Spatially and temporally high-resolution polarimetric weather radar measurements provide the undisputed core information for an in-depth evaluation of NWP models. In addition to improvements in quantitative precipitation estimation, polarimetric radars provide insights into precipitation microphysics and the 3D distribution of hydrometeors. This study exploits measurements of the polarimetric X-band Doppler radar (BoXPol) in the city of Bonn, Germany. It is installed at 50.73052∘ N, 7.0716638∘ E on a 30 m tall building next to the Institute for Geosciences, Department of Meteorology, University of Bonn, at 99.9 m above mean sea level (MSL) see also.

and introduced so-called quasi-vertical profiles (QVPs) to present polarimetric radar observations in a time versus height format. To generate QVPs, the azimuthal median is calculated from standard conical scans measured at higher elevation angles, and the range coordinate is transformed into height. Here we use the 18∘ elevation scan with 100 m range resolution. One key advantage is the inherent noise reduction from the averaging process, which sometimes enables the detection and quantification of small but meaningful vertical gradients in the polarimetric radar variables. Furthermore, QVPs are well suited to study the temporal evolution of processes and to directly compare with other mostly vertically pointing sensors and with model simulations in particular. QVPs represent the average conditions within the cone spanned by the radar scan with decreasing resolution with height. If the precipitation is not uniform within the cone, errors from the averaging process are larger, but the advantage of a significant noise reduction clearly dominates for microphysical studies of widespread stratiform rain as presented in this paper.

The variables – horizontal reflectivity ZH, differential reflectivity ZDR and cross-correlation coefficient ρhv – are masked where ρhv<0.7 to exclude clutter and bins without significant weather signal from the attendant QVP calculations. Calibration offsets for ZH and ZDR are estimated following and . After differential phase ΦDP is masked where ρhv<0.95 and ZH<0 dBZ, the measurements are smoothed with a median filter using a 1.1 km moving window (i.e. including 11 range bins). The melting-layer detection algorithm of is applied to each ray of smoothed ΦDP and the identified bins are removed. A linear interpolation of ΦDP across the melting layer is performed that excludes the component of backscattering differential phase δ and enables the estimation of an average specific differential phase KDP in this region. Least-squares fitting on a moving 3.1 km window is used to estimate KDP based on the smoothed ΦDP without melting-layer contamination. Finally, the QVP of KDP is calculated using the same azimuthal median approach.

We study an event of widespread stratiform rain passing the Bonn area and monitored by BoXPol on 16 November 2014 between 00:00 and 10:00 UTC. Figure  shows the QVPs during this time, illustrating only moderate reflectivities ZH around 20 to 25 dBZ near the surface and attendant ZDR values typical of rain. The melting layer is observed at around 1.5 km and significant ZH values are observed up to 6 km. Enhanced ZDR values up to 0.4 dB indicate pristine crystals near the cloud top, while decreasing ZDR, together with increasing ZH toward lower levels, indicates ongoing aggregation or riming processes. Enhanced KDP values above the melting layer are observed in the first half of the observation period especially, pointing towards enhanced number concentrations of ice particles and thus ice water content (IWC), which is in line with higher ZH below the melting layer and thus higher rain rates in the first half of the observation period. ρhv is mostly close to 1, except for in the melting layer where values decrease to 0.92 to 0.95, in line with statistics of polarimetric variables performed in stratiform precipitation observations at X band . Pristine crystals, together with decreasing signal-to-noise ratio, also result in a ρhv reduction near the cloud top.

This study evaluates the partitioning of total ice water content in the Consortium of Small-scale Modelling (COSMO) model with a two-moment bulk microphysics scheme (henceforth, SB2M). The extended version of the SB2M is used, which includes a separate hail class described in , and . An additional dynamic saturation adjustment was turned on to reduce the time step sensitivity of model microphysics and precipitation . More details about the dynamical core and other physical schemes are available from .

SB2M predicts the mass densities ρq and number densities ρn of cloud droplets, rain, cloud ice, snow, graupel and hail, which are the zeroth and first moments of the particle mass distribution (PMD) that is assumed to follow a modified gamma distribution (MGD): 1f(x)=N0xμexp⁡(-λxν), with x being the particle mass and parameters μ and ν determining the shape of the distribution. The specific hydrometeor mass q and specific number n can be derived by q=ρq/ρ and n=ρn/ρ, with ρ being the total density (air, vapour and hydrometeors).

