Introduction
The continuous observation of ice-crystal habit is a key component for an
improved characterization of mixed-phase clouds with remote-sensing
techniques . considered the shape of ice
particles to be the largest source of errors in existing size and number
concentration retrievals that are based on combined lidar and radar vertical
observations. For instance, the authors reported that the assumed ice
particle shape can cause changes in the calculated effective size and number
concentration of up to 200µm and 90L-1,
respectively. In existing microphysical models, an accurate representation of
ice particle shape plays an important role as the shape parameterizes
size–mass–terminal velocity relations of the ice phase
, the depositional growth rate
, and scattering properties of the ice crystals
. Moreover, knowledge of the ice
particles' shape provides a potential for the retrieval of the particle number size distribution. Such
a retrieval can be based on the cloud radar Doppler spectra and known
relations between size and terminal velocity for different particle habits
. presented a retrieval of the number
size distribution based on the moments of Doppler spectra obtained with
a 35 GHz cloud radar. The authors estimated the uncertainties of the
retrieval associated with the ice particle habit and found those to be 60 and
40 % in ice water content and median ice particle size, respectively. Continuous
information about the number size distribution of ice particles can later on
be helpful for a better understanding and characterization of the efficiency
of heterogeneous ice formation, which currently is subject of numerous studies
.
Cloud radar is one of the most promising remote-sensing instruments for
particle shape determination. Recent investigations of
show the potential of the multi-frequency
approach in the separation of snow particle habits when Mie scattering is
present. According to , the approach is most effective for
a median volume diameter exceeding 2 mm. Often, characterization of
smaller ice crystals is required. For example, in mid-level mixed-phase
clouds the typical size of ice crystals is about an order of magnitude lower.
Another powerful tool for the shape estimation of cloud particles is
cloud-radar polarimetry. The polarimetric approach is known to be effective
in the case when cloud particles can be approximated using the well-known
spheroidal model . presented
theoretical considerations about the potential of polarimetric cloud radars
for the shape classification of ice crystals. The author analyzed modeled
elevation dependencies of polarimetric products that could be measured with
several polarimetric configurations. ,
, and experimentally evaluated the
proposed polarimetric configurations that were emulated using rotatable
quarter- and/or half-wavelength phase plates. The plates were mounted into
the waveguide system of a ground-based Ka-band radar, operated by the Wave
Propagation Laboratory of the National Oceanic and
Atmospheric Administration. A number of studies present polarimetric
measurements of winter clouds taken by airborne
and ground-based cloud radars
. Often such measurements were
compared with the microphysical properties of the ice crystals observed in
situ with aircraft or on ground. Despite the observational evidence that
polarimetric variables are sensitive to the shape of particles, which was
confirmed by the above-mentioned studies, further investigations in this area
are required to realize an operational quantitative characterization of
particle shape . An approach to quantitatively
obtain the particle shape and orientation from weather radar observations of
polarimetric parameters was, e.g., presented by , but
their retrieval has limitations in the discrimination between oblate and
prolate particles.
Even though the potential of different polarimetric configurations for
a detailed shape retrieval of hydrometeors were evaluated in the
above-mentioned studies, many cloud radars are operated in simpler
configurations. The widely used spaceborne 94 GHz cloud profiling radar aboard
the CloudSat satellite has no polarization capabilities at all . Other systems operate in a depolarization mode (also
known as polarization diverse mode). In this mode the radar emits a wave with
a certain constant polarization state (usually linear or circular) and
receives co-polarized and cross-polarized components of the backscattered
wave. This is, e.g., the case for the default setup of MIRA-35
as well as the Ka-band Zenith-pointing Radar
(KAZR) of the US Department of Energy (DoE) Atmospheric Radiation Measurement (ARM) program. Normally such radars provide only one polarimetric
product – the depolarization ratio – which is the ratio of the returned
power in the cross-polarized channel to the returned power in the
co-polarized channel. If only the depolarization ratio is used to derive an
estimate of ice particle shape, an assumption about the distribution of ice
crystal orientation has to be made as described in .
concluded that not only power relations but also the
correlation between the orthogonal components of the received wave should be
analyzed for the characterization of both shape and orientation distribution.
In this paper we propose an approach to simultaneously estimate the shape and
orientation of ice particles. The algorithm utilizes elevation dependencies
of differential reflectivity ZDR and correlation coefficient
ρHV that are related to the output of a spheroidal scattering
model. The method is applied to polarimetric observations obtained with a new
modification of the scanning 35 GHz cloud radar of type MIRA-35 with hybrid
polarimetric configuration.
The paper is organized as follows. Section contains the
description of the technical implementation of the hybrid mode in the cloud
radar, calibration issues, and processing considerations. The approach for
the retrieval of the shape and orientation distribution is presented in
Sect. . A case study showing the application of the method is
given in Sect. . Conclusions and further considerations are
presented in Sect. .
MIRA-35 with hybrid mode
MIRA-35 is a magnetron-based 35 GHz cloud radar produced by METEK GmbH,
Elmshorn, Germany. Several measurement sites in Europe operate radars of this
type in the framework of Cloudnet, which is part of the Aerosols, Clouds and
Trace gases Research Infrastructure (ACTRIS), because of their high
sensitivity and reliability
.
describe the technical implementation of MIRA-35,
accuracy issues, and operational statistics based on more than
10 years of continuous measurements. Recently, a MIRA-35 was installed
on board the research aircraft HALO . Main operational
parameters of MIRA-35 are listed in Table .
Parameters of MIRA-35 used in the operational mode.
Peak power (kW)
30
Beam width for 1 m antenna (∘)
0.6
Pulse length (ns)
200
Pulse repetition frequency (kHz)
5
Minimum range (km)
0.15
Maximum range (km)
15
Range resolution (m)
30
Number of pulses for fast Fourier transform (FFT)
256
Number of spectra for averaging
200
Sensitivity at 5 km (dBZ)
-55
Typically, cloud radars of type MIRA-35 emit linearly polarized waves. The
corresponding operation mode is denoted as the linear depolarization ratio
mode (LDR mode). Often, LDR measurements taken with vertically pointed cloud radars are used for clutter
filtering and a reliable detection of the melting layer
. At the same time the applicability of the LDR mode for
the shape estimation is limited because of its high sensitivity to the
orientation of cloud particles .
For the shape studies presented in this paper we used the hybrid mode. This
mode is also known as the Simultaneous Transmission and Simultaneous
Reception (STSR) mode and is often used in weather radars . In hybrid mode
a radar transmits horizontal and vertical components of the signal
simultaneously; thus, expensive high-pulse-power polarization switching is
not required. As will be shown below, the hybrid mode is capable of providing
polarimetric parameters that allow for a quantitative estimate of particles
shape and orientation characteristics.
This section is devoted to the technical realization, calibration, and the
data processing of the new hybrid-mode radar. In Sect. we
present the implementation of the horizontal and vertical channel of the
radar and describe the phase adjustment procedure. An overview of the general
data processing is given in Sect. . The correction of the
data for the differences of amplifications and electrical path lengths in the
horizontal and vertical channel is described in Sect. . The
representation of the measured data in a 45∘ rotated polarization
basis, which permits the depolarization ratio to be retrieved, is presented in
Sect. . In Sect. it is explained how
antenna effects on polarimetric measurements are corrected. The spectral
polarimetric variables are derived in Sect. . The applied
approach to increase the signal-to-noise ratio in the hybrid mode is
presented in Sect. .
