Retrievals of ice microphysics using dual-wavelength polarimetric radar observations during stratiform precipitation events

Ice growth processes within clouds affect the type as well as the amount of precipitation. Hence, the importance of an accurate representation of ice microphysics in numerical weather and numerical climate models has been confirmed by several studies. To better constrain ice processes in models, we need to study ice cloud regions before and during monitored precipitation events. For this purpose, two radar instruments facing each other were used to collect complementary 10 measurements. The C-band POLDIRAD weather radar from the German Aerospace Center (DLR), Oberpfaffenhofen and the Ka-band MIRA-35 cloud radar from the Ludwig Maximilians University of Munich (LMU) were used to monitor stratiform precipitation in the vertical cross-section area between both instruments. The logarithmic difference of radar reflectivities at two different wavelengths (54.5 and 8.5 mm), known as dual-wavelength ratio, was exploited to provide information about the size of the detected ice hydrometeors, taking advantage of the different scattering behavior in the Rayleigh and Mie regime. 15 Along with the dual-wavelength ratio, differential radar reflectivity measurements from POLDIRAD provided information about the apparent shape of the detected ice hydrometeors. Scattering simulations using the T-matrix method were performed for oblate and horizontally aligned prolate ice spheroids of varying shape and size using a realistic particle size distribution and a well-established mass-size relationship. The combination of dual-wavelength ratio, radar reflectivity and differential radar reflectivity measurements as well as scattering simulations was used for the development of a novel retrieval for ice 20 cloud microphysics. The development of the retrieval scheme also comprised a method to estimate the hydrometeor attenuation in both radar bands. To demonstrate this approach, a feasibility study was conducted on three stratiform snow events which were monitored over Munich in January 2019. The ice retrieval can obtain ice particle shape, size and mass which are in line with differential radar reflectivity, dual-wavelength ratio and radar reflectivity observations when a suitable mass-size relation is used and when ice hydrometeors are assumed to be represented by oblate ice spheroids. A furthermore finding was the 25 importance of the differential radar reflectivity for the particle size retrieval directly above the MIRA-35 cloud radar. Especially for that observation geometry, the simultaneous slantwise observation from the polarimetric weather radar POLDIRAD could reduce ambiguities in retrieval of the ice particle size by constraining the ice particle shape.