The size–mass and velocity–mass relations of different hydrometeors are parameterised by the following power laws: 2D=agxbg,3vT=avxbv, with (maximum) particle diameter D; terminal fall velocity vT; and parameters ag, bg, av, and bv.

Note that the PMD given in Eq. () is equivalent to the modified gamma particle size distribution (PSD) 4g(D)=N0bgag-1bg(μ+1)Dμ+1bg-1exp⁡-λagνbgDνbg, when transformed to the diameter space using the power law in Eq. () e.g..

The shape parameters μ and ν of the MGD remain constant for each hydrometeor class, and N0 and λ can be diagnosed from the two prognostic moments. However, if rain is below cloud base in the sedimentation–evaporation regime, its μ depends on the mean diameter to better capture the strong effects of these two processes on the shape of the rain size distribution.

To mitigate unphysical effects on the mean spectral particle mass x‾=q/n coming from the separate advection and sedimentation of q and n, it is very important to impose some minimum and maximum allowable mass limits for x‾ (xmin⁡ and xmax⁡) at relevant places during the model time stepping. This is done by clipping n so that x‾ stays within [xmin⁡,xmax⁡]. For reference, all fixed parameters which were used in this study are summarised in Table .

The cloud droplet nucleation parameterisation is based on the lookup table of , which parameterises the number of activated cloud droplets just above cloud base depending on the updraught speed w, ambient cloud nuclei (CN) concentration, mean and standard deviation of an assumed log-normal dry CN size distribution, and aerosol solubility, based on 1D rising-parcel simulations with a very detailed bin microphysical scheme. For this study, continental aerosol with CN concentration NCN=1700×106 m-3, log-normal standard deviation ln⁡(σs)=0.2, mean radius of aerosol size distribution R2=0.03µm and solubility ϵ=0.7 is used; w is chosen to be the prognostic grid-scale updraught because the table values already include subgrid effects of a disturbed turbulent flow. Similarly, the ice nucleation parameterisation is based on and . The large-scale concentration of aerosols of this parameterisation for heterogeneous ice nucleation are chosen as Ndust=162×103 m-3, Nsoot=15×107 m-3 and Norganics=177×107 m-3.

For ice-phase processes, interactions between different hydrometeors involving collisions (e.g. riming, aggregation, ice multiplication) play an important role in the partitioning of the IWC. These interactions are parameterised using collision integrals and collision and sticking efficiencies , which are activated according to certain particle mean size and temperature thresholds. In this study, we focus on two of these parameters, motivated by the case study below.

The first parameter is the critical mean diameter of cloud ice particles Dice for conversion to snow through aggregation of cloud ice. If the mean cloud ice size, i.e. 5D‾i=agi(qi/ni)bgi, is larger than Dice, self collection leads to the production of snow, otherwise ice remains as ice. agi and bgi are the size-mass parameters for cloud ice, and qi and ni are its specific mass and number, respectively. Perturbations in Dice affect the ice to snow partitioning and also the size of the resulting snow particles.

The second parameter is the temperature threshold Tgr below which the production of graupel by riming of cloud ice and snow with supercooled rain is allowed. If T<Tgr, a certain part of the rimed cloud ice and snow particles are converted to the graupel class, otherwise no cross-class transfer happens. This pathway for graupel production may also be slightly controlled by Dice because larger snow exhibits more riming.

As with most bulk cloud microphysical schemes without a prognostic melted fraction, SB2M most likely systematically underestimates the distances that melting particles may fall until melting completely (i.e. the melting-layer thickness). This is because SB2M instantaneously transfers the amount of meltwater formed during one model time step from cloud ice, snow, graupel and hail to the rain class. As a consequence, the melting hydrometeors shrink too quickly, fall too slowly and completely melt too quickly in the SB2M. We acknowledge this limitation in the SB2M scheme.

