Quantitative hail monitoring in an alpine area: 35-year climatology and links with atmospheric variables

Authors

  • Emanuele Eccel,

    Corresponding author
    1. IASMA Research and Innovation Centre - Fondazione Edmund Mach - Environment and Natural Resources Area Via Mach, 1—38010 San Michele all'Adige, Italy
    • FEM Via Mach, 1-38010 S. Michele, Italy.
    Search for more papers by this author
  • Piero Cau,

    1. IASMA Research and Innovation Centre - Fondazione Edmund Mach - Environment and Natural Resources Area Via Mach, 1—38010 San Michele all'Adige, Italy
    Search for more papers by this author
  • Kathrin Riemann-Campe,

    1. International Max Planck Research School of Earth System Modelling (IMPRS), Meteorologisches Institut, Universität Hamburg, Bundesstrasse 55, 20146 Hamburg, Germany
    Search for more papers by this author
  • Franco Biasioli

    1. IASMA Research and Innovation Centre - Fondazione Edmund Mach - Food Quality and Nutrition Area Via Mach, 1—38010 San Michele all'Adige, Italy
    Search for more papers by this author

Abstract

Hail climatology is usually weakly known and unsatisfactorily standardised in measurement techniques. Trentino, in the Italian Alps, boasts a 271-hailpad network operated since 1974, covering nearly the whole of the regional agricultural area. Many hail indices, concerning both extensive and energetic features of hailstorms, were investigated in a 35-year period, seeking for climatic trends. The results show that, despite a slight, non-significant trend of decrease in the number of events and in the hit surfaces, most energetic indices, which are directly correlated to the damage to crops, have increased in the period, some at considerable rates. Particularly, indices referring to extreme values show the clearest trends. The correlation with atmospheric variables from ECMWF's reanalysis (ERA-40) was considered. Data were processed at six gridpoints, to calculate three instability-related indices. Other ten variables were considered, either integrated over the atmospheric column or at separate atmospheric levels. Correlations between seasonally averaged single atmospheric predictors and hail indices show a varied record of cases, where only some pairs of atmospheric predictors and hail indices give positive results. Statistical links were also sought using a multivariate method involving principal component regression (PCR) and partial least square regression (PSLR) techniques. Despite the more general approach allowed by these methods, only some hail indices respond to the attempt of setting up satisfactory statistical models. The principal-component predictors are built with many atmospheric variables, warning against a simplified use of correlations of some hail indices with few atmospheric predictors. Particularly, it is shown that the number of events is not a useful index for assessing general climatic features of hailstorms, and that the use of one instability index alone—like convective available potential energy (CAPE)—does not allow a thorough description of the links between atmospheric precursors of hail and its real occurrence. Copyright © 2010 Royal Meteorological Society

1. Introduction

Hail is a meteorological phenomenon which affects the different climatic regions of the world differently. Too warm air masses aloft, on one hand, and the lack of convectivity required for the triggering of hail-generating cumulonimbus clouds, on the other hand, do limit the occurrence of hailstorms in either too warm or too cold climates, respectively. Hence, just a small portion of the Earth's surface is significantly affected by this phenomenon, namely the middle latitude regions (between about 30 and 50°), related to the average position of the upper level jet and close to mountain areas. Among these regions, one comprises a large band of Europe, including the Italian peninsula, and particularly its northern regions (Berz and Siebert, 2000). The Alpine range lies nearly parallel to the westerly upper level jet. For this reason, both sides of the Alps can be, alternatively, downwind or upwind from the main flow, causing a high frequency of hailstorms.

Owing to the large variability, hail climatology is usually weakly known and unsatisfactorily standardised in measurement techniques. To date, the majority of climatic investigations on hail have been based either on documentary evidence, mainly from damage surveys (Dessens, 1986; Olcina Cantos, 1994; McMaster, 1999; Changnon et al., 2001; Webb et al., 2001; Piani et al., 2005; Schuster et al., 2005), or on ‘present weather’, qualitative observations at meteorological observatories (Kotinis-Zambakas and Nikolakis, 1989; Steiner, 1989; Mesinger and Mesinger, 1992; Changnon and Changnon, 2000; Changnon et al., 2001; Zhang et al., 2007; Xie et al., 2008; García-Ortega et al., 2010). However, in some areas, locally implemented hailpad networks did produce quantitative, impactometric measurement series (Dessens and Fraile, 1994; Sànchez et al., 1996; Eccel and Ferrari, 1997; Vinet, 2001; Fraile et al., 2003; Giaiotti et al., 2003 Berthet et al., 2010). An investigation on the number of published works based on hailpad data analysis shows the increasing interest in this kind of investigation in recent decades (Palencia et al., 2009). Of course, the latter investigations have the advantage of relying on true physical measurements of the hail events, rather than on their simple occurrence or on an estimate of their extent by the assessment of damages. Therefore, the impactometric approach is able to record changes in the energy-related quantities of hailstorms over time—and not only in their occurrence—with a far larger accuracy and with a far more reliable resolution, irrespective of crop values, insurance policies, time of occurrence of events, and so on.

Horticultural crops are particularly endangered by hail, considering that damage can depreciate crop value by affecting its outward appearance, even in cases when the crop is harvested. If a raw energetic threshold of damage to a generic crop can be determined in about 50 J m−2 (Morgan, 1990), calibrations trials carried out at the Fondazione Mach (Montefinale et al., 1983) showed that fruit may display aesthetic damages at 10–20 J m−2, where energetic fluxes are calculated on the vertical component of fall velocity.

Trentino, northern Italy, is an important region for the production of valuable grapes and apples; this has fostered the setup of a dense hail monitoring network, covering nearly the whole of the agricultural area. The network has been in operation since 1974. The length of the survey period allows us to infer good climatological information, and to draw some remarks on the observable changes.

