We are using data from the “Biogenic Aerosols – Effects on Clouds and Climate” BAECC; campaign to train, validate, and test ensembles of ANNs. During BAECC, in situ observations of snow were collocated with Ka- and W-band radar measurements at a site in Hyytiälä, Finland. The ensembles of trained ANNs are then applied to observations collected during the “TRIple-frequency and Polarimetric radar Experiment for improving process observation of winter precipitation” TRIPEx-pol; in Sect. . The motivation to use these data is twofold. First, this allows us to demonstrate that the ANNs are able to generalize to different meteorological conditions and radar settings and to check whether the predictions are consistent between the Ka- and W-band setup. Second, the riming retrieval can additionally be compared with expected signatures of riming in triple-frequency radar observations. Another validation study is performed using data obtained at the Leipzig Institute for Meteorology (LIM) on 19 March 2021 in Sect. . In this data set, W-band radar data are complemented by ground-based in situ observations of graupel and snowflakes. In Sect. , we apply one set of ANNs to a graupel case measured by the same W-band radar during the “Dynamics, Aerosol, Cloud And Precipitation Observations” (DACAPO-PESO) field experiment in Punta Arenas. In this section, each of the four measurement setups is briefly introduced.

Masses of individual snowflakes can be retrieved by applying hydrodynamic theory to PIP observations of particle velocity and size . A data set containing observed snow particle number size distributions, along with retrieved particle masses collected between 2014 and 2015 in 5 min temporal resolution, is freely available on GitHub . Using these retrieved masses, m, and the maximum dimensions of the observed particles, Dmax, we first estimated the rime fraction. The mass of unrimed snow, mus, is assumed, as in and , as follows: 1mus=α⋅Dmaxβ, where the values for α and β are α=0.0053 and β=2.05 (in centimeter–gram–second units). The rime fraction is then defined, as in , as follows: 2FRPIP=1-IWCusIWC=1-∫mus(Dmax)⋅N(Dmax)dDmax∫m(Dmax)⋅N(Dmax)dDmax.

Here, IWCus is the estimated ice water content for unrimed snow with the same N(Dmax) as the observed particles. It is obtained by integrating mus computed from Eq. () over the measured particle number size distribution N(Dmax). FRPIP values smaller than zero were removed. In the next step, continuous PIP sampling periods longer than 1 h were identified for which KAZR and/or MWACR observations are available as well. This results in six snow cases between 1 February and 20 March 2014, which are listed in Table .

During BAECC, a turbulent surface layer was often present, resulting in a broadening of the Doppler spectra and impacting their width and other higher-order moments relevant for the training. The following sampling procedure for the training data set was chosen, striving to achieve the best possible spatiotemporal match between remote sensing and in situ observations, while at the same time avoiding the sampling of spectra which are strongly impacted by surface induced turbulence. We compute the turbulent eddy dissipation rate (EDR) for 5 min time periods and determine r, the lowest range at which EDR is <10-3 m2 s-3. This threshold was determined empirically in a sensitivity study in which spectral broadening was simulated using the convolution of a spectral broadening term σT with measured Doppler spectra. The time Δt it takes for the particle to travel from height r to the surface can be estimated using the measured MDV at r, making the assumption of temporal and spatial coherence, meaning that the properties measured at time t and r will be the same as the properties at time t+Δt at r+Δt⋅MDV(t,r). Note that negative MDV values indicate downward motions. A schematic for the visualization of the applied sampling technique is shown in Fig. . For each PIP measurement, the rime fraction was obtained using Eq. (). All the KAZR and MWACR spectra at range r, which were matched with a 5 min PIP measurement, were extracted, and Ze, MDV, and the skewness were computed. MDV was corrected for air density change as a function of altitude . An additional measure of the width of the spectra was computed and stored; the SEW is defined as the distance (in meters per second) between the left edge and the right edge above the noise threshold. This threshold is the mean noise, according to , plus 3 standard deviations of the noise. SEW offers the advantage that it is, in contrast to the spectrum width, not weighted by the reflectivity, making it more sensitive to broadening of the spectrum due to small peaks, e.g., caused by liquid water. While SEW and skewness are not among the traditional radar moments, they are often available; e.g., the ARM MicroARSCL product contains the skewness and edges of the spectra .

