1. Introduction

2. Materials and Methods

2.2. Hail data.

Reported hail falls, used in this study was used in previous studies [52,57], and comes from three different sources, namely: Romanian National Meteorological Administration (RNMA), ESWD (European Severe Weather Database) and media and local newspaper . The dataset from RNMA represents a total of 242 hail days from 18 weather stations from 1979-2017. 29 hail days were taken from ESWD reports, the database used in studies at the continental level [28,29,58] as well as at the regional level [59,60]. The third data source is represented by large hail reports from the local newspapers archive. These types of meteorological phenomena reports, including data from past centuries, have been used in climatological studies that have been carried out [61,62,63].

Figure 1. Geographical position of north-eastern Romania at continental (a) and country (b) scale; spatial distribution of the mean hail days per year (c), monthly distribution of the hail events (d), and hourly distribution of the hail events (c) for 1981–2020.

Figure 1. Geographical position of north-eastern Romania at continental (a) and country (b) scale; spatial distribution of the mean hail days per year (c), monthly distribution of the hail events (d), and hourly distribution of the hail events (c) for 1981–2020.

2.3. Convective Parameters

The convective environment of hail storms was studied using 23 instability parameters from two data sources. Data from sounding stations in the vicinity of the studied area, namely Bucharest-Băneasa, Cluj-Napoca, Cernăuți and Odesa, as well were used reanalysis data from ERA5. Sounding data were downloaded from the web server of the University of Wyoming [64] The spatial density of air sounding stations from the studied territory is very low, and the atmosphere sounding is carried out at most twice a day. The use of aerial survey data was done according to the criterion of proximity. Data from the sounding station closest to the place where the hail phenomenon was reported were thus used. For a comparison the convective parameters, was used ERA5 database [65]. From ERA5 was used a number of 14 instability indices such as CAPE, CIN, TT, KI and the values of temperature, relative humidity, dew point and wind speed and direction at 850 hPa, 800 hPa, 700 hPa and 500 hPa levels. Convective parameter values for 378 hail days were analyzed at 00:00 UTC and 12:00 UTC. The 23 instability indices used are divided into five categories, namely particle theory indices, moisture indices, temperature indices, kinematic indices, and complex indices. They are presented synthetically in tab no. 1.

Statistical analyses were run only for the convective period during which the hail occurs, namely from April to October and for the 00:00 (03:00 AM local time) and 12:00 PM GMT (12:00 PM local time) of the day. Analysis of parameters values at 00:00 was made to evaluate the condition prevailing hailstorm development. Parameters values at 12:00 PM were considered those that characterize the convective environment during the manifestation of the phenomenon trying to capture the convective developments in the afternoon, the classical daytime period for hail occurrence.

Table 1. Parameters used in study.

Table 1. Parameters used in study.

	Group	Index Name	Acronym	Unit of Measure
1	Parcel parameters	Convective available potential energy	CAPE	J/kg
2		Convective Inhibition	CIN	J/kg
3		Lifted index	LI	-
4		Showalter index	SI	°C
5		Lifted condensation level	LCL	m
6		Equlibrum level	EL	m
7		Cloud vertical extent	H_Cl	m
8		Parcel’s max vertical velocity (square root of 2 X CAPE)	Wmax	m/s
9	Temperature indices	Freezing level	FL	m
10		2 m - 700 hPa lapse rate	LR_0-7	°C/km
11		800 - 500 hPa lapse rate	LR_5-8	°C/km
12	Moisture indices	Relative humidity at 850 hPa pressure level	RH850	%
13		Relative humidity at 700 hPa pressure level	RH 700	%
14		Relative humidity at 500 hPa pressure level	RH 500	%
15		Mean mixed layer MIXR (average MIXR in the lowest 500 m)	MLMIXR	g/kg
16		Precipitable water	PW	mm
17	Kinematic indices	0-6-km AGL wind shear - deep-layer shear	DLS	m/s
18		Velocity of the main stream	Vw	Km/h
19	Compositeindices	K index	KI	K
20		Total totals	TT	K
21		Bulk-Richardson Number	BRN	-
22		Severe Weather Threat Index	SWEAT	-
23		DLS x Wmax	WMAXSHEAR	m2/s2

3. Results

3.1. Convective Parameters Values

3.1.1. Parcel Parameters

CAPE mean values from the two databases are approximately 200 J/kg (Figure 2). The median values are about 433 J/kg in the case of ERA5 and 505 J/kg for the asounding data. These are comparable to those of small hail size days in central and western Europe obtained in other studies [15,27]. In Switzerland, for the cases with weak and isolated convective storms, the average value of CAPE from the 12 UTC sounding data was 400 J/kg, and in the Czech Republic, in the case of strong convective storms in more than 80% of the cases, the value was 322 J /kg [66]. Can be seen a difference , especially for higher values than the median quartile, between ERA5 and sounding data. The 75th and 90th percentile values from sounding are about 100 J/kg lower than those calculated with ERA5 data. CAPE maximum values recorded in sounding data was 4351 J/kg on 24.06.1987 and from ERA5 it was 3918 J/kg on 18.06.2016. The parameter Wmax being obtained from taking the square root of the double CAPE, is characterized by the same statistical distribution of values and also by a similar spatial distribution.