This work starts with the climatic analysis of hail measured continuously and homogeneously for 35 years; the evidence and the nature of time trends are discussed. Then, the atmospheric information inferred by the ECMWF's re-analysis database ERA-40 is associated to seasonal hail indices in order to ascertain the existence of links between hail indicators and atmospheric instability. The latter investigation, associated with climatic models, might shed light on the possibility and limits of projecting hail recurrence in the future.

2. Materials and methods

2.1. The geographic and climatic context

The orography of Trentino (central-eastern Italian Alps—Figure 1) is characterised by a system of valleys, among which the longest is, by far, Adige Valley. In general, climate in Trentino can be ascribed to the humid, temperate, oceanic type, particularly in the pre-alpine areas, more open towards the Po Plain and the Adriatic Sea. Some areas show features of transition to a more continental-alpine climate, cooler and often drier, more typical of the inner mountain valleys. Most of the area covered by the hail monitoring network falls into a Köppen ‘Cfb’ class (temperate, middle latitudes climate, with no dry season). Precipitation amounts are generally distributed over two maxima, in autumn (main) and in spring (secondary), although in some mountain areas rainfall peaks in summer (Eccel and Saibanti, 2007). Indeed, moving from the main valley bottoms to higher and inner areas, the contribution of summer thunderstorms to the total annual rainfall increases, due to orography-induced mechanisms fostering convective instability. For the same reason, as in other alpine and pre-alpine regions, hailstorms are more frequent and more intense in mountain areas (Eccel and Ferrari, 1997).

Figure 1.

The hail monitoring network in Trentino

2.2. The hail monitoring network

The hail monitoring network in Trentino (Figure 1) was established in 1974. The monitored sites have increased from an initial number of 232 to the present number of 271 since 1985. Only minor changes over the network (expiry of sites and addition of new ones) occurred in the past years. The measuring sites are disposed according to a network having elements of about 2 km side, as regular as possible. It covers the main agricultural areas, and ranges in elevation from 70 to 1260 m a.s.l. (Figure 2). Data are collected from May to September, and exceptionally earlier or later, if important events occur before or after the standard measurement season. The series has been analysed for the period 1975–2009 (35 years).

Figure 2.

Number of hail monitoring sites per altitude class

The network measurements are performed by ‘Schleusener-type’, 15 cm × 15 cm polystyrene hailpads, covered with a 0.135-mm-thick aluminium sheet (Schleusener and Jennings, 1960). The pads are mounted horizontally on bearings fixed at 1 m from the ground. Each hailstone leaves a dent on the aluminium sheet, whose depth (and hence, its horizontal dimensions) is proportional to its kinetic energy. After inking, dents are counted and measured.

The calibration of hailpads was described by Montefinale et al. (1983). Only the vertical component of kinetic energy was considered. The hailstone diameter is calculated through the proportionality between kinetic energy (assessed from the dent size) and hailstone size (Morgan and Towery, 1976). The kinetic energy (Ek) of a falling hailstone is given by:

equation image(1)

where mh = hailstone mass, vt = vertical fall (terminal) velocity and, for a single (supposed spherical) hailstone:

equation image(2)

where ρ = hailstone ice density, Vh = volume, dh = diameter.

Terminal velocity (vt) comes from equilibrium between gravity and friction, which is, in turn, directly proportional to the diameter of the falling ball and to its velocity, so that:

equation image(3)

Finally, kinetic energy, resulting from Equation (1) by substituting Equation s (2) and (3), is

equation image(4)

Data are recorded after each hailstorm; one event is identified by a date, with no discrimination about the recording area. Each dent is described by one of seven diameter classes, each identifying a specific kinetic energy. The total energy is calculated from the product of the number of hailstones in each class and the relevant specific kinetic energy for class.

2.3. Atmospheric data

Since Doswell et al. (1996) introduced the ingredients-based method of forecasting, many studies have used this approach to identify and improve the forecasting of different types of convective severe weather including hail occurrence (e.g. Rasmussen and Blanchard, 1998; Craven and Brooks, 2004; Groenemeijer and van Delden, 2007; Kaltenböck et al., 2009). The above-mentioned studies report that instability and vertical wind shear (VWS) between 0 and 6 km above ground level are favourable for developing hail events.

2.4. CAPE and CIN

Instability is expressed by convective available potential energy (CAPE; Moncrieff and Miller, 1976), which determines the energy available to develop cumulus convection. The potential energy is assessed by integrating the difference of virtual temperature of an idealised air parcel and its environment (Emanuel, 1994). An air parcel is assumed to rise from a well-mixed layer (ML) over the lowest 100 hPa of the atmosphere. If the virtual temperature within the parcel (Tvp) exceeds that of its surrounding atmosphere (Tve), the parcel has reached the level of free convection (LFC). From LFC, the parcel rises freely now, thanks to its lower density, until it reaches the level of neutral buoyancy (LNB), where its density is the same as that of the surrounding air. The integration of the virtual temperature difference between the LFC and the LNB is calculated by:

equation image(5)

where Rd denotes the gas constant of dry air and p is pressure.

However, large amounts of CAPE do not necessarily lead to strong convective storms. A stable boundary layer can prevent convection from happening, if no external forcing leads to near surface air ascent. The stability within the boundary layer is expressed by convective inhibition (CIN; Colby, 1984). The energy needed by the parcel to rise from the ML to the LFC is estimated by CIN:

equation image(6)

Strong VWS favours the development of convective storms by separating the updraft region from the downdraft one, allowing warm moist air to rise, leading to the formation of cumulus clouds. If the moisture within the ascending air cools, condensates, and falls out as rain, it also cools the warm air below preventing the cumulus cloud from further deepening. If the wind velocity increases with height, the cumulus cloud tilts in the direction of the wind, causing the rain to fall in a region different from that of ascent. In this case, the cumulus can develop further, leading to a convective storm.

