AMTAtmospheric Measurement TechniquesAMTAtmos. Meas. Tech.1867-8548Copernicus PublicationsGöttingen, Germany10.5194/amt-10-2239-2017Evaluation of radar reflectivity factor simulations of ice crystal
populations from in situ observations for the retrieval of condensed water
content in tropical mesoscale convective systemsFontaineEmmanuele.r.j.fontaine@reading.ac.ukhttps://orcid.org/0000-0002-7240-3381LeroyDelphineSchwarzenboeckAlfonsDelanoëJulienProtatAlainDezitterFabienGrandinAliceStrappJohn WalterLilieLyle EdwardUniversité Clermont Auvergne, Laboratoire de Météorologie
Physique, Aubière, FranceLaboratoire Atmosphère, Milieux et Observations Spatiales, UVSQ,
Guyancourt, FranceCenter for Australian Weather and Climate Research, Melbourne,
AustraliaAirbus, Toulouse, FranceMet Analytics, Toronto, CanadaDepartment of Meteorology, University of Reading, Reading, UKEmmanuel Fontaine (e.r.j.fontaine@reading.ac.uk)13June2017106223922527October201624October201629March201710April2017This work is licensed under the Creative Commons Attribution 3.0 Unported License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/3.0/This article is available from https://amt.copernicus.org/articles/10/2239/2017/amt-10-2239-2017.htmlThe full text article is available as a PDF file from https://amt.copernicus.org/articles/10/2239/2017/amt-10-2239-2017.pdf
This study presents the evaluation of a technique to
estimate cloud condensed water content (CWC) in tropical convection from
airborne cloud radar reflectivity factors at 94 GHz and in situ measurements
of particle size distributions (PSDs) and aspect ratios of ice crystal
populations. The approach is to calculate from each 5 s mean PSD and
flight-level reflectivity the variability of all possible solutions of m(D)
relationships fulfilling the condition that the simulated radar reflectivity
factor (T-matrix method) matches the measured radar reflectivity factor. For
the reflectivity simulations, ice crystals were approximated as oblate
spheroids, without using a priori assumptions on the mass–size relationship
of ice crystals. The CWC calculations demonstrate that individual CWC values
are in the range ±32 % of the retrieved average CWC‾ value
over all CWC solutions for the chosen 5 s time intervals. In addition, during
the airborne field campaign performed out of Darwin in 2014, as part of the
international High Altitude Ice Crystals/High Ice Water Content
(HAIC/HIWC) projects, CWCs were measured independently with the new IKP-2
(isokinetic evaporator probe) instrument along with simultaneous particle
imagery and radar reflectivity. Retrieved CWC‾s from the T-matrix
radar reflectivity simulations are on average 16 % higher than the direct
CWCIKP measurements. The differences between the CWCIKP and
averaged retrieved CWC‾s are found to be primarily a function of the
total number concentration of ice crystals. Consequently, a correction term
is applied (as a function of total number concentration) that significantly
improves the retrieved CWC. After correction, the retrieved CWC‾s
have a median relative error with respect to measured values of only -1 %.
Uncertainties in the measurements of total concentration of hydrometeors are
investigated in order to calculate their contribution to the relative error
of calculated CWC‾ with respect to measured CWCIKP. It is shown
that an overestimation of the concentration by about +50 % increases the
relative errors of retrieved CWC‾s by only +29 %, while possible
shattering, which impacts only the concentration of small hydrometeors,
increases the relative error by about +4 %. Moreover, all cloud events
with encountered graupel particles were studied and compared to events
without observed graupel particles. Overall, graupel particles seem to have
the largest impact on high crystal number-concentration conditions and show
relative errors in retrieved CWC‾s that are higher than for
events without graupel particles.
Introduction
Clouds play an important role within the hydrological cycle, radiative
transfer, and heat balance of the Earth. Thus, improving knowledge of ice
hydrometeor properties and understanding of related processes is important
for improving numerical weather forecast and global climate models, as such
models use simple schemes to describe the ice hydrometeors' properties. As a
consequence, significant differences in the representation of ice properties
in clouds (Li et al., 2005, 2007) lead to large variations in the
quantification of ice cloud effects on climate evolution (Intergovernmental
Panel on Climate Change Fourth Assessment Report). Among different ice
properties, the spatiotemporal distribution of cloud condensed water content (CWC) is a key parameter for
evaluating and improving numerical weather prediction (Stephens et al., 2002). Increasingly, remote sensing tools are used to study cloud
properties such as hydrometeor size distributions (ice or water), liquid
and/or ice water content, ice particle shape (spherical, hexagonal, etc.), and precipitation rate. In particular, the radar (at
different frequencies of 5.5, 9.4, 35, 94 GHz) is the most common
measurement technique used to measure clouds properties. Radar reflectivity
factors are an integral value of all backscattering cross sections from all
hydrometeors within the radar sampling volume, which makes the radar a
complex measurement device for estimating cloud properties.
The methodology applied in this study to simulate 94 GHz radar reflectivity
factors is based on assumptions about individual cloud particle properties.
If hydrometeors are droplets, then Mie solutions can be applied to the
Maxwell equations; however, this is not the case for non-spherical ice
crystals. Discrete dipole approximations
(DDA; Draine and Flatau, 1994; Liu, 2008) can
be used to calculate backscatter cross sections for complex shapes and thus
tackle this question for ice crystals. However, in order to apply DDA
simulations to ice crystal radar reflectivity factors, a classification of
ice hydrometeor habits is essential. Unfortunately, more than 50 % of ice
crystal images classified using automated or manual shape recognition
techniques from ground-based and airborne measurements are typically
identified as irregular (i.e. they are not identified as a specific habit).
This statement still holds when using very-high-resolution imaging such as
from the Cloud Particle Imager (2.3 µm resolution; e.g. Mioche, 2010).
Hogan et al. (2011) used the oblate spheroid
approximation to simulate radar reflectivity factors at 3 and 94 GHz. For
their calculation of the ice fraction in horizontally oriented oblate
spheroids, these authors used a constant axis ratio of 0.6 and used the
mass–size relationship from Brown and Francis (1995),
originally from Locatelli and Hobbs (1974), to derive CWCs and radar reflectivity factors. Even though a mass–size
relationship for ice crystals with constant coefficients has been utilized,
the study of Hogan et al. (2011) claimed minimal errors between measured and
simulated radar reflectivity factors, even smaller than the calibration
uncertainty of the cloud radar.