The resulting extracted training data set includes 105 115 Ka-band and 209 965 W-band radar observations, along with the FRPIP retrieved from the corresponding PIP measurements. It is available on GitHub (10.5281/zenodo.5751820; last access: 16 January 2022). A 3D plot of three of the contained features (Ze, SEW, and skewness) colored by FRPIP is shown in Fig. c. The video supplement contains an animated visualization of the same variables.

The retrieval described in this section reflects a regression problem. Machine learning techniques are used to relate Doppler cloud radar moments and SEW to FRPIP, using a fully connected neural network. Multiple ANN models are trained to make predictions, given many input (features) and output (target) pairs, with the goal to search for a function that both fits the given data well and is also able to generalize to new values . For the steps described in the following, tools provided in the Python library of Sklearn , were used.

We acknowledge that several sources of uncertainty impact the riming predictions and only some of them can be quantified. For the training data set, assumptions about the density of unrimed snow and the viewing-geometry-corrected Dmax were made. The m–D relation used to derive the mass of unrimed snow is assumed to overestimate mus by a maximum of 5 %. Furthermore, errors are introduced by the spatiotemporal matching of radar and PIP observations. To grasp the overall effect of measurement uncertainties which propagate into the FRANN predictions, a sensitivity study was performed. We assumed an error of 0.2 dBZ for Ze, one Doppler bin for MDV and SEW, and 0.2 for the skewness and added this uncertainty to selected Doppler spectra. This was accomplished by random picking of n=10000 samples from a Gaussian distribution defined by the measured values as the mean and above errors as the standard deviation. The resulting standard deviation in the predicted FRANN is approximately 1 %. In addition to the 5 % uncertainty from the mass of unrimed snow, and other error sources which cannot be quantified, we propose assuming an overall uncertainty of approximately 10 % due to the training data. This uncertainty has to be added to the uncertainty of the ANN models (Table ).

In addition to using the BAECC data set for training, validation, and testing, we also capitalize on the fact that these data have already been extensively studied with respect to microphysical growth processes, and several well-defined case studies are available. We evaluate the performance of our newly developed riming estimation technique for a 1 h period between 22:00 and 23:15 UTC on 21 February 2014, which is part of the 10 % of the labeled data that were retained for the test set. Riming started at around 17:00, with the LWP reaching its maximum value of more than 1000 g m-2 at around 22:00 UTC Fig. e; see. Parts of the focus period considered here between 22:00 and 23:15 UTC have been previously analyzed in detail by, e.g., , , , and . Fig.  shows Ze, MDV, spectral width, skewness, and SEW measured by the KAZR. The case is characterized by a seeder–feeder situation, where a frontal snow cloud merges into a mid-level mixed-phase cloud. In the mixed-phase cloud, SLW layers are present at 0.7 to 0.9 km and slightly below 3 km. As snow starts to fall from the frontal (seeder) cloud into the lower-level (feeder) cloud, intense riming happens along a slanted fall streak feature at around 22:40 to 22:45 UTC, resulting in Doppler spectra with multiple peaks . During the following time period, a transition from strongly rimed particles to unrimed snow aggregates at between 23:03 and 23:10 UTC was observed by .

Figure  shows the predicted FRANN for the two different ANN ensembles and the two different radar frequencies, respectively. The ensembles yield very similar predictions, which is remarkable given the fact that ANN 2 does not use MDV as input feature. The surface-induced turbulent layer close to the ground is masked with gray pixels where EDR exceeds the threshold of 10-3 m2 s-3. For the W band, columns where the estimated attenuation exceeded 10 dBZ were masked. For all four configurations, a clear increase in FRANN is visible at around 22:40 UTC when snow starts falling from the seeder cloud through the SLW layers in the lower-level, mixed-phase (feeder) cloud. This is the period for which reported riming signatures in Doppler spectra featuring multiple peaks. Unfortunately, due to low precipitation intensity at the ground, no PIP-based FR retrieval was available for this time period (Fig. f). However, a continuous decrease in LWP points to the depletion of SLW by the strong riming (Fig. c). Later, after around 22:50 UTC, the predictions differ between Ka and W band. While the two ANN ensembles trained on Ka-band data only predict riming during a short period around 23:00 UTC, the FRANN predictions in the W-band setup remain elevated up to a range of around 4 km. The Ka-band ANNs are apparently able to detect the transition from increased riming to less riming around 23:05 UTC, which was reported in existing studies of the event. Around this time, the LWP has reached its minimum, indicating that no SLW for further riming is available in the column. Coinciding with this period from around 23:05 UTC onwards, the FRANN is very low (≤ 0.5) throughout the cloud system, which is in accordance with the measured decrease in FRPIP (Fig. f).

This first case study is promising with respect to the usability of our trained ANNs to predict riming from cloud radar moments. Furthermore, the similarity between ANN 1 and 2 for both radar frequencies shows that their application might be possible even without the use of MDV.

To answer the question of whether the developed methods are able to generalize to conditions that are different to the ones they were trained on, it is required that another data set be considered. For this reason, the two ANN sets are applied to data from a different site and obtained by radars with different settings. We will first focus in more detail on the 24 November 2018 case from the TRIPEx-pol campaign. This precipitation event has been analyzed with respect to rain and ice microphysics by , who found strong signatures of aggregation during the period from 06:45 to 07:45 UTC and riming during a shorter time interval at around 09:00 UTC.

Figure  shows the radar moments measured during the period from 02:00 to 11:30 UTC on 24 November 2018. The period, characterized as aggregation by , clearly shows up as a patch of increased signal in the DWRX,Ka between the 1 and 4 km range, while, during the riming period around 09:00 UTC, an obvious increase in absolute MDV values can be observed in a similar range interval, along with an increase in SEW.

In Fig. , the predictions of the two ANNs are shown side by side for W band and Ka band. In both cases, the CloudNet classification mask was used only to apply the ANNs to those parts of the cloud which were classified as ice or ice and liquid. For the two different frequencies, and for the two ANNs, the predicted FRANN features are very similar. For the aggregation period, which has the strongest signal in the DWRX,Ka (Fig. c), from approximately 06:45 to 07:30 UTC, some riming is predicted; however, there are relatively low values. During the riming period, which clearly shows up as increased MDV in Fig. b between 08:00 and 09:00 UTC, strong riming is predicted for both wavelengths and by both ANN sets. Again, it is remarkable how the MDV features in Fig b can be discovered even in the predictions by ANN 2, which does not use MDV (Fig. c, d). Despite the differences in scattering properties and attenuation due to the hydrometeors at the Ka and W bands, as well as the different noise levels of the two radars, the retrieved FRANN is rather similar. The common time–height grid in the TRIPEx-pol data set allows for a convenient direct comparison of the two radar frequencies for each of the ANN setups. The correlation of the predicted FRANN values for all considered TRIPEx-pol cases is high for both ANN sets, and the R2 of the Ka- vs. W-band-based predictions are 0.73 for ANN 1 and 0.81 for ANN 2, respectively.

As mentioned earlier on, riming and aggregation can produce distinct signatures in the triple-frequency space of the X-, Ka- and W-band reflectivity. When considering a plot with DWRX,Ka on the abscissa and DWRKa,W on the ordinate, observations obtained during riming events fall onto a line at low DWRX,Ka (pink line in Fig. ). Aggregates, in contrast, tend to yield a hook-like feature, due to the comparably large size at which DWRKa,W is in saturation because of Mie scattering. This conceptual model was presented by and further explored by , who found that not only the density but also the shape parameter of the particle size distribution and the internal structure of aggregates can have strong impacts on triple-frequency signatures.

In Fig. , we plotted the observations for which an increased FRANN > 0.5 was predicted by the ANNs on 2D histograms in the triple-frequency space and colored by the median FRANN of all the observations in the respective pixel. A pink line is drawn along the line of the increasing median volume diameter expected for rimed particles (according to Fig. 15 in ). With respect to frequency of occurrence (not shown here), the largest portion of the pixels for which a FRANN>0.5 was predicted falls around that line for both ANN sets and both frequencies. This finding suggests that both ANN ensembles for both frequencies are capable of predicting elevated FR values.

The findings in the previous sections motivate the need for additional comparisons to in situ observations. The 19 March 2021 Leipzig case is characterized by a wintertime convective mixed-phase cloud system, with the cloud top at 3–4 km, and with embedded strong snow and graupel showers. Cold air aloft, combined with some solar warming near the ground, causes weak instability. Additional lifting, e.g., due to convergences, triggers showers and, as in this case study, is even sufficient to cause thunderstorms.

In Fig. , the first two moments of the cloud radar Doppler spectra during that day are shown, along with the SEW. Around 15:00 UTC, a strong updraft is visible in the MDV, followed by strongly negative Doppler velocities coinciding with increased Ze and SEW values. Around that time, alternating graupel and snow showers were observed in the Leipzig area. This case is moderately convective, and most of the data would be excluded by filtering criteria such as the convection index κ used in the approach by .

Figure a and b show the ANN predictions for the time between 14:00 and 19:00 UTC. In the panels below (Fig. c), hydrometeors observed by the VISSS are shown for three selected time periods. In both ANN predictions, a clear transition from very high (around 1) to very low (≤0.4) FRANN values at around 15:00 UTC is visible. This change can be confirmed by the VISSS observations. In the period from 14:40 to 14:50 UTC, the images show dense and roundish particles (rimed aggregates and graupel). In contrast, during the period from 15:00 to 15:10 UTC, fluffy, unrimed aggregates are observed. Later, from approximately 15:45 to 16:20 UTC, the FRANN features increased values throughout the vertical column (≈0.7–1.0), but these are not as pronounced as in the period before 15:00 UTC. VISSS images taken during the period from 15:50 to 16:00 UTC reveal a mixture of particles which have different sizes and degrees of riming. Small hydrometeors, with diameters well below 1 mm, coincide with aggregates and graupel particles having sizes of several millimeters. The ANN predictions fit extremely well with these observations. In the first case, very high FRANN values around 1 are predicted, whereas in the second case, the predicted riming indices are below 0.4. In the third case, even though a portion of the column is masked due to the EDR threshold, it is visible that intermediate FRANN values are predicted by both ANNs. This leads to the assumption that the ANNs are not only capable of detecting strong riming but are also sensitive to the degree of riming or the fraction of rimed particles compared to the total hydrometeor population. In this case, and in the previously presented results, the predictions of ANN 1 and 2 are strikingly similar. These findings show that predicting riming is possible – even without the use of MDV. It has to be acknowledged, though, that the vertical distribution of FRANN cannot be verified by the VISSS observations. Since the ANNs proved to perform well for this wintertime convective case, this could open a door to detect and even quantify riming in convective systems.

The previous findings make us confident that ANN 2 can be applied to the W-band radar data in the DACAPO-PESO data set. We do not apply ANN 1 because it would be biased by the orographic wave motions. Here, we analyze a case observed on 21 February 2019 (Fig. ) from 13:30 to 22:00 UTC. A precipitating cloud system, with a cloud top around 2.5 to 3 km, is present from around 15:00 to 18:00 UTC. Above, a mid-level cloud, topped at around 6 km and with varying cloud base, is observed. Especially in the higher-level cloud, in the range between 3 and 6 km, a wave pattern is visible in the MDV (Fig. b), including a prominent downdraft around 18:00 UTC, with MDV ≈ -2 ms-1. Precipitation reached the ground between 15:00 and 18:00 UTC, and another precipitation event occurred at around 21:00 UTC. At 16:30 UTC, marked by the red cross in Fig. d, graupel particles were observed on the ground at the site.

In Fig. d, the FRANN predicted by ANN 2 is shown. The predicted FRANN is only increased in the lower part of the cloud system up to around 3.5 km range, which probably contains liquid water. No increased FRANN values are predicted for the higher part of the cloud system. The maximum in FRANN predictions is reached around 16:30 UTC, coinciding with the observation of graupel particles.