Simplified block diagrams of typical LDR (a) and
hybrid (b) modes of MIRA-35. Components, added for the
implementation of the hybrid mode from the LDR mode, are shown in
yellow color. OMT is an orthomode transducer. See details in the
text.
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Implementation and phase adjustment
The implementation of the hybrid mode was based on a standard scanning
MIRA-35 cloud radar configured for the LDR mode. Simplified schemes of
traditional LDR mode and the implemented hybrid configuration are shown in
Fig. . In the hybrid mode, high-frequency power, generated by the magnetron-based
transmitter, is split into two channels by a 3 dB coupler. A second
circulator is added to decouple the high-power transmission line from the
sensitive receiver in the vertical channel. Note that here we only show
changes that were implemented in order to realize the hybrid mode. Details
about the standard LDR configuration can be found in .
It is known that the exact polarization state of the transmitted radiation
depends on the phase shift between the orthogonal components of the
transmitted signal ΔφT (transmission phase
difference). Often, polarimetric weather radars use an arbitrary elliptical
polarization as the transmission phase difference
ΔφT is not adjusted to a certain value. We decided
to first evaluate the hybrid mode with the transmission phase difference
ΔφT adjusted to 0∘, i.e., linear
polarization of the transmitted radiation. In the future a circular or
elliptical polarization state of the transmitted signal can be easily
implemented by shifting ΔφT. Adjustable ferrite
phase shifters for the peak power of 15 kW at Ka-band are expensive and, in
addition, introduce extra power losses which will result in worse
sensitivity. Instead, in order to adjust the phase shift, we slightly changed
the path length of the horizontal channel by inserting throttle plates
(Fig. ) between the waveguide flanges. Changing of the
transmission phase shift ΔφT requires
throttle plates to be inserted right after the 3 dB coupler. In MIRA-35 the 3 dB
coupler is installed inside the receiver unit and cannot be easily reached. Thus, due
to the construction design of MIRA-35 we inserted throttle plates after the
circulator no. 1 (see Fig. b). Introducing the additional
phase shift after the circulator leads to changes of the phase shift induced
in the receiving paths ΔφR (reception phase
difference). The reception phase difference ΔφR can
be removed during processing (Sect. ).
Throttle plates used for the phase adjustment. The thickness
of the plates is 0.05 mm (a), 0.1 mm
(b), and 0.28 mm (c). The introduced phase
shift is 1.8∘ (a), 3.4∘ (b),
and 9.1∘ (c).
![]()
To characterize phase shifts induced by the radar hardware, a polarization
basis should be defined. For the description we use the Cartesian
polarization basis (exey), shown in Fig. ,
throughout the paper. In the description basis, the total phase difference
between the horizontal and vertical channels ΔφΣ
measured in the configuration shown in Fig. b can be
represented as follows:
ΔφΣ=φx-φy=Δφtp+Δφps︸ΔφT+Δφbs+Δφrp+Δφps︸ΔφR,
where φx and φy are the phases of the signals in the horizontal and
vertical channel, respectively, Δφtp is the phase
shift caused by the difference in the electrical path lengths between the
transmission channels, Δφps is the phase shift
introduced by the phase shifter, Δφbs is the phase
shift produced by atmospheric scatterers, and Δφrp is
the phase shift caused by differences in the electrical path lengths of the
reception channels.
Antenna of MIRA-35 system mounted on the scanning unit. The
description polarization basis is shown. The unit vector
ez shows the propagation direction of the transmitted
radiation.
![]()
We measured the phase shift Δφrp based on previously
documented antenna measurements . For the measurements an
external test transmitter was used. The test transmitter generates continuous
linearly polarized radiation. The frequency of the test transmitter was set
close to the operational frequency of the radar transmitter. The frequency of
the radar local oscillator was adjusted to center the receiver bandwidth to
the signal of the test transmitter. The rotatable antenna system of the test
transmitter permits the orientation β of the transmitted
polarization to be changed with respect to the unit vector ex of the description
basis. The radar was placed approximately 40 m away from the test
transmitter. The radar was operated in the receiving-only mode. Antennas of
the radar and the test transmitter were pointed to each other. A detailed
description of the test transmitter and the measurement procedure can be
found in . Measurements conducted at β=45∘
showed Δφrp denoted as α3(0,0)
in to be -2∘. Note that these measurements were
performed before introducing throttle plates.
Knowing Δφrp, we added throttle plates into the
horizontal channel in order to measure the introduced phase shift. Plates
(Fig. ) with thickness of 0.28, 0.1, and 0.05 mm
introduced a phase shift of 9.1, 3.4, and 1.8∘, respectively.
It should be noted that the wavelength in the waveguide λg is
10.8 mm which is longer than the one in vacuum
Sect. 2.2. Calculated values of
Δφps for λg are 9.3, 3.3, and
1.7∘, respectively.
It is known that randomly oriented particles do not produce a backscattering
differential phase shift . Therefore, for vertical
observations of clouds we can assume Δφbs=0. In this
case Δφtp can be estimated from the measured total
phase difference ΔφΣ observed by the vertically pointed
radar using Eq. (). Measurements performed without installed
throttle plates resulted in ΔφΣ=-21.6∘ and,
thus, Δφtp=-19.6∘. In order to adjust the
transmission phase difference ΔφT as close to
0∘ as possible we inserted throttle plates with a total thickness
of ∼0.6 mm into the horizontal channel. This introduced
20.5∘ of additional phase shift Δφps and
resulted in the transmission phase difference ΔφT=-0.9∘ and the reception phase difference ΔφR=18.5∘.
During the operation the frequency of the magnetron can vary with temperature
within ±1 MHz. Such variations of the operational frequency
causes changes of ΔφΣ. Measured changes of
ΔφΣ due to the frequency variation of the magnetron do
not exceed ±1∘, which can be considered as not significant.
Nevertheless, during the operation we have found that variations in ambient
conditions can lead to changes of ±8∘ in
Δφrp. Significant changes in
Δφrp usually took several days. We do not consider
reasons for the Δφrp variations in this paper. To
account for these changes, periodical vertical observations in light rain are
required. Assuming Δφtp and
Δφps to be constant Δφrp can be
found using Eq. ().
Processing of the coherency matrix
MIRA-35 is a coherent cloud radar. Two receivers calculate in-phase (I) and
quadrature (Q) parts for the vertical and horizontal components of the returned
signal. Further we denote the horizontal and vertical component by indexes h
and v, respectively. Ih, Iv, Qh,
and Qv components are obtained for every pulse cycle and range
gate. Fast Fourier transformation (FFT) over Ih+iQh and Iv+iQv, calculated from
NF pulses, is used to estimate discrete complex spectra
S˙h(ωk) and S˙v(ωk),
respectively. Here ωk denotes a Doppler frequency of a spectral
component k=0,…,NF-1:
ωk=kfrπNF,
where fr is the pulse repetition frequency. Details of the
I/Q and spectrum computation in MIRA-35 data processing are given by
.
Using Ns complex spectra S˙h(ωk) and
S˙v(ωk), the spectral form of the 2×2
coherency matrix can be calculated as follows:
B(ωk)=Bhh(ωk)B˙hv(ωk)B˙vh(ωk)Bvv(ωk).