Evaluating output of NWP models with observations requires their data in a consistent and comparable parameter space, typically either in model space (e.g. hydrometeor mass and number densities) or observation space (e.g. radar reflectivity and further polarimetric radar variables). Conversion of the numerical model output into radar observables is done by means of a polarimetric radar forward operator. Particularly for model evaluation, it is important that the model and forward operator (FO) are consistent regarding parameters that affect the forward modelled observables. Many of these, including the phase partitioning of hydrometeors during melting, the shape and orientation of particles, and the heterogeneous microstructure of frozen hydrometeors, are insufficiently constrained by the direct model output, and assumptions need to be made. When implicit assumptions exist in the numerical model, it is advantageous to ensure that the FO makes use of equivalent assumptions.

In this study, we apply the Bonn Polarimetric Radar forward Operator (B-PRO v2.0) . B-PRO is a research-oriented polarimetric radar FO, which has been built onto an early, non-polarimetric version of EMVORADO , the German Meteorological Service's operational radar FO. Below we explicate the B-PRO implementation and settings directly related to polarimetry. Further aspects are detailed in Appendix .

B-PRO calculates and outputs polarimetric radar parameters on the spatial grid given by the numerical model field input. This means that no beam integration and antenna pattern are taken into account, and hence the output ZH and ZDR are to be considered unattenuated (or perfectly attenuation-corrected) variables. In addition, no simulated measurement errors are included, making the output variables take on their intrinsic values. A software interface between the COSMO model and B-PRO ensures consistent microphysics, specifically the same hydrometeor-class-dependent particle size distributions and size-mass relations used in the SB2M in Eqs. () and () and Table . The shape and orientation of the hydrometeors, which are the primary properties that characterise anisotropic scattering, are not at all constrained by the COSMO model. Instead, different parameterisations are applied by the FO. Apart from the cloud liquid class, hydrometeors are modelled as homogeneous oblate spheroids. Their shape is described by the aspect ratio (AR), defined here as the ratio of the semi-minor and semi-major axes of the spheroids (following ). The spheroids are assumed to have no preferential orientation, with their maximum cross section parallel to the horizon on average and with canting angles α out of the horizontal following a Gaussian distribution with a specified width σcanting, i.e. μα=0∘ and σα=σcanting see. The applied hydrometeor-class-dependent parameterisations for the frozen hydrometeors are given in Table . For rain, the AR parameterisation of and σcanting=10∘ is used following . The shapes and orientations of melting particles are derived as melting fraction-dependent weighted-mean values of the respective frozen hydrometeor and rain (see Appendix  for details on the melting model). Scattering properties of the spheroids are calculated applying the T-matrix method for particles with a fixed orientation for canting angle α=0∘, with the properties of particles with an orientation distribution then derived using the angular moments method of .

Compared to , several modifications to B-PRO have been implemented within this study. Melting particle shape and orientation calculations have been adapted to consistently follow the approach of . For cloud ice, the fairly spherical and unoriented crystals (AR = 0.9–0.7, σcanting = 40∘) resulting in insignificant polarimetric signatures have been replaced by more oriented (σcanting = 12∘) and more non-spherical particles following a shape parameterisation by . In addition, the range of sizes considered for cloud ice, representing single crystal particles in COSMO, has been largely extended (from the original upper integration limit, Dintupper, of 200 µm to 4 mm) consistent with COSMO (mean) size limits of cloud ice and providing a better coverage of particle sizes contributing to the cloud ice bulk properties. The considered size range of snow, representing aggregated ice particles in COSMO, was also found to not sufficiently cover the sizes contributing significantly to bulk scattering (both regarding single particle scattering properties as well as the PSD-predicted number density). Therefore, the size ranges of snow, graupel and hail were extended. The calculation of effective density and volume-equivalent diameter of the spheroids, which are inputs to the particle effective refractive index and T-matrix calculations, respectively, from D, x and AR have been revised and corrected for both frozen and melting hydrometeors.

A summary of the shape and orientation parameterisations used as a baseline in this study (B-PROdef) is given in Table . The table further details implementations or choices for further FO parameters like the melting scheme, effective medium approximation (EMA; see also Appendix ) and particle size ranges.