Fontaine et al. (2014) also used the oblate spheroid
approximation for ice crystals to calculate CWC in mesoscale convective
systems (MCS), and Drigeard et al. (2015) used the
Fontaine et al. (2014) results to simulate radar
reflectivity factors at 5.5 GHz. Although simulations of radar reflectivity
factors agreed with reflectivity observations at 94 and 5.5 GHz, no direct
bulk measurements of CWC were available to evaluate the retrieved CWCs.
A simpler way to calculate CWC from radar reflectivity factors is based on
empirical Z–CWC or Z–CWC–T relationships. Such relationships have been
established in earlier studies, either with or without direct measurements
of CWC (Protat et al., 2016, 2007; Hogan et al., 2006),
for different types of clouds and at different geographical locations
(tropics, continental, mid-latitude). When no direct simultaneous
measurements of CWC are available, Z–CWC (and Z–CWC–T) relationships are
established by using constant mass–size relationships (for CWC calculations
from particle size distribution (PSD) measurements) and most of the time these studies use m(D)
coefficients suggested by Brown and Francis (1995). As a matter of fact this
would mean that mass–size coefficients are constant and are linked neither
to temperature nor to the variability of PSDs or the type of clouds. In
Fontaine et al. (2014), these simplistic assumptions were not used. This
more sophisticated method allows for a more dynamic solution with varying
mass–size coefficients related to the variability of microphysics (PSD and
aspect ratio of ice crystals). Fontaine et al. (2014) end up with the
retrieval of an average CWC calculated as a function of time from multiple
possible m(D) solutions for the T-matrix simulations of the radar
reflectivity factor (Ze) simulations compared to measured Z. The method has
been established and published without validation from simultaneous direct
measurements of CWC.
During the High Altitude Ice Crystals (HAIC; Dezitter et al., 2013)/High
Ice Water Content (HIWC; Strapp et al., 2016) airborne field campaign
performed out of Darwin, the Falcon-20 (F-20) from SAFIRE (Service des
Avions Français Instrumentés pour la Recherche en Environnement)
measured on the same aircraft 94 GHz Z, PSD, aspect ratios of hydrometeors,
and independently CWC. The objective of our study is to use this
comprehensive HAIC/HIWC dataset to evaluate the method presented by Fontaine
et al. (2014).
The next section of this paper presents the dataset of the first HAIC/HIWC
airborne campaign and associated data processing. The principle of the cloud
radar reflectivity simulation method (Fontaine et al., 2014) is then briefly
recalled. The third section is dedicated to the evaluation of the Fontaine
et al. (2014) method by comparing averaged in retrieved
CWC‾s from the T-matrix simulations with direct measurements
of CWCIKP. Moreover, the study suggests correction functions for
calculated CWC‾ (based on T-matrix simulations of the reflectivity
factors) as a function of temperature, largest size of hydrometeors in PSDs,
and ice crystal concentrations. Then, two further sections are dedicated to
the estimation of possible uncertainties in the measurements leading to the
corrected CWC‾ retrievals and the impact of graupel particles on
those retrievals. Finally, the study ends with a discussion and conclusion
section.
Data processing
The HAIC/HIWC projects were designed to investigate the microphysical
processes responsible for engine damage observed when commercial aircraft
divert around convective cores. First HIWC studies (Mason et al., 2006)
indicated that this new form of icing (now referred to as ice crystal icing)
was due to the production of high concentrations of small ice crystals by
deep convection. In this context 23 flights were performed over the Darwin
area, mainly over the ocean north of Australia, during the monsoon season.
Three of the 23 flights were dedicated to the calibration of the instruments
and are not included in this study. The dataset includes more than 17 000
data points where all parameters are synchronized and averaged over 5 s. As one of the priority of the HAIC/HIWC projects was to measure
high ice water content and the variability of CWC as a function of distance
from the convective cores at typical altitudes flown by commercial aircraft,
the flight strategy was to fly long legs at constant altitude at
-50, -40, -30, and -10 ∘C
and to get as close as possible to the most convective zone of the MCS (see
Fig. 2 in Leroy et al., 2017), thereby avoiding red aircraft radar echoes
at normal gain as commercial aircraft would also do. More details on HAIC/HIWC
projects and implemented flight strategy can be found in Dezitter et al. (2013), Leroy et al. (2016, 2017), Protat et al. (2016), and Strapp et
al. (2016).
In situ microphysical measurements and radar reflectivity data used in this
study were provided by three types of instruments, which were mounted
on board the F-20 for the HAIC/HIWC Darwin campaign.
(1) The 94 GHz multi-beam Doppler cloud radar RASTA measured both cloud radar
reflectivity factors and 3-D cloud dynamics below and above the flight level.
The uncertainty on the measured reflectivity is about ±1 dBZ (e.g.
Protat et al., 2009). We only use radar vertical antennas (zenith, nadir)
producing vertical profiles of the radar reflectivity along the flight
trajectory. Radar reflectivity factors are interpolated at the flight
altitude using validated gates (typically 180 m above and below the
aircraft) to retrieve the most likely radar reflectivity at flight altitude.
RASTA has a vertical resolution of 60 m and 0.7∘ beam width.
(2) Two optical array probes (OAPs), the 2-D-Stereo probe (2-D-S) from SPEC
(Stratton Park Engineering Company, Inc.) and the Precipitation Imaging Probe
(PIP) from Droplet Measurement Technologies (DMT) were used.