Introduction
The ice phase is the predominant cloud phase at mid and higher latitudes (Field and Heymsfield, 2015). Ice clouds can 30 cause a cooling effect at the surface by reflecting the shortwave, incoming solar radiation but they can also contribute to warming of the atmosphere by trapping the longwave, terrestrial radiation (Liou, 1986). Their influence on the radiation budget of the climate system strongly depends on their top height as well as on ice crystals habits and effective ice crystal size (Zhang et al., 2002). Ice growth processes, such as deposition, riming and aggregation, play a leading role in the formation of precipitation and are a central topic in many ice cloud studies. A misrepresentation of these processes in numerical weather 35 models can lead to high uncertainties and therefore, they need to be constrained as accurately as possible. Brdar and Seifert (2018) presented the novel Monte-Carlo microphysical model, McSnow, aiming for a better representation of aggregation and riming processes of ice particles. When numerical weather models are used to predict microphysics information about ice hydrometeors (e.g. Predicted Particle Properties (P3), Part I, Morrison and Milbrandt, 2015), we need to investigate under https://doi.org/10.5194/amt-2021-216 Preprint. Discussion started: 21 October 2021 c Author(s) 2021. CC BY 4.0 License. which conditions each ice growth process occurs. To better understand these mechanisms and improve their representation in 40 models, more precise microphysics information (e.g. size, shape and mass) through ice retrievals based on measurements, is needed.
Many studies showed how millimeter-wave radar measurements can be used to retrieve ice water content (IWC) profiles in clouds (e.g. Hogan et al., 2006). However, stand-alone single-frequency radar measurements cannot constrain microphysical properties such as ice particle size and shape simultaneously without using empirical relations. Dealing with more parameters 45 (e.g., IWC, size and shape) more measurements are needed. Thus, observations or simulated radar parameters are often combined with other remote sensing instruments, e.g. with lidars, to retrieve microphysics properties such as the effective radius of cloud ice particles (Cazenave et al., 2019), or with infrared radiometers (Matrosov et al., 1994) to retrieve the median diameter of the ice particles size distribution. Another way to gain microphysics information is to use multi-frequency radar observations as they exploit the scattering properties of ice particles in both Rayleigh and Mie regime. To this end, frequencies 50 are chosen with respect to the prevalent ice particle size. In the case of dual-frequency techniques, one frequency is chosen to be in the Rayleigh regime (e.g. S-, C-or X-band), where particle size is much smaller than the radar wavelength, and the other is chosen to be in the Mie regime (e.g. Ka-, Ku-or W-band), where particle size is comparable or larger than the radar wavelength. The scattering of radar waves is sensitive to the size and number concentration of particles. The radar reflectivity factor z is defined as the sixth moment of the particle size distribution ( ) and is thus designed to be proportional to the to 55 the Rayleigh scattering cross section of liquid spheres: where, : the radar reflectivity in linear scale, : the number concentration, 60 : the geometric diameter of the particles.
This definition can be also expressed in logarithmic terms: This definition, however, cannot be directly applied to snow due to the varying density, the irregular shape and larger size of ice particles which cause deviations from the Rayleigh into the Mie scattering regime. Nevertheless, an equivalent radar 65 reflectivity factor Ze can be derived from the measured radar reflectivity η when the dielectric factor of water | | = 0.93 is assumed: where: : the radar wavelength. In the Rayleigh regime, the radar reflectivity factor Z or the equivalent radar reflectivity factor Ze (for 70 simplicity reasons referred also as radar reflectivity in this paper) is proportional to the sixth power of the particle size, while in the Mie regime Ze scales with the second power of the particle size. In both regimes Ze scales linearly with the particle number concentration. The logarithmic difference of these radar reflectivities in Eq. (2), known as dual-wavelength ratio (DWR), is a parameter that can be used to infer the size of the observed hydrometeors in the atmosphere as it increases with the particles size: with λ1 > λ2 the radar wavelengths, ze,λ1, ze,λ2 the radar reflectivities of the two radar bands in linear scale (units: mm 6 m −3 ) and Ze,λ1, Ze,λ2 the radar reflectivities of the two radar bands in logarithmic scale (units: dBZ). The DWR method has been used in https://doi.org/10.5194/amt-2021-216 Preprint. Discussion started: 21 October 2021 c Author(s) 2021. CC BY 4.0 License. many ice studies before. Matrosov (1998) developed a DWR method to estimate the snowfall rate R, supplementing experimental Ze-R relations with a retrieved median size, while in Huang et al. (2019) the DWR was used for Quantitative 80 Precipitation Estimation (QPE) from the combination of Ku-and Ka-band which were accounted to be Rayleigh and Mie region, respectively, for the detected particles sizes. In other studies, such as Hogan and Illingworth (1999) and Hogan et al. (2000), DWR from airborne and ground-based radars was used to estimate ice crystals sizes as well as IWC for cirrus clouds.
Sometimes two DWR measurements are combined to exploit the information in triple-frequency radar measurements. Kneifel et al. (2015) used the triple-frequency method (DWRX, Ka and DWRKa, W) to derive ice particle habits information from three 85 snowfall events measured during the Biogenic Aerosols Effects on Clouds and Climate (BAECC) field campaign (Petäjä et al., 2016). The triple-frequency method was also used by Leinonen et al. (2018b) to develop an algorithm that retrieves ice particle size and density as well as number concentration using airborne radar data from the Olympic Mountains Experiment (OLYMPEX, Houze et al., 2017).
Beyond DWR techniques, polarimetric radar measurements are used in many snowfall rate estimation studies. E.g. 90 Bukovčić et al. (2018) used polarimetry to study the snow water equivalent rate and IWC. Except for such studies, polarimetry is an advantageous tool to obtain information about ice particles, e.g. their size distribution and their shape. Additional characteristics, like the orientation and canting angle distribution, as well as the variable refractive index of melting or rimed ice crystals have specific polarimetric radar signatures. Polarimetric weather radars can provide observational parameters including Ze, differential radar reflectivity (ZDR), linear depolarization ratio (LDR), reflectivity difference (ZDP), cross-95 correlation coefficient (ρHV), differential propagation phase (φDP) and specific propagation phase (KDP). These parameters have been widely used in classification schemes of atmospheric hydrometeors. Höller et al. (1994) developed one of the first algorithms to distinguish between rain, hail, single or multi-cells. Subsequently, this algorithm was extended to estimate hydrometeor mass concentrations (Höller, 1995). Straka et al. (2000) developed a method to distinguish hydrometeor types using radar observations and model calculations at a wavelength of 10 cm. Other studies suggested to use polarimetry to 100 investigate growth processes of snow and their signatures on dual-polarization and Doppler velocity radar observations . Tiira and Moisseev (2020) developed an unsupervised classification of snow and ice crystals particles exploiting profiles of polarimetric signatures on radar variables. The most important growth processes of ice particles were studied using several years of the Ikaalinen C-band radar data, in Hyytiälä forestry station in Juupajoki, Finland.
Scattering simulations as well as polarimetric radar simulations can be used to extract additional information regarding 105 the microphysical properties of the observed hydrometeors. However, in the case of ice particles this can be challenging due to the large complexity and variety in shape, structure, size and density of ice crystals. Many scattering algorithms have been developed to calculate the optical properties of ice particles. One of the most known, the Discrete-Dipole Approximation (DDA, Draine and Flatau, 1994), can be used to calculate the scattering properties of realistic ice crystals and aggregates.
Snow hydrometeors with size in the millimeters order of magnitude are found to have low densities and therefore, the Self-110 Similar Rayleigh-Gans Approximation (SSRGA, e.g. Hogan and Westbrook, 2014;Hogan et al., 2017;Leinonen et al., 2018a), that is applicable for "soft spheres", can be used. The term "soft" indicates homogeneous ice particles composed of an ice and air mixture and a real part of the refractive index close to 1. A well-proven approach is the soft spheroid particle model which uses the effective medium approximation (EMA) to model the refractive index of ice crystals and aggregates, e.g. the Bruggeman or Maxwell-Garnett models as in Garnett and Larmor (1904). Many studies, e.g. Hogan et al. (2012), have shown 115 that soft spheroid ice particles can provide quite realistic radar signals in scattering simulations. In the same study, it was also found that the majority of particles in ice clouds can be well-represented by horizontally aligned oblate spheroids with an axial ratio value of 0.6.
In this study, we developed an ice microphysical retrieval scheme using a simple particle model, simulations and novel combination of radar observations for ice hydrometeors. In this way, we are able to simultaneously retrieve median size, aspect 120 ratio and ice water content of ice particles. For the computation of scattering parameters, the ice particles are assumed to be https://doi.org/10.5194/amt-2021-216 Preprint. Discussion started: 21 October 2021 c Author(s) 2021. CC BY 4.0 License. spheroids. In this way, we are able to vary parameters such as median size, aspect ratio and ice water content independently, which serve as degrees of freedom of the ice spheroids, and calculate their optical properties without much computational cost as in other scattering algorithms (e.g. DDA, Draine and Flatau, 1994) that are used for more realistic ice crystal shapes simulations. Moreover, using spheroids we can better understand the ambiguities between the aforementioned degrees of 125 freedom. Here, more sophisticated models of specific ice crystals could introduce additional challenges to sort a collection of ice shapes along these degrees of freedom or to define variables like the aspect ratio. The single scattering properties of the ice spheroids are calculated using the T-matrix scattering method as described by e.g. Mishchenko and Travis (1994) and Mishchenko et al. (1996). The averaging over particle orientations and the calculation of radar variables for whole size distributions are done using PyTMatrix (Leinonen, 2014). Combining ice scattering simulations and radar measurements we 130 present an ice microphysics retrieval that resolves the ice water content, the median size and the apparent shape of the detected ice particles. The apparent shape (for simplicity the term shape will be used in this study) describes the average observed aspect ratio which is strongly connected to the particle orientation including small oscillations out of this plane. Although vertically pointing radars are useful for Doppler spectra observations (e.g. Kneifel et al., 2016;Kalesse et al., 2016), they cannot provide sufficient polarimetric measurements, e.g. ZDR, that can be useful to estimate the shape of the ice particles due 135 to their observation geometry. In this work, we can estimate the shape of the ice hydrometeors using ZDR measurements from a scanning weather radar. For size retrievals we use simultaneous range-height indicator (RHI) scans from a scanning cloud radar, 23 km apart from the weather radar, to obtain dual-wavelength observations for the same observation volume. As we aim to use DWR and ZDR measurements from two different locations, we are focused on homogeneous case studies with large clouds and in which hydrometeor attenuation can be considered to be negligible. Therefore, we have selected cloud cross-140 sections from stratiform snowfall cases where water hydrometeors are unlikely to occur. To exclude liquid hydrometeors and melting layers (ML), an ice mask was developed and applied to the observational dataset. Future studies will also include wet particles to improve the representation of melting and riming processes in numerical weather models.
This publication is organized as follows: In Sect. 2 the instruments used to produce the measurements dataset are described. In Sect. 3 the measurement strategy and the error assessments of the radar observations as well as the T-Matrix 145 scattering simulations are presented in detail. Section 3 demonstrates the methodology to combine DWR and polarimetric measurements along with the scattering simulations in order to retrieve microphysical properties of ice particles. In addition, the attenuation correction methods are described. In Sect. 4, some retrieval results along with their uncertainties as well as statistical results of the ice microphysics retrieval are presented. Furthermore, the limitations of this study and the performance of the ice retrieval in different areas of the radars cross-section are fully discussed. In Sect. 5, the conclusions for the presented 150 approach are drawn.

Instruments
This feasibility study to combine two spatially separated weather and cloud radars was conducted in the scope of the IcePolCKa project (Investigation of the initiation of Convection and the Evolution of Precipitation using simulatiOns and poLarimetric radar observations at C-and Ka-band), which is part of the Polarimetric Radar Observations meet Atmospheric 155 Modelling (PROM) Priority Program (Trömel et al., in review, 2021). For the DWR dataset the synergy of two polarimetric radars, the C-band POLDIRAD weather radar at German Aerospace Center (DLR) in Oberpfaffenhofen Munich, and the Ka-  Fig. 1, left) is a polarization diversity Doppler weather radar operating at C-band at a frequency of 5.504

