream G-550HALO or HIAPER (up to Mach
0.75, corresponding to ∼ 250 m s-1). The extent of such
corrections underlying both the geometric and the thermodynamic perspective,
and their impact on the measured data, is discussed in the following for
actual measurements from three (out of eight) underwing probes deployed on
the HALO aircraft.
Instrumentation related to cloud particle microphysics
The three selected instruments are PMS-type underwing probes which are
commercially available from the instrument manufacturer Droplet Measurement
Technologies (DMT, Boulder, CO, USA) with the general purpose of
investigating the microphysical properties of cloud elements and
hydrometeors. One particular measurement technique the three instruments have
in common is based on the principle of OAPs as
described by Knollenberg (1970). Advanced developments of the OAP measurement
method led to the shadow cast imaging instruments of different types (Korolev
et al., 1991, 1998; Korolev, 2007; Lawson et al., 2006) that
are currently in use. The HALO underwing probes to be discussed are as
follows.
The CCP combines two detectors:
the Cloud Droplet Probe (CDP), detecting forward scattered
laser light due to particles penetrating the CDP detection area (Lance et
al., 2010) as an advanced development of the Forward Scattering Spectrometer
Probe (FSSP) technique (cf. Dye and Baumgardner, 1984; Baumgardner et al.,
1985; Korolev et al., 1985);
the CIPgs, which records
2-D shadow cast images of cloud elements that cross the individual CIPgs
detection region.
CCP measurements overall cover a particle diameter size range from 2 to
960 µm. The performance of the specific CCP instrument used in this
study is demonstrated by earlier investigations related to clouds in the
tropical convective outflow (Frey et al., 2011), concerning polar
stratospheric clouds (Molleker et al., 2014) or within low-level
mixed-phase clouds in the Arctic (Klingebiel et al., 2015) when deployed at
much slower flight velocities (< 170 m s-1).
The Novel Ice eXpEriment – Cloud, Aerosol and Precipitation
Spectrometer (NIXE-CAPS) described by Meyer (2012) also combines two
measurement techniques:
The CAS-DPOL module (Cloud and Aerosol Spectrometer) is
based on the principle of forward scattering detection similar to the CDP
(cf. above) but, instead of using an open-path detection region (CDP), the
CAPS is equipped with an inlet tube. In addition, the CAS-DPOL discriminates
between spherical and aspherical particles by measuring the change of
polarisation of laser light that is scattered by single particles (cf.
Baumgardner et al., 2001, 2014).
Additionally, NIXE-CAPS is equipped with a CIPgs instrument (cf. CCP).
With NIXE-CAPS cloud particles with diameters between 0.6 and
∼ 950 µm are detected. Note that the thermodynamic correction
derived here applies as such to particle number concentrations measured
particularly with the OAPs (the CIPgs probes and the PIP) since the flow
conditions inside the inlet tube of the CAS-DPOL differ from those of the
open-path instruments.
The PIP detects precipitating cloud elements and hydrometeors by means of
particle-induced shadow projection onto a diode sensor, allowing for a 2-D
particle imaging similar to the CIPgs. In comparison to the CIPgs, the PIP
setup features an increased detection volume that covers larger particle sizes
with 100 µm < Dp < 6400 µm.
Diagrams and images of the different instrument heads of
quasi-streamlined design. Top: Cloud Combination Probe (CCP) with
90∘ angled wedge. Middle: combined probe head of 90∘ angled
wedge and additional winglet of NIXE-CAPS. Bottom: Precipitation Imaging Probe (PIP) with half-sphere probe head.
One major difference between CCP, NIXE-CAPS and PIP is the
instrument-specific design of the probe heads. As shown in Fig. 6, CCP is
equipped with a 90∘ angled wedge. NIXE-CAPS combines a wedge of the
same shape with an additional aerodynamic winglet that may significantly
contribute to the effective cross-sectional area of the NIXE-CAPS body. PIP
is equipped with a half-sphere front cap. The different instrument heads have
individual extension tips. Between the tips a free laser beam crosses the
freely flowing sample air through which the particles pass. The sample area
As of the probes, where the instrument is sensitive for particles
crossing the open laser beam, is located almost half way between the tips.
One further important difference of the three instruments is their mounting
position on HALO with respect to the aircraft fuselage (cf. Fig. 1b). PIP is
mounted closest to the aircraft fuselage under the portside wing. NIXE-CAPS
and CCP are positioned under the starboard wing on the intermediate and
outbound hardpoints, respectively. Thus, with the three selected instruments
the full range of available underwing probe positions with respect to the
aircraft fuselage of HALO is covered.
Specific correction factor ξ for HALO instruments
The continuous measurements of the parameters v1 (TAS), v2 (PAS),
T1 (static air temperature), p1 (static ambient pressure) and
p2 (static pressure at the probes) during flight allow for deriving the
factors for the geometric correction PASTAS and
the thermodynamic correction ξ as a function of TAS with 1 Hz temporal
resolution. Hence, individual ξ corrections are obtainable at any time
during the measurement with pitot-equipped instruments. Figure 7 shows the
comparison of calculated ξ and PASTAS
corrections (synonymous for using TAS instead of PAS for Nmeas,
cf. Sect. 2.1) as a function of TAS. The unadjusted data from 6 out of a
total of 11 ML-CIRRUS flights are shown. In sum, for the following, the
1 Hz resolved data of more than 35 flight hours are treated.
It needs to be noted that throughout the ML-CIRRUS measurements the PAS of
the PIP was systematically affected due to the malfunction of a temperature
sensor; i.e. a broken temperature sensor in the PIP's pitot tube provided a
constantly false temperature output of about 320 K. This caused a false
measurement of the PIP's PAS which, however, never exceeded a 10 %
deviation compared to the PAS measured by the other cloud probes. Thus, the
resulting falsification of the PIP's PAS was reconstructed by adopting
exclusively the missing temperature data from a pitot tube of another
underwing probe (e.g. the CCP) which was functioning normally. The
reconstruction of the PIP's PAS – still comprising the PIP's own pressure
measurements – may contain uncertainties. However, calculations show that
temperature deviations of ±20 K (as well as with ±10 K) employing
the adopted temperature values cause the resulting PAS to vary by about
±5 % (±3 %). Thus, the uncertainty of the PIP's reconstructed
PAS is minor compared to the uncertainty that is generally presumed for the
PAS measurement which exhibits a significantly higher sensitivity to measured
pressures.
Comparison of two different instrument-specific corrections applied
to data acquired on HALO during ML-CIRRUS. The geometric correction
PASTAS causes a general downscaling of measured
concentrations of 20 % up to 35 % for NIXE-CAPS and CCP. Thereby
PASTAS is highly variable, ambiguous and shows
certain dependences on the instrument's wing position. Instrument-specific
ξ values exhibit higher compactness over the TAS range and show reduced
dependence on the wing position. The data are from six ML-CIRRUS flights and
include outliers due to freezing of the pitot tubes or due to distortions
from isoaxial flow accompanied with manoeuvres such as tight turns.
Relevant parameters for determining ξas a function of TAS for
the CCP. (a) The absolute difference of measured pressures (p1,
p2) and velocities (v1, v2) and the difference of measured
temperature T1 to calculated T2. (b) The ratio of
pressures p1p2 and temperatures T2T1 as
used in Eq. (7) to illustrate respective effectiveness in the
ξ correction.
Correlations between individually measured static pressures and PAS
for each instrument pair. The p correlations (upper panels) indicate
consistency as the data follow the 1 : 1 relationship (dashed red lines).
The PAS correlations (lower panels) reveal systematic deviations from the
1 : 1 relationship which may be attributed to the instruments' different
geometry or underwing position.
During the flight on 29 March 2014 (red data points) the factors
PASTAS and ξ as a function of TAS
occasionally show significant deviation from the generally observed course.
This deviation can unambiguously be apportioned to disturbed PAS
measurements. The PAS chart is subject to disturbances either due to freezing
conditions causing the pitot tube to be tamped or due to non-isoaxial airflow
caused by flight manoeuvres like tight turns. Very few and relatively short
periods of PAS disturbances also occurred during the flight on 11 April 2014
(pink data points).
The ξ correction is a monotonous function of flight velocity that has
increasing effectiveness for each of the three instruments. Contrarily, the
PASTAS correction appears to be systematically
effective over the full range of air speeds, even at the lowest aircraft
velocities – while the scatter of PASTAS by
∼ 2–10 % may result from small-scale turbulence or non-isoaxial
airflow. However, the geometric correction with
PASTAS causes a general reduction of the values
measured with CCP and NIXE-CAPS of not less than 20 %, even reaching
35 % for NIXE-CAPS (cf. Fig. 7). For CCP the values of ξ and
PASTAS are most compact. The variability, in
particular of PASTAS, increases for NIXE-CAPS
over the complete TAS range. For PIP the ξ factor is comparably variable
at flight velocities greater than 140 m s-1.