The elements of the coherency matrix B(ωk) are
calculated as follows:
Bhh(ωk)=〈S˙h(ωk)S˙h*(ωk)〉,B˙hv(ωk)=〈S˙h(ωk)S˙v*(ωk)〉,B˙vh(ωk)=〈S˙v(ωk)S˙h*(ωk)〉,Bvv(ωk)=〈S˙v(ωk)S˙v*(ωk)〉,
where * is the complex conjugation sign and 〈〉 denotes
averaging over Ns spectra. The real elements
Bhh(ωk) and Bvv(ωk) are the power
spectra in the horizontal and vertical channels, respectively. In MIRA-35
with the LDR mode these spectra represent co- and cross-polarized components
of the received signal, respectively, and are used for the calculation of the
radar reflectivity factor at horizontal polarization Zh, mean
Doppler velocity, Doppler width, and LDR .
A recent modification of the MIRA-35 software permits one to additionally
calculate and store the complex element B˙hv(ωk). It
is necessary to note that B˙hv(ωk)=B˙vh*(ωk). Therefore, storage of the element
B˙vh(ωk) is not required. Storing the elements
Bhh(ωk), B˙hv(ωk), and
Bvv(ωk) in usual operational mode
(Table ) requires approximately 700 MBh-1 which
is about 100 times less than storing the I/Q data.
Correction of the coherency matrix for differences of channels
The spectral form of the coherency matrix B(ωk) allows
for the calculation of spectral polarimetric variables. Advantages of such
a representation have been shown for weather radar applications
. Before the calculation of polarimetric parameters the
elements of the coherency matrix B(ωk) were corrected
for the effect of differential amplification in the horizontal and vertical
channels. We define the spectral components ωn (n∈k) where
both Bhh(ωk) and Bvv(ωk) are at least
30 dB higher than the mean noise levels Nh and
Nv, respectively. The mean noise levels in this paper represent
a noise level in a spectral line and can be determined by averaging the power
spectra over the last range gates where no scatterers are present or by
applying the Hildebrand–Sekhon algorithm .
In order to correct the difference in the amplifications we calculate
a coefficient Ka:
Ka=Bhh(ωn)-NhBvv(ωn)-Nv.
Note that Nh and Nv in Eq. () can be
neglected because of high signal-to-noise ratios (SNRs) of signals used. For
the calculation of Ka we used rain observations with the
vertically pointed radar. In this case particles can be considered as spheres
and do not change the polarization of the scattered wave. Data containing
scattering from insects, that typically cause depolarization, should be
avoided. For a rain event on 1 May 2014 we measured a Ka value
of 1.46±0.02.
The effect of differences in the amplifications and the electrical
path lengths on the components of Eq. () can be corrected
as follows:
B˙hv′(ωk)=KaB˙hv(ωk)e-iΔφR,Bvv′(ωk)=KaBvv(ωk).
The additional phase shift, introduced in
B˙hv′(ωk), removes the reception phase
difference ΔφR. The spectra
Bhh(ωk), Bvv(ωk), and
Bvv′(ωk) are shown in Fig. . We
denote the coherency matrix with the corrected elements as
B′(ωk).
(a) Uncalibrated power spectra in the horizontal
(blue line) and vertical (green line) channels. Displayed
observations were obtained with the vertically pointed radar in
light rain. (b) Uncalibrated power spectrum in the
horizontal channel (blue line) and corrected power spectrum in the
vertical channel (green line). The same data as in (a) are
used. Mean noise levels of Bhh and
Bvv′, estimated using the Hildebrand–Sekhon
algorithm, are 0.153 and 0.169, respectively. Note that this case
was chosen to illustrate the correction. Due to low signal-to-noise
ratios, such spectra were not used for the calculation of the
coefficient Ka (see
Sect. ).
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As mentioned in Sect. , the calibration of the receiver
slowly fluctuates during operation. This causes variations of ±0.06 in
Ka. The range of Ka can be constrained by
performing recalibrations during light rain.
The Jones vector of a received signal represented in the
description (a) and slanted (b) polarization
basis.
![]()
Representation of the coherency matrix in the slanted basis
It is known that the antenna coupling produces biases in polarimetic
variables. Such biases hamper shape and orientation retrievals. The antenna
coupling can be directly determined in LDR-mode cloud radars from vertical
measurements in light rain or drizzle when particles can be assumed to be
spherical. In this case the cross-polarized returned signal is caused only by
the coupling . In cloud radars with the hybrid mode
the estimation of antenna influence is not straightforward as the major part
of the returned signal in both channels is produced by scatterers. In this
section we show the representation of the coherency matrix
B′(ωk) in the polarization basis rotated by
45∘ with respect to the description one. The Jones vector of
a received signal in description and slanted basis is shown in
Fig. . Such representation provides the co-polarized and
cross-polarized components that would be measured by a cloud radar with
slanted polarimetric basis. These components can be used for the correction
algorithm proposed by . In addition, the change of the
polarization basis makes it possible to calculate the depolarization ratio
and the co-cross-channel correlation coefficient that cannot be directly
measured in the hybrid mode.
The corrected coherency matrix B′(ωk) can
be represented in the linear basis rotated by 45∘ with
respect to the description basis:
BS(ωk)=FTB′(ωk)F,
where T is the transpose sign and F is the rotational
operator:
F=1211-11.
The elements of BS(ωk) can be
calculated as follows:
Bxx(ωk)=12{Bhh(ωk)+Bvv′(ωk)-2Re[B˙hv′(ωk)]},B˙xc(ωk)=12{Bhh(ωk)-Bvv′(ωk)+2iIm[B˙hv′(ωk)]},Bcc(ωk)=12{Bhh(ωk)+Bvv′(ωk)+2Re[B˙hv′(ωk)]}.
In the slanted basis we use the indexes c and x to denote the
co-polarized and cross-polarized components, respectively. Note that
these components would be directly measured by a cloud radar with the
slanted polarimetric basis.
The coherency matrix BS(ωk) can be
considered as the coherency matrix measured in the slanted-linear-depolarization ratio mode (SLDR mode) that was used for the shape
classification by . In the SLDR mode and
hybrid mode with transmission phase difference ΔφT=0∘ the transmitted signals have the same polarization
state. The difference between these polarimetric configurations is the
45∘ rotation of the receiving basis that we perform in
Eq. (). Note that Eq. () allows for
representation of the coherency matrix measured in the SLDR mode on a horizontal–vertical basis and, thus, can be used to retrieve
polarimetric variables such as ZDR and ρHV.
For the subsequent data analysis we define spectral components
ωp where the backscattered signal is detected in the
elements Bcc(ωk) and
Bxx(ωk). The threshold applied for the detection
is calculated as follows:
BTc,Tx=Nc, x1+QNs.
In Eq. () Nc, x is the mean power of noise of
Bcc(ωk) and Bxx(ωk), respectively. We
use the value of Q=5 which is applied for the thresholding in the
operational MIRA-35 radars .
Further we remove the mean noise levels from the elements
Bcc(ωp) and Bxx(ωp):
Bcc′(ωp)=Bcc(ωp)-Nc,Bxx′(ωp)=Bxx(ωp)-Nx.
