Evaluation of modeled summertime convective storms using polarimetric radar observations

Ensemble simulations were conducted for three summertime convective storms over a temperate region in northwestern Germany using the Terrestrial Systems Modeling Platform (TSMP). The simulated microphysical processes were evaluated with polarimetric observations from two X-band radars, with the help of a forward operator applied to the model data. TSMP was found to generally underestimate the convective area fraction, high reflectivities, and the width/magnitude of so-called differential reflectivity (ZDR) columns indicative of updrafts, all leading to an underestimation of the frequency 5 distribution for high precipitation values. The statistical distributions of ZDR and specific differential phase (KDP ) were however similar, while the cross-correlation coefficient (ρhv) was poorly simulated, probably due to little variability of assumed hydrometeor shapes and orientations in the forward operator. The observed model bias in the ZDR columns could be associated with small size of supercooled raindrops and poorly resolved three dimensional flow at km-scale simulations, besides the treatment of freezing process in the model, which warrants further research. 10

and Zrnic, 2019) (α = 0.28 and β = 0.03). These coefficients are not used for the hail inflicted segments for which we do not know the actual attenuation and differential attenuation-the above method only provides estimates of attenuation-corrected Z H and Z DR . We acknowledge this uncertainty in the estimates of attenuation corrected radar observations. 190 We also further interpolated the polarimetric radar data from the native polar coordinates to cartesian coordinates at 500 m horizontal and vertical resolution using a Cressman analysis with a radius of influence of 2 km in the horizontal and 1 km in the vertical. While, the data in native polar co-ordinates is used for investigating polarimetric signatures, the gridded data allows for easy comparisions with their model-simulated equivalents. Ground clutter and non-meteorological scatterers are known for having significantly decreased values of ρ hv compared to precipitation (Zrnic and Ryzhkov, 1999;Schuur et al., 195 2003). A threshold of 0.8 in ρ hv was imposed in the gridded data to ensure that clutter is filtered out without removing useful meteorological information.
Besides, the observations from the X-band radars, the RADOLAN (Radar Online Adjustment; Ramsauer et al. (2018), Kreklow et al. (2020)) data from the German national meteorological service (DWD, Deutscher Wetterdienst) is also used for evaluating the modeled precipitation. RADOLAN is a gauge adjusted precipitation product based on DWD's C-band weather The first case (5 July 2015) is a northeastward propagating deep convective hail-bearing storm crossing Bonn. The storm was connected to low-pressure system west of Ireland with an occluded front crossing Norway and the cold front extending over the western part of middle Europe producing pre-frontal convergence zones over western Germany, where a moisture tongue 210 ahead of the cold front produced instability and drew warm moist air mass from the south. Scattered notheasterly propagating storms were prevalent throughout the day, with an isolated deep convective storm passing directly over the Bonn radar from 1500 to 1600 UTC. Acccording to the European Severe Weather Database (ESWD), large hail (2 -5 cm in diameter) was observed over the Bonn region, including damaging lightnings further north, and heavy precipitation with severe wind (further north-east).

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The second case (13 May 2016) is chracterized by scattered convective storms over Rheinland Pfalz, Germany, connected with a low pressure system over the Norwegian sea with an occluded front over northern and a cold front over southern Germany. The southward propagating cold front provided the necessary lift to release the potential instability associated with a warm moist air mass below 700 hPa over the region between the occlusion and the cold front. The ESWD reported heavy rainfall over the Frankfurt area resulting in flooding and damage to property. The third case (6 July 2017) consists of deep convective clouds propagating eastwards over Bonn. On that day, a warm front over middle of Germany separated a relatively cool northern, from a warm southern Germany. A low pressure system over the North Atlantic produced an occlusion west of UK moving eastward, which pushed the western edge of the warm front-disturbing it into a wave like feature. The induced anticlockwise rotation of the warm front produced the necessary lift to release the potential instability associated with the warm and moist southerly air mass. The ESWD reported scattered severe 225 wind around the Bonn region and heavy precipitation south of Mainz including large hail.