The events when the pitot tube was frozen or affected by misaligned inflow
(mainly attributed to the measurements made on 29 March 2014 and to a limited
number of measurements made on 11 April 2014) were removed from the data set,
which effectively reduces the data set volume by less than 3 %.
For CCP measurements (data set as treated for Fig. 7) the parameters for
calculating ξ according to Eq. (7) are shown in Fig. 8a as a function
of TAS. Displayed are the absolute differences of measured pressures
(p1, p2) and velocities (v1, v2). The difference of the
squared velocities v1 and v2 (Eq. 7) is implicitly included in
calculated T2. Moreover, the difference between measured temperature
T1 and the calculated temperature T2 is shown. At a maximum TAS of
255 m s-1 the compression impact causes a Δv of up to
75 m s-1, a ΔT of up to 16 K and a Δp of about
30–60 hPa. The values of ΔT and Δp upstream of an underwing
probe may appear surprisingly high but are largely consistent with the
results of a fluid-dynamical simulation at similar flow velocities
(200 m s-1) for another underwing probe geometry (Abdelmonem et al.,
2016). Moreover, these observations are largely consistent with the results
of theoretical considerations regarding the thermodynamic processes inherent
with the compression of air (cf. Appendix A). In Fig. 8b the results of the
pressure expression p1p2 (green data points) and temperature
fraction T2T1 (black data points), as applied in Eq. (7),
are displayed as a function of TAS, illustrating the respective effectiveness
of each term to calculated ξ. The inversion to Namb causes
Nmeas to be reduced by a factor of up to 0.8 to compensate for
the induced pressure increase. In contrast, the compression-induced heating
of air needs to be corrected by a factor of up to 1.07.
Coefficients of the statistical analyses of derived ξ values:
(1) quadratic regression with parameters and standard deviations (σ);
(2) linear correlation of the instrument-specific ξ values. Both the
ξ parameterisations and correlations from HALO measurements are
based on > 130 000 single 1 Hz data points
(> 36 flight hours).
Regression for parameterisation of ξ as a function of HALO-TAS: f=y0+a⋅x+b⋅x2CCPNIXE-CAPSPIPy0±σ0.99 ± 2.04 ×10-40.99 ± 2.36 ×10-40.99 ± 2.06 ×10-4a±σ3.18 ×10-4± 2.34 ×10-62.55 ×10-4± 2.71 ×10-63.10 ×10-4± 2.35 ×10-6b±σ-3.40 ×10-6± 6.48 ×10-9-3.30 ×10-6± 7.54 ×10-9-3.37 ×10-6± 6.54 ×10-9r20.990.980.98Linear regression of instrument-specific ξ inter-correlation: f=y0+a⋅xCCP versus NIXE-CAPS PIP versus NIXE-CAPSPIP versus CCPy0±σ-0.04 ± 2.26 ×10-4-0.05 ± 5.09 ×10-4-0.01 ± 4.73 ×10-4a±σ1.03 ± 2.49 ×10-41.05 ± 5.60 ×10-41.01 ± 5.20 ×10-4r20.990.970.97
Note that for a TASmax of 255 m s-1 the compression-induced
heating increases the temperature of the air sample by a ΔTmax of
16 K. Assuming that the air gets compressed over a distance of ∼ 0.5 m
upstream of the instrument (cf. Wendisch and Brenguier, 2013, Sect. 6.2.1
therein), then, for the given flight velocity, the airborne particles are
exposed for an overall duration of about 2 ms to a continuously heating
environment, ending up at the ΔTmax of 16 K. The shrinkage, i.e.
the evaporative loss of size, of an airborne ice particle of 2 µm
initial diameter is at most ∼ 5 % after a 2 ms lasting exposure to
a ΔTmax of 16 K (at any initial air temperature of 190–245 K)
at a static pressure of 300 hPa, as calculated from the mass rate change
(Pruppacher and Klett, 2012; Spichtinger and Gierens, 2009). The shrinkage
increases vigorously for particle of initial sub-micron size. Moreover, the
compression of air over a distance of ∼ 0.5 m upstream of the
instrument causes a Δpmax of 60 hPa (cf. Fig. 8a). If scaled to
the dimensions of a droplet of millimetre-sized diameter (smaller particles
are affected to lesser extent) the potential droplet deformation due to
compression may be negligible.
In Fig. 9 the comparison of respectively measured p2 is shown together
with the correlation of the PAS as derived from the dynamic pressure
proportion of the pitot tube measurements. The correlations of the
individually measured p2 between NIXE-CAPS and CCP (Fig. 9, upper-left
panel) and between PIP and CCP (Fig. 9, upper-right panel) agree almost in
line with the displayed 1 : 1 relationship (dashed red lines). Thus, the
p2 measurement of the instruments does not seem to be significantly
affected either by the individual probe head design or by the respective
wing position. Note that the calibrated pressure transducers commonly
integrated in the individual probes are of the type Honeywell, model 142PC15A
with a specified linearity within ±0.4 % of the output signal span
for the pressure range between 140 and 1030 hPa.
The dynamic pressure for calculating the air speed results from the total
pressure, impacting on the pitot's forward-facing congestion tube, subtracted
by the static pressure that is detected at the pitot tube's flanks. Hence,
the PAS comparison between NIXE-CAPS and CCP (Fig. 9, lower-left panel)
exhibits a systematic discrepancy of about 5–10 m s-1 by which the
resulting PAS of the CCP exceeds the NIXE-CAPS measurements over the entire
velocity range. This may result from different calibrations of the respective
pitot tube or it could be an effect of the instrument's wing position. For
comparably much smaller flight velocities (< 100 m s-1),
previous studies demonstrated that the air flow field changes along the wing
span with different impact on instruments positioned outboard or inboard at
an aircraft's wing (Drummond and MacPherson, 1985; MacPherson and
Baumgardner, 1988). It is also likely that the systematically stronger
deceleration of air flow upstream of NIXE-CAPS is caused by its winglet (cf.
Fig. 6), which may increase the probe's cross-sectional area compared to that
of the CCP. The comparison between the PIP's reconstructed PAS and the
measured PAS of the CCP is also shown in Fig. 9 (lower-right panel) but the
agreement among the PAS data may benefit from the implicit dependency of the dependency of the
PIP's reconstructed PAS on the imported temperature data from the CCP (cf.
remark above). However, a potential but unlikely deviation of the adopted
temperature from a true temperature at the PIP's position by up to ±20 K
would shift resulting comparisons by at most 5 % in either abscissa
direction.
Parameterisation of ξ as a function of TAS for the three
different instruments deployed on HALO during the ML-CIRRUS mission.
Parameterisation coefficients are provided in Table 1. The fit curve (black)
is covered by the lines (blue) of the narrow confidence band.
For providing a parameterisation of ξ values as a function of TAS the
data set needs to be reassessed by accounting for the limited periods of
tamped or malfunctioning pitot tubes. For the following, those periods that
were identified to be affected by an inoperative pitot tube have been removed
from the data set. In Fig. 10 the derived ξ factor is depicted as a
function of TAS. The parameterisation results from fitting a quadratic
regression (Table 1) to the given data set. For each instrument the
individually derived parameters of v2 (PAS) and p2 (static air
pressure at the probe) are used, such that the ξ factors are also
individually determined for each instrument. The regression fits in Fig. 10
are provided together with the 95 % confidence band (blue lines) and the
95 % prediction band (red lines). Note that the 95 % confidence band
is very narrow, even covering the black regression fit because the data set
used for these regressions is large and the data variability is small. The
fit parameters are summarised in Table 1 and the regressions always reveal
values of r2 greater than 0.98, which confirms the solidity of the
functional relationship between ξ and TAS.
Correlations of instrument-specific ξ. The deviation from the
1 : 1 relationship (dashed black lines) as a function of the aircraft true
air speed (TAS) is strongest at the PIP position (portside, innermost).
Coefficients for the correlations are provided in Table 1. The fit curve
(black) is covered by the lines (blue) of the narrow confidence band.
Resulting particle number concentration after application of
different correction procedures to the data acquired during the
ACRIDICON-CHUVA mission flight “AC13” on 19 September 2014 between
20:00:40 UTC (72 040 s of day) and 20:32:00 UTC (73 920 s of day), over
the Amazonian basin, Brazil. Left panel: the time series of total particle
concentration measured with CCP and PIP. Right panel: the resulting particle
size distribution, merged from CCP (CDP and CIPgs) and PIP measurements. As a
consequence of used binning scheme of OAP data the inertia correction with
μ is applied to the particle size bin of Dp= 97 ± 25 µm and to all larger sizes
(μ= 0.8, cf. Eq. 9).