Several atmospheric variables and indices (list in Appendix 2) were computed diagnostically at 6 gridpoints surrounding the hail monitoring area (Figure 3) from the 6-hourly reanalysis of the European Centre for Medium-Range Weather Forecasts ECMWF (ERA-40; Kållberg et al., 2005) on a 1.125° grid between 1958 and 2001.

Figure 3.

Positions of the ERA40 (1–6) gridpoints. On the frame: latitude and longitude (degrees)

2.5. Combination of CAPE and wind shear

The above mentioned studies analysed CAPE and vertical wind shear derived from observations (Rasmussen and Blanchard, 1998; Craven and Brooks, 2004), ECMWF analyses (Kaltenböck et al., 2009) and a combination of observed and simulated data (Groenemeijer and van Delden, 2007). They relate median values of CAPE and vertical wind shear to several categories of severe weather with hail being either an exclusive category or being combined with strong wind and/or weak tornadoes (Craven and Brooks, 2004). The comparison of these CAPE values with those derived from the ERA-40 data is handicapped by the form of computation. CAPE is derived assuming an idealised rising air parcel. The starting position of the parcel, as well as the role of the moisture within the parcel (after condensation, moisture can either stay within the parcel or fall out as rain) yields several types of CAPE with large differences in their magnitudes. For the different hail categories, median CAPE values range from 537 J kg−1 (1000 m mixed layer-based parcel, Rasmussen and Blanchard, 1998) for storms producing hail sizes less than 5 cm in diameter, to 1072 J kg−1 (most unstable parcel, Groenemeijer and van Delden, 2007) for hail exceeding 3 cm in diameter. In contrast, the median values of 0–6 km wind shear cover a smaller range of 10.8 and ∼13 m s−1 (Rasmussen and Blanchard, 1998; and Craven and Brooks, 2004, respectively) for hail smaller than 5 cm, and 12.3 m s−1 (Groenemeijer and van Delden, 2007) for hail diameters exceeding 3 cm. In addition, Craven and Brooks (2004) combined CAPE and 0–6 km wind shear by multiplication to yield the ‘Significant Severe Parameter’ (SigSev) in m3 s−3, with a lower threshold of 10 000 m3 s−3 for the combined hail–wind category. However, Kaltenböck et al. (2009) reported that a combined parameter of CAPE and wind shear does not discriminate better between severe weather types than its single components.

2.6. Statistical processing

Measurement and collection of hail data at the detail of each single class of hailstone diameter allows a huge amount of information. A general climatology of hail in Trentino has been published with a 20-year dataset (Eccel and Ferrari, 1997). The dataset is nowadays much longer (36 years); however, it is not the aim of this work to provide a full, high-resolution hail climatology. This work focuses on the more general trends of hail in the whole region, and it analyses relationships with atmospheric parameters retrieved from the ERA-40 archive.

Single hail reports were aggregated by event (each identified by one single day) and by hail season (year). Extreme values were investigated (absolute maxima and 90th percentile values). Threshold filtering was tested, leaving out the smallest events, which have little significance in terms of damages. Also a log-transformation was tested, looking for possible improvement in correlation with atmospheric parameters. To avoid the effect of the increase of monitored sites during early years of the network operation, cumulative energy indices were divided by the monitored area of each year (4 km2 for each hailpad site), producing a measure of ‘energy density’. An explanation of all hail indices used in this work is given in Appendix 1.

In both atmospheric and hail variable analysis, to tackle the generally non-gaussian nature of data, two non-parametric tests were used beside the Pearson test on the significance of linear trends: Mann-Kendall and Mann-Whitney ‘U’ test. The latter consists of testing the null hypothesis of no-difference in series obtained by splitting the original series in two parts and allows us to check the increase or decrease of median values between the earlier and later portions of the time series.

The analysis of the link with the atmospheric parameters involved a preliminary exploratory, univariate analysis of each liable predictor with selected hail indicators, and a subsequent multivariate analysis. The datasets were arranged in two matrices with 27 rows (years from 1975 to 2001, the last year with available ERA-40 observations). The predictor matrix (X) had 66 columns for the atmospheric variables and the predictand matrix (Y) had 14 columns for hail indices. X and Y columns were standardised before further analysis. Data exploration on both matrices was performed by principal component analysis (PCA).

For both datasets we expected strong collinearity related to the correlation among variables and to the intrinsic nature of the problem and, therefore, we decided to investigate the problem by multivariate methods aiming at a prediction of hail parameters. For small, highly collinear datasets both partial least squares regression (PLSR) and principal component regression (PCR), as described in Martens and Naes (1989) and references therein, provide often optimum performances. Both methods allow the setting of prediction models based on a smaller set of new latent variables and usually have similar performances (Mevik and Wehrens, 2007). PLSR builds the new variables trying to describe the amount of the predictor (X) variance that has a maximum covariance with the predictand (Y) matrix while PCA, on the contrary, independently maximises the overall variance of the two matrices. For this reason, PLS usually needs a smaller set of predicting variables than PCR, allowing a simpler data interpretation. PLSR can provide models to calibrate both the whole Y matrix (PLS2) and one dependent variable at a time (PLS1). The former case allows better data description and exploration, but the latter has often smaller prediction errors.

Supervised multivariate calibration methods, as PLSR and PCR, need to be validated on samples that have not been used for the model setup. In the case of small datasets, as in the present study, a leave-one-out procedure is preferable: the training set (all elements but one) are used to build a prediction model, whose performances are then tested on the remaining element. The procedure is iterated until all elements have been left out once. The model performance is summarised in the root-mean-square error of cross-validation (RMSECV; Martens and Naes, 1989). The only free parameter in the PLSR and PCR models, the number of components used, must be set using only the training set. Calculations were performed with the statistical software R (R Development Core Team, 2008) using the package ‘pls’ (Mevik and Wehrens, 2007).