POLDIRAD (
GHz (λ = 54.5 mm, in Eq. 2). The radar is located at DLR, Oberpfaffenhofen, 23 km southwest of Munich at 48°05'12" N and 11°16'45" E at an altitude of 602.5 m above mean sea level (MSL). Since 1986, POLDIRAD has been operated at the roof of Institute of Atmospheric Physics (IPA), DLR for meteorological research purposes (Schroth et al., 1988). The weather radar 165 consists of a parabolic antenna with a diameter of 4.5 m and a circular beam width of 1°. A magnetron transmitter with a power peak of 400 kW and a Selex ES Germatronik GDRX digital receiver with both linear and logarithmic response are synchronized with the polarization network of the receiver, which can record the linear, elliptic and circular polarization of each radar pulse (Reimann and Hagen, 2016). POLDIRAD has the capability to receive the co-and cross-polar components of the horizontal, vertical, circular and elliptical polarized transmitted electromagnetic waves. In this way it provides several polarimetric 170 variables, e.g. ZDR, ρHV etc., which can be used to obtain additional information about the size, shape, phase, and falling behavior of the hydrometeors in the atmosphere (Straka et al., 2000;Steinert and Chandra, 2009). Depending on its operational mode, the maximum range that can be reached is 300 km (for a pulse repetition frequency of 400 Hz, a pulse duration of 2 μs and a range resolution of 300 m), making it a suitable instrument for nowcasting in the surrounding area of Munich. For the present study POLDIRAD's maximum range was 125 km with a pulse repetition frequency of 1200 Hz, a pulse duration of 1 175 μs and a range resolution of 150 m. The system can also be operated in the STAR mode (simultaneous transmission and reception). Here, we used the alternate-HV mode (alternate horizontally and vertically polarized transmitted electromagnetic waves) which allows measuring the cross-polar components of the back-scatter matrix. The technical characteristics of POLDIRAD are presented in Table 1. GmbH, Elmshorn, Germany) with a frequency of ca. 35.2 GHz and a wavelength λ = 8.5 mm (Görsdorf et al., 2015), which is λ2 in Eq. (2). The cloud radar, which is operated by the Meteorological Institute Munich (MIM) as part of the Munich Aerosol Cloud Scanner (MACS) project (also referred as miraMACS, Ewald et al., 2019), is located on the roof of the institute at the LMU at 48°08'52.2'' N and 11°34'24.2'' E and 541 m above MSL. The transmitter consists of a magnetron with a power peak 185 of 30 kW which typically transmits radar pulses of 0.2 μs with a pulse repetition frequency of 5 kHz, corresponding to a range resolution of 30 m. The 1 m diameter antenna dish produces a beam width of 0.6°. The MIRA-35 cloud radar emits horizontally polarized radiation and measures both vertical and horizontal components of the backscattered wave. Hence, it has the capability to perform LDR measurements. The cloud radar usually points to the zenith, but can also perform RHI scans at different azimuths and plan-position indicator (PPI) scans at different elevations angles. Although the maximum radar range 190 for this setup is 30 km, only 23 km range was recorded during the RHI scans performed for the purpose of this study. The technical characteristics of MIRA-35 are presented in Table 1.    This study intends to investigate microphysical properties of ice hydrometeors that are known to affect the type of precipitation (e.g. stratiform or convective) aiming to improve their representation in numerical weather models. To address this, an ice microphysics retrieval scheme has been developed. In this way, the microphysical properties of ice hydrometeors are revealed for stratiform snow precipitation cases. In this section, our approach is presented in detail and demonstrated using 205 a case study example from 30 th January 2019 when a snowfall event took place over the Munich area.

Measurements strategy and data preprocessing
Coordinated RHI measurements with POLDIRAD and MIRA-35 have been collected during three snowfall days on 9 th , 10 th and 30 th January 2019, with some ice particles reaching the ground where both radars are located (602.5 m for POLDIRAD and 541 m for MIRA-35, both heights above MSL). 59 RHI scans were executed from the two radars at almost the same time 210 (time difference between RHIs was estimated less than 15 s) with a temporal resolution which was adjusted to the precipitation rate. POLDIRAD scanned between 0°-35° elevation towards MIRA-35 (northeast direction, azimuth of 73°), while MIRA-35 scanned between 0°-90° elevation towards POLDIRAD (southwest direction, azimuth of 253°) as well as 91°-169° elevation in a backward northeast direction but still inside the common cross-section (Fig. 2). With this setup, the cross-section between the two radars as well as beyond the MIRA-35 position was fully covered to record the development and microphysics of 215 precipitation cells and fall streaks. During the snow events, Ze measurements from the two radars were performed and interpolated onto a common rectangular grid (50 × 50 m 2 ). The 0-height of this grid is defined to be the height above MSL, while POLDIRAD and MIRA-35 locate at 602.5 m and 541 m height above MSL. In Fig. 3a  the two radar systems during the RHI scans from 30 th January 2019 at 10:08 UTC is presented. For the MIRA-35 Ze measurements we applied a calibration offset of 4 dBZ as derived in Ewald et al. (2019). Studying only snow cases no strong 220 effects of hydrometeor attenuation are expected (e.g. Nishikawa et al., 2016). However, an iterative method to estimate hydrometeor attenuation has been developed. Additionally, both Ze datasets are corrected for gaseous attenuation using the ITU-R P.676-11 formulas provided by International Telecommunication Union (ITU) in September 2016 (ITU-R P.676, 2016).
Both methods are fully described in Sect. 3.3. After the interpolation of both radar reflectivities in the common radar grid, we calculated the DWR (Fig. 3b) using Eq. (2). Since DWR is defined as the ratio of Ze at two wavelengths, it is independent of 225 number concentration N. Therefore, it exploits the difference in the received radar signal due to Mie effects to give size information. To avoid unwanted biases by measurement artefacts, DWR values lower than -5 dB and higher than 20 dB were excluded. Furthermore, errors from other sources, e.g. beam width mismatch effects (beam width 1º for POLDIRAD and 0.6º for MIRA-35), are considered (fully explained in Sect. 3.1.2). Besides DWR measurements, polarimetric observations were used to study the shape of ice particles. POLDIRAD can provide polarimetric measurements of ZDR ( Fig. 3d) defined as, 230 where, : the signal received or reflectivity factor at horizontal polarization, : the signal received or reflectivity factor at vertical polarization. Following the definition of ZDR, it is zero if the received signal in both polarization states is the same, i.e. spherical targets. For elongated, azimuthally oriented particles ZDR is found 235 to be greater (oblate particles) or less than zero (vertically aligned prolates), depending on the orientation of their rotational axis to the horizontal polarization state (e.g. Straka et al., 2000). Only ZDR values between -1 dB and 7 dB were considered to be atmospheric hydrometeors signatures. Moreover, the ZDR calibration was validated using additional measurements (described in detail in Sect. 3.1.2). For the ZDR panel ( Fig. 3d), reasonable boundaries for optimal visualization purposes were used in the colormap. 240 When Ze, ZDR and DWR measurements are combined (Fig. 3), one can already get a first glimpse on the prevalent ice microphysics. Especially below 3 km height, between 20-30 km from POLDIRAD, the large values of Ze accompanied with the large values of DWR (greater than 5 dB) and the low values of ZDR (lower than 1 dB) indicate the presence of large and quite spherical ice particles. In the following, quantitative ice microphysics will be revealed by the combination of Ze, DWR and ZDR measurements with scattering simulations for a variety of ice particles. 245

Ice mask and noise filters application 250
As already mentioned, the current version of the ice microphysics retrieval only accounts for ice particles. Hence, radar datasets should be filtered accordingly and an ice mask should be applied. The implementation of the ice mask using threshold from polarimetric radar variables, i.e. MIRA-35 LDR, POLDIRAD ZDR and ρHV, as well as temperature sounding data (shown in Fig. 4), are fully presented in Appendix B.