(3) An Isokinetic Evaporator Probe (IKP-2: Davison et al., 2016) that provides
direct CWC measurements was also used. The IKP-2 is a second-generation version of the
prototype IKP (Davison et al., 2008), which was downsized for the F-20. The
IKP-2 was developed to provide reliable measurements of CWC in deep
convective clouds at temperatures colder than -10 ∘C, up to at
least 10 g m-3 at aircraft speeds of 200 ms-1, and with a target
accuracy of 20 %. The IKP-2 samples the cloud particles isokinetically,
evaporates them, and measures the resulting humidity of the evaporated
particles and background air. CWC (hereafter CWCIKP given in g m-3)
is then obtained by subtracting the water vapour background measurement from
the IKP-2 total hygrometer signal. System accuracy estimates are better than
20 % for CWC greater than 0.25 g m-3 for temperatures lower than
-10 ∘C (Davison et al., 2016). Accuracy increases with decreasing
temperature due to the exponential decrease in background humidity, which
drives much of the IKP-2 error. For example, at -56 ∘C, system accuracy was
estimated at better than 4 % for CWC greater than about 0.1 g m-3.
The 2-D-S and the PIP record monochromatic 2-D shadow images of cloud
hydrometeors (ice and/or water) along the flight trajectories. The 2-D-S
records images of hydrometeors in the size range 10–1280 µm at a 10 µm pixel resolution, whereas the PIP records images in the size range
100–6400 µm and beyond (perpendicular to photodiode array and
reconstruction of truncated images parallel to the array) at a 100 µm
pixel resolution. For both probes, PSDs were
produced by image analysis into number concentrations per unit volume of
sampled air as a function of their size.
In this paper, the size of ice hydrometeors is given in terms of the maximum
diameter Dmax (e.g. see Leroy et
al., 2016, for definition). The size of truncated images and sampling
volume are corrected using the method presented in Korolev
and Sussman (2000). This reconstruction method allows extrapolating
hydrometeor sizes to a maximum size of 2.56 mm for 2-D-S and to 12.8 mm for
PIP.
In addition, many artefacts can bias PSD estimates from 2-D image analysis.
Therefore, supplementary post-processing is needed to retain only the
natural ice particles. One of the most important causes of artefacts is the
shattering of hydrometeors on the tips of OAPs. During the first
HAIC/HIWC field campaign in Darwin, the newest anti-shattering tips were
used for 2-D-S and PIP to reduce the shattering from large ice crystals. In
addition, analysis of the time-dependent (along the flight trajectory) interarrival time spectra was performed to determine the cut-off time, which
separates natural hydrometeors images from artefact particles
(Korolev and Isaac, 2005; Field et al.,
2006; Korolev and Field, 2015). It has been shown that both mitigation
techniques are needed to maximize the removal of shattering artefacts
(Jackson et al., 2014). Furthermore, OAP
images (for both 2-D-S and PIP) of splashed hydrometeors were removed
using the ratio between their projected surface area and the surface defined
by the box Lx × Ly (e.g. see Dx and Dy in Leroy et al., 2016), where Lx is
the projection of the size of each hydrometeor along the flight trajectory,
and Ly is the projection along the array of diodes. Images with an area
ratio less than 0.25 were considered as splashed particles and removed. This
threshold has been calculated statistically and allows the removal of larger
splashed ice crystals as well.
Another important correction is related to the sizing of out-of-focus
hydrometeors. In our study, the size of out-of-focus particles was corrected
using the method presented in Korolev (2007). In addition, noisy pixels
(satellite pixels) which may affect hydrometeor images were eliminated
thereby applying the method described in Lawson (2011). These single-pixel noisy pixels
are not firmly attached to the hydrometeors' images
and therefore must be removed to get the best estimation of the true
diameter (e.g. Dmax).
Finally, high number concentrations of ice particles lead to gaps in the
sampling times of OAPs due to insufficient time to record all
hydrometeors images. This probe effect (also called OAP overload or dead
time) was taken into account and would otherwise lead to an underestimation
of the number concentration of hydrometeors. While the 2-D-S probe overload
times are directly registered, the PIP overload is estimated by comparing
the number of images in the PIP files to the separately registered total
particle counts of particles that passed through the laser beam. The ratio
of counted particles (1-D information) to recorded particle images (2-D
information) is used to correct for the concentration. During an OAP
overload, 1-D counted particles may reach 15000 while only about 10 000 have a
recorded image, which would result in an uncertainty of 50 % on the
concentration of hydrometeors, without overload correction
(Fontaine,
2014). Further details on post-processing of 2-D-S and PIP data are given in
Leroy et al. (2016). The individual 2-D-S and PIP PSDs were merged into a
composite PSD using the algorithm described in Eq. (1). The resolution of
the composite PSD is 10 µm (by interpolating the PIP raw PSDs at the
2-D-S resolution), and PSDs are averaged over 5 s time intervals for improved
large particle statistics. The transition zone for changing from 2-D-S to PIP
data in the composite spectrum (see equation below) is from a Dmax of
805 µm (median diameter for a size bin) to 1205 µm.
N(Dmax) is given per litre.
∑Dmax=15Dmax=12845NDmax⋅ΔDmax=∑Dmax=15Dmax<805N2-D-SDmax⋅ΔDmax+C1Dmax⋅∑Dmax=805Dmax<1205N2-D-SDmax⋅ΔDmax+C2Dmax∑Dmax=805Dmax<1205NPIPDmax⋅ΔDmax+∑Dmax=1205Dmax=12845NPIPDmax⋅ΔDmax,
where C1(Dmax)+C2(Dmax)= 1, with
C2(Dmax)=Dmax-8051205-805.
Retrievals of CWC from radar reflectivity simulationsSimulations of radar reflectivity factors: Ze
This section reviews the method used in Fontaine et al. (2014). The principle of the technique is to retrieve CWC from simulations
of radar reflectivity factors (Ze), calculated from OAP image information and
compared to measured RASTA radar data. The data were collected in tropical
MCSs that formed over the African continent and over the Indian Ocean during
two aircraft campaigns dedicated to the Megha-Tropiques project (Roca et
al., 2015). The main drawback of these experiments is that they do not
include direct measurement of CWC. The Fontaine et al. (2014) method uses oblate spheroids (Hogan et al.,
2011) to approximate the backscatter cross section (Qback) of natural
hydrometeors. In Eq. (2) below, Ze is defined in mm6 m-3:
Ze(As‾,ficeDmax)=1000⋅λ4π5⋅Kw-ref⋅∑Dmax=15Dmax=12845NDmax⋅QbackAs‾,ficeDmax⋅ΔDmax,
with
fice=min1,mDmaxβπ6⋅ρice⋅Dmax3,
where
mDmax=α⋅Dmaxβ,
and
As‾=∑Dmax=15Dmax=12845AsDmax⋅PiDmax,
where
PiDmax=NDmax⋅Dmax3⋅ΔDmax∑Dmax=15Dmax=12845NDmax⋅Dmax3⋅ΔDmax.