The correlation between noise in the orthogonal components is negligible and,
thus, does not influence the element B˙xc(ωp)
significantly. We represent the resulting coherency matrix as follows:
BS′(ωp)=Bxx′(ωp)B˙xc(ωp)B˙xc*(ωp)Bcc′(ωp).
Correction of the coherency matrix for the antenna coupling
We decompose the coherency matrix
BS′(ωp) into non-polarized and
fully polarized parts :
BS′(ωp)=AS(ωp)I+BS(ωp)D˙S(ωp)D˙S*(ωp)CS(ωp),
with the condition:
BS(ωp)CS(ωp)-|D˙S(ωp)|2=0,
where I is a 2 × 2 unit
matrix. AS(ωp), BS(ωp),
CS(ωp), and D˙S(ωp) can
be calculated with the following equations
:
AS(ωp)=12SpBS′(ωp)-Sp2BS′(ωp)-4detBS′(ωp)1/2,
BS(ωp)=12Bxx′(ωp)-Bcc′(ωp)+Sp2BS′(ωp)-4detBS′(ωp)1/2,
CS(ωp)=12Bcc′(ωp)-Bxx′(ωp)+Sp2BS′(ωp)-4detBS′(ωp)1/2,
D˙S(ωp)=B˙xc(ωp).
Here Sp is the matrix trace and det is the matrix determinant.
Applying the method described by , we remove the influence
of antenna coupling on the elements AS(ωp),
BS(ωp), and CS(ωp). Note that in
this study the fully polarized part of the co-polarized component is
described by CS(ωp). The calculated variables are denoted
as AS′(ωp),
BS′(ωp), and
CS′(ωp), respectively. The corrected value
D˙S′(ωp) can be found using
BS′(ωp), CS′(ωp)
in Eq. (). Reverse rotation of the slanted basis allows for
the calculation of the elements A(ωp), B(ωp), and
C(ωp) in the description basis:
A(ωp)=AS′(ωp),B(ωp)=0.5BS′(ωp)+CS′(ωp)+2ReBS′(ωp)CS′(ωp)eiargD˙S(ωp),C(ωp)=0.5BS′(ωp)+CS′(ωp)-2ReBS′(ωp)CS′(ωp)eiargD˙S(ωp).
Spectral polarimetric variables
From A(ωp), B(ωp), and C(ωp), spectral
polarimetric variables can be obtained. In the following, we omit the word
“spectral” for brevity. Differential reflectivity
ZDR(ωp), correlation coefficient
ρHV(ωp), differential phase shift
φDP(ωp), SLDR(ωp), and
co-cross-channel correlation coefficient ρCX(ωp) are defined as follows:
ZDR(ωp)=A(ωp)+B(ωp)A(ωp)+C(ωp),ρHV(ωp)=B(ωp)C(ωp)[A(ωp)+B(ωp)][A(ωp)+C(ωp)]1/2,φDP(ωp)=argB˙hv′(ωp),SLDR(ωp)=AS′(ωp)+BS′(ωp)AS′(ωp)+CS′(ωp),ρCX(ωp)=BS′(ωp)CS′(ωp)[AS′(ωp)+BS′(ωp)][AS′(ωp)+CS′(ωp)]1/2.
In order to check the quality of the polarimetric measurements of MIRA-35 in
the hybrid mode, we performed vertical-stare measurements of a cloud system
that passed over the METEK site on 1 May 2014. Figure
shows SNR (a) and the polarimetric variables (b–f) derived with
Eqs. ()–(), respectively. Presented parameters were
obtained for the spectral line for which the maximum signal was observed. From 17:45 to 18:00 UTC
a melting layer is visible at 1.7 km height, indicated by enhanced
values of SNR and SLDR. Below the melting layer light rain occurred whereas
ice crystals were present above. The comparison of
Fig. b–f with (a) shows that the polarimetric
parameters could not be obtained for all data points because the quality
criterion of Eq. () is not fulfilled when the SNR is too
low. At a lower SNR, the influence of noise becomes significant resulting in
high biases and variability in all polarimetric variables.
It can be seen in Fig. b and d that on
average values of ZDR and φDP in clouds and precipitation are close to
0 dB and 0∘, respectively, which is the case when particles
can be considered as spheres or randomly oriented in the polarization plane.
Areas with slightly increased values of ZDR and
φDP are caused by noise as these areas are in correlation
with decreasing SNR, especially along cloud edges. Insects are characterized
by values of ZDR and φDP that lie outside of
the color bars.
In rain, the correlation coefficient ρHV is 1, which is
consistent with high values of this parameter observed by polarimetric
weather radars . Slightly lower values of
about 0.995 were observed in areas with ice particles producing slight
depolarization. In the highly depolarizing melting layer, ρHV
is below 0.95.
Values of SLDR measured vertically in rain, in the melting layer, in
ice areas, and in regions dominated by scattering from insects are
consistent with direct measurements of LDR
. Values of
ρCX for meteorological scatterers are 0 as it follows
from theoretical considerations . Insects can be
considered as point depolarizing targets and therefore produce high
ρCX .
Polarimetric variables obtained for the time period from 17:55 to 18:00 UTC
and the height range from 500 to 1700 m, where light rain was
observed, are close to those that would be measured in rain by a hypothetical
ideal radar, i.e., ZDR=1 (0 dB),
φDP=0∘, ρHV=1,
SLDR =0 (-∞ dB), and ρCX=0 in the limit
approximation given in. For the comparison and the estimation
of the antenna quality, we show values of polarimetric parameters without the
correction for antenna coupling in Table . We calculated these
variables by inserting the elements AS(ωp),
BS(ωp), and CS(ωp) instead of
AS′(ωp), BS′(ωp),
and CS′(ωp) in
Eqs. ()–().
Polarimetric variables calculated without the correction for the
antenna coupling. Values are based on measurements with the vertically
pointed cloud radar in light rain on the 1 May 2014. The statistics are based
on the height range from 500 to 1700 m and the time period from 17:55
to 18:00 UTC.
Variable
Mean value
Standard deviation
ZDR
1.011 (0.048 dB)
0.017
ρHV
0.9976
4.8×10-4
φDP
-0.16∘
0.35∘
SLDR
1.2×10-3(-29.3dB)
2.2×10-4
ρCX
0.089
0.046
Sensitivity issue
Splitting the transmitting power into two channels in the hybrid mode worsens
the radar sensitivity by 3 dB. In the case when only power spectra
Bhh(ωk) and Bvv(ωk) are available,
noncoherent averaging can recover up to 1.5 dB .
The availability of the full coherency matrix permits the application of
coherent averaging based on Eq. () which can potentially improve
the radar sensitivity by up to 3 dB. Thus, the sensitivity loss due
to splitting can be balanced out by the sensitivity gain due to coherent
averaging. Applicability of the coherent averaging to weather radars was
previously shown by .
Coherent averaging can be applied when the received signals in the
horizontal and vertical channels are in-phase. In the case of
elliptical or circular polarization of the transmitted signal, an
additional phase shift can be introduced during processing to fulfill
this requirement. As shown in Sect. , in our case the
transmission phase difference is ΔφT=-0.9∘,
which is considered to be sufficiently low to neglect effects of the
phase difference on SNR.
