1. Introduction
Concern about the environment, including natural disasters and climate changes, has increased significantly during the last decade. Thunderstorms are a major cause of natural disasters in the alpine region (Fig. 1) during the summer season. Despite all of these well-known observations, the investigation of the preconvective environment of thunderstorms has been neglected in Europe in comparison to the United States where in general more severe thunderstorms occur (Newton 1967; Modahl 1979; Wilson and Schreiber 1986; Rockwood and Maddox 1988; Johns and Doswell 1992; Mueller et al. 1993; Fuelberg and Biggar 1994). Analyses of the behavior of thunderstorms in Switzerland are important, since the alpine area of Switzerland (Fig. 1) belongs to the most preferred regions in Europe for the initiation of thunderstorms (Collier and Lilley 1994).
The general preconditions for the initiation of thunderstorms are well known and have been summarized by, for example, Doswell (1987) and Johns and Doswell (1992): 1) conditional instability, 2) a moist layer of sufficient depth in the lower or midtroposphere, and 3) a source of lift to initiate the convection. The formation of thunderstorms is an interaction between these conditions on different scales (Doswell 1987): “It is proposed that convective systems depend primarily on large-scale processes for developing a suitable thermodynamic structure, while mesoscale processes act mainly to initiate convection.” Hence, it follows that thunderstorms can be initiated by mesoscale processes even when the synoptic conditions are not ideal. However, the intensification or further development of these thunderstorms on a large scale is unlikely.
Forecasting thunderstorms is one of the most difficult tasks in weather prediction, due to their rather small spatial and temporal extension (Orlanski 1975) and due to the lack of horizontal and vertical resolution of the operational numerical models (Anthes 1976; Lilly 1990). Therefore, a variety of different thermodynamic and kinematic parameters have been derived from sounding data during the past 40 yr (see the appendix). Each of them indicated the thunderstorm potential of an air mass (Peppler and Lamb 1989). Studies on the efficiency of different stability indices for the thunderstorm prediction have been presented by several authors, for example, Neumann (1971), Anthes (1976), Reap and Foster (1979), Stone (1985), Andersson et al. (1989), Schultz (1989), Jacovides and Yonetani (1990), and Lee and Passner (1993). Additionally, one of the above-mentioned authors (Schultz 1989) comments: “However, there have been relatively few studies of the behavior and the relative effectiveness of the various indices. This is unfortunate, because in addition to providing practical information to field forecasters, these studies invariably result in useful insights into the physical characteristics of thunderstorms and their environments.” The present study tries to give some useful insights into the physical characteristics of thunderstorms and their prefered environments in Switzerland. The improvement of the thunderstorm prediction is important, especially for the prevention of injuries to people and damaged cars in contrast to the more unavoidable damages of buildings and in agriculture.
The state of the meteorological observation material in Switzerland has now reached a point that makes it possible to perform studies of thunderstorm environments comparable to studies from the United States. The aim of this paper is to investigate the relationship of different thermodynamic and kinematic parameters to the initiation of thunderstorms in Switzerland. This has been done by considering radiosounding data, data from a lightning detection network, and reports of hail damage from the Swiss Hail Insurance Company (see section 3). First the traditional stability indices presented in the appendix are tested for the thunderstorm prediction in northern Switzerland (see section 4). The results of these tests and the calculation of mean temperature soundings and hodographs for different days with no, isolated, and widespread thunderstorms over a 5-yr period (1985–89) lead to the development of new thunderstorm indices especially adjusted to the conditions in northern Switzerland: the so-called SWISS (stability and wind shear index for thunderstorms in Switzerland) indices (see section 5).
The aim and the content of the present study have many similarities to a recently presented paper by Fuelberg and Biggar (1994) about the preconvective environment of summer thunderstorms over the Florida panhandle. However, they have examined a smaller dataset from two summers (1990 and 1991) and compared only five different stability indices [TT, K, SLI (surface lifted index), SI850, and LI (lifted index)]. No new thunderstorm indices were developed for the investigated area.
2. Severe thunderstorms in Switzerland
Studies dealing with severe thunderstorms in Switzerland are quite rare. A climatological study of the mesoscale structure of severe precipitation events by using radar information has been published recently by Schiesser et al. (1995). The results show that about 40% of the mesoscale convective systems were moving into Switzerland from the west or southwest, while the rest of the systems were initiated within the borders of Switzerland. Most thunderstorms (66%) formed over western Switzerland. Less common was the formation of thunderstorms in the central and eastern parts of Switzerland (15%). The mature stage of the severe thunderstorms was observed most frequently in the central parts of Switzerland along the foothills of the Alps.
The characteristics of 42 severe hailstorms observed during an international field project “Grossversuch IV” (1977–82) in central Switzerland have been investigated by Houze et al. (1993). The hodographs in the environment of these storms showed wind shear values just about one-half to two-thirds of the values associated with supercell storms over the central United States. The Swiss wind shear vector generally veers clockwise with height through the lowest 5–6 km with a tendency for a lower-tropospheric southwesterly jet at the 700-hPa level. In comparison this jet is observed at the 850-hPa level in the U.S. cases. The clockwise veering of strong lower-tropospheric wind shear (associated with warm air advection) accounts for the predominance of right-moving hailstorms (Rotunno and Klemp 1982) as observed over the central United States. In contrast, Houze et al. (1993) observed that the Swiss hailstorms are nearly equally divided between left- and right-moving storms. The reason for this equal division was attributed to orographical effects on the local airflow in the region where the storms developed. Houze et al. (1993) also found that the values of convective available potential energy (CAPE) (see the appendix) are quite variable for the observed storms during Grossversuch IV, reaching from 340 to 2340 J kg−1. The CAPE values tend to be smaller on average than similar values associated with supercellular storms in the central United States, which may exceed 2500 J kg−1.
The most severe Swiss hailstorms nevertheless have significant features of supercell storms (Schmid et al. 1993). The updraft rotation accompanying supercell storms is believed to be generated by the stretching and tilting of streamwise vorticity associated with the environmental wind shear (Davies-Jones 1984; Rotunno and Klemp 1985). In a recent study presented by Schmid and Huntrieser (1994) the wind field in the environment of supercell storms in Switzerland was investigated. The results show the presence of substantial wind shear and helicity (Lilly 1986) in the vicinity of Swiss supercell storms. Helicity is on the order of 100–200 m2 s−2, which means that the “streamwise vorticity” hypothesis suggested by Davies-Jones (1984) is a reasonable explanation for the observed vortex signatures (Moller et al. 1994).
Recently, Huntrieser et al. (1994a,b) and Huntrieser (1995) analyzed the synoptic and mesoscale environment of the most severe Swiss hail days since 1950. The most common features of these severe cases can be summarized as follows: 1) “low-index” situation, 2) trough or cut-off low over the Bay of Biscay, 3) on the leeward side of the trough is a shallow depression located over France, 4) the associated cold front extends far southward and separates the maritime subtropical air from the maritime polar air, 5) in the warm sector of the depression the warm and moist air from the Iberian Peninsula [“Spanish plume,” see Morris (1986)] is transported to central Europe with southwesterly winds, 6) at the same time cold advection in high altitudes becomes apparent with the approach of the trough, 7) the result is a distinct increase of instability, 8) especially strong thunderstorm developments are to be expected if the cold front reaches Switzerland in the late afternoon or evening, and 9) CAPECCL > 600 J kg−1 and the vertical wind shear of the lowest 6 km exceeds 5 m s−1 per 6 km (see the appendix).
3. Method
a. Definition of thunderstorm days
This study includes thunderstorm days north of the Alps in Switzerland. The observation area is indicated in Fig. 1 between the bold dashed line with the arrows and the northern border of Switzerland. Thunderstorms have been studied during a 5-yr period (1985–89) from May to August (615 days).
An automatic mesoscale network (ANETZ) operated by the Swiss Meteorological Institute (SMI) delivers meteorological data with a temporal and spatial resolution of 10 min and 20–25 km, respectively, since 1978. The 36 weather stations in the observation area are supplied with lightning counters that record the near (≤5 km) and distant (5–25 km) lightning sum for each hour. The reports of hail damage from the Swiss Hail Insurance Company are also useful for thunderstorm statistics. From each community in Switzerland with insured agriculture, each single day with hail damage is reported to the insurance company. The communities in the observation area are small and cover an area of ∼10 km2 on average. In addition the operational radar images produced by the SMI contain information about the occurrence of thunderstorms. These images have a temporal and spatial resolution of 10 min and 2 km × 2 km, respectively.
To determine the thunderstorm days in the observation area, lightning reports were used in addition with hail damage reports to determine the most severe thunderstorm days. From the range and the spatial resolution of the lightning counters it is assumed that nearly each thunderstorm occurring in the observation area is registered. A comparison between the radar images (criterion for a thunderstorm day: occurrence of a radar echo of at least 47 dBZ = 30 mm h−1 rainfall intensity) and the lightning reports (near and distant) was carried out at the beginning of the investigations using 4 months of data, which resulted in almost the same sample of defined thunderstorm days when using the near lightning reports (Huntrieser 1995). In comparison distant lightning reports were sometimes false due to corona discharges near the mountain peaks, and three reporting stations had to be excluded from the study. Finally, the near lightning reports from 33 ANETZ stations were considered for the investigation. Since no radar images were available for the southern part of Switzerland during the investigation period, no comparison with the lightning reports from the ANETZ stations in this area was possible. Therefore, this part of Switzerland was excluded from this study.
In this study it is assumed that the radiosounding in Payerne represents the preconvective conditions over the whole observation area (∼250 km × 100 km). A further assumption is that both daily radiosoundings (from 0000 and 1200 UTC) must represent the daily preconvective situation. This criterion can only be fulfilled if the thunderstorms occurring during the afternoon (1240–2340 UTC, first and last lightning counts) are considered. During this time period about 80% of the radar detected severe hail cells occurred during the years 1983–94 (Gruppe für Radarmeteorologie 1995). Days with thunderstorms before 1240 UTC are excluded from the study because the 1200 UTC radiosounding is no longer representative of a preconvective environment. Without this criterion, neither daily radiosoundings is available for a comparison. Days with incomplete soundings (e.g., when wind data were missing or when the sounding was interrupted too early) were also excluded. Altogether the original dataset (615 days) was reduced by 99 days. The remaining 516 days were then divided into (a) days without thunderstorms: no ANETZ stations have reported near lightnings between 1240 and 2340 UTC, and (b) days with thunderstorms: at least one ANETZ station has reported at least one near lightning between 1240 and 2340 UTC. In addition, the days with thunderstorms were further stratified into (c) days with isolated thunderstorms: the criterion for “days with thunderstorms” is fulfilled, but the criterion for “days with widespread and severe thunderstorms” is not fulfilled; and (d) days with widespread and severe thunderstorms: at least 12 ANETZ stations have reported near lightnings between 1240 and 2340 UTC and in addition (as a severity criterion) at least 20 communities have reported hail damage.
The remaining 516 days were thereafter divided into 357 days without thunderstorms (69%) and 159 days with thunderstorms (31%). The days with thunderstorms were once more stratified into 139 days with isolated thunderstorms (87%) and 20 days with widespread and severe thunderstorms (13%).
b. Thermodynamic and kinematic parameters
Only thermodynamic and kinematic parameters, which represent stability and vertical wind shear (the latter influencing the convective strength and organization), were calculated from the radiosondes in Payerne (z0 = 491 m). The parameters are listed below in this section and an overview (parameter, code, key references, equations, remarks) is given in the appendix. The majority of the stability indices include only the temperature and humidity values at critical standard pressure levels for the calculation of the stability. These indices were developed in order to give the forecaster an indication of how stable or unstable the conditions are that predominate the atmosphere. In contrast to the calculation of these stability indices, the more recently developed CAPE is an integral value of the convective available potential energy throughout most of the troposphere, including more than just values from the critical standard pressure levels. This means that the CAPE parameters presented below are useful for the determination of the convective strength and that the non-CAPE stability indices are more successful by the decision stable or unstable environment (that means if an air mass has any thunderstorm potential at all).