Note that in Eq. (2) λ is the emitted wavelength of the radar and
Kw-ref is the dielectric constant of liquid water at the same frequency.
Qback is a function of the ice fraction (fice; Eq. 3) in the
spheroid and the axis ratio of the oblate spheroid (here denoted As‾,
see Eq. 5). fice is thereby a function of the mass–size relationship
(see Eq. 3). Equation (3) also limits the mass of an ice hydrometeor to the
mass of an ice sphere of diameter Dmax. fice also allows the
calculation of the dielectric properties of the ice spheroids
(Maxwell Garnet, 1904;
Drigeard et al., 2015).
As‾ (Eq. 5) is the average aspect ratio of all hydrometeors and is
calculated every 5 s according to N(Dmax) and Z. Pi (Eq. 6) is a weighting
function that has been defined to account for the volume occupied by the
hydrometeors in the sampled volume. As(Dmax) for a particle is defined as
the ratio of the width (radius perpendicular to Dmax) divided by
Dmax. In Fontaine et al. (2014) the calculation of As‾ only
considers all hydrometeors with sizes Dmax≤ 2005 μ which
contribute on average to 95 % of Ze (Drigeard et al., 2015). Since the
processing of 2-D-S and PIP has been further improved by Leroy et al. (2016), we decided to consider all hydrometeors from 15 µm to 1.2845 cm
for As‾ calculation. Note that a comparison of the As‾
calculation utilized in Fontaine et al. (2014) with the new As‾
calculation results in a decrease of As‾ of less than 3 %, which
has a negligible impact on the retrieval results.
Note that the constant aspect ratio of 0.6 used in
Hogan et al. (2011) is rather close to the peak of the
As‾ frequency distribution presented for African monsoon MCS and also
oceanic MCS over the Indian Ocean (Fontaine et al., 2014). The average
aspect ratio calculated for the HAIC/HIWC dataset is 0.55, which is then
very similar to respective average values for the various datasets sampled
over the African continent, United Kingdom, Indian Ocean, and north of Australia.
Condensed water content (CWC) as a function of time for two
HAIC/HIWC flights during the Darwin 2014 flight campaign. In black is
CWCIKP; in red is the average CWC‾ deduced from all possible
simulations (varying β and constraining α) of the measured
Z. Blue-to-green colour band shows CWC(βi) calculations when
β varies from 1 (blue) to 3 (green). (a) Results for flight
9;
(b) results for flight 12.
In Fontaine et al. (2014) the exponent β of the m(D) power law
relationship has been constrained as a function of time from the ice
particle images. For this study, no a-priori assumptions on the mass–size
relationship of hydrometeors have been chosen and therefore a variational
approach has been applied to calculate CWC from Ze reflectivity factor
simulations. For a given but variable exponent βi the
corresponding pre-factor αi is calculated to match the measured
reflectivity Z with the simulated Ze. βi is varying stepwise
between 1 to 3 by increments of 0.01. Thereby, the range of potential
solutions are explored using the oblate spheroids approximation with the
T-matrix method (Mishchenko et al., 1996) calculating
Qback of each spheroid. Hence, for a given 5 s data point, 201
calculations of αi and 201 calculations of corresponding
CWC(βi) are performed (see Eq. 10):
CWCβi=103⋅∑Dmax=15Dmax=12845NDmax⋅αi⋅Dmaxβi⋅ΔDmax.
For each 5 s data point, from the 201 possible CWC(βi) values, an
average value CWC‾ is deduced (Eq. 11):
CWC‾=1Ntot⋅∑βi=1βi=3CWCβi,
where Ntot≤ 201, since the minimum value allowed for αi is the mass of an empty sphere (air density).
Figure 1 shows two examples (flights 9 and 12) with
all possible CWC(βi) retrievals (colour band), average CWC‾
(red line), and CWCIKP measured by the IKP (overlaid black line). The
example in Fig. 1a shows results from flight 9,
in which the F-20 research aircraft flew in the more stratiform part of the
cloud system (w∼ 0 m s-1), whereas results from flight 12 shown
in Fig. 1b represent a case with more
signatures of convective updrafts. Overall, Fig. 1 demonstrates that the variational retrieval method produces a large
variability of possible CWC(βi) for each 5 s data point. In general,
the average CWC‾ (red line) is close to CWCIKP. The bandwidth of
all possible solutions CWC(βi) as a function of time is calculated
from the difference ΔCWC = max(CWC(βi))–min(CWC(βi)) between the
maximum and the minimum values of CWC(βi). On average, it is found
that ΔCWC accounts for 61 % of CWC‾ (with 64 % for the
median relative error) for the entire dataset (20 flights performed over
Darwin area). Finally, the calculations reveal that 80 % of the HAIC dataset
satisfy the condition CWCIKP=CWC‾± 32 %, where no a
priori assumptions on mass–size relationships were applied and βi linearly varies between 1 and 3, thereby producing equally eligible
solutions CWC(βi) that are finally averaged to produce a 5 s data
point for CWC‾.
(a) Ratio of cumulative sum of simulated Ze over measured total Z as a
function of Dmax for three chosen (αi,βi)
solutions (β=1, 2, and 3). (b) Ratio of the cumulative sum of ice
crystal mass over the CWC‾ for constant β (β= 1, 2, and 3), represented as a function of Dmax. Full lines represent
median and dashed lines 25th and 75th percentiles for entire
dataset with blue lines for β= 1, black lines for β= 2, and
red lines for β= 3.
In general, and for each given 5 s data point, maximum CWC is obtained for
β= 1 and minimum CWC for β=3. For β= 1, ice
hydrometeors below Dmax= 200 µm (sometimes even below 300 µm) may reach the maximum density of 0.917 g cm-3, while for
β= 3 the density of oblate spheroids is constant as a function of
Dmax (see Eqs. 3–4), where the density of icy spheroids is equal to
0.917 ×fice).