Half of CIN values from air sounding stations are close to 0, those from ERA5 have a median value of 70 J/Kg and extreme values exceeding 300 J/kg. We can aproximate this value of convective inhibition on hail days as available convective energy once it has been overcome. The lifting condensation level (LCL) at 12:00 UTC calculated from sounding and ERA5 data, which can be associated with cloud base, located at altitudes higher than 900 m for 90% of the analyzed hail days . In the case of the data from 00:00, the LCL was located at altitudes higher than 800 m for 75% of the analyzed hail days.

LI and SI values ​​being calculated in a similar way also have similar statistical distribution. The difference between the two indices lies in the lower values ​​of LI compared to SI. The values ​​of the lower quartiles of LI lower than -2 that characterize a moderately and strongly unstable environment denote the existence of a moist, unstable layer in the layer at the soil surface. We can associate the higher SI values ​​with a much lower frequency of an unstable, moist layer at altitude corresponding to the 850 hPa level.

The EL values, with much greater variability compared into those of the LCL, also greatly influence the height of the clouds (H_Cl). In most cases the vertical cloud extent was recorded between 3500 and 8000 meters at 00 UTC and 4000 and 9000 m at 12 UTC. Being calculated only from air sounding data, some values of EL and H_Cl are close to 0, as a fact due to the large distance of the stations of aerial sounding toward of hailstorm location.

Figure 2. Box-and-whisker plots for parcel theory parameters The median is represented as a horizontal line inside the box, the edges of the box represent the 25th and 75th percentiles, while whiskers represent the 10th and 90th percentiles.

Figure 2. Box-and-whisker plots for parcel theory parameters The median is represented as a horizontal line inside the box, the edges of the box represent the 25th and 75th percentiles, while whiskers represent the 10th and 90th percentiles.

3.1.2. Temperature Parameters

The vertical profile of temperature distribution in the atmosphere on hail days brings essential information on the 'hail growth zone'. The freezing level is correlated, with the size of hail recorded on the ground [67,68,69,70]. This parameter has the advantage of having a spatial and temporal homogeneity of values, especially for small regions like the studied area. Generally, the FL value on hail days was between 2500 and 3500 m (Figure 3). At the beginning of the convective season, values lower than 2500 m can be recorded in April and values higher than 3500 m in July and August. The other two indices in this category LR_0-7 and LR_5-8 provide an image of some thermal and humidity characteristics of the low troposphere, respectively of the middle troposphere (Figure 3). LR_0-7 represents, from this point of view, in general the situation in the first 3 km of the troposphere. Its values from 12 UTC, in the case of both data sources, are between 6.5 and 9.5 0C/Km indicating the presence of an amount of moisture located below the planetary boundary layer.

3.1.3. Moisture Parameters

The humidity parameters have a similar distribution in the case of both data sources, especially in the case of RH 850 and RH 500 (Figure 4). Differences showup in the case of RH700 where the interquartile values calculated from the ERA5 data are lower. The average value of these parameters calculated for all hail days analyzed begine from 75% in the case of RH850 till 50% in the case of RH500. Values distribution for MLMXR and PW are similar the two time intervals studied. Mean value around 9 kg/g for MLMXR is also specific for large hail cases in western Europe [27]. Over 75% from hail cases in the dataset used had PW values exceeding 22 mm, with a median value of 27 mm.

3.1.4. Kinematic Parameters

For all analyzed hail cases, DLS mean value is around 10 m/s for sounding data from 00 UTC and 8 m/s for those from 12UTC (Figure 5). The similar values are found in central and western Europe [15,27] and greater (around 15 m/s) for the hailstorm in USA [29,71]. DLS upper quartile values exceed 10 m/s and maximum 20 m/s. Vw has values between 7 and 19 km/h, being a very useful index for determining the movement of convective clouds. Its values can be correlated with the speeds of air masses that cause atmospheric instability in the studied territory or with relief and microclimate conditions in the case of local convections.