3. Results

3.1. Statistical distributions of hail indices

Hail is a rare event, and, as such, the statistical distribution of its quantitative indices is intrinsically non-normal. Being directly associated with damage, kinetic energy of hailstones is the most important hail quantity. Kinetic energy is proportional to the 4th power of the diameter (Equation 4), so single measures are expected to fit better with a log-normal distribution than with a Gaussian one (Eccel and Ferrari, 1997). The pdf of the whole kinetic energy record (each referring to one site and one record) is represented in Figure 4(a), while in Figure 4(b) the pdf of the log-values is represented. Figure 4(c) represents the ‘Q–Q plot’ (sample vs theoretical quantiles), where the theoretical distribution is a log-normal with mean and standard deviation assessed by the whole sample. A visual assessment of the histograms shows the similarity of the distribution to a log-normal, ascertainable by both Shapiro and Pearson normality tests on sub-samples of the total observational set; however, the Q–Q plot shows some differences in the tails of the distribution.

Figure 4.

Distribution (frequency) of hail kinetic energy for report: (a) raw values; (b) logs; (c) “Q-Q plot”: comparison between theoretical (log-normal) and sample distributions

Some of the annually aggregated hail indices display a quasi-normal distribution, while some do not, as can be seen from Figure 5, representing the pdfs of some of them. This result suggests non-parametric tests for the detection of time trends.

Figure 5.

Statistical distribution of occurrence of three selected annual hail indices. Upper panels: raw values. Lower panels: logs. See Appendix 1 for the meanings of acronyms

3.2. Hail-time trends

Only the features that are relevant for a general treatment of temporal behaviour of annual hail indices are investigated in this work. The first year of the series was discarded, due to the lower number of monitored sites and some doubts on the quality of recordings; then, series refer to the period 1975–2009. Non-parametric (Mann-Kendall and Mann-Whitney) tests on time trends were carried out.

Results (Table I) show that all the significant trends are positive. Among these, both average and ‘extreme’ (90th percentile) values show a clear, significant increase, in the range of 1.22–1.69% per year (range limited to the significant trends). In general, extreme values show more significant trends than maximum values. On the contrary, the number of hail days (days with at least one hail record) is decreasing, but not significantly at the 5% level (for this reason values are not shown in the table). Even less significant is the decrease of the cumulative hit surface. The time series whose trend values are reported in Table I are represented in Figure 6.

Figure 6.

Time series of anomalies of hail indices with significant trends (see Table I) and regression lines. See Appendix 1 for the meanings of acronyms

Table I. Trends of annual hail indices (1975–2009) expressed as % variation per year on the mean values (see Appendix 1 for legend). p MK: non-parametric Mann-Kendall's p-value. p MW: non-parametric Mann-Whitney p-value. Only trends with p < 0.10 for both methods are reported. Values in bold are significant with p < 0.05 for both methods
 Trend (% yr−1)p MKp MW
cum_hit_surf_dens
hail_days
m_surf_ev
dens.cum.en.
m.en_rep+ 1.350.0070.009
sd.en+ 1.220.053
m.en.ev.+ 1.440.0050.001
m._tot_en.ev+ 1.550.072
max.en_rep
extr.en_rep+ 1.480.0110.006
tot_en_max_ev
tot_en_extr_ev+ 1.690.0380.015
ratio_extr_to_tot_en_ev
ratio_max_to_tot_en_ev

3.3. Time trends of atmospheric variables

Time trends for annual series were assessed for the period of joint availability of hail data and ERA-40 (1975–2001). Aiming at summarising the representation of this analysis for variables expressed on pressure levels, only the one best correlated to hail indices was considered. Results are summarised in Table II, where the sign of the trend is shown only for cases with p < 0.05 according to the Mann-Whitney test. In general, no atmospheric variable shows a significant trend on all the 6 gridpoints. With the exception of vertical velocity (W), there is never discordance in the signs of significant trends. Taking into consideration only the atmospheric variables with significant trends of the same sign in at least 3 gridpoints, a decrease of CAPE can be inferred (especially significant on the southern, plain area), of relative humidity aloft, and of potential vorticity (PV) in the middle-lower atmosphere (the atmospheric level of vorticity, 925 hPa, is too low for being meaningful at mountain gridponts). The only increasing variable is CIN.

Table II. Mann–Whitney test: sign of the trends for atmospheric variables at the six gridpoints (P1…P6) considered (positions shown in Figure 3), for the period 1975–2001 (coincident with hail recording). Empty cells: non-significant at p − 0.05. @XXX denotes the level, in hPa, displaying the highest calculated time trend. See Appendix 2 for meanings of acronyms
1975–2001P1P2P3P4P5P6
CAPE max  
CIN 12UTC + ++ 
TCW mean      
TCWV mean      
TD mean+  +  
MSLP 12 UTC      
SigSev      
VO@925   
W@775 +  
RH@400 
Q@400      
PV@775   

A decrease in CAPE in combination with an increase in CIN reveals that conditions favourable for convective storms become less frequent; this would explain the lower occurrence of hail days. On the other hand, the trend in vertical velocity does not confirm this explanation: its sign is ambiguous, but pointing to an increase in absolute (negative) values (enhanced convection) in two points out of the significant three. The total water vapour content in the atmospheric column (TCW) shows no trend, while relative humidity (RH) aloft has significantly decreased in almost all the grid. This can be explained with a general increase of atmospheric temperature, not associated to a similar increase in the water content of air.