In Fig. b it can be seen that the mean noise levels
in the receiving channels are different. This can hamper the procedure
of increasing the sensitivity. Therefore, we adjust the mean noise
levels using the coefficient Kn:
Kn=NhNv.
For the rain case on 1 May 2014 we found Kn to be 1.32±0.14. Long-term fluctuations of
Kn are of the same order of magnitude as for Ka.
Using Kn instead of the coefficient Ka in
Eqs. () and (), we corrected the elements
Bvv(ωk) and B˙hv(ωk) for
different noise levels, which were then inserted into Eq. () to
perform the coherent averaging.
Another factor that can affect the utilization of Eq. () is the
differential phase shift introduced by the propagation and backscattering
properties of the scatterers. As mentioned in Sect. , the
orientation of particles can be assumed to be distributed uniformly in the
polarization plane when the radar is pointed vertically. In this case both
backscattering and propagation differential phase shift are 0. Nevertheless,
differential phase effects should be accounted for in the case of utilization
of the 35 GHz cloud radar at low elevations for precipitation observations.
For instance, showed that at 35 GHz, the
propagation and backscattering differential phase shift in rain stronger than
5 mmh-1 can exceed 1∘ km-1 and 5∘,
respectively. Note that in this paper we do not consider corrections for the
differential phase shift introduced by scatterers.
Power spectrum in the horizontal channel (blue line) and
power spectrum after coherent averaging (green line). The same data
as in Fig. are used.
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The results of Eq. () are shown in Fig. for an
arbitrary example case. It can be seen that maximums in
Bcc(ωk) and Bhh(ωk) are 0.93 and
0.56, respectively, while the standard deviations of noise are 0.01 and 0.011
(arbitrary units), respectively. The noise levels of
Bcc(ωk) and Bhh(ωk) are 0.16. Note that
all the values are given in arbitrary units. Thus, the SNR calculated from
Bcc(ωk) is nearly 2 times higher than the one calculated
using Bhh(ωk). The power spectra
Bcc(ωk) can be used for the standard processing, i.e., for
the detection and the estimation of spectral moments. In this case the total
power transmitted by the radar instead of the power transmitted in the
horizontal channel should be used for the calculation of reflectivity.
In Fig. the height–time cross sections of SNR
calculated from Bhh(ωk) and
Bcc(ωk) are shown. For the thresholding and the
SNR calculation we use the standard processing implemented in MIRA-35
cloud radar . It can be seen that the coherent
averaging results in more data points, which is especially of benefit
for the detection efficiency of high-level clouds.
Shape and orientation retrieval
As shown in Sect. the cloud radar with the hybrid
mode permits us to obtain the set of spectral polarimetric variables
(Eqs. –) that are not available in the
LDR mode. In this section we show how this additional information can
be used to quantitatively estimate shape and orientation of cloud
particles. The approach presented in the following is based on
a combination of established spheroidal models
that were developed to
describe the polarimetric variables.
Time–height cross sections of signal-to-noise ratios
calculated from Bhh (a) and Bcc (b)
measured at Elmshorn, Germany, on 1 May 2014. The
number of data points (especially in high-level clouds) in panel (b)
is higher in comparison with (a) because of
higher sensitivity.
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Backscattering model
It is known that particles with sizes much smaller than the wavelength of
a radar can be approximated by a spheroid. shows that
this approximation is valid in the case of ice-particle observations with
cloud radars. Scattering properties of a spheroid are often described using
the Jones representation in the linear polarization basis by a 2 × 2 backscattering matrix:
S=S˙hhS˙hvS˙vhS˙vv.
Time–height cross sections of the signal-to-noise ratio in the
horizontal channel (a), differential reflectivity
ZDR (b), correlation coefficient
ρHV (c), differential phase shift
φDP (d), slanted linear depolarization
ratio SLDR (e), and co-cross-channel correlation
coefficient in the slanted basis ρCX for the
measurements taken at Elmshorn, Germany, on 1
May 2014.
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The elements of the backscattering matrix S are calculated as
follows ch. 2:
S˙hh=k024πϵ0α1+α2-α1sin2θsin2φ,S˙hv=S˙vh=k024πϵ0α2-α12cosψsin2θsin2φ+sinψsin2θsinφ,S˙vv=k024πϵ0α1+α2-α1cos2ψsin2θcos2φ+sin2ψcos2θ+sin2ψsin2θcosφ2,
where k0 is the wavenumber, ϵ0 is the vacuum permittivity, ψ is the angle between the unit vector
ez (Fig. ) and the zenith direction. The angle ψ
is further denoted as the elevation angle. θ and φ are angles
defining the orientation of the spheroid, which is illustrated in
Fig. . α1,2 are polarizability elements:
α1,2=Vϵ0ϵr-1Λ1,2.
In Eq. () V is the volume of the spheroid,
ϵr is the relative permittivity, and Λ1,2 can be
found as follows:
Λ1,2=1ϵr-1λ1,2+1,
where λ1,2 are depolarizing factors. The depolarizing
factors for prolate and oblate spheroids are described as follows:
λ2(prolate)=1-b2b2-1+12bln1+b1-b;b2=1-1ρg2,ρg≥1,
λ2(oblate)=1+f2f21-1ftan-1f;f2=1ρg2-1,0<ρg≤1,λ1=1-λ22.
In Eqs. () and () ρg is the axis
ratio of the spheroid.
In the following, we consider only ice particles. In the microwave
region the real part of ϵr for pure ice is approximately
3.168. The imaginary part is several orders of magnitude lower than
the real part and, therefore, we neglect it. In this
case the elements of the backscattering matrix S are real
numbers.
Further we define the polarizability ratio:
ρe=α2α1.
ρe is a function of permittivity and axis ratio ρg and is
independent of particle volume V. As was shown in a review of
, the permittivity and density of ice crystals are
related almost linearly. The relationship between ρe, ρg,
and particle density is shown in Fig. .
The backscattering matrix of N particles dispersed in a certain
volume can be written as follows:
SΣ=∑j=1NSje2ik0rj,
where Sj and rj are the backscattering matrix and the
distance from the radar of the jth particle, respectively.
Assuming complex amplitudes of the horizontal and vertical components
of the transmitted signal
E˙ht=E˙vt=1, the polarization state corresponds to the one of a wave emitted
by an ideal hybrid-mode radar with a transmission phase difference
ΔφT=0∘.
The complex amplitudes of the horizontal
E˙hr and vertical
E˙vr components of the
received signal can be derived as follows:
E˙hr=S˙hhΣE˙ht+S˙hvΣE˙vt,E˙vr=S˙hvΣE˙ht+S˙vvΣE˙vt,
where S˙hhΣ,
S˙hvΣ,
S˙vhΣ, and
S˙vvΣ are elements of the backscattering
matrix SΣ.
Implementation of the subsequent modeling approach is based on the
following assumptions.
V, θ, φ, ρg are not correlated with each other.
All particles have the same axis ratio ρg.
φ is uniformly distributed in the range from -π to π.
The scattering is noncoherent.
Multiple scattering is neglected.
Propagation effects are neglected.
We assume that particles falling with the same terminal velocity have
comparable size and shape. In this case the first two assumptions are
reasonable when polarimetric variables for a certain spectral line are
modeled.