Accumulated Precipitation
First, we examine the model simulated ensemble precipitation with the RADOLAN data. Overall, the spatial pattern of ensemble averaged accumulated precipitation resemble the RADOLAN estimates, but the frequency distribution produced by 230 the ensemble members underestimate high precipitation for all three cases leading to a weak precipitation gradient in the ensemble average. For the first case ( Fig. 2 a), the model simulated accumulated precipitation is stratified according to four global models used for IC/BC. The members using GME data produce average accumulated precipitation and a frequency distribution for average accumulated precipitation (< 30 mm) closest to RADOLAN. The model does, however, underestimate average accumulated precipitation (> 30 mm) for all ensemble members as also visible in the spatial pattern of the ensemble 235 averaged accumulated precipitation. While the large-scale extent of the precipitating area is comparable between model and RADOLAN, the precipitation amount especially in the northwestern domain is underestimated. For the second case ( Figure   2b), all ensemble members underestimate the average accumulated precipitation compared to RADOLAN; also its frequency distribution for high precipitation is weaker compared to the first case. All ensemble members for second case, underestimates average accumulated precipitation (> 10 mm). For the third case ( Fig. 2 c), the model misses the precipitation observed over 240 the western part of the domain for all ensemble members except of one, and the simulated frequency distribution of accumulated precipitation exhibits a larger spread. This could be attributed to the switch in the ensemble generator for large scale atmospheric forcing data.

River discharge
Overall, the model generally does not produce sufficient base flow compared to the GRDC observations ( Figure 3), which we 245 mainly attribute to the still coarse grid resolution compared to actual river widths (Schalge et al., 2019). The model does, however, produce reasonable daily mean discharge compared to GRDC data for rivers with catchment areas covered by the storm's precipitation. The spatial pattern and intensity of simulated precipitation as such exhibits strong controls on the simulated discharge. In the first case study, the model ensemble exhibits a spread in the simulated discharge with varying precipitation amounts for Lippe river (two different locations) in North-Rhine Westphalia and Ems river in the north-western Germany. Similarly, the model ensemble also exhibits a spread in the simulated discharge for Nettebach in North-Rhine Westphalia and Wied river in Rhineland-Palatinate for the second case.

Polarimetric Signatures
For a given precipitation type, polarimetric variables are expected to cluster in a specific region of the multi-dimensional space (Zrnic and Ryzhkov, 1999). Thus as one evaluation method, we compare the respective clustering between simulations and 255 observations for similar stages of convection, which we identify via the Convective Area Fraction (CAF, area fraction of a storm with radar reflectivity >40 dBZ at 2 km height a.g.l; Fig. 4) and by a qualitative exploratory analysis of the model ensembles and the observed storm evolution. For the first case, the observed storm CAF decreases while approaching the radar and increases again while moving away from the radar. Especially, the ensemble members initiated and forced with GME model (relatively dark lines) show a similar behaviour but underestimate CAF compared to observations. For the second case, CAF gradually 260 increases for all ensemble members as in the observations, but CAF is underestimated in the earlier storm phase (before 1100 UTC). For the third case, the simulated CAFs of the model ensembles have a wider spread, probably caused by a switch in the way the ensemble is generated from March 2017 onwards. While few ensemble members simulate the storm much earlier than observed (relatively dark lines), the CAF of one ensemble member, better matches the observations and exhibits also a storm evolution (dark line) quite similar to the observations.