3.4. Hail correlation with atmospheric variables

The exploratory analysis of the correlations between atmospheric variables and hail quantities yielded interesting hints. Given the large amounts of relationships and the ramifications of choices in the atmospheric variables (gridpoints, different time aggregations, different pressure levels, application of detrending and of log-transformation), results have been strongly summarised in order to allow their representation in a synoptic table (Table III). In it, only the highest values of Pearson's R2 are given, choosing the best couple of series between each hail index and each atmospheric variable at: (1) gridpoint (nr. 1–6); (2) time aggregation (6-hourly mean or value at 12 UTC—only for CAPE: maximum in the day); (3) baric level, for variables given over baric levels in ERA-40 (Table II); and (4) either raw or time-detrended series.

Table III. Pearson's R2 between annual hail indices and atmospheric variables (see Appendices 1 and 2 for the meaning of acronyms). (a) Atmospheric variables averaged over four 6-hourly values per day; (b) average of the values calculated at 12 UTC time. Unreported values are not significant at p < 0.05. Values reported come from inference of either raw (plain character font) or detrended (italics) series and are the maxima attained. R2 with p < 0.01 are in bold. Neither lines nor columns with less than two significant R2 values are reported
(a)
Seasonal means (6-hourly values)Variables integrated over the atmospheric column (best over 6 points)Variables on 7 pressure levels (best over levels and over 6 points)
Hail indicesCAPECINTCWTCWVSigSevWVORHQPV
cum_hit_surf_dens0.3880.4830.1860.1810.228
hail_days0.3430.1680.2540.2260.1620.203
m_surf_ev0.1500.2750.3640.444
m.en_rep0.1640.1920.195
m.en.ev.0.1610.2840.193
m._tot_en.ev0.1810.175
max.en_rep0.1730.150
extr.en_rep0.2100.1910.153
tot_en_extr_ev0.160—0.1860.2030.1570.185
ratio_extr_to_tot_en_ev0.1620.1690.2160.2030.177
(b)
Seasonal means (values at 12 UTC)Variables integrated over the atmospheric column (best over 6 points)Variables on 7 pressure levels (best over levels and over 6 points)
Hail indicesCAPECINTCWTCWVSigSevWVORHQPV
cum_hit_surf_dens0.4020.5650.1480.154
hail_days0.4350.1850.2650.2570.197
m_surf_ev0.1530.3160.2480.3470.167
m.en_rep0.2010.1740.240
m.en.ev.0.2270.2270.1490.183
m._tot_en.ev0.1690.1720.2320.2070.167
max.en_rep0.2170.1590.236
extr.en_rep0.1640.1620.2220.1990.217
tot_en_extr_ev0.1820.1880.2190.1970.2420.212
ratio_extr_to_tot_en_ev0.2150.1920.2110.4100.175

Log-transformation did not yield general improvements of the correlations, so the corresponding results are not reported.

In general, the results show that: (1) none of the variables considered show significant correlations with the whole set of the six gridpoints and some atmospheric variables considered are never significantly correlated with any hail index; (2) CAPE, SigSev, W and PV show, in general, the highest correlation with some hail indices, mostly better after detrending of both atmospheric and hail indices; all the three variables are useful measures for assessing atmospheric convectivity; (3) the most highly correlated hail indices all refer to either the number of hail days or to the extension of the hit surface; with the only exception of the ratio of extreme event to total annual energy, correlations of energetic indices with atmospheric variables are always lower than 0.3; and (4) use of residuals after detrending both hail indices and atmospheric variables shows ambiguous effects on correlations.

To ascertain the role of enhancement/inhibition of hail generation, daily data were aggregated with different SigSev and CIN thresholds. It can be seen (Figure 7) that a combination of SigSev > 10000 m3s−3 and CIN < 50 J kg−1 provides a good discrimination between days with and without hail. The frequency density of days without hail is represented by the first class of aggregation (values = 0 for each hail index). The discrimination is good for the hit surface and for both mean and maximum kinetic energy, negligible for the total kinetic energy measured by the network.

Figure 7.

Comparison of daily hail indices frequencies according to a combination of atmospheric instability enhancement/inhibition indices. Full dots: SigSev > 10000 m3s−3 and CIN < 50 J kg−1. Open dots: all other cases

3.5. Multivariate analysis: data exploration and model calibration

The algorithms of the R package ‘pls’ have been implemented for both PLSR and PCR, linking atmospheric variables to hail indices. Model skills do not differ much between the two cases, so results can be presented together.

The atmospheric variables reported by ERA-40 at baric levels were included only for the best correlated ones. Variables entered the model at all the six chosen points of the ERA-40 grid. The result of a PCA on predictors and predictand matrices is represented in Figure 8, while Figure 9 represents the cumulative explained variance with increasing number of components. It can be seen that the number of components required is relatively low for the Y matrix, where 5 components successfully describe more than 97% of the variance, and rather high for the X matrix, where 14 components are needed to attain a similar value.

Figure 8.

First and second principal components of PCA analysis of both predictor matrix (left panel) and predictand matrix (right panel)

Figure 9.

Cumulative explained variance for PCA models with increasing number of principal components for the predictor (X) and predictand (Y) matrices

The analysis did not encompass the creation and use of principal components on hail predictands, which would have involved hardly interpretable compositions of indices. Nevertheless, it may be worth observing that some hail indices are strongly correlated, especially those that reflect different measures of kinetic energy. Scatterplots of the most correlated hail variables (annual values) are given in Figure 10. For example, as expected, the standard deviation of kinetic energy is strongly correlated to both extreme (90th percentile) and maximum energy, and the same is true for mean energy with respect to its 90th percentile.

Figure 10.