The impact of β on Ze and on the retrieved CWCs is illustrated in
Fig. 2. One can notice that for different values of β (β= 1, 2, 3) the corresponding value of α can be found such that the
cumulative sum of Ze as a function of Dmax normalized by the measured
radar reflectivity factor Z (in mm6 m-3; Fig. 2a.) is
equal to 1. The respective cumulative mass of ice crystals (as a function of
Dmax) then is normalized by CWC‾ (Fig. 2b). This CWC ratio may deviate from 1, whereas the normalized cumulative
sum of Ze has been equal to 1, independently of chosen β. For β=1, Ze is reached sooner (Dmax≈ 1700 µm) than for
β= 3 (Dmax≈ 3000 µm). The likely explanation is
that with increasing β, the backscattered energy is increased for
large hydrometeors and the mass contribution of smaller hydrometeors is
considerably reduced since the contribution of numerous smaller hydrometeors
(compared to larger hydrometeors) on retrieved CWC is decreasing with
increasing β.
(a) Relative errors of CWC‾ with respect to CWCIKP (as
defined in Table 1) as a function of total PSD number concentration
NT. The errors are presented with and without the three suggested
correction functions for CWC‾. (b) Number of 5 s data points used for
the statistics on the y axis as a function of NT intervals.
CWC deviations from T-matrix simulations of reflectivity with respect to
IKP direct measurements
This section focuses on the potential error in CWC retrievals from T-matrix
simulations of radar reflectivity factors (at frequency of 94 GHz) for
populations of ice hydrometeors approximated with oblate spheroids.
Therefore, the relative errors of retrieved CWC‾ with respect to
reference CWCIKP (measured by the IKP-2 probe) are calculated and then
analysed as a function of microphysical properties of ice hydrometeors such
as total concentration (NT; Fig. 3), temperature T (Fig. 4), maximum size
of hydrometeors in PSDs (max(Dmax); Fig. 5), total cloud water content
CWCIKP (Fig. 6), and radar reflectivity factors Z (Fig. 7). Blue lines in
Figs. 3–7 (upper charts) display median trends
obtained when the relative errors of CWC‾ are plotted as a function
of the crystal number concentration NT, the temperature T, the maximum
encountered crystal size max(Dmax), the CWCIKP, and the radar reflectivity
Z. Bottom and top whiskers of the error bars represent the 25th and
75th percentiles of the relative error of CWC‾ (with respect to
CWCIKP). Lower charts in Figs. 3–7 illustrate the number of samples used
for the calculation of the respective data points in discrete intervals of
NT, T, max(Dmax), CWCIKP, and Z. The other curves in Figs. 3–7
represent the retrieved CWCs with applied corrections as a function of
NT (red curves), T (grey curves), and max(Dmax) (black curves) and are discussed
in Sect. 3.3 with the correction functions.
Same as Fig. 3, but represented as a
function of temperature T on the x axis.
Same as Fig. 3 but represented as a
function of the maximum size of hydrometeors max(Dmax) on the x axis.
From Fig. 3 (blue line) it appears that CWC‾ resulting from T-matrix
simulations approximating ice hydrometeors with oblate spheroids is poorer
at the lower (NT < 100 L-1) and higher (NT > 5000 L-1)
ranges of number concentrations. In particular, the reference CWCIKP is
underestimated for small NT and overestimated for larger NT.
Furthermore, Fig. 4 (blue line) seems to illustrate that this method
increasingly overestimates with decreasing temperature (blue line in
Fig. 4). For example, CWC‾ exceeds
CWCIKP at 220 K (±5 K) by about 25 %. Finally, the relative
errors of CWC‾ with respect to CWCIKP slightly but continuously
increase with the maximum size of hydrometeors within the respective data
point (blue line in Fig. 5), where the relative
error of CWC‾ reaches +25 % when max(Dmax)= 1 cm versus
∼ 0 % for max(Dmax)= 800 µm.
Mean relative errors, 10th, 25th, 50th, 75th,
and 90th percentiles (in %) of retrieved
CWC‾s with respect to CWCIKP. Black numbers
are for the entire dataset and bold numbers are respective relative errors
for graupel events only.
Relative errorMean10th25th50th75th90thCWC‾-CWCIKPCWCIKP⋅100%19-142163254(83)(6)(32)(75)(101)(133)CWC‾⋅f(NT)-CWCIKPCWCIKP⋅100%2-24-12-11228(16)(-25)(-7)(7)(32)(54)CWC‾⋅f(T)-CWCIKPCWCIKP⋅100%4-24-1111534(59)(-5)(16)(51)(77)(100)CWC‾⋅f(max(Dmax))-CWCIKPCWCIKP⋅100%3-26-1201433(53)(-11)(14)(44)(68)(96)Correction functions for CWC retrievals from T-matrix simulations of
reflectivity
Because of the above findings, three different types of corrections are
studied in order to (i) quantify the limitations of the oblate spheroid
approximation and (ii) suggest suitable correction functions that use
in situ measured quantities over the entire dataset with CWCIKP larger
than 0.1 g m-3. These corrections are performed using the inverse of the
original relative errors (blue lines) in Figs. 3–5 and aims at reducing
the median relative errors to 0 %. The impact of these corrections on
relative errors as a function of NT, T, and max(Dmax) is added to
Figs. 3–7.
Red lines in Figs. 3–7 represent the relative error of CWC‾×f(NT)
after applying a correction function f(NT) as a function of NT with
fNT=0.84⋅-0.3012⋅log10NT3+2.658⋅log10NT2-7.758⋅log10NT+8.493.
Grey lines in Figs. 3–7 represent the relative error of CWC‾×f(T) after
applying a correction function f(T) as a function of T with
fT=0.84⋅0.006528⋅T-0.517.
Black lines in Figs. 3–7 represent the relative error of CWC‾×f(max(Dmax))
after applying a correction function f(max(Dmax)) as a function of
max(Dmax) with
fmaxDmax=0.84⋅2.092.10-9⋅maxDmax2-3.869.10-5maxDmax+1.15.