Under all above-mentioned assumptions the elements of the coherency
matrix can then be found as follows:
B^hh=〈E˙hrE˙hr*〉=F11+P1T1+F2P2T1+F3P2T2,B^vv=〈E˙vrE˙vr*〉=F11+F4P1+F5P1T1+F6P2+F7P2T1+F8P2T2,B^hv=〈E˙hrE˙vr*〉=F11+F9P1T1+F10P1+F10P2T1+F11P2T2.
In Eqs. ()–():
F1=N〈α1〉k024πϵ02,F2=12sin2ψ,F3=4-5sin2ψ8,F4=4F2,F5=cos2ψ-2sin2ψ,F6=sin4ψ,F7=72sin2ψ-5sin4ψ,F8=12-358sin2ψ+358sin4ψ,F9=12+12F5,F10=2F2,F11=14cos2ψ-sin2ψ,P1=ρe-1,P2=ρe-12,T1=〈sin2θ〉,T2=〈sin4θ〉.
Averaging in Eqs. (), (), and () is
performed over N particles.
Geometry of spheroid orientation. Adopted from
. In the case of ψ=0∘, x,
y, and z correspond to ex, ey, and
ez, respectively. ON is the symmetry axis of the
spheroid.
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Dependencies of polarizability ratio ρe on axis ratio of
a spheroid ρg for different densities of ice.
![]()
Probability density function of Θ for different values
of R. Adopted from .
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We model the probability density function of orientation angle θ by
the function adopted from :
W(Θ)=1-R22π11-R2cos22Θ+Rcos2Θπ2+arcsinRcos2Θ1-R2cos22Θ3/2,-π2≤Θ≤π2,
where R is a factor defining the width of the distribution, Θ=θ-θ0, with θ0 being the preferable orientation of
particles. We consider the preferable orientation to be horizontal, i.e.,
θ0=0 for oblate spheroids and θ0=π/2 for prolate
spheroids, which is consistent with . The advantage of
using Eq. () is that it permits us to model a variety of cases,
including a delta distribution (R=1), uniform (R=0), and fully chaotic
distributions. In Fig. W(Θ) for different values
of R is shown.
Using Eqs. ()–() the coefficients T1 and
T2 can be calculated as follows:
T1=∫-π/2π/2sin2Θ+θ0W(Θ)dΘ,T2=∫-π/2π/2sin4Θ+θ0W(Θ)dΘ.
Dependencies of T1 and
T2 on R for oblate and prolate
spheroids.
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The calculated values of T1 and T2 are shown in Fig. . For
further analysis it is convenient to use the degree of orientation ρa,
introduced in . The degree of orientation ρa is
related to the parameter T1 as follows:
ρa=1-2T1.
considered ρa only for θ0=0, for which
ρa lies in the range from 0 to 1. In the case θ0=π/2 values
of ρa are in the range from -1 to 0. Thus, the absolute value of
ρa represents the degree of orientation, while the sign indicates the
preferable orientation of particles (either 0 or π/2).
The modeled polarimetric variables can be represented using
Eqs. ()–():
Z^DR=B^hhB^vv,ρ^HV=|B^hv|B^hhB^vv,SLDR^=B^hh+B^vv-2ReB^hvB^hh+B^vv+2ReB^hv,ρ^CX=|B^hh-B^vv+2iImB^hv|B^hh+B^vv-2ReB^hvB^hh+B^vv+2ReB^hv.
Retrieval technique
proposed a shape and orientation retrieval
algorithm based on ZDR and ρHV observed by
a weather radar. The authors showed that the algorithm is applicable
for cloud areas with ZDR>4 dB where the
backscatter signal is dominated by oblate particles. When
ZDR<4 dB the algorithm can not distinguish between
oblate and prolate particles.
and showed that an
appropriate classification of ice particles in clouds requires
scanning in the elevation angle. Therefore, the shape and orientation
retrieval, described below, requires measured elevation scans of
differential reflectivity and correlation coefficient. We use scans in
the elevation from -60 to 60∘ (0∘ corresponds to
the zenith pointing). Thus, from every scan cycle, two half-scans are
obtained for the shape classification.
Using Eqs. ()–(73) look-up tables of
Z^DR(ρa,ψ,ρe),
ρ^HV(ρa,ψ,ρe),
SLDR^(ρa,ψ,ρe), and
ρ^CX(ρa,ψ,ρe) can be calculated. We use
values from -1 to 1 for ρa, from -60 to 60∘ for ψ,
and from 0.3 to 2.3 for ρe. The chosen range of ρe covers the
possible values for ice shown in Fig. . The cross sections of
modeled polarimetric variables for elevation angles 0 and 60∘ are
presented in Fig. . Left and right columns in
Fig. represent elevation angles ψ of 60 and
0∘, respectively. Values of ρa=-1 (upper part of diagrams)
characterize particles with horizontally oriented symmetry axis; ρa=0
is typical for uniformly distributed orientation angles θ; ρa=1
(lower part of diagrams) describes a vertically oriented symmetry axis of
particles. It should be noticed that ρa∼-0.4 specifies the so-called
fully chaotic orientation of particles which can be
considered as a special case of reflection symmetry . In
this case the polarimetric variables do not depend on ψ, and
ZDR and ρCX are 0 dB and 0, respectively.
Values of ρe<1 designate oblate particles; ρe=1 represents
spherical particles or particles with low density; ρe>1 corresponds to
prolate particles.
Modeled differential reflectivity Z^DR
(a and b), correlation coefficient
ρ^HV (c and d), slanted linear
depolarization ratio SLDR^ (e and
f), and co-cross-channel correlation coefficient in the
slanted basis ρ^CX (g and
h).
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In Fig. a ZDR is larger than 0 dB in the
lower left and in the upper right corners of the diagram. These corners
correspond to horizontally aligned oblate and prolate particles,
respectively. In contrast, in the upper left and in the lower right corners,
particles are oriented vertically and thus produce ZDR lower than
0 dB. Additionally, oblate particles can produce larger
ZDR than prolate ones, in consistency with and
. For zenith pointing (Fig. b)
ZDR values are 0 dB because of the reflection symmetry
. Figure c and d show that
ρ^HV is equal to 1 for spherical and horizontally aligned
oblate particles. At ψ=60∘ values of ρ^HV
decrease with decreasing |ρa|. This behavior is especially noticeable
for particles with ρe<0.5 and ρe>1.8. The relation between
ρ^HV and |ρa| is consistent with the findings of
. Figure e shows that values of
SLDR^ are dominated by ρe and only slightly depend on
ρa. This feature was previously described in and
. showed that in hybrid mode at
the zenith pointing ρ^HV is equal to the degree of
polarization. In this case SLDR^ and
ρ^HV can be related as follows:
ρ^HV∼1-2SLDR^.
The relation given by Eq. () can be clearly seen in
Fig. d and f. Figure g shows that
ρ^CX is mostly defined by ρa, i.e., by the
orientation of particles. This was previously found by
. For spherical particles (ρe=1) we use the
limit approximation ρ^CX=0 . As
mentioned above ρ^CX is equal to 0 in the case of
reflection symmetry, i.e., when ψ=0∘
(Fig. h).
In this paper we consider the retrieval based on ZDR and
ρHV only. Nevertheless, the same approach can be
applied to SLDR and ρCX that can be measured
directly by cloud radars operating in the SLDR mode.
It is known that the Doppler velocity measured by a cloud radar is
defined not only by the terminal velocity of particles, but also by air
motion. Thus, Doppler spectra measured at different elevation angles
usually have different shapes and mean values. In the following, we
however have to assume that the maximums of spectra (spectrum peak),
measured at a certain altitude and at different elevation angles,
correspond to particles of similar microphysical properties.
Due to the spatial inhomogeneity of a cloud or in the case of a low SNR,
some data points in a half-scan can be missing. Also some altitudes
cannot be reached by the radar at certain elevation angles. Therefore,
we apply the algorithm only to the altitudes where more than 50 %
of data points of polarimetric variables in a half-scan are present.
For simplicity, we describe the retrieval for one altitude only. We use
denotations ZDR(ψ) and ρHV(ψ) which
correspond to differential reflectivity and correlation coefficient,
calculated for the maximum spectral line at the elevation angle ψ,
respectively.
Using the scans of polarimetric variables and the look-up tables we calculate
the following error functions:
EZDR(ρa,ρe)=∫ΨZDR(ψ)-Z^DR(ρa,ψ,ρe)2dψ,ERHV(ρa,ρe)=∫ΨρHV(ψ)-ρ^HV(ρa,ψ,ρe)2dψ,
where Ψ represents elevation angles ψ for a certain
half-scan.
In order to classify particles as either prolate or oblate we search
for the minimum of EZDR(ρa,ρe). We define values
of ρa and ρe, with corresponding
EZDR(ρa,ρe) that do not exceed the minimum
EZDR by a factor of 1.1. For these values of ρa and
ρe we determine the lowest value of
ERHV(ρa,ρe). In the case when the minimum of
ERHV corresponds to ρe≤1, particles are
classified as oblate spheroids. Otherwise the particles are prolate
spheroids. It should be noted that without the correction for the
antenna coupling (see Sect. ) the algorithm can not
reliably discriminate spheroids with polarizability ratios in the
range from 0.8 to 1.2.
After the classification we determine ρe and ρa for every
elevation angle within ranges from 30 to 60 and from -60 to
-30∘. These ranges have been chosen considering that
polarimetric variables do not allow for the reliable discrimination
between different properties of particles at elevation angles close to
the zenith. We calculate the following function:
Es(ρa,ψ,ρe)=ZDR(ψ)-Z^DR(ρa,ψ,ρe)2+10ρHV(ψ)-ρ^HV(ρa,ψ,ρe)2.
We have not optimized the weighting factor in Eq. (). It
was set to 10 considering that errors in ZDR are about 1
order of magnitude higher than errors in ρHV. For every
elevation angle ψ we find values of ρe and ρa,
corresponding to the minimum of the function
Es(ρa,ψ,ρe). We emphasize that the retrieval allows
for the estimation of the polarizability ratio ρe. The estimation of
the exact axis ratio ρg from ρe requires knowledge of
density of ice crystals which has to be assumed or measured.
Range–altitude cross sections of (a) signal-to-noise
ratio, (b) differential reflectivity ZDR, and
(c) correlation coefficient ρHV, taken at
Cabauw, the Netherlands, from 18:16 to 18:20 UTC on 20
October 2014. Shown parameters are calculated for the maximum
spectral lines (spectral peaks).
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Case study
In this section we present a case study to demonstrate the applicability of
MIRA-35 with hybrid mode for the particle classification technique described
above. The data set was acquired during the ACCEPT (Analysis of the
Composition of Clouds with Extended Polarization Techniques) campaign which
was conducted at Cabauw, the Netherlands, in October and November 2014.
Throughout the ACCEPT campaign the radar was operated with the number of
averaged spectra Ns=20 which corresponds to an averaging time
of 1 s. Within every 15 min the radar performed two elevation
scans from -60 to 60∘ at an angular speed of
0.5∘s-1. One half scan between ±60 and 0∘
was thus performed within 120 s. The two scans were conducted
perpendicular to each other in azimuth direction.
In Fig. range–altitude cross sections of SNR, differential
reflectivity, and correlation coefficient calculated for the maximum spectral
lines are shown. These observations were taken in one azimuth plane on 20
October 2014 from 18:16 to 18:20 UTC. Two cloud layers at 2.7–3.5 and
4–5.2 km height are visible. We denote these layers as 1 and 2,
respectively. Between the layers a clear gap is present, thus seeding of ice
crystals from the upper layer into the lower layer can be
assumed to be absent. Temperatures at the tops of layers 1 and 2 derived with
a collocated microwave radiometer HATPRO were about -6 and
-14 ∘C, respectively.
Measured (blue crosses) and approximated (red solid curve)
elevation dependencies of differential reflectivity (a) and
correlation coefficient (b), and logarithms of
EZDR (c) and ERHV
(d). Measured data correspond to 3 km height of the
left half-scan of Fig. . According to the classification
scheme described in the text, this case corresponds to
a polarizability ratio of 1.6 (prolate
spheroids).
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Measured (blue crosses) and approximated (red solid curve)
elevation dependencies of differential reflectivity (a) and
correlation coefficient (b), and logarithms of
EZDR (c) and ERHV
(d). Measured data correspond to 4.7 km height of
the left half-scan of Fig. . According to the
classification scheme described in the text, this case corresponds to
a polarizability ratio of 0.4 (oblate
spheroids).
![]()
Height–time cross sections of (a) equivalent radar
reflectivity factor Zh, the mean (b) and standard
deviation (c) of polarizability ratio ρe, and the mean
(d) and standard deviation (e) of degree of
orientation ρa, taken at Cabauw, the Netherlands, on 20
October 2014. The equivalent radar reflectivity factor
Zh was measured by a collocated vertically pointed
35 GHz cloud radar MIRA-35 with LDR mode and with 1 s
averaging. The red rectangle shows the time period which corresponds
to Fig. .
![]()
In Figs. and a detailed analysis of
the case introduced in Fig. is presented for altitudes of 3 and
4.7 km (layer 1 and 2), respectively. Well-pronounced elevation
dependencies in the differential reflectivity can be seen for both layers. At
elevation angles of |ψ|=60∘ the differential reflectivity
reaches values of ∼3 and ∼5 dB for the layers 1 and 2,
respectively. In vertical pointing direction (ψ=0) the differential
reflectivity is close to 0.5 and 0 dB, respectively. Thus, for both
layers the differential reflectivity has its minimal value at 0∘
elevation and increases at higher |ψ|.
In contrast to the differential reflectivity, the elevation dependencies of
the correlation coefficient have different behavior for layers 1 and 2
(Figs. b and b). In layer 1
ρHV has its minimum at |ψ|=0∘ whereas it shows
increased values at higher |ψ|. In layer 2 ρHV has
a maximum at |ψ|=0∘ while at higher |ψ| the values of
ρHV are slightly lower.
Figures c, d and c and d show the
error functions EZDR(ρa,ρe) and ERHV(ρa,ρe),
respectively. We use the algorithm described in the Sect.
to distinguish between oblate and prolate particles at a certain altitude.
The polarizability ratio determined using Fig. c and d is
∼1.6, while the one from Fig. c and d is ∼0.4.
Thus, the spheroid types of the ice particles observed in layer 1
(3 km) and 2 (4.7 km) are classified as prolate and oblate,
respectively.