Scatterplots of the most correlated standardised hail descriptors. See Appendix 1 for the meanings of acronyms

For all hail variables we set prediction models both based on PLSR and PCR and evaluated them by leave-one-out cross-validation. The predictive skill of the models is very different for the different hail descriptors and only for few variables in the whole set of predictands can interesting indications be derived. For these variables the performance of PLS1 is only slightly better than that of PLS2 and very similar to PCR. The minimum error in prediction is achieved with about 5 components for PLSR1 and PLSR2 and with about 14 components for PCR. In general, PCR yields better predictions than PLSR, yet employing a much higher number of components. Hence, the latter approach strongly hampers interpretation purposes on the nature of the causal connection between atmospheric forcing and hail production. Then, we limit our discussion to the PLSR1 case.

The following hail indices were considered suitably modellable by atmospheric predictors: (1) annual mean kinetic energy; and (2) annual extreme kinetic energy for report.

Figure 11 represents cross-validation scatterplots for these two hail kinetic energy indices. Every predicted value was estimated on a different model set without using it. Root-mean-squared errors of cross-validation (RMSECV) of the pls-PCR models for the two abovementioned variables are in the range of 0.6–0.7 (referred to standardised variables), with R2 values of 0.58 and 0.45, respectively, for the two variables. Permutation tests (Welch, 1990) confirm that these values are highly significant (p < 0.002).

Figure 11.

Measured vs predicted values for kinetic energy annual values: (a) mean; (b) “extreme” (90th percentile)

4. Discussion

One problem when addressing hail climatology is the coarseness of surveying networks associated to the heterogeneity of hail measurement techniques (often hail incidence is estimated by indirect data as agricultural damage assessments or insurance refunds paid to growers). Past studies in other regions of the world have found results that may be apparently contrasting. For France, in the period 1989–2009, Berthet et al. (2010) found results similar to ours, with a strong increase in hailstorm intensity, but not in their frequency. Cao (2008) found an increase in intense hail events in Ontario in the period 1979–2002, while for the USA, Changnon and Changnon (2000) found different results within the 65 studied areas, with hail activity peaking on average around the half of the past century, then following a weak negative trend. Schuster et al. (2005) report a decrease in the number of hailstorms in Australia in the last 15 years of the examined period 1953–2003. For the period 1980–2005 Xie et al. (2010) found contrasting, but non-significant time trends in hail diameters of severe hailstorms in four Chinese regions (the study did not consider the frequency of events). As far as regards the number of hail days investigated over a wide area covering most of China, Xie et al. (2008) found no trend in the 60s and 70s, and a decrease from the 80s. Interestingly, the authors found a general increase in CAPE values till the 90s.

The latter work prompts us to observe that, if the present investigation had been limited to the number of hail days, the result for the studied area would have been similar to that of Xie et al. (2008): a weakly significant decrease. On the contrary, an increase of several energetic parameters was observed in Trentino. A look at the time series (Figure 6) suggests an evident increase in most energetic hail indices from about 1977 or 1978 to, roughly, 2003–2006. On the contrary, ‘extensive’ indices (number of hail days, cumulative surfaces—aggregated both over the season and over the single event) are stable or in (weakly significant) decrease. In general, the temporal behaviour of extreme values is more regular than that of maximum annual values, whose trends are never significant due to their large scattering. This is consistent with the intrinsically non-gaussian distribution of hail, offsetting the maxima to values often outside the normal range. Then, statistics of extreme events (in this study: 90th percentiles), rather than statistics of absolute maxima, can be better dealt with and the relevant results may be more useful.

The overall cumulative kinetic energy does not show any time trend; nevertheless, the majority of indices related to intense hail events do: mean energy per report and its standard deviation, the average and the extreme energetic figures of single events, all suggest that hail phenomenon has increased in intensity, if not in its average values. As a general rule, it can be concluded that, in Trentino, hail has enhanced the extreme behaviour of its energetic aspects, roughly maintaining the constancy of the extensive indices, like frequency of occurrence (number of hail days—or ‘events’) and cumulative hit surfaces. This is true both in the raw sample of single observations (increase of mean, standard deviation, and 90th percentile of energy), and in aggregated fields, like the events (increase of the cumulative energy of the 90th percentile event).

Taken one by one, no single atmospheric variable, averaged over the whole yearly seasons, shows a high correlation with hail indices. The better correlated seems to be CAPE and the SigSev (which are particularly significant, assessing atmospheric instability integrated along the whole tropospheric column), vertical velocity (W) and potential vorticity (PV), all of them also fostering convection and, hence, cumulonimbus formation. However, none of the three shows high correlation with more than one or two hail indices. Moreover, results are different when atmospheric variables are averaged over the four daily ERA-40s measures or over the values at 12 UTC (1 pm local time), and even before and after temporal detrending of series, applied to avoid artificial trend drifts due to independent time trends in the pairs of series.

There may be more than one reason for this. The first is the limited lifespan of hailstorms: the typical duration of an event is at least one order of magnitude lower than the time resolution of predictors from ERA-40 database (either 6 or 24 h, depending on the chosen aggregation time). The second is the limited coverage of the measurement network: 1626 km2, about 7.5% of the 21724 km2-wide area subtended by the 6-points grid extrapolated from ERA-40; given the strictly local scale of hailstorms (Dessens, 1986), in spite of the high space resolution of the hail network, the area is still undersampled. The third is the existence of threshold effects in the hail triggering mechanisms. In Trentino, hail is recorded by the network, on average, in about one-fifth of days of the monitoring period (May–September); during the other four-fifths of the days atmospheric variables may even lead to thunderstorms, but they get no effect on hail formation (or better, on its detection). However, the introduction of thresholds on CAPE brought no improvements in correlations with hail indices (results not shown). In contrast, the combination of SigSev > 10000 m3 s−3 and CIN < 50 J kg−1 is able to discriminate between days with and without hail occurrence. Dupilka and Reuter (2005) found that in Alberta the plain value of CAPE was not enough to discriminate among storm categories (including tornado-generating and hail-generating), the distribution of CAPE along the vertical atmospheric column being required for a true enforceability of its discrimination skill. Xie et al. (2010) found that, in China, the effects of several atmospheric forcing agents affect the time trend of the maximum hail diameter in annual series. A model developed by the authors shows that the antagonism of atmospheric agents may lead to non-univocal effects, scarcely predictable (like in the case of the increase of CAPE, leading to increased updraft in cumulonimbus clouds, and, on the other hand, of the freezing-level height, leading to enhanced melting of hailstones).

The fourth (and probably not the last) is the difference between re-analysis data and true atmospheric status. As an example, Niall and Walsh (2005) report scatterplots of CAPE values as estimated by NCAR reanalysis versus values calculated by radiosounding, showing a very poor match. We found a similar result when comparing daily CAPE data from Milan-Linate, Italy (45.43N, 9.28E, WMO station code: 16080) from University of Wyoming's radiosounding database, to those at the closest ERA-40 gridpoint (45.42N, 10.125E—point nr. 4, Figure 3), for the period 1997–2001. The gridpoint and the station are 66 km apart, and they both lie in the Po Plain area. This disagreement is likely due to the difference of the two ways of assessing CAPE: in reanalysis, it comes from assessment of atmospheric quantities averaged at a gridpoint, and provides an estimation of its value in a mean gridbox that includes both southern Alps and Po Plain areas, whereas station data come from the integration of direct measurements.

The use of a multivariate regression model like PLSR or PCR confirms these findings. The first components are made out of the contribution of many variables (Figure 12), each one appearing for either some or all the 6 gridpoints selected. An interpretation of the meteorological meaning proves difficult, and only some general features of the model can be inferred. For some predictors, at least for component 1, there seems to be a tendency in clustering the contribution of alpine gridpoints (1, 2, and 3) and the Po Plain ones (4,5, and 6). The most striking predictors are CAPE, CIN, W, RH for component 1, pointing to the importance of atmospheric instability indices. Component 2 has a more balanced sharing of loadings among the predictors, with the exception of W, and cannot be easily categorised. Component 3 emphasises the role of atmospheric water-related variables: TCW, TCWV, Td, and Q. Another study carried out in northern Italy (Giaiotti and Stel, 2006) did show the importance of water vapour in affecting hailstone size distribution.

Figure 12.

Composition loadings (first three principal components) of the latent variables used in the prediction model of hail mean kinetic energy. Each set of six variables represents one predictor over the six ERA40 gridpoints. See Appendix 2 for the meanings of acronyms

The feasibility of qualitative climatic projections for hail rests upon the definition of clear statistically significant relationships among atmospheric predictors and hail indices. Some authors have tried this path, but results are hardly comparable with one another due to differences in the geographic locations and in the methods. With the help of a sophisticated cloud microphysics scheme in an AO-GCM model, Leslie et al. (2008) simulated hail occurrences for the area of Sidney Basin for the next five decades, finding decadal oscillations, but no clear trend. Trapp et al. (2007) simulated the future of intense thunderstorms in USA by applying an instability index (derived from CAPE and vertical wind shear) to the projections of a regional climate model, finding a trend of increase of conditions favourable to the development of strongly convective systems, implicitly including hailstorms. Niall and Walsh (2005), after finding a positive correlation between CAPE and hail, simulated projections of no-increase of hail occurrence and damages in southeastern Australia for the next decades. For the same region, also McMaster (1999) assumes a probable future decrease in hail damages. On the contrary, for Tuscany (central Italy), Piani et al. (2005) projected an increase in the number of hailstorms (especially in spring) for the next decades, but it is worth observing that the authors claim that the latter feature is probably driven by the increase of the simulated precipitable water amount, and opposed by the expected decrease in atmospheric lapse rate. On the contrary, processing of model ECHAM5 climatic projections for the alpine area, where hail is an eminently summer phenomenon, seem to show an increase in summer atmospheric instability (CAPE), and no trend in summer Total Column Water (TCW) (data not shown). Moreover, the most recent climatic simulations confirm the strongly expected reduction of summer precipitation in the ‘Mediterranean’ area, including the Southern Alps (van der Linden and Mitchell, 2009).

This short review of the most recent studies on hail climatology leads to the awareness of the difficulty in projecting hail fate for the next decades: addressing the simplest hail indicators may lead to an under-representation of the problem, and the choice of some predictors instead of all the possible ones may determine an incomplete representation of the causal connection between atmospheric status and hail. For instance, the simple use of CAPE alone for modelling hail in the period 1975–2001 (overlapping period for ERA-40 and Trentino hail database), would yield a decrease in hail indices like the annual cumulative hit surface due to a decrease of CAPE in the period (Table II), whereas the recorded series gives no significant trend (Table I). The case of summer 2003 is representative of how an approach based solely on the most intuitive seasonal climatic features may mislead prognostic assertions on hail occurrence. Despite the permanent absence of cyclonic circulation patterns, associated with unusually high temperatures and moisture deficit over most of Europe (Garcia-Herrera et al., 2010), summer 2003 was one of the highest on the record (or the absolute highest) for hail occurrence, namely for important indices like total and extreme kinetic energy (Figure 6).

Finally, it may be interesting to consider possible links between hail occurrence and large-scale atmospheric circulation patterns, even if the numerical results are not shown in the present work.

On the extra-tropical northern Hemisphere, CAPE and CIN are correlated to the North Atlantic Oscillation (NAO), whose effects spread to northern Italy (Riemann-Campe et al., 2010). The location of the storm track and thus CAPE and CIN vary with the NAO.

Giaiotti et al. (2003) found that only a few regions in Europe seem to show some correlations (either positive or negative) of the number of hail days with the North Atlantic Oscillation Index (NAOI), Trentino not being among these. As a corollary of our analysis we considered also the other hail indices, and found no significant correlation with three time aggregations of NAOI: the whole year, summer, and winter (referred to both the previous and the following season).

Actually, analysing the atmospheric conditions linked to the presence of hail over the Middle Ebro Valley region (Spain), García-Ortega et al. (2010) showed that several patterns are associated with the occurrence of hail: their clustering gives place to synoptic situations that, in general, reflect the different convection-triggering mechanisms over the area. Albeit the remarkable geographic and climatic differences between the Iberian Peninsula and our southern alpine investigation area, the work shows that hailstorms can be generated by diverse meteorological conditions. Hence, analyses of links between hail occurrence and large-scale circulation patterns are strongly prone to the complexity of the phenomenon.

5. Conclusions

In some regions of the world, hail is an important agent of damage endangering agricultural crops. Hail is also an infrequent phenomenon, whose direct quantitative measurement requires a dense and costly network. Thus, direct observational time series are scarce. The latter, if including hailpad measurements, are particularly valuable, kinetic energy being directly linked to the effect of hailstone impact. In Trentino, the presence of a high-density impactometric network since 1974 gives an excellent chance of inferring climatic features of hail measures including energetic indices.

Analysis of time trends of annual series in the last 35 years (records from May to September) shows an asymmetric shift in hail: whereas some metrics like the number of hail days (events) or the cumulative hit surface remained substantially unchanged, showing a slight non-significant decrease, while most energetic indices show a considerable, even if irregular, increase in the period. This seems clearer for the extreme values indices, like the 90th percentile measures. It may be concluded that, in Trentino, hail seems to have extremised its behaviour.

With the present study, we think some more detail has been added to the links between atmospheric instability and hail. Aiming at eventual applications of the knowledge of hail climate to climate model simulations for downscaling purposes, analyses were carried out on the relationships between hail and annually aggregated atmospheric instability indices. The ERA-40 dataset allowed the use of a large amount of gridded atmospheric data. Generally speaking, one result of this analysis is the complexity of the statistical correlations which can be set up among predictors (atmospheric variables) and predictands (hail indices). Not all hail indices show clear relations with atmospheric variables. CAPE, and above all, its combination with vertical wind shear, the SigSev, index taken by themselves, seem to have the highest predictive skill. Inconsistent signals come from the positions of gridpoints on which atmospheric parameters are calculated.

Aiming at producing a more general prediction model, the use of a multivariate approach with PCR and PLSR showed an acceptable skill for a few important energetic hail indices. However, the number of atmospheric variables used for the creation of the predictors is high, encompassing different measures of dynamic features and temperature- and humidity-derived quantities. This prompts to a twofold reading of the results. At one hand, the feasibility in predicting some hail climatic features is shown by this analysis, even with some caveats. On the other hand, the outcomes of the present investigation warns against simplistic formulations in the search of correlations between hail and potential climatic atmospheric predictors; results show that many variables independently contribute to the composition of atmospheric predictors, and that some can act as antagonists to the most intuitive indices of atmospheric instability.

Eventual steps of the work envisage the use of the developed know-how to try to build statistical models more oriented to climate forecasting, by use of climatic model outputs, and to extend the investigation to the real-time prediction, shifting the focus to meteorological models and their use for forecasting purposes.

Acknowledgements

We acknowledge the DKRZ, DWD, and ECMWF for providing us with their data. Thanks to Claudio Dalsant for his over-30-year patient work in the maintenance of the hail network, and to Stefano Corradini, Alessandro Biasi, Giambattista Toller, and Fabio Zottele for the database management. We wish to thank the two anonymous referees for their useful suggestions.

Appendix 1. Annual Hail Indices and Units

  • cum_hit_surf_dens = cumulative hit surface density ( = cumulative hit surface/total monitored surface) (−)

  • hail_days = nr. of hail days (or events: one event ≡ one hail day) (−)

  • m_surf_ev = mean surface for event (km2)

  • dens_cum_en. = density of cumulative kinetic energy (J m−2)

  • m.en_rep = mean energy per report (one report ≡ recording of one event at one site) (J m−2)

  • sd_en = standard deviation of kinetic energy (per report) (J)

  • m_en_ev = spatial mean kinetic energy for event (J m−2)

  • m_tot_en_ev = mean total kinetic energy per event (MJ)

  • max_en_rep = max kinetic energy for report (J m−2)

  • extr_en_rep = extreme (90th percentile) kinetic energy for report (J m−2)

  • tot_en_max_ev = total kinetic energy for maximum annual event (MJ)

  • tot_en_extr_ev = total kinetic energy for extreme (90th percentile) event (MJ)

  • ratio_extr_to_tot_en_ev = extreme (90th perc.) event kinetic energy/total annual kinetic energy (−)

  • ratio_max_to_tot_en_ev = maximum event kinetic energy/ total annual kinetic energy (−)

Appendix 2. Atmospheric Indices and Units

At the ground level or integrated over the atmosphericcolumn

  • CAPE = mixed layer (100 hPa) pseudo-adiabatically Convective Available Potential Energy (J kg−1)

  • CIN = mixed layer (100 hPa) pseudo-adiabatically Convective INhibition (J kg−1)

  • TD = 2 m dew point temperature (K)

  • TCWV = total column water vapour (kg m−2)

  • TCW = total column water (kg m−2)

  • MSLP = mean sea level pressure (Pa)

  • VWS = 0–6 km above ground level vertical wind shear (m s−1)

  • SigSev = Significant Severe Parameter (m3 s−3)

At 7 atmospheric baric levels between 925 hPa and400 hPa

  • T = temperature (K)

  • Q = specific humidity (kg kg−1)

  • RH = relative humidity (%)

  • PV = potential vorticity (K m2 kg−1 s−1)

  • W = vertical velocity (Pa s−1)

  • VO = relative vorticity (s−1)

  • U = zonal wind velocity (m s−1)

  • V = meridional wind velocity (m s−1)

Ancillary