This paper is devoted to the experimental quantitative characterization of
the shape and orientation distribution of ice particles in clouds. The
characterization is based on measured and modeled elevation dependencies of
the polarimetric parameters differential reflectivity and correlation
coefficient. The polarimetric data are obtained using a newly developed
35 GHz cloud radar MIRA-35 with hybrid polarimetric configuration and
scanning capabilities. The full procedure chain of the technical
implementation and the realization of the setup of the hybrid-mode cloud
radar for the shape determination are presented. This includes the
description of phase adjustments in the transmitting paths, the introduction
of the general data processing scheme, correction of the data for the
differences of amplifications and electrical path lengths in the transmitting
and receiving channels, the rotation of the polarization basis by
45

The continuous observation of ice-crystal habit is a key component for an
improved characterization of mixed-phase clouds with remote-sensing
techniques

Cloud radar is one of the most promising remote-sensing instruments for
particle shape determination. Recent investigations of

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

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

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

The paper is organized as follows. Section

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

Parameters of MIRA-35 used in the operational mode.

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

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

This section is devoted to the technical realization, calibration, and the
data processing of the new hybrid-mode radar. In Sect.

Simplified block diagrams of typical LDR

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.

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

Throttle plates used for the phase adjustment. The thickness
of the plates is 0.05

To characterize phase shifts induced by the radar hardware, a polarization
basis should be defined. For the description we use the Cartesian
polarization basis

Antenna of MIRA-35 system mounted on the scanning unit. The
description polarization basis is shown. The unit vector

We measured the phase shift

Knowing

It is known that randomly oriented particles do not produce a backscattering
differential phase shift

During the operation the frequency of the magnetron can vary with temperature
within

MIRA-35 is a coherent cloud radar. Two receivers calculate in-phase (

Using

The elements of the coherency matrix

A recent modification of the MIRA-35 software permits one to additionally
calculate and store the complex element

The spectral form of the coherency matrix

In order to correct the difference in the amplifications we calculate
a coefficient

The effect of differences in the amplifications and the electrical
path lengths on the components of Eq. (

The additional phase shift, introduced in

As mentioned in Sect.

The Jones vector of a received signal represented in the
description

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

The corrected coherency matrix

The elements of

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

For the subsequent data analysis we define spectral components

In Eq. (

Further we remove the mean noise levels from the elements

The correlation between noise in the orthogonal components is negligible and,
thus, does not influence the element

We decompose the coherency matrix

Applying the method described by

From

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

It can be seen in Fig.

In rain, the correlation coefficient

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

Polarimetric variables obtained for the time period from 17:55 to 18:00 UTC
and the height range from 500 to 1700

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

Splitting the transmitting power into two channels in the hybrid mode worsens
the radar sensitivity by 3

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 Fig.

For the rain case on 1 May 2014 we found

Another factor that can affect the utilization of Eq. (

Power spectrum in the horizontal channel (blue line) and
power spectrum after coherent averaging (green line). The same data
as in Fig.

The results of Eq. (

In Fig.

As shown in Sect.

Time–height cross sections of signal-to-noise ratios
calculated from

It is known that particles with sizes much smaller than the wavelength of
a radar can be approximated by a spheroid.

Time–height cross sections of the signal-to-noise ratio in the
horizontal channel

The elements of the backscattering matrix

In Eq. (

In the following, we consider only ice particles. In the microwave
region the real part of

Further we define the polarizability ratio:

The backscattering matrix of

Assuming complex amplitudes of the horizontal and vertical components
of the transmitted signal

The complex amplitudes of the horizontal

Implementation of the subsequent modeling approach is based on the
following assumptions.

All particles have the same axis ratio

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:

Geometry of spheroid orientation. Adopted from

Dependencies of polarizability ratio

Probability density function of

We model the probability density function of orientation angle

Using Eqs. (

Dependencies of

The calculated values of

The modeled polarimetric variables can be represented using
Eqs. (

Using Eqs. (

Modeled differential reflectivity

In Fig.

The relation given by Eq. (

In this paper we consider the retrieval based on

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

Using the scans of polarimetric variables and the look-up tables we calculate
the following error functions:

In order to classify particles as either prolate or oblate we search
for the minimum of

After the classification we determine

We have not optimized the weighting factor in Eq. (

Range–altitude cross sections of

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

In Fig.

Measured (blue crosses) and approximated (red solid curve)
elevation dependencies of differential reflectivity

Measured (blue crosses) and approximated (red solid curve)
elevation dependencies of differential reflectivity

Height–time cross sections of

In Figs.

In contrast to the differential reflectivity, the elevation dependencies of
the correlation coefficient have different behavior for layers 1 and 2
(Figs.

Figures

After the classification of the spheroid type we obtain the polarizability
ratio

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.

In Fig.

In Fig.

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

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
(

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

The research leading to these results has received funding from the European Union Seventh Framework Programme (FP7/2007–2013): People, ITN Marie Curie Actions Programme (2012–2016) in the frame of ITaRS under grant agreement no. 289923. The ACCEPT campaign was partly funded by the European Union Seventh Framework Programme (FP7/2007–2013) under grant agreement no. 262254. Edited by: M. Kulie