After the classification of the spheroid type we obtain the polarizability
ratio ρe and the degree of orientation ρa for every elevation
angle in the following range: 30∘≤|ψ|≤60∘. Using
the obtained values we calculate mean and standard deviation of ρe and
ρa for every altitude. In order to estimate the influence of
uncertainties in ZDR and ρHV on the retrieval of
ρe, we applied the algorithm to the measurements in light rain on 7
November 2015, from 20:30 to 21:00 UTC. The precipitation intensity during
the chosen time period was about 1 mm h-1 as it was observed by a
disdrometer on-site. We assume that raindrops have a spherical shape which is
characterized by the polarizability ratio of 1. Values of retrieved ρe
were mainly 1±0.02.
We applied the algorithm to the polarimetric observations from 13:30 to
19:30 UTC of 20 October 2014. The results are presented in
Fig. . Figure a shows the time–height cross
section of the equivalent radar reflectivity factor from a collocated
vertically pointed cloud radar MIRA-35 with LDR mode. The time period
corresponding to the elevation scan that is shown in Fig. is
indicated by the red rectangle in Fig. a. Several cloud layers
at different heights were observed during the measurement. High-level clouds
with a cloud top at around 8 km height were observed from 13:30 to
14:30 UTC and 15:00 to 17:00 UTC. Reflectivity values for these cloud
layers mostly exceeded -10 dBZ which is high enough to calculate
polarimetric variables. From 15:00 to 20:00 UTC a thick mid-level cloud with
a top at 5 km height was observed. At 16:40 UTC strong ice
formation, indicated by high values of the radar reflectivity, was observed.
Melting of ice particles resulted in a short precipitation event reaching the
ground. Later the cloud experienced seeding from the high-level cloud above.
After 18:15 UTC the cloud split into two thin cloud layers with cloud tops at 5 and 3 km height.
Different ambient conditions within these layers caused, as it will be shown
below, different types of ice crystals. At about 2 km height thin
low-level cloud layers appeared from 13:00 to 17:00 UTC. These cloud layers
did not have a large enough SNR and/or were spatially inhomogeneous and,
therefore, were filtered out by the retrieval algorithm.
In Fig. b and c mean and standard deviation of the
polarizability ratio are presented. It can be seen that the high-level clouds
(above 5 km height) are characterized by a polarizability ratio of
0.85±0.07. According to Eqs. () and () this
can be caused either by ice particles of quasi-spherical shape or of low
density or both. Low density (<0.1 gcm-3) of ice particles in
cirrus clouds was, e.g., reported by . Ice particles in
the mid-level cloud with the top below 5 km height showed values of
ρe≈0.43±0.17, which indicates a strongly oblate shape and
a high density of ice particles (Fig. ). From 15:50 to
16:30 UTC the polarizability ratio increased to values of
ρe≈0.83 ± 0.1 towards the bottom of the cloud. These
signatures were accompanied by an enhancement of the effective radar
reflectivity factor (Fig. a). Thus, the larger particles were
more spherical and/or less dense, which is a clear indication of particle
growth due to aggregation and/or riming processes. The capability to identify
these processes can be especially useful for the investigation of
precipitation formation. It can be seen in the virga shown in Fig. a, which partly reaches the
ground, that the areas in which aggregation or riming occur can produce
precipitation. From 18:15 to 19:15 UTC a thin cloud layer with prolate ice
particles was observed at 3 km height. These particles are
characterized by ρe≈1.5±0.2.
In Fig. d and e the mean and standard deviation of the
degree of orientation are shown, respectively. Areas where the
spheroid shape of the ice particles was classified as strongly oblate
or prolate are characterized by |ρa| values of ∼0.7 and
∼0.95, respectively, i.e., particles are oriented nearly
horizontally which is consistent with theoretical studies
. The low standard deviation
of |ρa| in these areas indicates that the orientation
distributions for different populations of ice particles are
similar. Observed high-level clouds and cloud areas with seeding had
considerably lower values of the degree of orientation with
|ρa|∼0.4–0.6. These values are indicative of a more random
orientation of ice particles around the horizontal alignment. The high
standard deviation of ρa in these clouds can be explained by
different orientation distributions of different populations of ice
particles.
Summary and conclusion
Existing backscattering models, assuming the spheroidal approximation
of cloud scatterers, allow for the estimation of parameters
(polarizability ratio and degree of orientation) connected with the
shape and orientation of particles. Accurate measurement of these
parameters by cloud radars requires a set of polarimetric variables.
In order to measure a variety of polarimetric variables, the new 35 GHz
cloud radar MIRA-35 with hybrid polarimetric configuration was implemented in
collaboration between the Leibniz Institute for Tropospheric Research
(TROPOS), Leipzig, Germany, and METEK GmbH, Elmshorn, Germany, within the
Initial Training for atmospheric Remote Sensing (ITaRS) project. The radar
emits the horizontal and vertical component of the transmitted wave
simultaneously, with the differential phase shift set close to 0∘.
The polarization calibration of the radar was performed using
an external test transmitter and vertical measurements in light rain. Additionally, the correction for the
antenna coupling was applied. Vertical observations with the radar under rain
conditions show the high accuracy of the polarization calibration.
The radar permits the measurement of spectral polarimetric parameters:
differential reflectivity, slanted linear depolarization ratio, correlation
coefficient, co-cross-channel correlation coefficient in the slanted basis,
and differential phase shift. The slanted linear depolarization ratio and co-cross-channel correlation coefficient are
derived using the rotation of the measured coherency matrix. Retrieved values
of these parameters are consistent with observations of cloud radars with the
LDR or SLDR mode. The algorithm for deriving the polarizability ratio and
degree of orientation of particles based on the differential reflectivity and
correlation coefficient was developed. The same approach can be applied to
the slanted linear depolarization ratio and co-cross-channel correlation
coefficient. It should be noted that the retrieval of ice particle shape from
the measured polarizability ratio additionally requires the information about
the density of ice particles.
The algorithm was applied to observations made during the ACCEPT campaign in
Cabauw, the Netherlands, where the new cloud radar was deployed in October
and November 2014. Vertical profiles of the polarizability ratio and the
degree of orientation were retrieved. The results show clouds with oblate
(ρe≈0.43±0.17), prolate (ρe≈1.5±0.2), and
quasi-spherical or low-density particles (ρe≈0.85±0.07). All
these clouds had different cloud top heights (5, 3, and 8 km,
respectively), indicating different ambient conditions of ice formation. Areas
in which aggregation and/or riming led to ice particle growth could be
detected. High absolute values of the degree of orientation observed in areas
dominated by oblate and prolate ice particles indicated their nearly
horizontal orientation. Orientation of slightly oblate or low-density ice
particles, detected in high-level clouds and in areas with seeding, was found
to be more random, though the primary orientation was horizontal.
In conclusion, the proposed algorithm provides valuable information about the
shape and orientation of ice crystals which is especially important for the
investigation of mid-level mixed-phase clouds. The retrieved vertical
profiles of ρe allow the change in the shape and orientation of ice
crystals to be tracked. Combined analysis of these profiles and Doppler
spectra of vertical velocity can be used for studies of size–shape–terminal
velocity relations of particles in the atmosphere.
recently showed a potential of combining the polarimetric and multi-frequency
approaches. Therefore, a synergistic use of the proposed algorithm and
multi-frequency analysis can yield additional information.