Without the above correction functions, retrieved initial CWC‾s are
larger than CWCIKP by about 19 % on average (with a median value of
+16 %; Table 1, first row). Therefore, all
three correction functions (Eqs. 9–11) have a median factor of 0.84
in common that reduces the initial CWC‾ such that CWC‾×f(X;X=NT, T, max(Dmax))
better matches CWCIKP. The expressions in parentheses of Eqs. (9)–(11) try to
redistribute the relative error in CWC‾ from T-matrix simulations
over the entire range of observed NT, T, and max(Dmax) values, but they have
negligible impact on the median relative error itself. Even though no
correction functions for CWC‾ have been proposed as a function of
CWCIKP and Z, Figs. 6 and 7 illustrate the impact of NT, T, and
max(Dmax) correction functions (Eqs. 9–11) on the redistribution of the
relative error also as a function of CWCIKP and Z.
Figure 3 reveals that f(NT) (Eq. 9) decreases
biases of retrieved CWC‾×f(NT) over the entire NT bandwidth,
while f(T) (Eq. 10) and f(max(Dmax)) (Eq. 11) do not change the shapes of the
relative error lines as compared to uncorrected CWC‾ relative errors
(Fig. 3). Also, the function f(NT) (Eq. 9) also generally decreases
relative errors of the CWC‾×f(NT) retrievals when plotted as a
function of T (Fig. 4) and as a function of max(Dmax) (Fig. 6). Furthermore,
the f(T) correction function (Eq. 10) reduces the differences between
CWC‾×f(T) and CWCIKP as a function of T (Fig. 4). However,
CWC‾s corrected as a function of T still show bias when
presented as a function of NT (Fig. 3, grey line) or as a function of
Z (Fig. 7, grey line). Finally, the f(max(Dmax)) correction function (Eq. 11)
reduces the relative error of retrieved CWC‾×f(max(Dmax)) as a function of
max(Dmax) in Fig. 5 but does not have much impact on the
shape of the relative error distributions as a function of NT, T,
CWCIKP, and Z (Figs. 3, 4, 5, 7) relative to uncorrected CWC‾
relative errors.
Same as Fig. 3 but represented as a
function of CWCIKP on the x axis.
Same as Fig. 3 but represented as a
function of radar reflectivity factors Z on the x axis.
In addition, rows 2–4 of Table 1 present mean (average), median, 10th,
25th, 75th, and 90th percentiles of the relative error after
applying the correction functions, with an obvious decrease of mean and
median values and corresponding shift of relative error distribution
percentiles.
Overall, the f(NT) correction seems most efficient to remove the CWC bias.
Heymsfield et al. (2013) showed that total
concentrations of ice hydrometeors tend to increase with decreasing
temperature in tropical MCS for temperatures -60 ∘C < T < 0 ∘C. This evolution of the increasing total
concentration of hydrometeors related to decreasing temperatures is
therefore suggested as the key to explaining trends in relative CWC errors
as a function of NT and T.
Figure 8 summarizes the above results by showing
probability distribution functions of CWC‾×f(X;X=NT, T, max(Dmax)) versus
CWCIKP. Imperfections of the corrections described by Eqs. (10) and (11) are clearly visible in Fig. 8c and d, where high CWCIKP
values are still overestimated (as in Fig. 8a) by CWC‾×f(T) and
CWC‾×f(max(Dmax)), respectively. The correction function f(NT) (Eq. 9)
produces the best results (Fig. 8b), where the
maximum of the probability distribution function in CWC‾×f(NT) versus
CWCIKP representation follows the line y=x.
Relative errors of retrieved prefactor αi,fshatt and
αi,50% with respect to αi in % for β= [1, 2, 3].
Probability distribution functions of CWC‾ on the y axis
calculated as a function of CWCIKP on the x axis. Probabilities are
represented by the colour scale and were normalized by the number of data
points. (a) No correction is applied to average CWC‾. (b) Correction
f(NT) described by Eq. (9) is applied to CWC‾. (c) Correction f(T)
described by Eq. (10) is applied to CWC‾. (d) Correction
f(max(Dmax)) described by Eq. (11) is applied to CWC‾.
Dashed black lines represent the shift of retrieved CWSs when Z is shifted by more or less 1 dBZ (RASTA uncertainty; Fontaine et al. 2014).
Uncertainties in ice particle concentrations and impact on
results
This section investigates the impact of uncertainties in crystal
concentrations on the CWC retrieval, with a particular focus on shattering
of ice crystals. As discussed in Sect. 3.2 the relative errors increase
with total number concentration, with overestimations by about 50 % of
CWCs for very large concentrations of hydrometeors, which can reach 104
hydrometeors per litre in most convective parts of sampled MCS
(Fig. 3a). In order to investigate the impact of
uncertainties of number concentrations on the retrieved CWC we apply two
different types of functions on the measured PSDs, in which both functions
increase the number concentrations of measured PSDs.
First, a function fshatt is applied to the PSD in order to increase
concentrations of hydrometeors in the first PSD size bin (5–15 µm) by
about 50 %, while concentrations of hydrometeors larger than 500 μ
remain unchanged. The function fshatt decreases in a logarithmic way
with Dmax from first bin to 500 µm. fshatt is applied to PSD
such that N′(Dmax)=fshatt(Dmax)×N(Dmax) and aims to produce new PSDs
where the optimized probe tips still would have produced shattered crystal
fragments and/or removal processing would have failed to remove numerous
shattered ice particles. Then, the retrieval method (see Sect. 3.1) is
applied to these new PSDs in order to calculate new values for αi and subsequently CWCi (hereafter αi,fshatt and
CWCi,fshatt). For the purpose of this Sect. 4, the method was only
applied for β= [1, 2, 3] in order to get a good idea of the
maximum impact of possible shattering artefacts. Results are presented in
terms of relative errors in Table 2 for αi,fshatt and Table 3
for CWCi,fshatt, respectively. Relative errors in (%) are calculated
with respect to coefficients αi and CWCi (for β= [1, 2, 3]) calculated in Sect. 3 for non-modified original N(Dmax) size
distributions and without correction functions discussed in Sect. 3.3.