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Based on the CAF time-series and qualitative exploratory analysis of storm evolution, we identified optimal locations (identified by square markers) and time intervals (solid lines bounded by vertical bars) for the comparison of the statistical distribution of polarimetric variables between observations and simulations.
Importantly, both synthetic and observed radar variables are affected by errors in forward operator and calibration/attenuation corrections respectively. The errors in the forward operator could mainly arise due to many assumptions that need to be 270 made regarding the hydrometeor scattering properties, melting parameterizations, effective medium approximations (EMA) etc. Similarly, errors in observed radar data might arise due to the assumptions made in the attenuation correction algorithm.
We acknowledge this limitation in the study, and concentrate more on patterns and not so much on the actual magnitudes of the polarimetric moments. 1530 UTC for the first case. The storm is characterized by high reflectivity (>50 dBZ) and differential reflectivity (> 2 dB) near the melting layer. An arc-like feature of high Z DR follows the leading eastern edge of the storm just below the melting layer with concurrent lower Z H values suggesting hydrometeor size sorting associated with storm inflow (Kumjian and Ryzhkov, 2012;Dawson et al., 2014;Suzuki et al., 2017). Fig. 5 b shows a cross-section of storm based on the gridded radar data.

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Its convective part between -20 and 5 km relative to BoXPol exhibits Z DR columns, anchored to lower levels and extending up to 6 km altitude associated with two strong updraft zones. Their different extensions suggest different updraft intensities including frozen drops aloft (Kumjian and Ryzhkov, 2008;Kumjian et al., 2014;Snyder et al., 2015). K DP columns (Ryzhkov and Zrnic, 2019;Snyder et al., 2017b) co-located with the Z DR columns with slight inward offsets are additional signs for updraft locations (e.g., van Lier-Walqui et al. 2016). The low (<0.7) cross-correlation coefficient (ρ hv ) near the inflow region 285 and the still low ρ hv (<0.92) along the strong convective core associated with high reflectivity probably indicates hail. The dominance of near-zero Z DR and reflectivity values between 20 and 25 dBZ above the melting layer in the anvil suggest the dominance of snow (Yuter and Houze Jr, 1995). The low ρ hv in the northern region at higher levels associated with relatively high Z DR and moderate K DP , are probably caused by horizontally oriented ice crystals.
As discussed in Sect. 5.1, the ensemble members initiated using GME data have similar storm evolutions as observed. So, 290 only these ensemble members are used here for the polarimetric comparisons. Fig. 6 shows the simulated polarimetric moments at lower levels up to the melting layer and cross-sections of polarimetric variables and simulated hydrometeors at 1455 UTC for one of the ensemble members (Fig. 4 a-dark solid line). At lower levels (1000 m a.g.l.), the southeastern flank of the storm has -as expected near the core of the storm -relatively high Z H and Z DR (also associated with relatively low ρ hv ) with lower magnitudes on the northwestern side. K DP has generally low magnitudes while ρ hv is generally high. Near the melting level 295 (4000 m a.g.l.), K DP present much lower magnitudes but ring like feature of Z DR with relatively low ρ hv is visible in the updraft region, which is a typical polarimetric signature found for supercell storm (Kumjian and Ryzhkov, 2008).
In all ensemble members, the storm is aligned in the northeast direction and has a strong updraft region in the southeasten edge characterized by a bounded weak echo region (BWER, see Fig. 6 c). The convective storm top extends up to 15 km height with Z H between 30 and 40 dBZ (which is relatively lower than the observed Z H ) co-located with the simulated hail shaft and 300 updraft (Fig. 6 d). The model also exhibits a narrow Z DR column extending up to 6 km altitude adjacent to the updraft region.
The simulated Z DR column is relatively smaller in width and magnitude (value) compared to the observations. The model also simulates high K DP (> 1 deg/km) along the top of the convective storm part, but no K DP columns are present in the updraft region as seen in the observations. Although, the simulated ρ hv is higher than observed, slight decrease can be observed in the updraft region with high Z H associated with hail, and below the melting layer.