The consistency of ξ for HALO instruments
Further insight into the properties of ξ is provided by Fig. 11, which
illustrates the correlation of individually derived ξ values for each
instrument. The ξ data are colour-coded according to TAS and the linear
correlation between the instrument-specific ξ data and TAS are derived.
The graphs also contain the very narrow 95 % confidence band (blue lines)
and the 95 % prediction band (red lines). The parameters for the linear
correlations shown in Fig. 11 are also summarised in Table 1. The
ξ values exhibit a strong correlation with a correlation coefficient
r2 larger than 0.97, which indicates ξ to be widely independent of the
instrument characteristics, such as wing position or design, in contrast to
PASTAS. Nevertheless, in detail the individual
ξ values obviously differ from each other, which is presumably connected
to the differently shaped probe heads and/or the instrument's distance to the
aircraft fuselage. Starting with neighboured instruments, i.e. comparing CCP
with NIXE-CAPS (Fig. 11, upper panel) and PIP with NIXE-CAPS (Fig. 11,
centred panel), an increasing deviation from the 1 : 1 relationship (dashed
black lines) appears. The comparison of corresponding results from the PIP
and the CCP (Fig. 11, bottom panel) depicts a smaller deviation of
ξ values from the 1 : 1 relationship. However, it must be emphasised
that the dependency of the PIP's reconstructed PAS on CCP temperature data
(cf. Sect. 3.2) has negligible impact on derived ξ. It remains
speculative to ascribe the ξ deviation to the individual instruments'
design, although it may explain this observation.
Altitude and flight velocity for the ACRIDICON-CHUVA mission flight
“AC13” on 19 September 2014 over the time period between 20:00:40 UTC
(72 040 s of day) and 20:32:00 UTC (73 920 s of day) and derived
corrections of ξ and PASTAS for CCP and PIP.
Inertia correction is applied with μ for particles with Dp > 96 µm.
Flight altitudeTASξ – CCPξ – PIPμ (Dp)PASTAS – CCPPASTAS – PIPin m (a.s.l.)in m s-1Average12 971.6221.750.900.890.80.730.76Maximum12 980.7226.890.910.890.80.740.77Minimum12 962.5215.120.890.880.80.720.74Effectiveness of ξ corrections on atmospheric particle measurements
In the following the derived ξ values are applied to data of atmospheric
cloud measurements that were performed during the HALO mission
ACRIDICON-CHUVA. The studies of various types of tropical convective cells
aimed at, amongst other characteristics, the microphysical properties of
cloud elements under variable conditions. Large contiguous cloud fields with
liquid or mixed-phase cloud particles were probed, occasionally over more
than 30 min without encountering cloud-free air. Relatively high particle
number concentrations were detected. For demonstrating the effectiveness of
the ξ correction a segment was selected from flight “AC13” on
19 September 2014 between 20:00:40 UTC (72 040 s of day) and 20:32:00 UTC
(73 920 s of day). During this flight period, at almost constant level
flight at about 13 km altitude (cf. Table 2), spheroidal particles were
mostly present and detected as such. Figure 12 shows a time series (left
panel) of the total number concentration (as 10 s running averages) derived
from measurements of both the CCP (CDP and CIPgs) and the PIP. Additionally,
a particle size distribution covering the full diameter detection range of
CCP and PIP is provided (Fig. 12, right panel) averaged over the complete
level flight period to reduce the counting error level to a minimum over the
full diameter range covered. In both graphics, the time series and according
particle size distribution are shown in four ways:
measured particle number concentration Nmeas (black);
the data corrected by values of ξ determined for each second of
measurement (green);
the data corrected by values of ξ (as before) and μ (Dp) (cf. Sect. 2.5) (blue);
the data set after correction with 1 Hz resolved factors of
PASTAS (red).
The averaged TAS (∼ 220 m s-1, cf. Table 2) over the depicted
time period suggests a ξ value that causes an effective correction of
Nmeas of about 10 %, read off Fig. 10. The averaged values of
calculated ξ for the CCP and PIP are indeed close to 0.9 (cf. Table 2).
The additional correction with μ (Dp) affects the particle
number concentrations in the spectral size bin of Dp= 97 ± 25 µm and those of larger sizes. However, a
correction with PASTAS would cause a downscaling
of Nmeas by up to 27 % (for the CCP-detected particle size
range, cf. Table 2) whereas the applied ξ corrects Nmeas with
regard to the air's compression systematically by about 10–11 %. Taking
the droplets' inertia into account, the applied correction by ξ and μ
(in total by about 13 %) effects a comparatively cautious change with
respect to Nmeas when predominantly smaller particles are
encountered (e.g. at the UTC times 72 110, 73 050, 73 140 or the period
between 73 070 and 73 700 s of the day). In periods when particles with
sizes Dp > 100 µm prevail the correction by
ξ and μ effectively depletes Nmeas by at the most
21 %.
In essence, the effective correction of Nmeas by ξ may not be
excessive but, by knowing the variables to determine ξ, a systematic bias
in measured particle number concentrations is easily eliminated. The
additional correction by μ (Dp) allows for further
approximation of Namb out of Nmeas. However, it needs
to be noted that μ is of varying effectiveness, depending on the particle
size and on the cloud particles' phase. The correction of Nmeas
by ξ and μ finally becomes very effective when surface, volume or
mass distributions are obtained from the OAP measurements. Furthermore, if,
for example, the cloud's liquid water content (LWC) or ice water content
(IWC) is extracted from OAP data, the compression correction in combination
with a carefully chosen inertia correction over the entire range of particle
sizes detected is essential to base any conclusion on reasonable data.
Correction factor ξ for other fast-flying aircraft
Provided that ξ was sufficiently proven to hold for large ranges of
atmospheric conditions and aircraft speeds, the question arises whether the
properties of ξ can also hold for other fast-flying aircraft.
Coefficients of the statistical analyses of derived ξ values for
CCP measurements on the Learjet-35A: quadratic regression with
parameters and standard deviations (σ). The ξ parameterisation is
based on > 12 000 single 1 Hz data points
(≈ 3.3 flight hours).
Regression for parameterisation of ξas a function of Learjet-TAS: cf. Table 1 CCP y0±σ0.99 ± 6.91 ×10-4a±σ3.74 ×10-4± 8.35 ×10-6b±σ-3.08 ×10-6± 2.48 ×10-8r20.97
In Fig. 13a the determined ξ values for each time of CCP measurement on
board the Learjet-35A are displayed from a single flight (over
3.3 flight hours) on 5 September 2013 during the AIRTOSS-ICE (AIRcraft TOwed
Sensor Shuttle) mission aiming at ice clouds (cirrus) over northern Germany
(Finger et al., 2016). The ξ values for one flight, when CCP was deployed
on an underwing position of the Learjet-35A, are parameterised by
means of a quadratic regression and according coefficients are summarised in
Table 3. The derived ξ values (green dots) as a function of TAS follow in
general the expected course and the data set is similarly compact over the
TAS range as previously shown for the HALO cases. However, the comparison of
the ξ fit from the Learjet-35A measurements with the
parameterised ξ from HALO flights (dark cyan line) reveals that ξ for
the Learjet-35A configuration generally causes a smaller correction
of Nmeas to reach Namb. As the instruments deployed
on board of HALO and the Learjet-35A are identical the systematic
difference in ξ indicates that the compression may depend on the
instrument–platform configuration. As ξ is principally a measure for the
compression strength, it seems that upstream of the CCP on the
Learjet-35A, for some reason, the air compression is weaker than on
HALO. Factually, the instrument configuration by using the AIRTOSS, which is
released from the Learjet-35A on a steel cable during flight (Frey
et al., 2009), displaces the CCP measurements to a certain distance (up to
4000 m) away from any potential source of disturbance or interference
provided by the aircraft. The data sets of two flights of the AIRTOSS-ICE
campaign were selected which provide all variables required to determine
ξ. Measurements during curved manoeuvres were discarded from further
analysis as the adaptation of the AIRTOSS's flight attitude to rough changes
in flight direction is delayed. Moreover, the CCP pressure data were adjusted
to account for the difference of static air pressure accompanied with the
lower flight altitude of AIRTOSS with respect to the Learjet-35A.
For the levitating CCP the calculated ξ values are displayed in Fig. 13b
(purple dots) exhibiting a strong scatter. However, hereby a dispersion of
ξ about a mean appears to be indicated that is close to the
ξ parameterisation fit of measurements with CCP when attached under the
Learjet's wing. Thus, a significant influence of the aircraft's wings or
the fuselage of the Learjet-35A on the underwing-mounted CCP is not
definitely verifiable. Concerning the difference of ξ resulting from
measurements either on the Learjet-35A or the G-550HALO we
can only surmise that a specific flow field is induced due to the specific
HALO configuration, by the aircraft fuselage and/or the wings' leading edge
and/or the pairwise configuration of the underwing instruments. Nevertheless,
by applying ξ the individual and systematic influences on the actual
thermodynamic conditions under which the measurements occur are, to a large
extent, accounted for – independent of the probably various and likely
interfering sources of disturbances on the measurement conditions.
Summary and conclusions
To determine particle number concentrations with respect to ambient
conditions from the measurements of underwing cloud probes on fast-flying
aircraft two corrections need to be applied on the data obtained under
measurement conditions from the free atmosphere.
The first correction refers to the compression of air occurring upstream of
the air flow obstacle provided by the instrument's body. Taking the
compression effect into consideration is of increasing importance with
increasing flight speeds (e.g. up to 250 m s-1). This first correction
accounts for the compressed state of the sample air volume probed per time
interval as indicated by an observable increase of the static air pressure
(and air temperature) in the instruments' detection region compared to
ambient conditions.
The particles' mobility to react on small-scale and fast changes in a flow
field, inducing a particle's displacement from its initial state, is a
function of the particles' individual mass (i.e. inertia). Thus, the second
correction refers to the particle inertia which impacts the penetration speed
of cloud particles while passing the instrument's detection region. Due to
the compression of air the flow in the instruments' detection region is
decelerated compared to the undisturbed state (at a certain distance away
from any obstacle) to which large cloud droplets (e.g. Dp > 100 µm) are unable to adapt fast enough.
However, strong indications were found that the penetration speed of smallest
particles (e.g. Dp < 70 µm) is more than
likely affected by the changed air flow conditions. As a consequence of the
particles' individual inertia, the penetration speed through the instruments'
detection region is not equal for all particles in a cloud. Thus, the general
assumption of the constancy of particle mixing ratios (particle number per
mass of air sampled) is not fulfilled over the entire cloud droplet size
range. Indeed, the mixing ratio between ambient and measurement conditions
likely remains constant only for small-sized particles which exhibit enough
mobility to adapt to the air compression. In contrast, large particles may
accumulate in the instruments' detection region due to their inability to
kinetically adapt to the changing air speed. Hence, without an inertia
correction of measured particle number concentrations, large particles may be
over-represented in the sampled air volume.
For the compression correction the factor ξ is introduced based on
thermodynamic considerations for inverting the data from the pressure and
temperature conditions during measurement to ambient conditions. An equation
is provided for deriving ξ that depends on the variables of static
pressure and temperature in the ambient (undisturbed) state as well as the
aircraft TAS. Additionally, the static pressure measurement
and the actually measured PAS at the individual probe are needed.
Provided that an underwing probe is equipped with a pitot tube for continuous
measurement of air speed and static pressure in the vicinity of the probe,
the instrument-specific ξ can be derived for each second of measurement
during a flight.
As the detector scanning of OAPs is triggered by the measured airflow
velocity, a significant deviation or falsification of the pitot-measured PAS
would result in visibly distorted images. Measurement flight sections
featuring predominantly liquid (spherical) cloud droplets were selected. For
these chosen measurement periods the grade of distortion of the recorded
images was apportioned to the deviation of the particle penetration speed
through the instrument's detection region by means of an automated OAP image
analysis. Small particles of Dp < 70 µm appear
to largely adapt to the decelerated air speed by reaching vp≈ PAS in the instruments' detection region. Larger droplets
with Dp > 100 µm seem to penetrate the
detection plane with PAS < vp < TAS, which is
attributable to the particles' inertia. The dependence of the inertia
correction on the particle size is expressed in the suggested correction
factor μ (Dp) to be applied to measured particle number
concentration Nmeas. For the particular case investigated the
correction of measured number concentrations with μ= 1 holds for
cloud droplets of Dp < 70 µm while a
correction with μ= 0.8 seems to suffice for cloud droplets with
100 µm < Dp < 225 µm. For
larger droplets (e.g. Dp > 225 µm, which
were not detected during investigated measurement periods) the inertia
correction may asymptotically approach a value of μ= 0.75. Only if
the particles' inertia inhibits a change of the particles' initial state may the
resulting particle penetration speed through the OAP detection region
satisfy the assumption that vp≈ TAS. However, the
generalized correction regarding the particle's inertia based on the
particle's size may not always be appropriate. Prior to applying such a
correction some careful considerations are required regarding the particles'
phase and habit. Cloud particles exhibit the largest material density when
they are liquid, whereas, if a cloud particle is frozen, its material density
(and inertia) is decreased compared to a liquid droplet of the same
geometrical size. Moreover, spatial structures of ice particles (e.g. if
evolved to dendrites, crystals, bullet rosettes or hollow needles) may
lead to increased mobility due to a decreased compactness of the particles.
At present there are three different approaches to treat particle
microphysical data obtained from underwing probes.
Without knowledge of the air speed and static pressure at the point
of measurement it is common practice to presume that particles always
penetrate the probe's sample area As with speeds equal to the
aircraft TAS. Taking this route, the compression of air due to the moving
instrument body and the compression-induced motion of particles out of their
ambient (undisturbed) state is ignored. As a consequence of the compression
upstream of a probe, the PAS at the point of measurement must be
systematically lower compared to TAS. Determining particle number
concentrations by using the TAS without adjustments regarding the compression
leads to an underrepresentation of particle concentrations that is not
negligible.
The measured particle number concentration Nmeas
(based on the recorded PAS; cf. Sect. 2.1 for details) does not represent the
ambient number concentration of cloud particles. The compression of air
causes a modification of the particle's environment and behaviour at the
point of measurement compared to ambient (undisturbed) conditions. Thus, the
measured particle number concentrations without any corrections may be
representative for the measurement conditions only. However, compared to
ambient particle number concentrations, the uncorrected Nmeas is
an overestimate of increasing strength with flight velocity. Note that an
uncertainty of Nmeas remains due to the PAS uncertainty which may
not considerably exceed 10 %.
Multiplying measured particle number concentrations Nmeas
with the ratio PASTAS, presumably deduced from
geometric considerations, with the attempt to hereby invert the measured
concentrations to ambient conditions lacks any physical rationale. The ratio
of air speeds does not account for the compression of air upstream of the
probe which is the major reason for the deviation of measured air speeds, PAS
and TAS. By using the ratio PASTAS, the increase
of pressure and the heating accompanied with the compression of air remains
fully ignored. Hence, this simplified correction procedure turns out to cause
an unreasonable reduction of particle number concentrations. This procedure
was shown to affect the results at surprisingly low aircraft speeds.
Therefore, the particle number concentration under measurement conditions
Nmeas (based on the recorded PAS, cf. Sect. 2.1) needs correction
to account for the compression of air and the compression-induced motion of
particles out of their ambient (undisturbed) state, which is a function of the
cloud particles' individual mass (i.e. inertia). The herein introduced
correction factor ξ covers the most important impacts accompanied by
the compression. It is suggested that the subsequent correction of the
measured particle number concentration with the factor μ (Dp)
to account for the particles' individual inertia be applied carefully.
Further effects may be considered which additionally concern the ability of
the cloud particles to adapt to sudden changes of the flow field upstream of
an underwing probe. CFD simulations by Korolev et al. (2013), for example,
indicate that the air speed locally varies along the sample volume. Thus, the
complexity of velocity corrections increases when an inhomogeneity of the
air speed distribution within the sample volume is also taken into
consideration.
If pitot tube measurements are not available, the provided
ξ parameterisation as a function of TAS serves as a guideline for
adaptation of the TAS to determine particle number concentrations.
The parameterisation also shows that the compression effect is comparatively
small for lower flight velocities. For a mean cruising speed, e.g. of the
M-55 Geophysica of about 170 m s-1, the systematic bias of
the number concentration obtained from CCP measurements may be at most
6 % in the case that the compression is not otherwise accounted for and
if the measured number concentrations are directly determined by using the
recorded PAS. Note that this potential bias of CCP measurements on board the
M-55 Geophysica is directly taken from the parameterisation of ξ
for the CCP on HALO (cf. Fig. 10) and therefore represents the uppermost
extreme. For slower aircraft, e.g. the POLAR 5 (a modified and
turboprop-engined Douglas DC-3) with cruising speed of about 70 m s-1
(Klingebiel et al., 2015) the potential bias of uncorrected CCP-measured
particle number concentrations is at worst 2 % and therefore lies well
within the measurement uncertainty. Calculated ξ from CCP measurements on
board the Learjet-35A, reaching flight velocities comparable to
those of the G-550HALO, reveals that the compression is generally
less expressed in the Learjet-35A configuration compared to that of
the G-550HALO. An increased compression effect on the
G-550HALO is not unambiguously connectable to a specific source. It can only be
surmised that on the G-550HALO a strengthened disturbance on the
thermodynamic conditions of underwing probe measurements is accompanied with
interferences of the aircraft fuselage and/or the wings' leading edge and/or
the pairwise configuration of the underwing instruments.