In this study we use the HCA of , hereafter referred to as HCA-Pejcic. In this two-step method, agglomerative hierarchical clustering is first applied to the polarimetric radar observations and Δz (i.e. the difference between observation height and 0 ∘C level). With the sigmoid transformation used in , Δz separates liquid and solid regions with a smooth transition around the freezing level height. The resulting clusters are identified based on state-of-the-art HCAs and merged into categories comparable to the model hydrometeor classes for rain, snow, cloud ice, graupel, hail and wet snow. In the second step, a modified method of is used to derive hydrometeor percentage (HP). Here, we use not only the centroids (mean values of the polarimetric moments) of the clusters as done originally, but we also calculate the covariance of the five dimensional observations. Instead of the exponential distribution used by , we use a multivariate normal distribution for the determination of the HP. This allows us to use the calculated centroids and covariances to determine the shape of the individual hydrometeor probability functions in five dimensions without parameterisation. Furthermore, the membership-function-based HCA of and adapted by (HCA-Zrnic) and (HCA-Dolan) are also used for comparison. HCA-Zrnic uses hydrometeor categories of vertically aligned crystals, horizontally aligned crystals, wet snow, dry snow, graupel/hail, rain/hail, hail, large drops, heavy rain, moderate rain and light rain. HCA-Dolan uses categories of big drops/melting hail, hail, high-density graupel, low-density graupel, vertically aligned ice, wet snow, aggregates, ice crystals, rain and drizzle. In these two methods, theoretically calculated membership functions are determined for each hydrometeor type and for each polarimetric variable and a temperature variable. As explained in and , the dominant classes are then determined by the highest score calculated over the membership functions.

Synthetic radar observations of the CTRL run are derived by running the FO with the B-PROdef setup using the model outputs. To minimise the FO computational cost, the domain was cropped to only cover the QVP extent, which is simply governed by the maximum diameter of the conical mask near the top of the precipitating system. FO calculations were performed for each 5 min step during 00:00–10:00 UTC, and QVPs were produced from the FO radar variable fields using a conical mask (see above). The resulting QVPs are shown in Fig. .

The cloud-ice-dominated upper levels show reflectivities up to 10 dBZ, similar to the observations (see Fig. a). The increase of ZH with decreasing height through the snow-dominated layers and towards the melting layer is somewhat stronger compared to the observations, with ZH reaching up to 30 dBZ just above the melting layer compared to ≤ 25 dBZ in the observations. The maximum ZH in the melting layer agrees fairly well with the observations, but the melting layer appears wider in the model-simulated radar data compared to the observations. This pattern continues below the melting layer, where the synthetic ZH is significantly higher and high ZH appear over much longer times.

Cloud ice, located at heights > 5 km, shows a clear polarimetric signature with ZDR from 0.2 up to 2 dB, KDP up to 0.2 ∘ km-1 and ρhv slightly decreased below 1. This is qualitatively in agreement with the observations; quantitative comparisons are not meaningful at these heights due to significant uncertainties in the observations. The snow-dominated layers are characterised by an evident lack of polarimetric signals in the synthetic observations, in clear disagreement with the observations showing KDP values of 0.1–0.2∘/km and ZDR values ranging from 0.2–0.5 dB. Within and below the melting layer, synthetic ZDR reaches a clearly higher maxima (2 to < 3 dB) compared to observations, although the range and frequency of KDP values agree fairly well there. Synthetic ρhv are clearly not similarly reduced in the melting layer as in the observations but show similar qualitative patterns. Below the melting layer, ρhv exhibits clearly lower values than in the observations.

The matter of synthetic ρhv in most regions being very close to 1 while observations show reduced values can likely be explained by shortcomings in the FO assumptions on hydrometeor shape and orientation. ρhv describes the correlation between the horizontally and vertically polarised returned radar signals and is sensitive to particle shape, composition and orientation; hence, it provides information about the diversity of the scattering particles within the observed radar volumes . This means that overestimating ρhv indicates too little variability of assumed hydrometeor shapes and orientations in the FO. Assuming hydrometeors of all categories and sizes to be homogeneous spheroids with identical shapes, at least for all particles of one category and size, as is the state of the art for the majority of polarimetric radar FOs, is clearly a simplification of the shape and microstructure variability of real-world hydrometeors. Simplifications are typical and necessary in modelling; however, the persistent overestimation of ρhv suggests that the current assumptions oversimplify and produce too little variety in the structure of particles and therefore fail to sufficiently reproduce observed ρhv levels. Similar issues have been identified, e.g. by . This current lack of forward modelling ability regarding ρhv limits the applicability of synthetic ρhv in data assimilation and in observation-equivalent-based model evaluation.

The lack of polarimetric signatures at the snow-dominated heights may be due to issues with the partitioning of cloud ice and snow in these layers but also due to the forward operator struggling to correctly model the scattering properties of snow aggregates. This is analysed in depth in Sect.  and .

Large regions of high ZH together with extremely high ZDR and comparably low ρhv (breaking the general pattern of synthetic values overestimating the observed one) below the melting layer suggest issues with the underlying COSMO modelled hydrometeor fields. Comparison to Fig. a indicates that the “curtains” of high ZH and ZDR do not coincide with high rain mixing ratios, and hence they are likely not due to rain. Instead, as suggested by the frozen hydrometeor mixing ratios (Fig. a–c) and their mean sizes (not shown), these are caused by graupel. This has also been confirmed by no-graupel runs of the FO (not shown) and has been observed during testing to occur independently of the choice of melting scheme settings in B-PRO; i.e. the FO results strongly suggest an overestimation of the graupel occurrence below the melting layer (ML).

Figure  shows the retrieved dominant hydrometeor types with HCA-Pejcic, HCA-Dolan and HCA-Zrnic. The HCA retrievals are only available up to an altitude of about 4.5 km (Fig. ) because KDP values became too uncertain at altitudes above (Fig. ). When comparing the dominant hydrometeor types, it can be seen that mainly snow is identified at temperatures above zero degrees. HCA-Zrnic and HCA-Pejcic show predominantly cloud ice at the upper edges of the precipitation and only between 06:00 and 07:00 UTC; from 09:00 UTC onward, cloud ice is also classified down to the height of the melting layer. HCA-Dolan classifies no cloud ice except for very small isolated areas between 05:00 and 07:00 UTC at approx. 2.5 km. In contrast to snow, only very small amounts of graupel are classified. Thereby, HCA-Pejcic shows that between 01:00 and 04:00 and 07:00 and 09:00 UTC graupel occurred directly above the melting layer, which can be only partially confirmed with the sagging of the melting layer (very visible in Fig.  at ρhv and ZDR) as an indicator of aggregation and riming. At the same time steps, smaller portions of graupel are classified by HCA-Zrnic. HCA-Dolan classifies rain above the 0 ∘C isotherm in these areas and HCA-Zrnic in the middle of the melting layer. Considering the scores calculated via the membership function in HCA-Zrnic and HCA-Dolan (not shown here), there are only minor differences between the scores for graupel, rain and wet snow in the same areas. Figure  shows the hydrometeor percentages derived from the HCA-Pejcic. Below the melting layer, all HCA classify rain and the hydrometeor percentage for rain is constant at 100 % and changes with height to wet snow. Graupel reaches up to 3 km altitude at 01:00 UTC but with only small proportions below 40 %. The proportions of cloud ice reach down to 3 km altitude between 01:00 and 03:00 UTC. In general, the different HCA indicate the dominance of cloud ice above 4 km, snow aggregates from 1.5 to 4 km (with sporadic appearances of cloud ice), wet snow in the melting layer and rain drops below the melting layer. Comparison between the above radar retrievals and the CTRL simulations (Fig. ) show two main differences in the partitioning of the IWC above the melting layer: (1) excessive graupel production above the melting layer which extends from 1 to 2 km and (2) a low concentration of cloud ice above 4 km with an absence of sporadic increases in cloud ice concentration above the melting layer. While the above deficiencies in the modelled hydrometeors in the CTRL run can be also observed in the synthetic radar variables compared to radar observations, with a thick bright band in the melting layer, stronger reflectivity above the melting layer and a lack of polarimetric signatures in the snow-dominated region, the contribution of possible errors in the assumptions used in the FO also can not be neglected. Thus, additional sensitivity studies with the model and FO are conducted to better understand the uncertainties in the model and the FO, which are discussed in detail in the following sections.