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In the updraft region, the modelled vertical velocity above 8 km reaches 40 m/s, dominated mostly by super-cooled raindrops around 6-9 km (see Fig. 6 d), which is an important source for hail growth. The strong updraft also generates a warm anomaly above the melting layer (see the 0 • isotherm), below which rain is also formed by melting of graupel and hail. Graupel dominates the frozen hydrometeor categories above the melting layer peaking at top of the updraft region. Ice crystals are located mostly above 8 km height, and the self-collection of these ice particles leads to the formation of snow which further 310 grows in size via aggregation. Low concentration of hails are also simulated on periphery of the peak updraft. Fig. 7 shows the PPIs of Z H , Z DR , K DP and ρ hv at 1.0 degree elevation from BoXPol at 1030 UTC for the second case. We find moderate reflectivities (35 -40 dBZ) and high Z DR (>2 dB) at around 1 km. According to the cross-section of storm based on gridded polarimetric radar data (Fig. 7 b), the storm has a wide Z DR column anchored to the lower levels and extending up 315 to 5 km. At this location, below the melting layer (approx. 2.5 km), Z DR is >2 dB while reflectivity is weak, which suggests size-sorting of rain drops. A large portion of the storm exhibits very low or negative Z DR above the melting layer, possibly indicating vertically oriented or conical graupel (Bringi et al., 2017). While other studies also have shown the presence of low and negative Z DR above melting layer for convective storms (e.g Suzuki et al. 2017;Hubbert et al. 2018), it is possible that for these convective cases, attenuation correction even with the advanced methods as we used here may at least partially contribute 320 to negative Z DR . Figure 8a,b shows the simulated polarimetric moments up to near the melting layer and cross-sections of polarimetric variables and simulated hydrometeors at 1050 UTC for one of the ensemble members (see Fig. 4 b-thick solid line). The southwards propagating storm is oriented in north-south direction. Regions with moderate to high reflectivities in the lower levels (1000 m a.g.l.) coincide with moderate to high Z DR , K DP and lower ρ hv suggesting heavy rain or rain/hail mixtures.

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Just above the melting level (3000 km a.g.l.), Z DR and K DP are much lower except on the western storm edges, where Z DR and K DP columns are found (but with weak magnitudes). According to the cross-section (Fig. 8 c) moderate reflectivities (30-50 dBZ) comparable to the observations, reach up to 6 km height while the storm top height extends up to 9 km. Narrow Z DR columns with lower ρ hv extend up to 7 km and signal high rain concentration and hail above the melting layer (Fig. 8d).
Again, the simulated Z DR column is much smaller in width and magnitude compared to the observations. A grid-scale K DP 330 extended upto 4 km above the melting layer is also visible but K DP generally, remains very low here except for some region near the storm top, which is also visible in the observations. Based on the modeled hydrometeors, Fig. 8 d indicates presence of super-cooled raindrops above the melting layer connected with updraft regions (5 m/s maximum vertical velocity at the left and right edges of the storm). However, the smaller size of raindrops (< 1 mm) are not sufficient to create strong Z DR magnitudes as observed in the Z DR columns. The vertical velocity 335 in the storm center is around 1 m/s and not included in the contour plot. The frozen hydrometeors are again dominated by graupel with high concentrations in the strong updraft region. Some hail is present adjacent to the updraft regions reaching down to the surface. Above 6 km height some cloud ice exists while this region is mostly dominated by snow. Fig. 9 shows the PPIs of Z H , Z DR , K DP and ρ hv at 8.2 degree elevation from BoXPol at 1400 UTC. The storm is characterized 340 by reflectivities > 50 dBZ and Z DR >2 dB near the melting layer. Its convective region (reflectivities > 50 dBZ) extends up to 12 km height and the correspoding lower ρ hv indicate presence of hail (Figure 7b). The convective core has also relatively high K DP values extending up to the storm top and including a wide Z DR column up to 5 km height. Both indicate lofting and growth of large rain drops by updrafts, which are also important for hail formation. This case also shows low to negative Z DR values above the melting layer, which could also be partially contributed by the attenuation correction algorithm. oriented from west to east and at lower levels characterized by a wide core of moderate reflectivity (40-50 dBZ) and high K DP , Z DR >2 dB along the edges, and low ρ hv produced by heavy rain and rain/hail mixtures. Near the melting level (4000 m a.g.l.), variable Z DR and Z H regions are found near the southeastern edge-characteristics of rain drop size-sorting. Overall, moderate reflectivities (30-50 dBZ). While, Z H at lower levels is comparable to observations, the relatively high Z H seen in the observations extending upto upper levels is underestimated by the model. The model also simulates a narrow Z DR column extending up to 5 km adjacent to the updraft region and relatively comparable to observation. This region also has relatively high Z DR than the background, extending upto 12 km height. The model also simulates high K DP along this convective part 355 of the storm. The simulated ρ hv is again generally high with slight decrease in the updraft region and below the melting layer.