Comparison of corrections for the CCP (a) with the CCP
attached to a Learjet-35A' underwing hardpoint (flight on
5 September 2013) during the AIRTOSS-ICE mission over northern Germany. The
PASTAS correction exhibits broad scatter and
ambiguities. Instead, the determined ξ values yield compactness over the
complete TAS range. For comparison the ξ parameterisation from
HALO measurements of the CCP is implied, illustrating the dependence
of ξ on the used measurement platform. (b) Instead of
PASTAS, the ξ values are shown for the CCP
when deployed in the AIRcraft TOwed Sensor Shuttle (AIRTOSS) released from
the Learjet-35A on a steel cable.
This study provides a starting point for further intensive instrumental
comparisons and investigation by means of combined measurement results of
cloud and aerosol probes from the accomplished HALO field missions ML-CIRRUS
and ACRIDICON-CHUVA. However, to make the measurements comparable, a common
standard of treating the data and of considering systematic influences on
the measurement is essential. This standard needs to be designed and agreed
upon before comparing or interpreting the data. The introduced correction
procedures may serve as one contributing factor accounting for the most
significant impacts resulting from the moving instrument body in the medium
air on fast-flying aircraft. Further flow disturbances due to aircraft
components (e.g. the impact of turbulence along the wings or the flow
impacts induced by the fuselage) are potentially not covered by
suggested procedures but may be subject of detailed CFD simulations.
Data availability
The meteorological and avionic data and the data products of the cloud probe
measurements on board HALO for both field missions, ML-CIRRUS and
ACRIDICON, are available at https://halo-db.pa.op.dlr.de/, maintained
by the German Aerospace Center (DLR), Institute of Atmospheric Physics,
Oberpfaffenhofen, Germany.
Instruments' basic data (i.e. pressure, temperature, PAS) as well as
raw image files are stored on individual databases and are accessible upon
request towards the operators of respective instrument (i.e. NIXE-CAPS:
IEK-7: Stratosphere, Water Vapor and Clouds, Forschungszentrum Jülich;
CCP; and PIP: Particle Chemistry Department, Max Planck Institute for
Chemistry, Mainz).
Data products from measurements on board the Learjet-35A are accessible
upon request to the operator of respective instrument (CCP: Particle
Chemistry Department, Max Planck Institute for Chemistry, Mainz).
Meteorological measurements and avionic data belonging to the Learjet-35A
field mission AIRTOSS-ICE were provided by enviscope GmbH, Frankfurt,
Germany.
Various ways of deriving the ξ correction
The derivation of ξ emanates from following different conditions, which
are illustrated in Fig. 1 for the air velocity v, the air pressure p, the
specific enthalpy h of a uniform system and the gravitational potential
ϕ.
Condition 1 – at the aircraft's air data boom: v1, p1,
T1, h1, ϕ1.
Condition 2 – upstream of the probe: v2,p2,T2,h2,ϕ2.
Bernoulli's law for compressible
gases and under the presumption of energy conservation reads as
12v12+h1=12v22+h2,
assuming that the gravitation potential ϕ1=ϕ2 since the
relative elevation between the air data boom and the underwing probe position
is negligibly small, i.e. < 10 m.
Assuming T2b as the reference, for which potentially
involved diabatic processes remain considered, the ratio
T2aT2b indicates the strength of deviation from this
reference. The ratio T2aT2b overall remains between
0.988 and 1.004 and the majority of data range at 0.99–1.0. Thus changes of
state accompanied with compression are almost entirely adiabatic. The ratio
T2aT2b deviates from the adiabatic threshold (black
line) by generally less than 1 %, and the deviation increases expectedly
with TAS potentially due to turbulence and accompanied mixing.
The occurrence frequency of T2aT2b values in
the data set displayed in Fig. A1.
The ratios ξIIξI and
ξIIIξI as a function of TAS for
the different underwing probes CIP, PIP and NIXE-CAPS, respectively. The
ratios overall remain between 0.985 and 1.045 indicating a strong agreement
between the differently derived ξ values. The comparison generally
exhibits a relative deviation of less than 5 % and, over a large range
of TAS (< 190 m s-1), of even less than 2 %. For all
instruments the correction factors ξI and ξIII
show best agreement.
For finite differences of the specific enthalpy (Δh=h2-h1) for an ideal gas such as the air, one can use
Δh=cpΔT.
wherein cp denotes the specific heat capacity of dry air (in
J kg-1 K-1) at a constant pressure.
For the further derivation we assume the following:
The pressures p1 (static air pressure) and p2 (static air
pressure at the probe during measurement) are measured with sufficient
certainty.
For velocities relative to undisturbed ambient cloud conditions the
velocity v1 equals the avionic TAS while v2 is the air speed
determined from the probe's pitot measurements, PAS.
Under undisturbed ambient conditions, for which p1 and T1
are valid, the particles' initial velocity relative to the aircraft flight
direction may be close to zero, or at least much smaller than v1 and
v2.
Subsequently, Eq. (A1) leads to
12v12-v22=h2-h1=cpΔT=cpT2-T1.
Hence, rather than the velocity ratio (cf. Sect. 2.2), the difference of
the squared velocities appears in the thermodynamic approach. With Eq. (A3)
the functional relationship between the aircraft air speed, reduced by
the compression-induced airflow velocity during measurement, i.e. the
expression v12-v22, is provided versus the relative heating of
the probed air with respect to ambient conditions. Consequently, the
resulting squared velocity difference implies the change of the particles'
motion in-line with the flight direction due to the compression.
The occurrence frequency of values of
ξIIξI and
ξIIIξI in the data set displayed
in Fig. A3.
Rearrangement of Eq. (A3) leads to
T2=T1+ΔT=T1+12⋅cpv12-v22.
The specific heat capacity cp of air ranges from about
1002.5 to 1006.4 J kg-1 K-1 for atmospheric temperature
conditions between 180 and 325 K (Dixon, 2007). Accepting an implied
uncertainty in the per-mill range, the product 2⋅cp in
Eq. (A4) may be replaced by 2008 J kg-1 K-1.
Substitution of T2 from Eq. (A4) into Eq. (5) leads to the
thermodynamic correction of measured particle number concentrations to
account for the compression of air upstream of the probe during flight:
Namb=Nmeas⋅p1p2⋅1+12008Jkg-1K-1⋅T1v12-v22=Nmeas⋅ξ.
By means of Eq. (A5) the thermodynamic correction factor ξ is introduced,
which basically equals the ratio of the probed volume and according ambient
volume (V2V1) of air and which is used for the following
discussions (Sect. 3 and also here in the following).
For the following considerations concerning the congestion-induced
compression of a gas volume occurring upstream of a flow obstacle, the
resulting increase of the gas' density is described by the factor
ξ=ρ1ρ2=p1p2T2T1,
by assuming the air to behave as an ideal gas, for which p⋅V=M⋅Rs⋅T, or rather p=ρ⋅Rs⋅T, with the static pressure
[p] = kg m s-2, the gas volume [V] = m3, the mass of
the gas [M] = kg, the gas temperature [T] = K, the gas density
[ρ] = kg m-3 and Rs, the specific gas
constant in units of J kg-1 K-1; while
J = kg m2 s-2.
The ambient conditions, at the data boom, are described by p1, T1
and the TAS =v1 in units of m s-1.
The measurement conditions, in the detection region upstream of the underwing
probe, are described by p2 and the PAS =v2 (in
m s-1), recorded data from the individual underwing cloud probes CCP,
PIP and NIXE-CAPS.
The consequences of the air compression are p1≤p2 and
T1≤T2.
Deriving ξ comprising most of the observational data
Here we assume that
the gas properties are those of an ideal gas,
the principle theorem of thermodynamics – the conservation of energy – is fulfilled,
the gas flow conditions follow Bernoulli's law.
This allows for expressing
12v12+h1+Φ1=12v22+h2+Φ2.
With the specific enthalpy [h] = J kg-1 and provided that
following assumption for the gravitational potential is valid Φ1≈Φ2, then the air temperature in the instruments
measurement region is determined by
T2=T1+v12-v222⋅cp,
from which the first expression for the ξ correction follows
ξI=p1p2T2T1=p1p21+v12-v222⋅cp⋅T1.
Deriving ξ by presuming an adiabatic change of pressure conditions
Exclusively relying on the measurements of the flow velocity in the detection
region and by assuming an adiabatic change of the pressure conditions due to
compression an additional assumption is added to those specified in Sect. A1:
T2T1=p2p1κ⇔T2T1-1κ=p1p2,
with the adiabatic exponent κ=Rscp.
The temperature T2 is calculated analogously to Eq. (A3). Thus, for
the ξ correction, a new expression follows:
ξII=p1p2T2T1=T2T1-1κT2T1=T2T1κ-1κ=1+v12-v222⋅cp⋅T1κ-1κ.
This approach bears a certain inconsistency: the compression-induced increase
of the air temperature in the measurement region (T2) may also comprise
diabatic processes, whereas for the compression-induced increase of the
static pressure exclusively adiabatic changes of state are assumed to occur.
Deriving ξ by presuming all changes of state as adiabatic
Relying only on the static pressure individually measured by respective
instrument, i.e. by the underwing probes and the data boom, a further
assumption to those specified in Appendix A1 is introduced: all changes of
state are exclusively adiabatic, i.e. they proceed without any energy
exchange with the environment.
Using Eq. (A10) the temperature T2 is calculated as
T2=T1⋅p2p1κ.
This allows for expressing the ξ correction as follows:
ξIII=p1p2T2T1=p1p2p1p2-κ=p1p21-κ.
Note that now the measured air flow velocities are entirely excluded from
consideration. The correction with ξIII relies only on the
static air pressures measured by the data boom (p1) and in the detection
region of the underwing probes (p2). Indeed, the pressure data may be
comparably accurate, even when obtained at high flight velocities, and thus
measured pressures exhibit certain robustness. Nevertheless, it appears
plausible that the compression strength depends on the absolute air flow
velocities; however, ξIII does not anymore account for the
values of v1 and v2.
Sensitivity tests
In the following the differently derived ξ corrections are evaluated
concerning their effectiveness and, by applying them to measurement data from the
ML-CIRRUS mission, concerning the comparability of the individual results.
The first appraisal aims at the question of whether the assumption of adiabatic
changes of state can be confirmed by the in-flight air temperature
measurements. Subsequently the agreement of the differently derived
ξ corrections (ξI, ξII, ξIII) is proven.
The temperature T2 obtained according to Eqs. (A2) and (A12)
is compared for each of the individual instruments. Therefore, we introduce
T2a=T1p2p1κ;T2b=T1+v12-v222⋅cp.
In the expression concerning the change of enthalpy dh=dq+αdp, with α=VM, the assumption of adiabatic change
of state is implied by setting dq=0, i.e. that exchange of heat
between the system and the environment is excluded, in accordance to the
principle theorem of thermodynamics. This assumption is likely valid as the
processes occur very rapidly. When considering that diabatic processes
occur, as for example due to mixing or friction, this means that
dq≠0 and consequently T2a≠T2b.
With the unprovable assumption that T2b constitutes the reference,
for which potentially involved diabatic processes remain considered; the
ratio T2aT2b would indicate the strength of deviation
from this insinuated reference. The ratio T2aT2b is
shown as a function of flight velocity in Fig. A1, the occurrence frequency
of T2aT2b values in the data set is displayed in
Fig. A2. For all instruments' data the ratio T2aT2b
remains between 0.988 and 1.004, whereas the majority of data ranges between
0.99 and 1.0. As a consequence, the assumption of adiabatic changes of state
accompanied with the compression appears justified. The deviation of the
ratio T2aT2b from the adiabatic threshold (black line
in Fig. A1) increases with the TAS, as can be expected
because the occurrence of turbulence and accompanied mixing with increasing
TAS is very conceivable.
In essence, the increasing air temperature upstream of the underwing probes
is accompanied with an almost ideal adiabatic compression at flight
velocities of up to 250 m s-1.
The differently derived ξ corrections (ξI, ξII,
ξIII) are compared, provided that – once more as an unprovable
assumption – ξI constitutes the reference. As ξI
mostly involves observational data, ξI is largely independent
of assumptions (e.g. the occurrence of exclusively adiabatic processes) that
may implicate constraints on the interpretation of the results. In the
following the ratios ξIIξI and
ξIIIξI are analysed from the
individual underwing probes, i.e. CCP, PIP and NIXE-CAPS, respectively. In
Fig. A3 the obtained ratios are displayed and in Fig. A4 the corresponding
occurrence frequencies. The resulting ξ ratios always remain between
0.985 and 1.045 which indicates a strong agreement between the differently
derived ξ that generally exhibit an absolute deviation of less than
5 %, in most cases of even less than 2 %. Furthermore, the factors
ξI and ξIII exhibit the best agreement,
regardless of the instrument for which the ξ values are determined. This
means that the approach which
assumes exclusively adiabatic processes to occur provides the most consistent
reproduction of ξI, whereas ξI at the most
involves the available observational data.
Conclusions
From the previous investigation the following conclusions arise:
The compression of air occurring upstream of the underwing probes
at flight velocities of up to 250 m s-1 appears to be described
consistently by an ideal adiabatic change of state.
The differently derived ξ corrections, i.e. ξI (based
on observational data) and ξIII (assuming exclusively adiabatic
changes of state accompanied with the compression), show the best agreement
while the correction with ξII (comprising exclusively the change
of pressure state as adiabatic) leads to the largest
deviation from what is expected for an adiabatic process.
For those underwing probes lacking an air flow velocity sensor the
implementation of a static air pressure sensor of appropriate accuracy
may provide a crucial improvement for obtaining a measure of the
compression strength at any given flight speed.
Automated spheroid recognition from OAP images
Distortions of particle images are caused, for example, by false measurements
of the speed of particles when they pass the OAP detector region. In terms of
shape any liquid cloud particle (with Dp < 2 mm) may
provide the reference for nearly perfect spherical bodies (Pruppacher and
Klett, 2012; Thurai et al., 2009) that are detected with an OAP. Thus, the
recorded images of such liquid (spheroidal) cloud elements occasionally could
exhibit significant distortions from spherical shape due to strong deviations
between the measured and the true particle speed. In such a case the aspect
ratio of the particle image deviates from unity and provides a measure for
the error of measured particle speed. Provided that a spherical particle
produces identical 2-D shadow images, independent from the particle's
rotation, the deviation of the image's aspect ratio from unity is
individually measurable for each particle image. To identify spheroids in the
recorded data, or rather to identify images that presumably emanate from
spherical cloud elements, an automatic procedure is used to systematically
categorise recorded particle images. Insinuating that the particles' images
always exhibit a certain degree of distortion, most of the images should
depict an ellipsoidal shape even though the initial cloud particle was
potentially spherical.
Ellipsoid particle in comparison to the fitted ellipse by using the
Bresenham algorithm. The green ellipse pixels denote events when the
approximated ellipse hits the particle image pixels (grey shaded). Red
ellipse pixels illustrate when particle image pixels are missed by the
approximation. The shade brightness of the particle image pixels (grey)
illustrates the different grades of shadowing generated by the particles on
the OAP diode array detector. The image background (lacking any particle
image information) is given in blue.
Of course the categorisation of an imaged cloud particle as spherical cannot
be exclusively based on an image's ellipsoidal character. Further criteria
are applied by limiting the data set to be analysed to a certain range of
ambient air temperatures (e.g. > 270 K) or pressure altitudes
(> 300 hPa) with the purpose of largely excluding ice particles
from the analysis, as these would likely impact and falsify the particle
categorisation.
However, one of the most important limitations for an automated
categorisation of particle images is the available pixel resolution of the
recorded images (which is 15 µm for the CIPgs-type instruments and
is 100 µm for the PIP-type OAPs, respectively; cf. Sect. 3.1). From
a cloud particle with Dp < 30 µm, for example,
the measurement information from the CIPgs is provided as a 2 × 2 pixel image.
Due to this low image resolution it is impossible to further
distinguish fine microphysical structures, e.g. if the particle surface is
smoothly rounded (indicative for liquid particles) or rather rough (ice
particles). Thus, for the further analysis only those particle images were
selected which consist of at least 5 pixels (75 µm) in either
direction along the image's main axes, i.e. the axis a (in line with the
flight direction and perpendicular to the OAP diode array) and the axis b
(in line with the OAP diode array).
One further effect that needs to be considered is the consequence of Fresnel
diffraction on liquid spherical particles passing the beam of the coherent
detection laser. This effect results in particle images exhibiting a bright
spot in the centre, referred to as the Poisson spot (Korolev, 2007). The size
of the Poisson spot depends on the distance (Zd) of the particle
from the object plane when passing the detection laser. With increasing
distance of a detected particle from the object plane the resulting image is
expanded in size and the image's edges get smoothed compared to those of the
original particle. Therefore, those images having a Poisson spot resulting
from Zd > 4 (cf. Korolev, 2007) are discarded from
further consideration. Furthermore, images exhibiting a non-continuous image
edge, which appear as open circles or c-shapes around a Poisson spot, are
also discarded. The approach of Korolev (2007) is used to retrieve the initial
size of the airborne cloud particle from the images having a Poisson spot and
that remain after previous selection.
To identify the ellipsoidal particle images in the remaining data set, the
Bresenham algorithm (Bresenham, 1965) is used to get the shape of particle
image approximated by an ellipse (cf. Fig. B1), bearing in mind that a circle
is a type of ellipse. The radii of the ellipse are iteratively fitted to the
length (a) and the width (b) of the particle image. The comparison of the
approximated ellipse with the particle image allows for categorising the
particle images. If the imaged particle is too small the available image
resolution (cf. above) impedes the approximation of the particle image as an
ellipse. Therefore, the resolution of the grid-plane for the ellipse
approximation needs to be increased (e.g. by a factor of 4) in comparison
to the pixel resolution of images taken. Thus, each image pixel
(15 µm × 15 µm) is subdivided by a 4 × 4 sub-grid for the
ellipse approximation such that an ellipse can be moved and
expanded/contracted on a grid of 3.75 µm mesh width when projected
onto the particle image plane. The implementation of a higher resolved
sub-grid has the following advantages:
The algorithm aligns the centre of the ellipse to the centre of the
particle image with improved accuracy in both cases, i.e. whether the number
of image pixels along the main axes is even or uneven.
The algorithm enables the adaption of the ellipse's shape to
the particle image by expanding or contracting the ellipse's axes on a finer
scale to resolve the following optimisation problem.
The optimisation problem is to approximate the ellipse that provides the
maximum of conformities and the minimum of nonconformities with the shape of
the particle image. In Fig. B1 a result of the automated approximation
process is illustrated. Fractions of the approximated ellipse that cause
nonconformities are coloured in red, while all conformities between the
approximated ellipse and the particle images are depicted in green. The
number of conformities ηconf. over the entire ellipse
ηtotal provides a criterion to automatically discard those
images from further consideration that significantly distinguish from an
ellipsoidal shape (e.g. irregular shapes, false images). The threshold for
this selection criterion was conservatively set to an acceptance value of
ηconf.ηtotal≥ 0.9 indicating an
ellipse as appropriate approximation to the particle image. The ratio of the
main axes' lengths ab of accepted ellipses is assumed
to represent the aspect ratio of the selected individual particle image. Of
course, some uncertainties are inherent in this approach. The largest
ambiguity arises from the optical resolution of the images. Consequently, the
remaining uncertainty of the obtained object size in either axis direction is
estimated with ±7.5 µm. The uncertainty of the aspect ratio
determined for the individual particle images is obtained as the largest
possible error that arises from the ratio
a+7.5µmb-7.5µm .
With the applied criteria, the computational spheroid recognition may provide an appropriate tool to
specifically select OAP image data which emanate with highest probability
from the detection of spherical particles that are most likely liquid
cloud droplets:
by limiting the analysed data set to a certain range of ambient
air temperatures and pressure altitudes;
by the automated discarding of false images or images that very
obviously emanate from particles of irregular (non-spherical) shape;
by the automated rejection of images that emanate from particles
passing the detection region too far away from the object plane, which would
certainly disturb any conclusion concerning the shape of detected particle;
and by the automated approximation of an ellipse to the particle
image with severe conformity criteria.
Acknowledgements
The authors thank the coordinators of the involved missions. We gratefully
acknowledge the technical support provided by C. von Glahn, K.-D. Wilhelm,
W. Schneider and T. Böttger. We thank M. Schnaiter, E. Järvinen,
M. Hermann, K. Kandler, and M. Baumgartner for the fruitful discussions as
well as the ML-CIRRUS team for the suggestions (ML-CIRRUS workshop, 25/26 November 2015).
Furthermore, the help and advice of R. E. Jubb is highly
appreciated as well as the very valuable and constructive suggestions of
D. Baumgardner, A. Korolev, C. H. Twohy and of an anonymous referee.
This work is based on data acquired during the DFG-supported (SPP1294) HALO missions
ML-CIRRUS and ACRIDICON-CHUVA, and this study was prepared with support by
the German “Bundesministerium für Bildung und Forschung” (BMBF) within
the joint ROMIC project SPITFIRE (01LG1205A). The AIRTOSS-ICE
campaign was supported by DFG through the projects BO1829/7-1 and
SP1163/3-1. Our research received funding from the European Research
Council under the European Union's Seventh Framework Program
(FP/2007-2013)/ERC grant agreement no. 321040 (EXCATRO). Financial support
from the Max Planck Institute for Chemistry and the Helmholtz Society is
gratefully acknowledged. We particularly thank all aircraft crew members and
operators of the research aircraft HALO and the GFD
Learjet-35A for their engagement.
Edited by: D. Baumgardner
Reviewed by: A. Korolev, C. H. Twohy and one anonymous referee
ReferencesAbdelmonem, A., Järvinen, E., Duft, D., Hirst, E., Vogt, S., Leisner, T., and
Schnaiter, M.: PHIPS-HALO: the airborne Particle Habit Imaging and Polar
Scattering probe – Part 1: Design and operation, Atmos. Meas. Tech., 9,
3131–3144, 10.5194/amt-9-3131-2016, 2016.
Baumgardner, D., Brenguier, J. L., Bucholtz, A., Coe, H., DeMott, P.,
Garrett, T. J., Gayet, J. F., Hermann, M., Heymsfield, A., Korolev, A.,
Krämer, M., Petzold, A., Strapp, W., Pilewskie, P., Taylor, J., Twohy,
C., Wendisch, M., Bachalo, W., and Chuang, P.: Airborne instruments to
measure atmospheric aerosol particles, clouds and radiation: A cook's tour of
mature and emerging technology, Atmos. Res., 102, 10–29, 2011.
Baumgardner, D., Jonsson, H., Dawson, W., O'Connor, D., and Newton, R.: The
cloud, aerosol and precipitation spectrometer: a new instrument for cloud
investigations, Atmos. Res., 59–60, 251–264, 2001.
Baumgardner, D., Newton, R., Krämer, M., Meyer, J., Beyer, A., Wendisch,
M., and Vochezer, P.: The Cloud Particle Spectrometer with Polarization
Detection (CPSPD): A next generation open-path cloud probe for distinguishing
liquid cloud droplets from ice crystals, Atmos. Res., 142, 2–14, 2014.
Baumgardner, D., Strapp, W., and Dye, J. E.: Evaluation of the Forward
Scattering Spectrometer Probe. Part II: Corrections for Coincidence and
Dead-Time Losses, J. Atmos. Ocean. Tech., 2, 626–632, 1985.
Bresenham, J. E.: Algorithm for computer control of a digital plotter, IBM
Syst. J., 4, 25–30, 1965.
Dixon, J. C.: Appendix B: Properties of Air, in: The Shock Absorber Handbook,
361–374, John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West
Sussex, England, 2007.
DMT: Droplet Measurement Technologies Inc., Data Analysis User's Guide,
Chapter II: Single Particle Imaging, DOC-0223, 2009.
Drummond, A. M. and MacPherson, J. I.: Aircraft Flow Effects on Cloud Drop
Images and Concentrations Measured by the NAE Twin Otter, J. Atmos. Ocean. Tech., 2, 633–643, 1985.
Dye, J. E. and Baumgardner, D.: Evaluation of the Forward Scattering
Spectrometer Probe. Part I: Electronic and Optical Studies, J. Atmos. Ocean. Tech., 1, 329–344, 1984.Finger, F., Werner, F., Klingebiel, M., Ehrlich, A., Jäkel, E., Voigt, M.,
Borrmann, S., Spichtinger, P., and Wendisch, M.: Spectral optical layer
properties of cirrus from collocated airborne measurements and simulations,
Atmos. Chem. Phys., 16, 7681–7693, 10.5194/acp-16-7681-2016, 2016.Frey, W., Eichler, H., de Reus, M., Maser, R., Wendisch, M., and Borrmann,
S.: A new airborne tandem platform for collocated measurements of
microphysical cloud and radiation properties, Atmos. Meas. Tech., 2,
147–158, 10.5194/amt-2-147-2009, 2009.Frey, W., Borrmann, S., Kunkel, D., Weigel, R., de Reus, M., Schlager, H.,
Roiger, A., Voigt, C., Hoor, P., Curtius, J., Krämer, M., Schiller, C., Volk,
C. M., Homan, C. D., Fierli, F., Di Donfrancesco, G., Ulanovsky, A.,
Ravegnani, F., Sitnikov, N. M., Viciani, S., D'Amato, F., Shur, G. N.,
Belyaev, G. V., Law, K. S., and Cairo, F.: In situ measurements of tropical
cloud properties in the West African Monsoon: upper tropospheric ice clouds,
Mesoscale Convective System outflow, and subvisual cirrus, Atmos. Chem.
Phys., 11, 5569–5590, 10.5194/acp-11-5569-2011, 2011.
Hinds, W. C.: Aerosol Technology: Properties, Behavior, and Measurement of
airborne Particles, 2nd edition, 5–21, John Wiley & Sons Inc., Hoboken, New
Jersey, 1999.Kärcher, B. and Lohmann, U.: A parameterization of cirrus cloud
formation: Homogeneous freezing of supercooled aerosols, J. Geophys.
Res.-Atmos., 107, 4010, 10.1029/2001JD000470, 2002.
King, W. D.: Air Flow and Particle Trajectories around Aircraft Fuselages. I:
Theory, J. Atmos. Ocean. Tech., 1, 5–13, 1984.
King, W. D.: Air Flow and Particle Trajectories around Aircraft Fuselages.
IV: Orientation of Ice Crystals, J. Atmos. Ocean. Tech., 3, 433–439,
1986a.
King, W. D.: Air Flow around PMS Canisters, J. Atmos. Ocean. Tech., 3,
197–198, 1986b.Klingebiel, M., de Lozar, A., Molleker, S., Weigel, R., Roth, A., Schmidt,
L., Meyer, J., Ehrlich, A., Neuber, R., Wendisch, M., and Borrmann, S.:
Arctic low-level boundary layer clouds: in situ measurements and simulations
of mono- and bimodal supercooled droplet size distributions at the top layer
of liquid phase clouds, Atmos. Chem. Phys., 15, 617–631,
10.5194/acp-15-617-2015, 2015.
Knollenberg, R. G.: The Optical Array: An Alternative to Scattering or
Extinction for Airborne Particle Size Determination, J. Appl. Meteorol., 9,
86–103, 1970.
Korolev, A.: Reconstruction of the Sizes of Spherical Particles from Their
Shadow Images. Part I: Theoretical Considerations, J. Atmos. Ocean. Tech.,
24, 376–389, 2007.
Korolev, A., Emery, E., and Creelman, K.: Modification and tests of particle
probe tips to mitigate effects of ice shattering, J. Atmos. Ocean. Tech.,
30, 690–708, 2013.
Korolev, A., Makarov, Y. E., and Novikov, V.: On the calibration of
photoelectric cloud droplet spectrometer FSSP-100, TCAO, 158, 43–49, 1985.
Korolev, A. V., Kuznetsov, S. V., Makarov, Y. E., and Novikov, V. S.:
Evaluation of Measurements of Particle Size and Sample Area from Optical
Array Probes, J. Atmos. Ocean. Tech., 8, 514–522, 1991.
Korolev, A. V., Strapp, J. W., and Isaac, G. A.: Evaluation of the Accuracy
of PMS Optical Array Probes, J. Atmos. Ocean. Tech., 15, 708–720, 1998.Krämer, M., Schiller, C., Afchine, A., Bauer, R., Gensch, I., Mangold,
A., Schlicht, S., Spelten, N., Sitnikov, N., Borrmann, S., de Reus, M., and
Spichtinger, P.: Ice supersaturations and cirrus cloud crystal numbers,
Atmos. Chem. Phys., 9, 3505–3522, 10.5194/acp-9-3505-2009, 2009.
Kulkarni, P., Baron, P. A., and Willeke, K.: Aerosol measurement: principles,
techniques, and applications, John Wiley & Sons, 25–71, 2011.Lance, S., Brock, C. A., Rogers, D., and Gordon, J. A.: Water droplet
calibration of the Cloud Droplet Probe (CDP) and in-flight performance in
liquid, ice and mixed-phase clouds during ARCPAC, Atmos. Meas. Tech., 3,
1683–1706, 10.5194/amt-3-1683-2010, 2010.
Laursen, K. K., Jorgensen, D. P., Brasseur, G. P., Ustin, S. L., and Huning,
J. R.: HIAPER: The Next Generation NSF/NCAR Research Aircraft, B.
Am. Meteor. Soc., 87, 896–909, 2006.
Lawson, R. P., O'Connor, D., Zmarzly, P., Weaver, K., Baker, B., Mo, Q., and
Jonsson, H.: The 2D-S (Stereo) Probe: Design and Preliminary Tests of a New
Airborne, High-Speed, High-Resolution Particle Imaging Probe, J. Atmos. Ocean. Tech., 23, 1462–1477, 2006.
MacPherson, J. I. and Baumgardner, D.: Airflow about King Air Wingtip-Mounted
Cloud Particle Measurement Probes, J. Atmos. Ocean. Tech., 5, 259–273,
1988.
Menter, F., Kuntz, M., and Langtry, R.: Ten years of industrial experience
with the SST turbulence model, Turbul., Heat Mass Transfer, 4, 625–632,
2003.
Meyer, J.: Ice Crystal Measurements with the New Particle Spectrometer
NIXE-CAPS, Schriften des Forschungszentrum Jülich, Energy & Environment,
160, ISBN:978-3-89336-840-2, Forschungszentrum Jülich GmbH, 2012.Molleker, S., Borrmann, S., Schlager, H., Luo, B., Frey, W., Klingebiel, M.,
Weigel, R., Ebert, M., Mitev, V., Matthey, R., Woiwode, W., Oelhaf, H.,
Dörnbrack, A., Stratmann, G., Grooß, J. U., Günther, G., Vogel,
B., Müller, R., Krämer, M., Meyer, J., and Cairo, F.:
Microphysical properties of synoptic-scale polar stratospheric
clouds: in situ measurements of unexpectedly large HNO3-containing
particles in the Arctic vortex, Atmos. Chem. Phys., 14, 10785–10801,
10.5194/acp-14-10785-2014, 2014.
Naumann, Z. and Schiller, L.: A drag coefficient correlation, Z. Ver. Deutsch
Ing., 77, 318–323, 1935.
Norment, H. and Quealy, A.: Three-dimensional trajectory analyses of two drop
sizing instruments: PMS OAP and PMS FSSP, AIAA 25th Aerospace Sciences
Meeting, 12–15 January 1887, Reno, Nevada, 1988.Norment, H. G.: Three-Dimensional Trajectory Analysis of Two Drop Sizing
instruments: PMS* OAP and PMS* FSSP, J. Atmos. Ocean. Tech., 5, 743–756,
1988.
Pruppacher, H. R. and Klett, J. D.: Microphysics of Clouds and Precipitation,
p. 397 and p. 551, DOI:10.1007/978-0-306-48100-0, Springer Netherlands, 2012.Spichtinger, P. and Gierens, K. M.: Modelling of cirrus clouds –
Part 1a: Model description and validation, Atmos. Chem. Phys., 9,
685–706, 10.5194/acp-9-685-2009, 2009.
Thurai, M., Bringi, V. N., Szakáll, M., Mitra, S. K., Beard, K. V., and
Borrmann, S.: Drop Shapes and Axis Ratio Distributions: Comparison between 2D
Video Disdrometer and Wind-Tunnel Measurements, J. Atmos. Ocean. Tech.,
26, 1427–1432, 2009.Voigt, C., Schumann, U., Minikin, A., Abdelmonem, A., Afchine, A., Borrmann,
S., Boettcher, M., Buchholz, B., Bugliaro, L., Costa, A., Curtius, J.,
Dollner, M., Dörnbrack, A., Dreiling, V., Ebert, V., Ehrlich, A., Fix,
A., Forster, L., Frank, F., Fütterer, D., Giez, A., Graf, K., Grooß,
J.-U., Groß, S., Heimerl, K., Heinold, B., Hüneke, T., Järvinen,
E., Jurkat, T., Kaufmann, S., Kenntner, M., Klingebiel, M., Klimach, T.,
Kohl, R., Krämer, M., Krisna, T. C., Luebke, A., Mayer, B., Mertes, S.,
Molleker, S., Petzold, A., Pfeilsticker, K., Port, M., Rapp, M., Reutter, P.,
Rolf, C., Rose, D., Sauer, D., Schäfler, A., Schlage, R., Schnaiter, M.,
Schneider, J., Spelten, N., Spichtinger, P., Stock, P., Walser, A., Weigel,
R., Weinzierl, B., Wendisch, M., Werner, F., Wernli, H., Wirth, M., Zahn, A.,
Ziereis, H., and Zöger, M.: ML-CIRRUS – The airborne experiment on
natural cirrus and contrail cirrus with the high-altitude long-range research
aircraft HALO, B. Am. Meteor. Soc., 10.1175/BAMS-D-15-00213.1, 2016.
Wendisch, M. and Brenguier, J.-L.: Airborne measurements for environmental
research: methods and instruments, John Wiley & Sons, 2013.
Willeke, K. and Baron, P. A.: Aerosol measurement, Principles, techniques and
applications, 3–36, Van Nostrand Reinhold: New York, NY, 1993.