Assessment of radar observations errors
Radar measurements are often affected by systematic or random errors. To assess their impact on the ice microphysics 260 retrieval developed in this study we need to investigate possible errors in POLDIRAD and MIRA-35 observations as well as all their sources.
The absolute radiometric calibration of both instruments is an important error source in DWR measurements. While the error of the absolute radiometric calibration of POLDIRAD is estimated to be ±0.5 dB following the validation with an external device (Reimann, 2013), the budget laboratory calibration of MIRA-35 following Ewald et al. (2019) is estimated to be ±1.0 265 dB.
In order to test for a systematic ZDR bias, we exploited POLDIRAD measurements during vertically pointing scans (also known as birdbath scans, e.g. Gorgucci et al., 1999) in a liquid cloud layer performed on the 4 th April 2019. The measurements indicated that ZDR has an offset of about +0.15 dB as ZDR values are expected to be near 0 dB for this case due to the spherical apparent shape of liquid droplets. In Fig. A1 (Appendix A), examples of radar reflectivity Ze, differential reflectivity ZDR as 270 well as a scatter plot showing the ZDR offset are presented.
Another error that should be considered is the random error, especially for ZDR measurements at low signal levels. To detect and filter out regions with high ZDR noise we compare the local (3 range gates) standard deviation ZDRstdv with the local mean ZDRmean. Subsequently, we only include regions where the signal ZDRmean exceeds the noise ZDRstdv by on magnitude. An example of this approach can be found in Fig. A2 (Appendix A). While we apply the retrieval to all cloud 275 regions, the described ice mask and noise filters are used during the statistical aggregation of retrieval results.
In our case of spatially separated radar instruments, an azimuthal misalignment between both instruments had to be excluded to obtain meaningful DWR measurements. To this end, we performed several solar scans with both instruments in spring 2019 to confirm their azimuthal pointing accuracy (e.g. Reimann and Hagen, 2016). Here, we found an azimuth offset https://doi.org/10.5194/amt-2021-216 Preprint. Discussion started: 21 October 2021 c Author(s) 2021. CC BY 4.0 License. of -0.2° for POLDIRAD and an azimuth offset of +0.1° for MIRA-35. Consecutive solar scans confirmed the azimuthal 280 pointing accuracy within ±0.1°. Despite the small azimuthal misalignment, the radar beam centroids of both instruments were clearly within the respective other beam width during our measurement period in 2019.
Besides an azimuthal misalignment, we also analyzed the temporal mismatch between both RHIs as well as the volumetric mismatch in the context of non-uniform beam filling. Although the RHIs from the radars were scheduled to be executed simultaneously, regions within the RHIs are measured at slightly different times by both instruments. This temporal mismatch 285 can lead to slightly different Ze radar observations from both radars in the context of horizontal advection of an inhomogeneous cloud scene. In the following we used this temporal mismatch to estimate the resulting DWR error for the example case shown in Fig. 3. Using wind data (Fig. 4) from the Oberschleißheim sounding station (source: Deutscher Wetterdienst, data provided by University of Wyoming; http://weather.uwyo.edu/upperair/sounding.html, last access: 10 June 2021), we converted the temporal mismatch (Fig. 5a) between the radar measurements for each pixel in the common radar grid to a spatial difference 290 ( Fig. 5c). To estimate the impact of this spatiotemporal mismatch (hereafter spatiotemporal error) we subsequently used these spatial differences to calculate DWR values between pixels in the spatially higher resolved MIRA-35 Ze measurements (Fig.   5e). Concluding the DWR error assessment, we also analyzed the volumetric mismatch caused by the different beam widths of the two radars. For spatially heterogeneous scenes, this volumetric mismatch can lead to artificial DWR signatures caused by a non-uniform beam filling. Here, the spatially higher resolved MIRA-35 Ze measurements (30 m range gate length) along 295 the RHI cross section were used as a proxy to obtain the spatial heterogeneity of Ze perpendicular to the RHI cross section. In a first step, the local beam diameters for each pixel in the common grid are calculated for POLDIRAD (Fig. 5b) and MIRA-35 (Fig. 5d). Then, moving averages along the Ze cross sections from MIRA-35 are performed using the corresponding local beam diameters. Hence, at each pixel of the common radar grid two averaged MIRA-35 Ze values are obtained; one corresponding to the local beam diameter of MIRA-35 and one corresponding to the local beam diameter of POLDIRAD. 300 Subtracting the averaged Ze for each pixel, we were able to estimate the error caused by the volumetric mismatch between both radar beams (Fig. 5f).

Scattering simulations for ice particles 310
Since the simple Rayleigh approximation of Eq. (1a) cannot be used for snow, the scattering calculations were performed using the T-matrix method implemented in the Python package PyTMatrix developed by Leinonen (2014). PyTMatrix is a package that can be easily adjusted to the user's needs via functions and classes regarding the desired preferences for particle shape, size, orientation, particle size distribution (PSD) and wavelength. Calculated scattering parameters, e.g. backscattering cross-section of single particles, can be used to compute radar variables which can then be compared to radar measurements 315 for the purpose of the presented work. As we intended to retrieve the apparent shape (expressed in terms of aspect ratio), the size and the mass of the detected ice hydrometeors, we used aspect ratio (AR), median mass diameter ( ) of the PSD, and ice water content (IWC) as three degrees of freedom of the simulated ice particles for the development of look-up tables (LUTs). Different LUTs for several angles of radars geometry (Fig. 2) were created. Their values were then interpolated to fit all possible radar viewing geometries and used in the ice retrieval. The a priori assumptions used in the simulations are fully 320 described in the following sub-sections.

Aspect ratio
For the scattering simulations we assumed that ice hydrometeors can be represented by ice spheroids in PyTMatrix. The shape of the particles is defined using the aspect ratio parameter. This is the ratio of the horizontal to rotational axis of the particle. From the description of the simulated ice spheroids in Fig. 6, it is obvious that oblate (shaped like lentil) and prolate 325 particles (shaped like rice) have AR larger and lower than 1.0, respectively, as z axis is selected to be the rotational axis. Using this principle, the representative value of axial ratio = 0.6 from Hogan et al. (2012) is calculated as AR = 1.67 for oblate ice particles in this study. The closest value of our AR simulations grid to 1.67, is AR = 1.60 and therefore, this number was used as a reference value for the simulation plots (Fig. 7, Fig. 8 and Fig. 9a). In this study, we also use the axial ratio (called sphericity S) to compare retrieval results when oblate and prolate ice particles are assumed. S is defined as the ratio of the 330 minor to major axis and therefore, for oblates and prolates is found to be smaller than 1, while for spheres is equal to 1. In this work, all prolate ice particles were assumed to fall with their maximum diameter aligned to the horizontal plane (hereafter referred as horizontally aligned prolates or horizontally aligned prolate ice spheroids) and thus, to be rotated 90° in the yz plane (Fig. 6). Furthermore, small oscillations out of this plane with a standard deviation of 20° are included to consider the flutter of ice crystals. 335

Mass-size relation 340
In many ice studies, a mass-size relation m(D ) can be used to provide information about the mass of the ice crystals and therefore, their effective density with respect to their size. Mass m of an ice particle is connected to its maximum diameter with a power-law formula, where, : maximum dimension of a spheroid in meters (m), 355 : mass of the particle in kilograms (kg). Another m(D ) that we use is the aggregates from Yang et al. (2000) (the simple term aggregates will be used in this study). This mass-size relation is used for an aggregated collection of geometrical hexagonal columns. The construction of these aggregates is fully described in Yang and Liou (1998). Assuming spheroids to represent the ice aggregates, the density and thus, the mass of the particles can be calculated using the and of Eq.
(6). The is used to describe the diameter of a spherical water particle with the same mass as an ice particle with maximum 360 dimension .
where is taken from Table 2 in Yang et al. (2000) and as well as are in microns.

