*3.2. Rain Microstructure Variation With Rain Type and Wind Direction*

Stratiform rain had smaller drops and lower drop concentrations compared to convective rain (Figure 5). The average D0 for stratiform rain was 0.77 mm compared to 1.24 mm in convective rain. Normalized drop concentration Nw in stratiform rain was around 2.24 <sup>×</sup> 104 mm−<sup>1</sup> m−3, while convective rain had an average of 1.4 <sup>×</sup> 104 mm−<sup>1</sup> <sup>m</sup><sup>−</sup>3. The overall average of D0 (0.81 mm) and Nw (2.17 <sup>×</sup> <sup>10</sup><sup>4</sup> mm−<sup>1</sup> <sup>m</sup><sup>−</sup>3) were closer to the values of stratiform rain since most rain intervals were of the stratiform type. The clusters in the values of D0 that appear in Figure 5 emerge from the combined

effect of the diameter range bins of the disdrometer measurements, and the logarithmic scales on the horizontal axis.

**Figure 5.** Scatter plot of D0 and (NW) for stratiform and convective rain. The vertical and horizontal lines represent the mean values of D0 and NW.

The distributions of D0 and NW values within each wind direction and rain type are illustrated in Figure 6. Similarly, the mean values of D0 and NW for different ranges of rain intensity within each wind direction and rain type are provided in Figure 7.

For stratiform rain, westerly circulations had larger drops and lower drop concentrations compared to easterly circulations. Especially SW had the largest mean D0 and the lowest NW. Easterly circulations were clearly characterized by the smallest drops and the greatest NW. The same pattern was present even when inspecting different classes of rain intensity within stratiform rain (Figure 7). With higher rain intensity, D0 increased too while NW decreased.

For convective rain, only few differences in the previously described patterns were obvious especially when examining the rain microstructure for different ranges of rain intensities. With the exception of SE which had a limited number of convective intervals compared to the remaining wind directions, the median diameter D0 was still the largest in SW and the smallest in NE, while NW was the largest NE and the smallest in Sw. XX and NW had similar NW values but NW exhibited larger drop sizes on average. The wind direction SE did not show any consistent pattern across rain intensity ranges.

When fitting a gamma function to the average rain drop size distribution within each wind direction in stratiform rain (Figure 8), easterly circulations had relatively lower concentrations of drops with a D0 larger than 1 mm compared to westerly circulations. On the other hand, westerly circulations, especially SW, had the lowest concentration of drops with D0 less than 1 mm. In convective rain, northerly circulations exhibited higher proportion of small drops (D0 < 1 mm) and a smaller proportion of large drops compared to southerly circulations. Fitting gamma distribution to rain microstructure was also performed event by event. An example of the fitting for individual events is presented in Figure A1, and the density plots of the gamma distribution parameters are provided in Figure A2.

**Figure 6.** Probability density plots of log10(NW) and D0 for each rain type and wind direction. Vertical thick lines show parameters averaged over all locations for convective (solid red line) and stratiform (dashed thick blue) rain and light lines represent averages for individual locations.

**Figure 7.** Rain microstructure for different rain intensities in stratiform and convective rain. Symbols on each colored line represent summary statistics for a wind direction. Each symbol represents the average median drop size D0 and the normalized drop concentration for a rain intensity range. The intervals were chosen to represent six equal sample sizes and were colored by mean rain intensity. Selected symbols that correspond to equal rain intensity were connected with differently dashed black lines for comparison.

**Figure 8.** Raindrop concentration per millimeter diameter and cubic meter for each wind direction in stratiform rain and convective rain. Points represent the one-minute average concentrations for each diameter range colored by wind direction. Colored lines represent the corresponding gamma distribution fits.

#### *3.3. Z–R Parameter Variation With Location, Rain Type and Wind Direction*

To investigate the influence of rain microstructure variability per wind direction on the rain intensity retrieval equation Z–R, the values of A and b were obtained for 2449 events (see Section 2.4). A density plot of the R and dBZ values for all the 9914 h included in these events is provided in Figure A3. An example of the Z–R equation fitting for one event using two methods is provided in Figure A4.

The average value of the prefactor A was clearly larger in convective rain (309) than in stratiform rain (239), while the exponent b value was similar for both rain types (1.53). The values of A and b were averaged for each location (black points in Figure 9; Figure 10), for each wind direction (colored points in Figure 9; Figure 10), and for each combination of location and wind direction (colored stars in Figure 9; Figure 10) in order to demonstrate the variability of A and b with these factors.

In stratiform rain, the range of both mean A and b for each of the ten locations (the grey area in Figure 9) is comparable to the range of the average values for the wind directions (the red rectangle in Figure 9). However, A and b value are smaller in eastern circulation (NE, SE) compared to remaining general wind directions, and they are outside of the range associated with the spatial variability.

In convective rain, no clear pattern was detected for the average values of A and b associated with the five wind directions. The range of A and b values for the different locations is much larger than the range associated with the five general wind directions, indicating a larger spatial variability compared to the variability associated with general wind direction.

When averaging the values of A and b for each combination of location and wind direction, a greater range is observed. In the case of stratiform rain, the pattern of these values is comparable to the one observed for the five general wind directions; SW circulations have larger A values, easterly circulations have smaller A values, while XX and NW circulations fall closely in between. The range of A and b values for each combination of the location and wind direction is larger in the case of convective rain. However, the small number of convective events needs to be considered in this case (see Table A1).

**Figure 9.** The parameters A and b of the radar rain intensity retrieval equation (Z = ARb) in both rain types using the first method of fitting (Equations (13)–(19)). A and b values are averaged by location (black dots), wind direction (colored circles), and the combination of both (colored stars). The grey area represents the range of A and b for the ten locations. The red rectangle represents the range of A and b for the five general wind directions.

**Figure 10.** The parameters of the radar rain intensity retrieval equation (Z = ARb) in both rain types using the second method of fitting (Equations (20)–(25)). A and b values are averaged by location (black dots), wind direction (colored circles), and the combination of both (colored stars). The grey area represents the range of A and b for the ten locations. The red rectangle represents the range of A and b for the five general wind directions.

#### **4. Discussion**

Our data indicate high frequency and high contribution of westerly and especially SW circulations to the rainy days over Bavaria, Germany. Easterly circulations have the least frequency and especially SE has the lowest share of rainy days. This is in agreement with the frequency of wind directions and proportions of rainy days of long-term studies for Germany for the period between 1995 and 2017 [28]. The high frequency and high contribution of westerly and southwesterly circulations to the number of rainy days is expected for this region since the main moisture flux is westerly [76].

Convection is responsible for 40% of rain amount in this region despite occupying only 10% of rain duration. Similar contributions of convective rain were reported for the Czech Republic [77] and in Switzerland [17]. Convective rain has typically higher rain rates and a distinct microstructure compared to stratiform rain. It is therefore essential to separate convective and stratiform rain prior to addressing rain microstructure, especially considering the variation in convective rain proportion with wind directions [17]. Southerly circulations generally have a higher proportion of convective rain compared to northerly circulations. A possible explanation is the strengthening and inhibition of convection and radiative cooling under different wind directions, which in turn has a major influence on the precipitation diurnal cycle over Germany [49]. Southerly circulations carry along warm air masses which intensify convection in the afternoon and inhibit radiative cooling in the early morning. Northerly circulations, in contrast, transport cold air masses, and therefore suppress convection and intensify radiative cooling.

Westerly circulations need special attention when addressing rain and microstructure, especially with the reported high contribution to rain duration and rain amount, and the expected increase in their frequency over Europe [78,79]. Westerly circulations are associated with larger rain drops than easterly circulations in stratiform rain, while easterly circulations have higher number of drops. This pattern is consistent for both stratiform and convective rain and across the ranges of rain intensity, except for SE circulations in convective rain, which was not well represented by data, accounting only for 0.6% of convective rain amount observed in this study.

Rain microstructure dependence on synoptic weather patterns has previously been reported for other locations in Europe. Northerly circulations in Leon, Spain, were associated with smaller drop sizes, while westerly and southerly circulations had larger rain drops [15]. This pattern was explained by the location of Leon to the south of the Cantabrian Mountains. Northerly circulation air masses precipitate prior to reaching Leon, leaving less humidity, lower rain intensities and smaller drops. Westerly and southerly circulations carry along higher humidity, leading to higher rain intensities and larger drops. For the Cévennes-Vivarais region in France, easterly circulations were associated with lower number of rain drops and larger drop size while most of the westerly circulations had the opposite traits [16]. The associations of rain microstructure with large-scale weather patterns observed in this and other studies are therefore not generally consistent, but region-specific. Different regions have different associated general air-mass characteristics, for example influenced by proximity to the sea or the presence of mountain massifs nearby. The origin of the air masses whether continental or maritime influences the rain microstructure and eventually influences the estimation of precipitation by radars [80,81]. Each class of wind direction used here has a mixture of both maritime and continental origins. It is however assumed that westerly circulations have a larger proportion of air masses with a maritime origin compared to easterly circulations.

The rain microstructure patterns in Bavaria have more in common with the patterns reported for Lausanne, Switzerland. Despite using different disdrometer types, schemes for rain type classification, and weather type classifications, and their different geographical locations in the Alps, easterly circulations were associated with higher number of drops per interval and smaller drop size compared to westerly circulations at both sites [17]. A plausible explanation for this is the variation of humidity and aerosol content in air masses between these wind direction clusters. Aerosols are particularly abundant in air masses which pass over Russia and Eastern Europe, especially over heavy industrialized areas [82,83]. These aerosols act as cloud condensation nuclei [84]. High availability of

cloud condensation nuclei increases the number of rain drops in the case of stratiform rain, increases the size of drops in local convection, but has no significant influence on rain microstructure in organized convection [85].

Differences in the load of cloud condensation nuclei under different circulations seem to be a plausible explanation for the rain microstructure differences observed in this study, especially in stratiform rain. The abundance of cloud condensation nuclei in easterly circulations in comparison with westerly circulations leads to higher number of rain drops. This in combination with the high (low) available humidity in westerly (easterly) circulations results in a larger (smaller) size of rain drops, respectively. For convective rain, easterly circulations comprise two wind directions, NE which has the smallest mean D0, and SE which has the largest mean D0. The larger size of raindrops in southerly circulations indicates the intensification of convection when the warm air masses are transported from the south, whereas northerly circulations bring colder airmasses. The rain type classification method used in this study does not differentiate local and organized convection, which makes it impossible to thoroughly compare with the findings of Cecchini et al. [85].

Our results may be useful for radar-based quantitative precipitation estimates (QPE), since Jaffrain et al. [75] demonstrated that the variation of A and b values in the Z–R retrieval equation is an important factor which should be accounted for. In their case study of Lausanne, Switzerland, spatial subgrid variability of rain microstructure was observed, which considerably influenced the quality of the estimation of rain rate. Using the same dataset, Ghada et al. [17] showed that the variability of A and b was larger than the subgrid spatial variability (in an area less than 1 km2) when weather types are considered. In our study, variation of rain microstructure parameters with wind directions in Bavaria led to significant variation in the values of Z–R parameters. The variations in the prefactor A and the exponent b by wind direction are of a similar magnitude as their spatial variations in the case of stratiform rain, but smaller than the spatial variations in the case of convective rain. The same patterns were obtained for the conventional and the alternative methods of Z–R parameters retrieval despite the absolute differences in the values of A and b. These small differences occur because the conventional method is more sensitive to the large values of Z while the alternative method is more sensitive to the density of scatter points where R is below 2.5 mm/h [75]. This difference needs to be addressed in future studies to quantify the exact influence on the estimation of rain intensity by actual radar measurements. Alternatively, the least-rectangles linear regression could be applied as a middle-ground solution.

Assessing potential benefits of considering the variations in Z–R parameters, Jaffrain and Berne [75] concluded that the subgrid spatial variability in rain microstructure may account for errors in rain estimates between −2% and +15%. Variability due to large-scale weather patterns in Z–R parameters is likely to exceed their subgrid spatial variability [17], and based on our study, is comparable with the spatial variability of Z–R parameters in stratiform rain on a regional scale. Consequently, the potential for a significant improvement in rain estimation when accounting for rain microstructure variability by wind direction is expected to be high for radar quantitative precipitation estimates based only on radar reflectivity Z.

However, using only disdrometer data for this purpose would be insufficient because disdrometers provide a direct measurement of rain microstructure, from which R and Z are calculated. These values are accurate local measurements if we assume an accurate measurement of rain microstructure. The next logical research step would be a proper assessment of the improvement potential. This should include the integration of empirical data of radar-based rain intensity estimates validated by ground observations within the different rain types, locations, and large-scale wind directions, as well as a thorough rain type classification based on available instruments, especially considering the available network of dual polarization Doppler radars across Germany. Even for precipitation estimates based on a rain-gauge adjusted system as currently operated by DWD [86], improving the Z–R relation would likely have a positive impact in the final quality of the product.