3.1.5. Composite Parameters

The TT and KI values indicates a moderately unstable environment with the probability of producing strong convective storms in limited areas (Figure 6). The values of these two indices calculated from ERA5 are lower than those calculated from sounding data. KI does not stand out with values higher than 40. Values above 50 in the upper quartile of TT can highlight situations in the first part of the warm semester when the instability was caused by cold air cores located at altitude (at the level of 500 hPa ). WMAXSHEAR is a composite index that has shown a good potential to forecast strong atmospheric instability but also to differentiate the degree of severity of convective phenomena [15,27]. The distribution of WMAXSHEAR values is closely related to that of CAPE from which the updraft velocity is estimated. It is noted that the values calculated from ERA5 are higher than those from the sounding are. For 00UTC only in 25% of cases, WMAXSHEAR indicates the possibility of some convection. Much more suggestive are the data from 12UTC (from both data sources) which have a mean value of 150 m2/s2. Thus, values indicated the presence of an environment with increased instability in 50% of cases.

Other two composite indices calculated from air sounding data, namely SWEAT and BRN have values that indicate the existence of a convective environment favourable to the development of potential hail just for only part of the cases analyzed in the study. In the case of SWEAT, the upper quartile values are between 150 and 300 (Figure 6). These values indicate a reduced probability of the occurrence of strong storms, but it must be considered that in its calculation parameters of moisture from the low levels of the atmosphere, parameters of instability, but also data related to the direction and speed of the vertical wind are used. Values in the lower quartile indicate an environment favorable to strong convection. The upper quartile includes values over 45 that characterize a weakly unstable environment.

Figure 6. Box-and-whisker plots for composites parameters. The median is represented as a horizontal line inside the box, the edges of the box represent the 25th and 75th percentiles, while whiskers represent the 10th and 90th percentiles.

Figure 6. Box-and-whisker plots for composites parameters. The median is represented as a horizontal line inside the box, the edges of the box represent the 25th and 75th percentiles, while whiskers represent the 10th and 90th percentiles.

3.2. Correlations among Parameters

Derivate indices from correlation matrix from sounding data at 00:00 UTC, show up a very strong correlations between indices of the same type or from different "families". Coefficient values of 0.9 or higher are actually autocorrelations occurring between indices that are calculated with the same thermodynamic variables. In this situation there are correlations betwin CAPE – BRN, LI –SI, KI – TT or PW – MLMIXR. Other autocorrelations are recorded between CAPE and indices calculated using its value: Wmax, WMAXSHEAR. Good correlations were considered those with values of rs greater than 0.5. The correlation matrix show two concentration with integer coefficients values over 0.5. The most obvious are the high correlations between the indices calculated based on the particle theory and those between them and the moisture parameters, respectively the composite parameters. Correlations with coefficient values close to 0.5 also show up between the MLMIXR and the composite indices.

Strong negative correlations are recorded between LI, SI and the other indicators due to the negative characteristic values of these two parameters. Other negative correlations such as those between EL and RH850 or FL and RH850 can be explained in terms of thermodynamic laws governing energy exchange in the lower and middle troposphere.

The correlation matrix between parameters calculated from sounding data at 12:00 UTC (Figure 8) shows the same pattern of rs coefficient values. The major difference lies in the higher correlation coefficient values between the particle theory-derived and moisture indices compared to the 00:00 UTC data. The index values at this time are the significant ones that characterize the convective environment, being the closest to the interval in which most of the hail falls occurred.

Correlation matrix for ERA5 parameters stand out significant correlations between the same types of thermo-dynamic parameters as indices derived from air sounding (Figure 9). Between CAPE and CIN exists a strong correlation only at 00:00 UTC observations. The correlation between night time CIN and CAPE and its lack at midday indicates that daytime heating and dynamical factors can convert convective inhibition into available energy for the development of convective hailstorms. At the case of the EL and LR_0-7 indices, a positive correlation present only from 12:00 UTC may be caused by cases where there is a reduced amount of moisture in the early troposphere. This situation involves the increase of the thermal gradient and implicitly of the air saturation deficit, which in turn causes the EL to increase.

Other good correlations are recorded between the relative humidity values at the three pressure levels, 850 hPa, 700 hPa and 500 hPa respectively. These indicate the presence of moist air layers in the lower and middle troposphere.

Figure 7. Correlation matrix for 23 instability indices derived from sounding data at 00:00 UTC. Spearman correlation coefficient (rs) values indicating strong correlations are marked with the darkest shades of red and green. Significance level α=0.05. Autocorrelations and insignificant correlations less than ║0.1║ are marked in gray.

Figure 7. Correlation matrix for 23 instability indices derived from sounding data at 00:00 UTC. Spearman correlation coefficient (rs) values indicating strong correlations are marked with the darkest shades of red and green. Significance level α=0.05. Autocorrelations and insignificant correlations less than ║0.1║ are marked in gray.

4. Discussions

Table 2. Strong linear correlations between index values derived from sounding and ERA5 at 00:00 UTC and 12:00 UTC of the 378 hail fall days analyzed.

5. Conclusion

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