Particle size distribution
In all calculations of our study, ice particle sizes were assumed to follow the normalized Gamma particle size distribution 365 of Bringi and Chandrasekar (2001) with a shape parameter μ = 4: where, : the intercept parameter,  ).
Although DWR can be used to retrieve median size of PSD without being much affected by the density of the ice particles (e.g. Matrosov, 1998;Hogan et al., 2000), it can be also used to retrieve when a mass-size relation is investigated as is significantly affected by the m(D ) used. For instance, Leroy et al. (2016) found that is significantly affected by the b exponent of the m(D ) and thus, from the mass and the density of ice hydrometeors. As we aim to investigate how 380 the choice of different parameters affects the results of the ice retrieval (mass, shape and median size), we were also focused on the median size. Along with the shape parameter and intercept parameter , soft spheroids with a defined AR were used to calculate Ze and specific attenuation A at both radar wavelengths, and ZDR only at 54.5 mm as this radar variable is only provided by POLDIRAD. For the refractive index calculation, the Maxwell-Garnett mixing formula was used (e.g. Garnett and Larmor, 1904). In addition to Ze, A and ZDR simulations, the IWC of the PSD was calculated. The that 385 corresponds to this value of IWC served as a factor for rescaling to the desired IWC values used for the simulations. The rescale factor was used for the new estimation of Ze, A and ZDR. In Fig. 7   The same figure also shows scattering simulations for ice spheroids with double and half the density of aggregates m(D ) (red dashed and dash-dotted line, respectively). This influence of density on retrieval results will be further discussed in a sensitivity study presented in Sect. 4.3.1. In addition, Fig. 8 also shows our DWR-ZDR measurements for low elevation angles (0°-10°) and for all 59 RHI coordinated scans as a blue shaded density histogram. The dark blue dashed isoline frames the 95 th percentile of our radar observations. In Fig. 8 it becomes apparent that the BF95 m(D ) relationship cannot explain our 410 radar observations very well as ZDR values drop fast with increasing DWR due to the fast decrease of density with size.
Therefore, BF95 will be excluded from further analysis. To compare BF95 with aggregates, some retrieval results using BF95 can be found in Sect. 4.3.1. The mass-size relationship for aggregate ice particles can obviously better explain the density histogram of our DWR-ZDR dataset, especially for particles with DWR > 4 dB.

Look-up tables structure 415
Using the aggregates m(D ), we proceed to the development of LUTs for different values of , AR, IWC and geometries covering the radar elevation angles presented in Fig. 2. of the Gamma PSD was varied between 0.1-3.02 mm in a logarithmic grid of 150 points. A minimum sensitivity limit of DWR = 0.1 dB was used in the simulations leading to different minimum retrievable according to the m(D ) and the AR used, but also the radar viewing geometry (more details about this topic can be found in Appendix C). IWC was varied between 0.00001−1 g m −3 in a logarithmic grid of 101 420 points. Scattering properties for spheroid oblate and horizontally aligned prolate ice particles were calculated and saved in  Fig. 9. For the creation of both panels we assumed the simulated radar beams to be transmitted horizontally towards each other (horizontal-horizontal geometry). For Fig. 9a Fig. 9b we chose IWC to be 0.50 g m −3 . ZDR values are found to be invariant for all simulated values of IWC when AR, and shape parameter μ of PSD as well as the m(D ) remained the same. All the aforementioned principles 430 are then used to implement a method for retrieving ice microphysics information from radar measurements.

Correction of attenuation
Before using the radar observations for the development of the ice retrieval algorithm, they need to be corrected for beam propagation effects. One major influence is the attenuation by atmospheric gases and by hydrometeors. This holds especially 440 true for the Ka-band radar measurements. Although snow attenuation in C-band can be mostly neglected especially for low density particles and low snowfall rates (Battan, 1973; Table 6.4), the corrections will be done in both radar bands for reliability purposes.

Gaseous attenuation
Both MIRA-35 and POLDIRAD radar reflectivities are corrected for attenuation caused by atmospheric gases. 445 Atmospheric water vapor can cause considerable attenuation of radar signals especially at the higher frequency (35.2 GHz) of our instrumentation. The gaseous attenuation for both radar bands is calculated using line-by-line formulas proposed by ITU-https://doi.org/10.5194/amt-2021-216 Preprint. Discussion started: 21 October 2021 c Author(s) 2021. CC BY 4.0 License. R P.676-11 model (ITU-R P.676, 2016). The corrections are implemented for oxygen and water vapor lines where the attenuation is expected to be significant. The gaseous attenuation formulas use atmospheric pressure, temperature and relative humidity for each RHI, obtained from ECMWF ERA5 reanalysis data (Hersbach et al., 2018). 450

Hydrometeors attenuation
Next to the gaseous attenuation, the hydrometeor attenuation needs to be considered, too. For this purpose, an iterative approach using the ice microphysics results is developed. In this way, both radar reflectivities are corrected to mitigate the impact of hydrometeor attenuation on the ice microphysics retrieval. For this approach, the retrieval algorithm is used twice.
A more detailed description of this method will be presented in Sect. 3.4 along with the developed ice retrieval scheme. 455

Development of ice microphysical retrieval
For the development of the ice retrieval scheme, radar measurements of Ze, ZDR and DWR are compared with the PyTMatrix scattering simulations described in Sect. 3.2. The retrieved parameters are IWC in g m −3 , of the PSD in mm, and AR of the measured hydrometeors. Considering their different ranges, we used normalized differences between simulated and measured values of DWR as well as Ze and ZDR at C-band. By minimizing these differences, the best-fitting microphysical 460 parameters are found. The microphysics retrieval is implemented in two steps using the minimization of the two following cost functions: where with Δ the difference between simulated and measured parameter is denoted. 465 Both ZDR and DWR are invariant to IWC when same values of and AR are used. Therefore, and AR are found in the first step, whilst the IWC is constrained in the second step. While the DWR merely contributes to the retrieval of , the ZDR measurement narrows down the solution of aspect ratio of the ice particles. As Ze at C-band is less affected by attenuation compared to Ka-band, it is better suited to estimate the IWC. After the retrieval of size and shape AR in the first step, the algorithm continues with these values with the retrieval of IWC in the second step by minimizing the cost function 470 J2 in the LUT. Completing these two steps, the microphysics retrieval has retrieved not only preliminary , AR and IWC but also the specific attenuation A at both radar bands which is used for the total attenuation estimation. As the ice retrieval produces results using radar measurements interpolated onto a cartesian grid, the estimated A at C-and Ka-band needs to be converted from cartesian to the original polar coordinates for the calculation of the total attenuation for each radar band. After A, in polar coordinates, is integrated along the radar beams, the total attenuation for each radar dataset is calculated and 475 converted back from polar to cartesian coordinates. Then, it is used to correct Ze for both radars. In the next step, the final microphysical parameters such as AR, IWC and are retrieved using the corrected Ze from both bands as well as ZDR from POLDIRAD. Figure 10 shows the process of attenuation correction and retrieval in more detail. An output example of the ice microphysics retrieval scheme for the already introduced case study from 30 th January 2019 at 10:08 UTC (Fig. 11-12) can be found in Sect. 4.1. The total attenuation for this case study is presented as a supplement material accompanying this paper.

Retrieval of ice microphysics
59 pairs of coordinated RHI measurements from POLDIRAD and MIRA-35 were investigated. Here, we use a case study from 30 th January 2019 at 10:08 UTC, already presented before, to demonstrate the output of the ice microphysics retrieval scheme. The microphysical properties of the detected hydrometeors are shown in Fig. 11 (assuming oblate ice spheroids and 490 LUTs for different radar viewing geometries) and Fig. 12 (assuming horizontally aligned prolate ice spheroids and LUTs for different radar viewing geometries). In Fig. 11a and Fig. 12a, the retrieved AR is presented. Both plots suggest that in the cross-section of the cloud between the two radars and especially, in the area which is below 3 km height at a distance 0-12 km away from POLDIRAD, more spherical ice hydrometeors are present. Further away at a distance 12-20 km from POLDIRAD, more aspherical particles with AR = 4.0 and AR = 0.3, for oblates and horizontally aligned prolates respectively, were found. 495 The same result is also supported from S plots in Fig. 11c and Fig. 12c where S > 0.6 for the spherical particles between 0-12 km distance and S < 0.6 for the aspherical particles between 12-20 km distance. The retrieved AR and S could explain well the ZDR measurements in Fig. 3d where more spherical particles have ZDR < 0.5 dB, while aspherical particles have ZDR > 0.5 dB. Overall, the ZDR measurements could be replicated better with the retrieval results using oblate ice spheroids with RMSE = 0.18 dB (with the term RMSE, the mean Root Mean Square Error over all grid points is meant) between the fitted 500 and measured ZDR for the whole scene, against RMSE = 0.25 dB when horizontally aligned prolate ice spheroids were used.
In Fig. 11b and Fig. 12b, the retrieved increasing towards the ground is an indication that large ice particles are present below 3km height compared to smaller particles that are dominant at higher altitudes. This is obvious in both oblates and horizontally aligned prolates results. Comparing this plot with the DWR measurements from Fig. 3b, we observe that the retrieved could reasonably explain DWR. The correlation between DWR and is found again to be better when oblate 505 ice spheroids are used. The RMSE for the fitted-simulated and measured DWR is 0.54 dB when ice oblates are used in the simulations, while RMSE = 0.81 dB when the ice particles were assumed horizontally aligned prolates. Although DWR and ZDR measurements are combined for the shape and size retrieval (minimization of J1 in Eq. 8), the spatial patterns agreement between DWR-and ZDR-AR/S plots indicate the strong correlation of DWR and ZDR with size and shape, respectively. to IWC values higher than 1×10 −3 g m −3 . Hence, the sensitivity of Ze to mass of the ice particles is again indicated for both spheroid shapes (oblates and horizontally aligned prolates). Nevertheless, the Ze RMSE for horizontally aligned prolate ice https://doi.org/10.5194/amt-2021-216 Preprint. Discussion started: 21 October 2021 c Author(s) 2021. CC BY 4.0 License. particles, is 0.34 dB whilst the RMSE is found 0.19 dB when ice oblates are used. All RMSE which serve as residual values for the ice retrieval are collected in Table 2. The lowest RMSE are found when oblate ice spheroids are assumed. Figure 13 shows averaged profiles of for both shape assumptions for the whole cloud cross-section measured on 30 th January 2019 515 at 10:08 UTC. The averaged profile for oblate ice spheroids is plotted in dark red, while the averaged profile for horizontally aligned prolate ice spheroids is plotted in red. Between the two shape assumptions the prolate assumption gives an on average by 0.36 mm larger profile. The respective shaded areas indicate the estimated error of when the calibration uncertainty of Ze and estimates of the spatiotemporal and non-uniform beam filling error discussed in Sec. 3.1.2 are considered. Here, the measurement errors are propagated to using a min-max approach: after the sum of the Ze 520 calibration uncertainties for POLDIRAD (±0.5 dBZ) and MIRA-35 (±1.0 dBZ) is added and subtracted to DWR values, the DWR error estimates for the spatiotemporal and non-uniform beam filling error are added. In that way we obtain two additional profiles which serve as upper and lower boundary for the estimate. For the investigated case study, the average error is estimated to be ±0.44 mm for oblate spheroids, while it is estimated to be ±0.48 mm for prolate spheroids.

Statistical overview
After investigating 59 pairs of RHI scans from three different snow events, we created stacked histograms with respect to temperature for a deeper insight of the retrieval. Particularly, all RHI measurements from 9 th January 2019 between 11:18−15:08 UTC, 10 th January 2019 between 09:08−17:08 UTC and 30 th January 2019 between 10:08−12:38 UTC were 545 compared to scattering simulations in LUTs for oblate and horizontally aligned prolate ice particles. Statistical results of the retrieved S, and IWC are presented in Fig. 14. In the first three panels of this figure, results for the retrieved parameters assuming oblate particles are presented, while in the last three panels, the same kind of results for horizontally aligned ice prolates are shown. At first glance, the majority of ice hydrometeors are found to be neither very spherical nor very elongated (green color panel plots, first column in Fig. 14). When oblate ice spheroids are used in the scattering simulations, the greater 550 part of retrieved S values is found to range from 0.3 to 0.6. With the assumption that ice hydrometeors can be represented by horizontally aligned prolates, the distribution is narrower with the majority of the detected particles to have S values ranging between 0.4−0.6. From the retrieval (red color panel plots, second column in Fig. 14), the results for oblates showed a narrower distribution shifted towards lower median mass diameters, while for horizontally aligned prolates the retrieved values are more broadly distributed towards larger values of (median value of both distributions can be found in Table 3). The 555 histograms for the retrieved IWC (blue color plot panels, third column in Fig. 14) are plotted using logarithmic x axis for visualization purposes. The statistical results showed that the greater part of the detected ice hydrometeors is found to have IWC values 1×10 −4 −1×10 −1 g m −3 (−4 to −1 in the logarithmic axis) when oblate ice spheroids were assumed. For horizontally aligned prolate ice particles, most of the detected ice hydrometeors are found to have IWC values between 3×10 −5 −3×10 −2 g m −3 (−4.5 to −1.5 in the logarithmic axis). The spikes in both and IWC histograms are merely caused from the strong 560 discrepancies between simulated and measured radar variables during the minimization of J1 and J2 in Eq. (8) color shades in all panel plots denote the different temperature groups in which the detected hydrometeors are separated. For both shape assumptions, it is observed that when temperature drops below −25 °C ice hydrometeors populations with IWC < 3×10 −3 g m −3 dominate the particles distribution. Furthermore, for higher temperatures the greater part of the log10IWC 565 distribution is shifted towards larger values in the logarithmic axis, denoting larger retrieved IWC.
For better interpretation of the ice retrieval results during the three investigated snow events, we further proceed with the calculation of some descriptive statistics presented in Table 3. The median of the retrieved properties for the observed particles distributions was calculated. With the assumption that the detected ice particles can be represented by oblate spheroids, we calculated the median retrieved sphericity S = 0.400, the median retrieved = 0.98 mm and the median retrieved IWC = 570 4×10 −3 g m −3 . On the contrary, when the observed hydrometeors were assumed to be horizontally aligned prolate spheroids, the median retrieved sphericity, the median retrieved median mass diameter and the median retrieved ice water content, were found S = 0.500, = 1.45 mm and IWC = 1.3×10 −3 g m −3 , respectively. Although the two median S are quite close, there are differences in the median and IWC between oblates and horizontally aligned prolates. For the latter, the median was calculated larger and the IWC was calculated lower than the respective values for oblate ice spheroids. Therefore, the shape 575 assumption seemed to affect the retrieved microphysical properties of the ice particles (also shown in Sect. 4.1). In Table 3 the 10 th and 90 th percentile of the detected hydrometeors retrieved parameters can be also found.

Discussion 585
One limitation of the current version of the ice retrieval is the need to make two significant a priori assumptions about the particle properties. The first assumption (discussed in Sect. 4.1) concerns the choice if we assume oblate or horizontally aligned prolate ice spheroids. In addition to the shape, we have to assume a suitable m(D ) relationship for the prevalent ice particles. For the three investigated snow events the selection of aggregates m(D ) over the BF95 has been partially discussed in Sect. 3.2. An extended explanation for this selection is presented in Sect. 4.3.1. 590

Unknown mass-size relationship
From the two m(D ) relations initially used in the scattering simulations, only the aggregates m(D ) was systematically used for the statistical analysis of this study. The BF95 mass-size relation was found to model too low ice particle densities. Although ice crystals are known to have lower densities when they grow larger (except for graupel or hail), BF95 prescribes near-zero density values for large particles. This leads to very low simulated ZDR values with increasing 595 particles size (Fig. 8). The ice retrieval results for the examined case study, using LUTs for oblate ice crystals and BF95 masssize relation, are presented in Fig. 15 along with the residual values of ZDR, DWR and Ze, expressed using RMSE values, in Table 4. The RMSE for ZDR and Ze are quite low and in the same order of magnitude like the RMSE for aggregates m(D ) for both oblate and horizontally aligned prolate shape assumptions (Table 2). However, the retrieved AR and S ( Fig. 15a and Fig. 15c) could not really explain ZDR measurements (Fig. 3d). The AR is almost unrealistically high, suggesting e.g. plates, 600 for the greater part of the cloud cross-section using BF95 m(D ). The RMSE for DWR with 2.84 dB was found to be quite high, suggesting that the retrieved (Fig. 15b) could not replicate DWR measurements (Fig. 3b). On the other hand, IWC ( Fig. 15d) showed a good agreement to the radar measurements as it could explain well POLDIRAD Ze (Fig. 3c). The retrieved values were found to be larger than the IWC values retrieved using the aggregates m(D ) for both shape assumptions.
Overall, the plots of retrieved parameters as well as the RMSE for ZDR, DWR and Ze reveal that the output of the ice retrieval 605 using the aggregates m(D ) and LUTs for oblate ice spheroids ( Fig. 11 and Table 2) were found to better explain the radar observations compared to the BF95 assumption. Figure 16 shows the residuals between the simulated and measured DWR for aggregates ( Fig. 16a) and BF95 m(D ) (Fig. 16b). For aggregates m(D ), the residuals are evenly distributed around 0 (mean value of +0.08 dB) suggesting that this mass-size relation can better explain our measurements in this case. In contrast, the measured DWR appeared to be higher than the simulated one for BF95 for the larger part of the cloud cross-section (reddish 610 areas) with a mean value of -1.45 dB.
To further investigate the significance of the m(D ) relation for the retrieval result, we conducted a small sensitivity study using the aggregates assumption from Yang et al. (2000) which suggests an almost constant effective density, ρeff, (approximately ρeff = 0.2 g cm -3 ) of ice particles with increasing size. Using this value as a reference, we created LUTs for oblate ice particles, once with twice and once with half the density of the aggregates mass-size relation (simulations shown 615 also in Fig. 8 with red dashed and dash-dotted lines). Retrieval results for ice oblates with twice the density are shown in the top panels of Fig. 17, while the bottom panels show the results for ice oblates with half the density of aggregates. Corresponding RMSE values for Ze are given in Table 4. Focusing on the IWC retrieval, we obtain lower IWC values (with an RMSE = 0.28 dB for Ze) for ice particles with twice the density of aggregates than the IWC values retrieved in Fig. 11d. Analogously, we retrieve larger IWC (with an RMSE = 0.15 dB for Ze) for ice particles with half the density of aggregates. In Table 4 the 620 residual values expressed as RMSE for DWR and ZDR can also be found. When the ice spheroids are denser, the DWR RMSE is 0.56 dB, while the DWR RMSE is 0.64 dB for the less dense ice spheroids. The RMSE for ZDR are found to be the same in both cases. However, the denser aggregates suggest the presence of more spherical particles compared to more aspherical particles when less dense aggregates are assumed.
The aforementioned examples indicate the limitations of the ice retrieval to provide realistic microphysics information 625 when a fixed mass-size relation is used. To overcome this weakness, but still keep our approach simple, a combination of

Particles shape and viewing geometry
The retrieval results in both Fig. 11 and Fig. 12 showed that some areas are affected more than others from the shape assumption inside the cloud cross-section. For instance, in the region above the Ka-band radar, the retrieved was found to be lower when oblate ice spheroids were used compared to horizontally aligned prolates. Conversely, the lower values of for ice oblates lead to a higher retrieved IWC. In these areas, the use of the polarimetric signature from POLDIRAD, i.e. ZDR, 650 is furthermore found to be crucial: not only to constrain the shape but also to reduce ambiguities between size and mass of the detected ice hydrometeors. To further evaluate the performance of the retrieval, 2d density histograms between retrieved and measured DWR were created for the oblate shape assumption, including all 59 RHI scans. The histograms are presented in Fig. 18 for elevation angles θC = θKa = 30° (Fig. 18a) and θC = 10°, θKa = 90° (Fig 18b). The first observation geometry (Fig.   18a) is a region located between both radar instruments, while the second one (Fig. 18b) located directly above the Ka-band 655 radar site. On top the density histograms, the DWR-D simulations for different values of AR are plotted with grey lines. In (Fig. 18a), the simulations as well as the retrieved are more closely distributed than in (Fig. 18b). The close distribution of the DWR-D lines in Fig. 18a suggests that the shape and the size retrieval are not strongly correlated in the region between both radar systems since the simulated DWR does not change much with AR. In the region above the Ka-band cloud radar, however, polarimetric measurements from the C-band weather radar POLDIRAD (i.e. ZDR) help to narrow down the solution 660 space of the size retrieval (Fig. 18b) by providing information about the ice particle shape. This behavior is fully explained in Fig. 19 where the radar beams passing through ice oblate spheroids are drawn. In Fig. 19a, the radar beams from the two instruments penetrate oblate spheroids with different AR with the same elevation angle θC = θKa = 30°. From the radar viewing geometry this is supposed to happen in cloud regions located between both radar instrument. In Fig. 19b, the elevation angle for C-band is θC = 10°, while the Ka-band points to zenith with θKa = 90°. In both cases, the radar beams penetrate three 665 different shaped ice oblates that are aligned with their maximum dimension in the horizontal plane and which are chosen to have the same . In Fig. 19a, the length of the Ka-band beam does not change dramatically inside the oblate ice particle.
In Fig. 19b, however, the MIRA-35 beam length through the oblate ice particle, and hence the DWR, is very sensitive on the aspect ratio. Therefore, the DWR-D relationship becomes quite sensitive to AR in this area, especially when particles are assumed to be horizontally oriented. From similar geometric considerations, the region between both radars at very low 670 elevation angles is another region in which the size retrieval benefits from the AR constraint. In the case of variable ice crystal shapes, ZDR from POLDIRAD is, thus, very helpful for the estimation.

Conclusion
In the present study, we combined dual-wavelength radar observations from the spatially separated weather radar POLDIRAD and cloud radar MIRA-35 to estimate the size of ice hydrometeors. Introducing a novel approach, we used the differential radar reflectivity from the weather radar to constrain the particle shape during the particle size retrieval. To this end, we calculated scattering properties for a variety of ice particles using PyTMatrix with AR, and IWC as degrees of 685 freedom for the simulated ice spheroids. Scattering simulations for all possible viewing geometries between the cross-section of the radar instruments were then compiled in LUTs and compared to radar observations implementing an ice microphysics retrieval scheme. Using the microphysics retrieval, we obtained AR/S, and IWC in ice cloud regions. Next to these parameters, we also calculated the attenuation by ice hydrometeors and corrected our radar observations. Besides attenuation, the uncertainty of the radar calibration has been considered. In addition, the impact of the spatiotemporal mismatch between 690 RHI scans and the volumetric mismatch between the radar beams on the measured DWR were analyzed. All aforementioned errors were subsequently propagated through the retrieval to obtain an error estimation.
Three snow events from January 2019 were used to test the ice microphysical retrieval. The retrieved parameters for shape, size and mass could reasonably explain the radar measurements of ZDR, DWR and Ze when the detected ice particles were assumed to be represented by oblate spheroids (smaller RMSE and retrieval errors than for horizontally aligned prolates) and 695 https://doi.org/10.5194/amt-2021-216 Preprint. Discussion started: 21 October 2021 c Author(s) 2021. CC BY 4.0 License. when the aggregates m(D ) from Yang et al. (2000), instead of the well-known BF95 assumption, was used. In the course of this study, the density of ice spheroids from BF95 turned out to be too low with increasing size. For that reason, BF95 could not produce pronounced polarimetric signals. Although the aggregates m(D ) could better explain our ZDR-DWR observations, their assumption suggests an almost constant density with increasing particle size, i.e. small ice crystals (columns or plates) appear to have the same density as larger ice particles (aggregates). Therefore, we still need a m(D ) relation 700 which describes a more realistic function between density and size. Here, additional measurements, e.g. Doppler velocity of ice hydrometeors, could be exploited in future studies to provide a more variable m(D ) relation instead of a fixed one. In conclusion, the assumption of the m(D ) relation together with the decision for oblate or prolate particles had the biggest impact on the retrieval. Within its uncertainty, the radar calibration has only secondary importance, while errors due to spatiotemporal and volumetric mismatches are considered to be even less important to the average retrieval profile. Non-705 uniform beam filling effects, however, can locally have strong impacts (of several dB) on DWR measurements. Subsequent studies certainly need to explore this effect for spatially separated radars in more detail and need to develop techniques to detect and filter out these regions.
Nevertheless, promising microphysics information can be obtained from the combination of dual-wavelength and polarimetric measurements from spatially separated radars. This combination, i.e. DWR and ZDR, can reduce the ambiguity 710 in retrievals caused by the variable aspect ratio AR of ice particles. While we found some influence of AR on retrievals in the region between both radar instruments and at high elevation angles (e.g. 30°), ZDR from POLDIRAD was very helpful to improve retrievals above the Ka-band cloud radar, or in the areas between both systems where the elevation angles of both radars are low. In these regions, ZDR measurements are essential to reduce the uncertainty in retrieval from DWR measurements of horizontally aligned ice oblates. 715 The current version of the ice microphysics retrieval scheme considers only dry ice particles. In future studies, this methodology will be extended to include wet particles as well. In this way, we aim for a better understanding of microphysical processes of ice growth, such as aggregation or riming, to improve their representation in future weather and climate models.
https://doi.org/10.5194/amt-2021-216 Preprint. Discussion started: 21 October 2021 c Author(s) 2021. CC BY 4.0 License. cases and as we assume that riming or melting ice is unlikely to occur, all hydrometeors above 4 km (height above MSL) and/or above ML were accounted dry. When the criteria were not met, the isotherm of 0 ºC was used as an auxiliary information 735 for ice above that height. The temperature data were obtained from the Oberschleißheim sounding station (about 13 km north of Munich), source: Deutscher Wetterdienst, data provided by University of Wyoming; http://weather.uwyo.edu/upperair/sounding.html, last access: 10 June 2021). Although the thresholds used in the ice mask were evaluated in precipitation cases where a ML was observed, the investigation of more precipitation cases to obtain more precise thresholds is needed. The necessity of sharpening the ice mask's thresholds is highlighted from Fig. B1 where an example of 740 ZDR observations during a thunderstorm observed over Munich on 7 th July 2019 is presented. Figure B1a shows ZDR without the application of any noise filters (described in Sect. 3.1), while in Fig. B1b the filtered and masked ZDR is plotted. Figure   B1c presents the origin of the masked ZDR values. On 7 th July 2019 at 08:22 UTC a melting layer was observed at 3 km and thus, ZDR was masked for ice hydrometeors at that height. However, the greater part of the cloud cross-section is masked using the 0 ºC isotherm revealing the need for more precise ice thresholds with evaluating more case studies with mixed-phase 745 cloud cross-sections. In the current study, only few ice hydrometeors were detected above the 0 ºC isotherm, making the sharpening of ice mask's thresholds not so crucial.

Appendix C: Estimation of minimum retrievable
For sensitivity purposes regarding DWR measurements we had to consider a minimum in our simulations. For this reason, we assumed a minimum value of DWR = 0.1 dB that can be observed by the two radars. The minimum retrievable depends not only on the viewing geometry of the two radars but also on the AR and the m(D ) used for the calculation of 755 the ice spheroids density. In Fig. C1 examples of the minimum retrievable for different radar geometries and m(D ) are presented. For this plot the aggregates m(D ) is used for red and dark red line plots. When the two radar beams are both simulated to be emitted horizontally the horiz-horiz definition is used, while when C-band beam is simulated be emitted horizontally and Ka-band towards zenith the horiz-vert label is used in the legend. As all ice spheroids are assumed to be aligned to the horizontal plane with small oscillations of up to 20° out of this plane, the minimum retrievable is, in general, 760 https://doi.org/10.5194/amt-2021-216 Preprint. Discussion started: 21 October 2021 c Author(s) 2021. CC BY 4.0 License. smaller when the radar beams are passing through the ice spheroids from the side. Assuming C-band beam emitted horizontally and for ice particles with the same size, Mie effects can be stronger for Ka-band beam when it penetrates the particles from the side (horiz-horiz geometry) rather than from below (horiz-vert geometry), as the beam path is longer inside the particle.
For horiz-horiz geometry, Ze,Ka values are lower and thus, DWR is higher than for horiz-vert geometry for same particle size. Therefore, the lowest minimum retrievable is smaller in horiz-horiz than in horiz-vert geometry. From the comparison of 765 red (aggregates m(D )) and blue (BF95 m(D )) color line plots, in which the radar beams are simulated to be emitted horizontally (C-band) and vertically (Ka-band), the minimum retrievable for aggregates m(D ) is larger compared to BF95, due to the higher effective density of aggregates. The less dense the particles are, the smaller the will be for the minimum DWR threshold of 0.1 dB. For the same geometry (C-band emitted horizontally and Ka-band emitted vertically) and both mass-size relations, the more aspherical the particles the larger the minimum retrievable due to the larger cross-section 770 of the horizontally aligned spheroids for the Ka-band beam. 10.24381/cds.bd0915c6. The author did not download the data to distribute them. The results contain modified Copernicus Climate Change Service information 2020. Neither the European Commission nor ECMWF is responsible for any use that 780 may be made of the Copernicus information or data it contains. Radar data from POLDIRAD weather radar from DLR as well as MIRA-35 cloud radar from LMU are available upon request to the authors.

Author contribution
In the framework of the IcePolCKa project ET, FE, MH and GK performed radar measurements during precipitation events.
ET developed the method used in this work and wrote the final paper under the consultation of FE. SG and TZ contributed to 785 this work with productive discussions during the development of the ice microphysics retrieval. All authors contributed helpful comments to the manuscript. https://doi.org/10.5194/amt-2021-216 Preprint. Discussion started: 21 October 2021 c Author(s) 2021. CC BY 4.0 License.