(Eqs. 9 to 11). The relative errors illustrate that the chosen concentration
increase of solely small hydrometeor sizes has very limited impact on
retrieved αi and CWCi. Indeed, we observe that the median
relative error of the prefactor αi,fshatt with respect to
αi is roughly -3 % for β= 1 and 0 % for β= 2
and β= 3. The 1st and 99th percentiles are shown in order to
demonstrate that the relative errors in αi,fshatt are small
over the entire dataset. Consecutively, median relative errors of
CWCi,fshatt with respect to CWCi are of the order of 4, 3,
and 1 % for β= 1, 2, and 3, respectively. The 99th percentile
of the relative error does not exceed 10 % in retrieved CWC.
Second, a simple concentration uncertainty factor of 1.5 is applied over the
entire measured size range, which increases the number concentration by
50 % such that N′(Dmax)=(1.5×N(Dmax)). Note that 50 % is approximatively
the missed number of ice crystal images by the PIP due to the
probe overload in high concentrations of ice crystals, though data have been
corrected for overload times (see Sect. 2 and Fontaine, 2014).
Simulations of the reflectivity factor with modified N′(Dmax) were performed
with resulting prefactor αi,50% and derived CWCi,50%.
Results of the comparison of αi,50% and CWCi,50% with
αi and CWCi, respectively, are also presented in Table 2 and
Table 3. Globally, this second scenario of concentration enhancement of
original PSD has a larger impact on retrieved prefactor (αi)
and calculated CWCi than was the case for the first scenario.
Indeed, adding 50 % to the concentrations of hydrometeors results in a
median decrease of prefactor αi,50% with respect to αi of -18 % for β= 1 and -20 % for both β= 2 and 3.
The forced decrease in α (from αi,50% to αi,) goes along with an increase of CWCi,50% with
respect to CWCi by about +29 % (for β=1) and +27 % for
β= 2 and 3. Indeed, for a given radar reflectivity factor we simulate
(and measure) the same Ze (and Z) for N′(Dmax) (and N(Dmax)) with decreasing α
(αi,50% compared to αi,), while the
CWCi,50% increases by almost 30 % (CWCi,50% case compared to
CWCi). Hence, if two different size distributions produce an identical
Ze, CWC can be significantly different. In other words, Ze may differ significantly for the same CWC associated
with two underlying different size distributions
even without considering uncertainties in concentration measurements.
For three cloud categories discussed in Sect. 5,
(a, c, e) show the number size distributions of ice crystals and (b, d, f) present the respective aspect ratio distributions of
ice hydrometeors as a function of crystal size on the x axis. Median
distributions are indicated by a solid line and the 25th and 75th percentiles
by
dashed lines. The red curves are used for events where graupel are
detected, whereas blue is used for events without graupel particles.
In addition, median relative errors of retrieved uncorrected
CWC‾s, corresponding median aspect ratios, and
number of observed events (for both graupel and non-graupel events) are
added as numbers in the figures.
Impact of graupel on retrieved CWCs
Graupel are more spherical than pristine ice crystal shapes and aggregates.
When approximating graupel particles as oblate spheroids in the T-matrix
calculations, their density is close to solid ice density and their aspect
ratio is close to 1. Hence, observations of graupel particles dominating the
crystal populations are investigated within the entire dataset to estimate
their impact on retrieved CWCs. A detection algorithm of virtually spherical
particles has been applied to PIP image data to select events where graupel
are observed. Most of these events are observed for NT > 2000 L-1, CWC > 1 g m-3. For those events, retrieved
CWC‾s also have relative errors larger than 100 %. Some
events are also detected for NT < 2000 L-1, but with relative
errors less than 30 %. Table 1 gives relative errors for graupel events
only (bracketed bold numbers). It shows mean and median relative errors of
retrieved CWC‾s without corrections and with correction
applied from Eqs. (9) to (11). The correction as a function of NT (Eq. 9) has
the largest impact on the relative errors (mean and median) for graupel
events. Indeed, mean relative errors of retrieved CWC‾s for
all graupel events are 83 % (without correction) and 16 % (after
f(NT) correction). Likewise, the percentages for the median
relative errors are 75 and 7 %, respectively, without and with correction.
Note that corrections as functions of max(Dmax) and T are less efficient in
reducing mean and median relative errors of retrieved CWC‾s
for graupel events.
In the following, three different microphysical categories are distinguished
in order to compare PSD and As(Dmax) of observed graupel events with respective non-graupel data:
CWCIKP > 2 g m-3 and NT > 2000 L-1 (Fig. 9a
and b),
1 < CWCIKP < 2 g m-3 and NT > 2000 L-1 (Fig. 9c
and d), and
1 < CWCIKP < 2 g m-3 and NT < 2000 L-1 (Fig. 9e and f)
Figure 9 shows median, 25th, and 75th percentiles of PSDs (Fig. 9a, c, and e) and size-dependent As(Dmax) (Fig. 9b, d, and f). Graupel
and non-graupel events are shown as red and blue lines, respectively. From
this figure, there is no evidence of significant differences between median
PSDs with and without detection of graupel particles (three left figures).
However, the median aspect ratio substantially changes for hydrometeors
larger than 1mm, with increased As(Dmax) for the graupel particle events
compared to non-graupel events. For all three graupel categories defined
above, the number of observations with graupel particles are smaller than
those without graupel particles. Indeed, for the event category where
CWCIKP > 2 g m-3 and NT > 2000 L-1 a total of 451
events without graupel particles and solely 130 events with graupel
particles are detected, with median relative errors in uncorrected retrieved
CWC‾s of +40 and +74 %, respectively. For the
event category with 1 < CWCIKP≤ 2 g m-3 and
NT > 2000 L-1, there are 1687 and 80 graupel and non-graupel events,
respectively, with median relative error of uncorrected retrieved
CWC‾s of +25 and +63 %, respectively. Finally, for
the third category (1 < CWCIKP < 2 g m-3 and NT < 2000 L-1) only 16 events are detected with graupel particles compared to 1701 events without graupel particles, with corresponding median relative errors
of +10 and +9 %, respectively. Graupel particles seem to have
smaller impact on this third category as compared to two other categories.
Most of the graupel events occur for high crystal number concentrations
(NT > 2000 L-1), thereby leading to higher median relative
errors in uncorrected retrieved CWC‾s as compared to the non-graupel events.
Discussion and conclusions
The objective of the present study was to evaluate with direct CWC
observations the CWC retrieval technique outlined in Fontaine et al. (2014),
based on matching simulated radar reflectivity factors from PSD measurements
with measured radar reflectivity factors at 94 GHz. Since mass–size
relationships are considered to be unknown, the reflectivity simulations
explore a wide range of possible solutions of (αi,βi), varying β in the range of 1 to 3. This produces a series of
possible CWCs for a given data point, one for each value of β. From
this series, the average value CWC‾ over all values of β is
calculated. On average it is found that the difference CWC(β=1)-CWC(β= 3) is approximately 64 % of
the average CWC‾. Of the Darwin data points, 77 % meet the condition of CWC(β= 3) ≤ CWCIKP≤ CWC(β= 1),
which goes along with the relation CWCIKP=CWC‾±32 %. However, the retrieved
CWC‾ values are generally larger than
CWCIKP by about 16 % (median value), which illustrates that the
approximation of ice oblate spheroids tends to underestimate the
backscattered energy of real reflectivity measurements of ice hydrometeors
at 94 GHz, and a constant factor of 0.84 could be applied as a first-order
correction of retrieved CWC‾.
One of the possible explanations is that the calculation of the average
aspect ratio from 2-D images (Eqs. 5 and 6) which has been adopted as the
flattening parameter utilized for the approximation of ice oblate spheroids
might be somewhat too large. A way to investigate impact and calculation of
axis ratio for ice oblate spheroids approximations would be to use
As(Dmax) instead of As‾ (Eq. 5) in simulations of radar
reflectivity factors.
This study also demonstrated that the total concentration of ice
hydrometeors could be used as input for a correction algorithm that
minimizes differences between CWC‾ and CWCIKP and that this
parameter was the best of several parameters evaluated for this purpose.
These differences, before correction, were found to increase with increasing
ice concentration, with CWC‾ underestimating CWCIKP at low ice
concentrations and overestimating CWCIKP at high concentrations.
Another attempt of explanation is the uncertainty of measured total crystal
concentrations, which could partly explain large relative errors at high
concentrations. Indeed, for very high concentrations we find a higher
relative error of about +50 % as compared to IKP measurements. However,
according to the results of Sect. 4 of this study, an uncertainty of
50 % in ice crystals concentrations can solely explain 30 % of the
relative errors. Likewise, concentration errors related to large crystal
shattering could not explain more than 35 % of the relative errors at
very high concentrations of ice hydrometeors. However, this cannot explain
the negative relative errors for low ice crystal concentrations. Also, at
very low ice crystals concentrations oblate spheroids approximation of
crystals could be not sufficiently adapted, since for low concentrations
real shapes of ice hydrometeors might be even more important due to the lack
of any averaging process over all possible shapes and possible orientations
as should be more likely the case for higher concentrations.
Moreover, graupel particles are found to substantially affect the relative
errors in retrieved CWC‾s in high total concentration
situations as compared to moderate total crystal concentration situations
with graupel. In the latter observed conditions, graupel may have been less
numerous and their impact on the aspect ratio of ice hydrometeors larger
than 1 mm becomes less important than at higher concentrations (NT > 2000). Despite the fact that most graupel events are found
during high crystal concentration conditions, the correction function
f(NT) appears to be very efficient in reducing the relative error in
retrieved CWC‾s when graupels are detected. Since the
suggested f(NT) correction has been established for the entire dataset and
is not exclusively designed for the graupel event correction of retrieved
CWC‾s, median relative errors of f(NT) corrected
CWC‾s of all graupel data are of the order of 7 % compared
to -1 % for the entire dataset (see Table 1).
This study does not focus on the mass–size relationship directly, but it
is clear that the coefficients of the m(D) relationship, and particularly its
exponent, considerably impact the simulation of radar reflectivity factors
on the one hand and CWC calculation on the other hand. In this context, we
recall that Fontaine et al. (2014) obtain different CWCs for one and the
same radar reflectivity factor, which is also valid reciprocally, where one
and the same CWC is related to a range of radar reflectivity factors, thereby
varying the β exponent and corresponding prefactors α in the
T-matrix simulations of the radar reflectivity factors. Hence, getting large
differences between calculated CWC (related to radar reflectivity
simulations) and measured CWC from IKP-2 does not mean that the oblate
spheroid approximation for Ze is wrong, but the difference stems primarily
from the choice of β (and respective α) of the mass–size
relationship. We are aware that a single m(D) power law is not sufficient to
assimilate all the complexity of the mass of ice hydrometeors. The main goal
of this paper is to evaluate the Fontaine et al. (2014) method of
calculating an average CWC from all possible solutions for (α,
β) without a priori assumption. The method has been already used in
further studies: Drigeard et al. (2015) and Alcoba et al. (2015). Finally,
the method allows constraining the effective density of ice hydrometeors and
also the simulation of radar reflectivity factors at different frequencies:
94, 9.4 and 5.5 GHz. The method will be used in the near future to
derive mass–size relationships for different size ranges of the ice
hydrometeors' size spectrum.
No data sets were used in this article.
The authors declare that they have no conflict of interest.
Acknowledgements
The research leading to these results has received funding from (i) the
European Union's Seventh Framework Program in research, technological
development and demonstration under grant agreement no.
ACP2-GA-2012-314314, (ii) the European Aviation Safety Agency (EASA)
Research Program under service contract no. EASA.2013.FC27, and
(iii) the Federal Aviation Administration (FAA), Aviation Research Division,
and Aviation Weather Division, under agreement CON-I-1301 with the Centre National de la Recherche Scientifique. Funding to support the Darwin
flight project was also provided by the NASA Aviation Safety Program, the
Boeing Co., and Transport Canada. Additional support was also provided by
Airbus SAS Operations, Science Engineering Associates, the Bureau of
Meteorology, Environment Canada, the National Research Council of Canada, and
the universities of Utah and Illinois. The authors thank the SAFIRE facility for
the scientific airborne operations. SAFIRE (http://www.safire.fr) is a joint
facility of CNRS, Météo-France, and CNES dedicated to flying research
aircraft.
Edited by: G. Vulpiani
Reviewed by: two anonymous referees
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