Case Three
Similar features of Z DR , K DP and ρ hv is also seen in the observed convective core.
The vertical velocity reaches to 10 m/s from 6-11 km in the updraft region where a low concentration of super-cooled rain drops is found up to 8 km (Fig. 10 d). Graupel again dominates the frozen hydrometeor categories above the melting layer, while snow further extends downwards upto 6 km height. Compared to the other two cases the simulated hail concentration is 360 higher and extends below the melting layer where it contributes to rain via melting.

Frequency distribution of polarimetric variables
Mismatches between space and time scales of simulated polarimetric moments compared to observations also needs to be addressed by monitoring ensemble properties of the convective event. So, the ensemble simulations are compared to the observations for similar storm evolution stages using contoured frequency altitude diagrams (CFADs; Yuter and Houze Jr 1995) 365 using the same extents and bin widths for observations and simulations.

Case One
We use the observations from 1445 to 1530 UTC, which encompasses the convective stage of the storm before it passes over the BoXPol. The CFADs from the X-band radar (Fig. 11 a) show a unimodal distribution of Z H which gradually narrows above the melting layer (around 4 km). The peak in the frequency distribution occurs around 20-25 dBZ with maximum reflectivities 370 well above 50 dBZ. The Z DR also exhibits a narrow unimodal distribution which further peaks (or narrows) above the melting layer with the mode around 0.25 dB, similar to the values reported by (Yuter and Houze Jr, 1995) for convective storms. The distribution broadens and shifts to values up to 4 dB below the melting layer peaking at around 1 dB near the surface. K DP exhibits a very narrow unimodal distribution throughout the vertical extent of storm with peak values around 0.1 deg/km. The distribution also broadens weakly from 7 km height downwards. ρ hv has a quite broader distribution peaking around 0.98 375 below 11 km height and shifting to 0.87 near the storm top.
The CFADs from the model ensemble were generated using five members from 1445 to 1530 UTC (Fig. 4 a-soild lines) which best matched the observed storm macrophysical features. The Z H distribution with maximum reflectivities generally below 50 dBZ peaks around 28 dBZ from 6 to 10 km, but shifts towards 15-20 dBZ at lower levels, which were found to be associated with grid cells with very low concentration of hydrometeors broadening of the distribution, compared to 380 observations. Z DR again exhibits a narrow unimodal distribution above melting layer peaking around 0.1 dB, which broadens below the melting layer with an additional peak at 2.6 dB. Unlike the unimodal CFADs from observations, the CFADs from the model ensemble produce two peaks below the melting layer. K DP shows a very narrow unimodal distribution similar to scale simulations. Future model evaluations with polarimetric radar data should focus on hyper-resolution simulations to better resolve the three-dimensional motion and microphysical processes associated with multivariate polarimetric signatures as well as uncertainty estimates in the attenuation correction of polarimetric moments for convective cases.

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Code and data availability. The source codes for the model and the forward operator used in this study are freely available from https:// www.terrsysmp.org/ and https://git2.meteo.uni-bonn.de/git/pfo respectively with registration. The codes for radar calibration and attenuation correction will be made available from https://github.com/meteo-ubonn/miubrt. The data used for the model runs including initial conditions for the soil-vegetation states are available from Deutscher Wetterdiest (https://www.dwd.de/DE/leistungen/pamore/pamore.html) and https: