Analysis of mesoscale convective systems with hail precipitation

Atmospheric Research 67 – 68 (2003) 573 – 588 www.elsevier.com/locate/atmos

Analysis of mesoscale convective systems with hail precipitation J.L. Sa´nchez a,*, M.V. Ferna´ndez a, J.T. Ferna´ndez a, E. Tuduri b, C. Ramis c a

Laboratorio de Fı´sica de la Atmo´sfera, Dpto. Fı´sica, Fac. de C. Biolo´gicas y Ambientales, Instituto de Medio Ambiente, Universidad de Leo´n, 24071 Leo´n, Spain b Instituto Nacional de Meteorologı´a, Centre Meteorolo`gic de les Illes Balears, Spain c Grup de Meteorologı´a, Departament de Fı´sica, Universidad de les Illes Balears, Spain Accepted 28 March 2003

Abstract Severe thunderstorms hit the Ebro Valley (Northeastern Spain) during the summer months, and hail precipitation is frequently registered. In this area, the spatial scale of storm cells is usually of 10 to 40 km. Nevertheless, in conditions of deep convection there may be precipitation systems on spatial scales from 40 to 500 km or larger. These types are known as mesoscale convective systems (MCS). Occasionally, there are long-lived mesoscale convective systems, termed mesoscale convective complexes (MCC), that cause intense precipitation and may produce hail. There are middle latitude classification criteria used to identify MCS and MCC from enhanced IR images, which may be derived from METEOSAT. This paper presents an analysis based on a classification of METEOSAT images for hail events in the Ebro Valley. The database consists of 72 of these hail events including 28 cases of MCS and 5 of MCC. In the remaining 36 cases, the convective air masses produced hail precipitation, but did not fulfill the classification criteria to be considered MCs. In addition, the paper includes a characterization of preconvective conditions according to different sounding variables. A logistic regressive analysis has been applied and the results show the difficulties encountered in forecasting the formation of MCs on the basis of preconvective variables. D 2003 Elsevier B.V. All rights reserved. Keywords: Satellite images; Sounding variables; Hailstorms

* Corresponding author. E-mail address: [email protected] (J.L. Sa´nchez). 0169-8095/03/$ - see front matter D 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0169-8095(03)00074-7

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1. Introduction It is a well-known fact that severe thunderstorms produce heavy rain and hail. Severe thunderstorms that produce this type of precipitation are consequently regarded as natural hazards and can be a cause for economic uncertainty. The regions with a higher frequency of hailstorms are mostly at middle latitudes and downwind of mountain ranges. Heavy rain (i.e. rainfall rates >50 mm/h) may affect hundreds of km2 and the area may be delimited rather easily. In contrast, delimiting the zones where hail precipitation has occurred is a difficult task. This is due to the fact that the affected zones cover generally a land area of only a few tens of km2. How can we identify the areas affected by hail and the characteristics of hailstones? In order to answer this question, we can check the information provided by hailpad networks (Fraile et al., 1991). Unfortunately, there are few areas where these networks are installed, and they generally cover just a few thousand km2 (Fraile et al., 1992). Establishing the ground truth is not an easy matter when dealing with hail phenomena. Alternatively, other observation methods may be employed, such as networks of observers scattered over a particular area. In this case, it is easy to determine whether there has been hail or not, and the approximate size of the hailstones can be estimated. This option requires a very dense network of observers (Changnon, 1977; Sa´nchez et al., 1996). Finally, there is a third option: making use of the information included in the database of the damages caused by hail on crops. This information indicates clearly the occurrence of hail in a particular area. However, there are a number of limitations that have to be taken into account:


The database refers to the months of the year when crops are insured. Hailstorms usually occur in the time of the year when crops are particularly sensitive to the impact of hailstones, so this database may contain interesting information. In this case, the damages caused by hailstones on insured crops are used in order to try and reach the ground truth of the hail event.
There is one disadvantage to this option. Some hail events are not included in the database, either because they did not damage any crops, or because the damaged crops were not insured. Nonetheless, this is not a major inconvenience, since hail affecting areas that are not insured usually cause damages in areas that do have crop insurance. Thus, taking into account this small disadvantage, the phenomena will still be recorded as ‘‘hail events’’. Insurance companies use these databases in order to estimate hail risk and to establish insurance premiums. In the United States, these databases have been used for both purposes (Changnon, 1999). This source of information allows us to approach the ground truth, since it tells us where and when most of the hail has fallen on a particular area (Changnon, 1971). However, there is a possibility that these databases actually contain an underestimate of the true number of hail events. In the Mediterranean areas of Europe, uninsured crops amount to about 50% of the total production. Consequently, we may have access only to what happens in the areas where crops are actually insured.

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There are numerous difficulties when trying to determine the ground truth in hail events, but in some cases it has been possible to analyze their climatological characteristics. Vinet (2001) established the first hail climatology in France making use of several sources of information, mainly hailpad networks. When hailpad network data were not available, Vinet checked hail risk estimations made by insurance companies and recorded in the insurance premium database. Changnon et al. (1997) followed a similar method in the USA. In Spain and other Mediterranean countries, insurance companies hold excellent databases that provide data about hail events in specific areas. Between the years 1991 and 2001, insurance companies paid out more than 2200 Mo (US$2300) in Spain in compensation for damages on crops caused by hailstorms. According to the data provided by the International Association of Hail Insurers, whose headquarters are in Zurich, Spain is the European country with the biggest losses in agriculture caused by hail. Italy and France come immediately after Spain. So, the data available show that the Mediterranean area should be considered a risk zone for losses on property and crops caused by hail events. Rivas Soriano and de Pablo (2002) have shown that the most intense convective activities originated by thunderstorms are concentrated in the northeast quadrant of the Iberian Peninsula. Vinet (2001) points out that in France, the line of hail risk marks the boundary between the Mediterranean and the Atlantic climate. Consequently, there is a general consensus that the Pyrenees is bounded by high-hail risk zones: to the south in the Central Ebro Valley and further north in the southwest of France. The Mediterranean Sea favors the formation of storms more so than the Atlantic Ocean in similar latitudes. According to the risk map estimated by Agroseguro (the Spanish company for crop insurance against hail), the economic impact caused by hail in the Central Ebro Valley may well amount to about 100 Mo annually. When the meteorological conditions favor the formation of thunderstorms, these structures are generally grouped together covering an area of tens of km2. There may be several active storm cells inside these structures. When one or several of them develop into severe thunderstorms they are known as severe mesoscale precipitation systems (SMPS). According to Weisman and Klemp (1986), SMPS are characterized by one or more areas with vigorous updrafts that may lead to strong winds, tornados, and heavy precipitation with or without hail and lightning. When there are SMPS in the Ebro Valley any of these phenomena may occur, although tornados are not so common as the rest of phenomena. Several cells may co-occur within one SMPS. The interaction among cells can be observed along a mesoscale and a synoptic scale. As this interaction increases, the degree of convective organization increases too, leading to the formation of mesoscale convective systems and/or mesoscale convective complexes, known as MCSs and MCCs. The real-time detection of the degree of convective organization in SMPS is important because it is linked to their severity. The structure of SMPS may be classified according to the degree of convective organization. Several classifications of SMPS have been put forward. Schiesser et al. (1995) use radar data to establish a structural classification of SMPS in Switzerland according to the degree of organization. Previous studies carried out

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by our team (Castro et al., 1992) describe the characteristics of storm cells in the Central Ebro Valley making use of data provided by a meteorological radar. But to reach a better understanding of the organization of severe convective hail events in the Ebro Valley, it is necessary to extend the spatial observation to identify those SMPS that can be classified as MCSs and MCCs because they affect wide areas. In these cases, the infrared satellite images provide valuable information, since SMPS structure may be examined in real-time and some of their physical characteristics can be measured, such as size, duration or maximum extent. In the case of torrential rain caused by SMPS in Mediterranean areas close to the Ebro Valley, these images have proved to be an effective tool improving our knowledge of the structure of mesoscale convective systems and mesoscale convective complexes (Maddox, 1980; Sa´nchez et al., 2001a; Cana et al., 1999). This paper contains the analysis of 72 hail events in the Central Ebro Valley between 1997 and 2001. The first step is the analysis of the IR images from METEOSAT that correspond to SMPS. The aim is to determine how many of the 72 hail events were caused by MCCs or MCSs. In other words, the paper will try to establish the degree of correspondence between hail falls causing damages and situations of highly organized convectivity. We will determine how many out of the 72 hail events can be considered MCS or MCC, and we will list some of their main characteristics. The second stage is an approach to the relationship between the qualitative organization of SMPS and the meteorological conditions on a mesoscale and a synoptic scale. This will improve the characterization of the meteorological conditions that favor the formation of MCSs o MCCs. The preconvective conditions will be analyzed and a dichotomous model will be set up to forecast (yes/no) the occurrence of MCSs or MCCs.

2. Study area, database and METEOSAT images 2.1. Geographical information The Ebro Valley is situated in the northeast quadrant of the Iberian Peninsula. The orientation of the Valley is NW – SE. The rugged mountains of the Pyrenees flank the Ebro Valley to the North, the Iberian Mountain Range flanks it to the SW, following the orientation of the basin, and the Mediterranean flanks it to the East. The Ebro is the largest river in the Iberian Peninsula, and it receives numerous tributaries coming from the two mountain ranges, which flank the Valley (see Fig. 1). The Central Ebro Valley is very flat and has high agricultural productivity. The orographic isolation of this plateau is confirmed by the scarce precipitation throughout the year, and especially in summer. Crops are spread all across the Central Ebro Valley. These crops are often within irrigation farming projects, they have a high yield and are of good quality. The agricultural production in the area is estimated to amount to about 900 Mo. The Ebro Valley produces mainly vines, market-garden produce, fruits and maize. All these products are very sensitive to hail precipitation, and therefore the economic losses are important. Farmers in this area have a high production, but it is

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Fig. 1. Location of the study zone, situated in the NE of the Iberian Peninsula, halfway between the Atlantic Ocean and the Mediterranean Sea.

very sensitive to adverse climatology. Storm phenomena are very frequent in the Ebro Valley, and on many occasions they lead to hail precipitation. 2.2. Haildays database In the Ebro Valley, there is a hailpad network available formed by 168 hailpads. The network has a square shape, with each square unit having sides of 4 km, thus covering a total land area of 2700 km2. The study zone in the Ebro Valley (see Fig. 1) covers a land area of approximately 50,000 km2. The hailpad network is far too small to register all or at least most hail events. It is therefore necessary to turn to the databases of damages caused on crops that were insured. The database contains information about several factors. It deals with the period between 1997 and 2001. 1. It contains the dates on which farmers were affected by hail damages on their insured crops. 2. It includes the names of towns and villages inside the study zone that were affected by hail. 3. The database may not have recorded all the areas with hail precipitation during one single hail event. But the convective organization in the study zone affects vast areas, so it is likely that the database includes most or all the SMPS that occurred between March and October from 1997 to 2001. According to the ground truth available, in this paper the term ‘‘hail event’’ will be used to refer to any situation where damages on crops were detected in one or several areas inside the study zone. Once the hail events were isolated, the IR images from METEOSAT corresponding to those events were analyzed.

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3. Classification of SMPS 3.1. Classification criteria In situations with SMPS, there are storms that develop in nearby areas. Every storm moves along a particular trajectory and can thus interact with itself or with other storms that are located in the same area. Synoptic factors condition the movement of SMPS, but subsynoptic factors may also influence their evolution and the formation of new SMPS, since there are two important mechanisms involved (Cotton and Anthes, 1989):


forced propagation, which results from external mechanisms, such as frontal boundaries produced by the outflows from decayed convective storms.
autopropagation concerning all those processes in which a thunderstorm regenerates itself or causes the generation of other cells inside the same SMPS. One or more convective systems may develop during the lifetime of each event. The bigger and more intense SMPS are, the more mechanisms are involved, and the more organized and complex SMPS are. This is the case of mesoscale convective systems (MCS) and mesoscale convective complexes (MCC). When the factors of forced propagation and/ or autopropagation are irrelevant compared to the synoptic factors, the convective organization is poor, but it does not lose its severe character and may still cause hail. Maddox (1980) and Maddox et al. (1986) set up a classification for characterizing convective systems that cause heavy precipitation in America. These mesoscale convective systems can be easily detected using IR images. Augustine and Howard (1991) defined classification criteria that distinguish between MCC and MCS based on enhanced satellite imagery. As pointed out by Augustine and Howard (1988), the area within a  52 jC threshold avoids ambiguity and is adequate to define the life cycle of MCCs and MCSs (Maddox used the  32 jC threshold). In Cana et al. (1999) and Sa´nchez et al. (2001a), these same criteria were applied in order to classify MCs in the Iberian Peninsula and they proved to be adequate in cases with torrential events in the Mediterranean area. In this paper, the data that have to be considered are the values reached by the minimum size of the Continuous Cold Cloud Shield, duration, shape, initiation, maximum extent and termination of the mesoscale convective system. The criteria used to establish whether an SMPS can be classified as an MCs (MCCs or MCSs) or not may be controversial, but their advantage is that they are widely used by various authors (Augustine and Howard, 1991) and the results for different areas can thus be compared. 3.2. METEOSAT and image processing Taking into account how fast SMPS develop and the fact that they may occur during day or night, one important fact is the observation of convective systems by means of images provided by satellites with a high time resolution. For this case, the high-resolution IR-band images of METEOSAT 7 (henceforth HR-IR-band) are the most appropriate ones, since they have a spatial resolution of 5  5 km.

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The procedure for analyzing the satellite imagery (Sa´nchez et al., 1992) provides the cloud top temperature, TTOP. The procedure consists of the following briefly summarized steps:


A geometric correction, using georeference methods for every image to locate cloud masses.
Use of algorithms to obtain cloud top temperatures, TTOP, from radiance data of images (following the instructions received by EUMETSAT, the organization that manages METEOSAT).
Method for obtaining the temperature contours of TTOP, so that it is easy to see in the processed image the area covered by an SMPS. METEOSAT 7 generates every day 48 HR IR-band images of the Ebro Valley, 1 every 30 min. The classification method describe above was applied to almost 3500 HR-IR-band images for this paper.

4. Results of SMPS classification Seventy-two hail events were classified according to the criteria in Sections 3.1 and 3.2. The results are shown in Fig. 2. This figure divides the 72 hail events in two MC groups (MCS or MCC) and a third group labeled ‘‘others’’. The latter group includes all SMPS that did not satisfy the criteria to be considered MCS or MCC. Fig. 2 shows that: 1. 30 of the 72 hail events that caused crop damages were associated with MCs. 2. Out of the 30 MCs, 4 were labeled as MCCs and 26 as MCSs. All four MCCs led to hail events. This means that even though MCCs only occur sporadically, there is a very high risk that they will produce hail precipitation.

Fig. 2. SMPS distribution using satellite imagery and classification criteria.

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Fig. 3. Distribution of maximum size in km2 reached by the TTOP V  52 jC contour for the 26 hail events with damages on crops that were classified as MCSs.

The satellite imagery showed that in 60 out of 72 cases, the TTOP temperature of the convective structure was at least  52 jC. Figs. 3– 5 present the maximum size of SMPS—expressed in km2—reached by the cloud masses with cloud top temperatures below  52 jC. These figures show that: 1. The cloud top temperatures of all MCCs and 8 of the 26 MCSs were at least  65 jC. 2. In 30 cases out of 72, the convective systems met the criteria to be considered MCC or MCS.

Fig. 4. Distribution of maximum size in km2 reached by the TTOP V  52 jC contour for the 4 hail events with damages on crops that were classified as MCCs.

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Fig. 5. Distribution of maximum size in km2 reached by the TTOP V  52 jC contour for the 30 hail events with damages on crops that did not fulfill the criteria to be regarded as MCs, but being SMPS were included in the group ‘‘others’’.

3. Another 30 hail events were not considered MCC or MCS, but were not too far from satisfying the criteria (see Fig. 5). 4. The remaining 12 events did not reach temperatures below  52 jC, but they were below  42 jC. The temperature at the base of storm cells in this part of the Iberian Peninsula is usually between 5 and 16 jC. Strong updrafts are detected in severe thunderstorms. Consequently, the formation of cloud drops is heavily influenced by processes of collision-coalescence, with strong updrafts that carry giant drops or hailstones. Evidence of giant drops has been found in strong updrafts (Sa´nchez et al., 1999). The tops of convective structures usually reach very low temperatures. Considering these low temperatures (below  40 jC), most of the water (or all) will freeze in those conditions. The distance between the cloud base and the cloud top is of approximately 12 to 14 km. In these circumstances, hailstones will be formed, will grow and will eventually reach the ground.

5. Meteorological variables that influence convective organization 5.1. Preliminary considerations on the selection of meteorological variables Storm formation depends on the preconvective environment. Several factors are involved in the development of convective activity, for example thermodynamic instability, convergence phenomena on a mesoscale that favor potential instability, and a source of humidity. Apart from these conditions, for thunderstorms to develop in a preconvective environment some mechanism has to be triggered, thus initiating the convection and

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destabilizing the lower layers of the atmosphere. Diurnal heating or lifting along a frontal or mesoscale boundary are the most common mechanisms triggering convection (Sa´nchez et al., 2001b). Preconvective conditions seem to have a clear influence on the organization of SMPS. How can this fact be noticed? The answer to this question implies the answer to another question: Do preconvective conditions in the Ebro Valley constitute a ‘‘meteorological signal’’ of the degree of convective organization before SMPS are formed and cause hail events? In previous papers (Sa´nchez et al., 1998a,b, 2001b), several models were established for short-term forecasting of thunderstorms and hailstorms in areas of the Iberian Peninsula close to the Ebro Valley. We found that forecasting of convective events with hail precipitation may be carried out with considerable success if the models use upper-air data, and the preconvective conditions are properly characterized. We have selected some variables obtained from upper-air data that will allow for a proper characterization of preconvective conditions, namely:


A first group of stability indices was calculated on the basis of data provided by the radiosounding carried out in Zaragoza shortly before the beginning of convectivity in the study zone: Showalter (1953), Total Totals (Miller, 1976), K (George, 1960) and Jefferson (Jefferson, 1963) indices, denoted by SI, TT, KI and JI, respectively.
A second group includes the Convective Available Potential Energy, knows as CAPE (Moncrieff and Miller, 1976). This is a vertical index measuring the cumulative buoyant energy in the free convective layer from the level of free convection (LFC) to the equilibrium level. CAPE has shown to be correlated with hailstorms in northwestern Spain (Lo´pez et al., 2001). The modification put forward by Doswell and Rasmussen (1994) has been used for calculating the CAPE index. This modification implies a virtual temperature correction. Both positive and negative buoyancy have been taken into account, and CAPE+ (usually named as CAPE) and CAPE  have been calculated, respectively. The CAP index, known as LSI, has also been added, because this index measures the ability of a stable layer to inhibit low-level ascent. LSI is determined by finding the maximum temperature difference between the environmental and the lifted parcel profiles, within the layer bounded by the lifted parcel level and the LFC.
The combination of variables that measure the vertical windshear intensity and of variables that measure the thermodynamic instability is a good tool for forecasting the type of convection (Weisman and Klemp, 1982). If the windshear is weak, the thunderstorms are likely to last for a rather short period of time and affect only small areas. However, strong windshear in unstable thermodynamic environments favor the formation of severe thunderstorms that are well organized and affect vast areas. A third group of indices has been included in order to account for this fact: the Storm-Relative Helicity (s-rH), which integrates the effects of streamwise vorticity and of the stormrelative winds through the inflow layer (Davies-Jones et al., 1990). This index is related to vertical windshear and to its ability to generate helical rotation in the updraft. The srH index has been calculated at 2 km, above sea level (asl), (SRH2) and at 3 km asl (SRH3). Its value will be expressed in m2 s 2.

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The last group includes indices that combine values of instability and windshear. The Bulk Richardson Number (BRN) (Moncrieff and Green, 1972) is the ratio between CAPE and a windshear vector difference (Weisman and Klemp, 1982). BRN is related to a situation that favors the occurrence of organized storm activity including the development of multicells and supercells (see Rasmussen and Blanchard, 1998 for details).

5.2. Preconvective conditions: classification criteria Two radiosonde launches were made daily, near Zaragoza (see Fig. 1) in the Central Ebro Valley, at 0000 and 1200 GMT. Zaragoza lies in the middle of the study zone, and therefore these radiosonde data may be considered representative of the valley’s meteorological conditions on a mesoscale. Time criteria were considered in order to determine representative data. When storm phenomena occur close to the area where the radiosounding is being carried out, the data are ‘‘contaminated’’ by convective currents. In these cases, the data provided by the vertical radiosounding cannot be considered representative of the preconvective conditions. On the other hand, when the preconvective conditions of a hailstorm are being established there should not be a long time span between the vertical radiosounding and the occurrence of the SMPS. How long can this time span be? We cannot establish in any accurate way the moment from which the strong updrafts of an SMPS may contaminate radiosounding data. It is even more complex to determine the area affected by an SMPS with the data available. Considering these facts, we may only suggest some subjective criteria that we believe are practical. The following three groups were established: 5 Group A: the radiosounding in Zaragoza at 1200 GMT was considered representative when SMPS started between 1300 and 2200 UTC. 5 Group B: the radiosounding in Zaragoza at 0000 GMT was considered representative when SMPS started between 0100 and 1000 UTC. 5 Group C: includes all the events that are not included in groups A and B. None of the events in group C was taken into account for the analysis, since the data provided by the radiosounding may not be considered representative of the preconvective conditions in these cases. 5.3. Results When these criteria were applied to the 72 hail events analyzed, 15 of these events were included in group C and were thus not taken into account for the analysis. LI, SI, TT, KI, JI, SRH2, SRH3, CAPE+, CAPE  and, BRN, were calculated for the 57 hail events on the basis of data provided by the radiosoundings of 1200 or 0000 GMT following the criteria of groups A and B. No CAPE values were found in 7 instances of the 57 hail events. This result is similar to the one found by Augus et al. (1988) in Florida and suggests that the presence of CAPE is not enough to predict SMPS. Consequently, the study focused on the 50 cases for which the values of the 10 variables could be obtained. Besides, the data provided by radio-

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soundings describe the preconvective conditions in which SMPS are formed that lead to hail events.

6. Analysis of preconvective conditions and their influence on the formation of MCs MCs developed in 22 cases out of the 50 hail events for which all 10 variables have been calculated. It is necessary to point out here that BRN is an index obtained from CAPE. (BRN is a function of CAPE and the wind shear.) In order to avoid redundant information, the CAPE index has been left out, leaving nine variables: LI, SI, TT, KI, JI, SRH2, SRH3, CAPE  and, BRN. Do these nine variables generate a meteorological signal that allows us to determine under what meteorological conditions MCs do develop or do not develop? A logistic regression analysis was used in order to answer this question. This type of analysis has been used in previous studies for establishing short-term forecasting models based on preconvective conditions (Sa´nchez et al., 2001b). This kind of analysis presents a two-fold advantage: 5 On the one hand, it includes all the variables that characterize preconvective conditions, combining them in such a way that they all provide their own information. In this case, we have used the nine selected variables. 5 On the other hand, it allows the establishment of a dichotomous forecast of particular meteorological phenomena: yes or no. In this case, the dichotomous forecast will refer to whether a hail event leads to the formation of MCs or not. The aim is to use the logistic analysis in order to establish a function that discriminates between two groups: MCs and no MCs. Following Kleinbaum (1994), we will define the logistic function in the following way: f ðzÞ ¼

1 1 þ ez

ð1Þ

where Z ¼ a þ b1 X1 þ b2 X2 þ . . . þ bk Xk

ð2Þ

and: Z explicative variable (see Kleinbaum, 1994 for details); Xi explanatory variables; a, bj with j = 1. . . k are unknown parameters. We may calculate them on the basis of the group of data formed by the explicative variables and the corresponding explanatory variables. The function defined in Eq. (1) may have any value between 0 and 1 and it may be described in terms of likelihood in the following way: 1

PðR ¼ 1AX1 ; X2 ; . . . ; XK Þ ¼ 1þe

 aþ

K X j¼1

! bj XJ

ð3Þ

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where P(R = 1jX1,X2,. . .,Xk) represents the conditional likelihood of R = 1 (explicative variable = 1), with the values {X1,X2,. . .,Xk}. In the case analyzed, k = 9, i.e. the number of variables that form groups 1 to 4 so that Z ¼ a þ bLI  ðLIÞ þ bSI  ðSIÞ þ bTT  ðTTÞ þ bKI  ðKIÞ þ bJI  ðJIÞ þ bSRH2  ðSRH2Þ þ bSRH3  ðSRH3Þ þ bBRN  ðBRNÞ þ bCAPE  ðCAPEÞ ð4Þ The values of the nine variables are known for every hail event in the sample. It is also known that in 22 hail events there were MCs and in 28 hail events there were not. We will assign f(z) the value 1 in 22 cases and the value 0 in the remaining 28 cases. The fitting process of all 50 hail events was carried out following the maximum likelihood method.

7. Results and discussion Once the function (Eq. (1)) was established, the sample was used to calculate skill scores. A 2  2 contingency table (see Table 1) is set up in a dichotomous forecast. The point here is to test whether the variables that characterize preconvective conditions can discriminate the meteorological conditions under which SMPS may be expected to form and lead to MCs, and distinguish them from those conditions under which this is less likely to occur. Table 2 shows the results for the cases analyzed here. In order to evaluate the success of a model based on contingency tables (Doswell et al., 1990), several skill scores are often used. Comparing the skill scores in Table 2 with the values corresponding to a ‘‘perfect’’ fit, we may conclude that the adjustment carried out in the 50 cases analyzed is moderately satisfactory. The frequency of hits is 0.65 and the probability of detection is 0.59. These results show that we have had a moderate success when attempting to establish the type of convective organization of SMPS that leads to hail events if the preconvective conditions are previously known. Nevertheless, it is still necessary to go deeply into their characterization on a mesoscale if the forecasting of this severe convective phenomenon is to be improved. It can be assumed that if CAPE is null, the convective organization will be very weak, and, as a result, no MCs and/or hail events will develop. On the other hand, if MCs and/or hail events are detected, this means that there is a good convective organization or that your categorization could be optimized. In seven hail events, CAPE null was found. Consequently, this is a paradoxical situation. Markowski et al. (1998) found that in

Table 1 Denotation of the elements in the contingency matrix Model

Observed

Yes No Total

Yes

No

Total

13 6 19

9 22 31

22 28 50

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Table 2 Skill scores found considering the 2  2 contingency table (Table 1) and the perfect fit

0 V POD V 1 0 V FOH V 1 0 V FOM V 1 0 V DFR V 1 0 V FAR V 1 0 V PON V 1 0 V FOCN V 1  1 V TSS V 1  1 V HSS V 1

Skill scores

Value obtained

Perfect fit

Probability of detection Frequency of hits Frequency of misses Detection failure ratio False alarm ratio Probability of a null event Frequency of correct null forecast True skill statistic Heidke skill score

0.59 0.68 0.27 0.29 0.32 0.79 0.71 0.38 0.38

1 1 0 0 0 1 1 1 1

convective conditions favoring the development of severe thunderstorms, s-rH could change up to an order of magnitude in distances under 100 km and in intervals of less than 3 h which requires us to be very careful with respect to how representative radiosounding data are. These aspects will have to be studied in detail to establish validity criteria in terms of time and space for every index. Several measures can be taken in order to improve the identification of convective situations that lead to hail events caused by MCs. Some good options are increasing the spatial and temporal frequency of soundings and looking for new and better tools.

Acknowledgements The authors thank Jose´ Luis Marcos, Antonio Vega and Laura Lo´pez for their help in applying the statistical model. The authors thank Noelia Ramo´n for translating the paper into proper English and Antonio Martinez for the figures. The authors also want to thank the reviewers for their useful comments. This work is based on a project supported by the project CICYT REN 2000-1210 CLI, ADV Terres de Ponent and Diputacio´n General de Arago´n.

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