The parameters include 1) wind shear: vertical wind shear of the horizontal wind (surface–3 km, 3–6 km, surface–6 km), and 2) stability indices: K index, TT index, Showalter index (850 hPa), modified Showalter index (700 hPa), modified Showalter index (CCL), modified Showalter index (LCL), surface lifted index, deep convective index, humidity index, Boyden index, KO index, SWEAT index, CAPE (surface), modified CAPE (850 hPa), modified CAPE (CCL), and modified CAPE (LCL).
c. Data analysis
Three methods were used to determine the thermodynamic and kinematic parameters with the strongest relationship to the initiation of thunderstorms in the observation area, namely, 1) skill scores, 2) probability distributions, and 3) mean temperature soundings and hodographs.
1) Skill scores
Skill scores are used in meteorology to verify weather predictions. Thunderstorm predictions have been evaluated with skill scores by, for example, Jacovides and Yonetani (1990), Lee and Passner (1993), and Collier and Lilley (1994). The investigated dataset is divided into a 2 × 2 contingency table with the elements A, B, C, and D as shown in Fig. 2. The most frequently used skill scores and their codes (CSI, POD, FAR, S, and TSS) are given in Table 1. Each of these elements has certain advantages and disadvantages, and is usually adjusted to particular situations. The disadvantage by applying CSI in comparison with TSS and S is that the correct prediction of the zero events D (Fig. 2) is not considered. Lee and Passner (1993) investigated the occurrence of thunderstorms near 14 sounding stations distributed all over the United States. A thunderstorm event was registered if the thunderstorm occurred within a 100-km area around the station over the 12-h forecast. They found that both skill scores TSS and S give about the same results. The reason is that thunderstorms occur rather frequently near the chosen sounding stations, actually in 34% of the cases. Only in cases of very rare events (<1%) was the skill score S superior, as demonstrated by Doswell et al. (1990). In the present study the most common skill scores like CSI, POD, FAR, S, and TSS were all calculated, but only the TSS values were considered for verification purposes.
2) Probability distributions
Another possibility to determine the most efficient predictand is to plot the probability distributions for a decision variable in different situations (Grosh and Morgan 1975; Mahrt 1977; Modahl 1979; McCoy 1986). In Fig. 3 two relative frequency distributions f0(x) and f1(x) are shown as examples for the idealized distribution (Gauss) of the decision variable x on days with and on days without thunderstorms. The value xG marks the threshold to separate the two probability distributions. In addition, the area below each of the relative frequency distributions corresponds to 100%. The size of the nonoverlapping area corresponds to the efficiency of the predictand. This area is shaded in Fig. 3 for the distribution f1(x).
3) Mean temperature soundings and hodographs
The comparison between mean temperature soundings and mean hodographs on days with and without thunderstorms deepens one’s insight into the thermodynamic and kinematic differences of these days. Several methods used to calculate mean temperature soundings and hodographs in the environment of supercells have been summarized by Brown (1993). He used a method that conserves significant features. In a study presented by Bluestein and Jain (1985) several mean temperature soundings and mean hodographs were calculated for different types of squall lines. Similar studies have been carried out by Maddox (1976) and Houze et al. (1990). In contrast to the method used by Brown (1993), a more classic method is used here. Before the mean temperature soundings were calculated, an interpolation at fixed levels was carried out in steps of 250 m except for the first interpolated point (491, 650, 900, 1150, =, 11 900 m). In addition the mean hodographs were also calculated. Hodographs connect the ends of wind vectors in different height levels. Before the mean hodographs were calculated, the wind values (divided into wind components u and v) were also interpolated at fixed levels.
For these calculations, only the months July and August were considered from 1985 to 1989 (310 days). The reason for this restriction is that a mean over all summer months (May–August) contains rather different temperature conditions. In contrast, July and August have about the same temperature and thunderstorm preconditions. For 51 days, no representative sounding was available (see section 3a) and as a result the dataset was reduced to 259 days. This smaller dataset was stratified into 183 days without thunderstorms, 64 days with isolated thunderstorms, and 12 days with widespread and severe thunderstorms—a total of 76 thundery days. The sample seems small. However, the results presented in section 4c are judged to be reliable since similar results were obtained from a preliminary study (not shown here) with a smaller dataset containing only 2 yr (1985 and 1989) instead of 5 yr (1985–89).
4. Results
a. Skill scores
For every thermodynamic and kinematic parameter described in section 3b five skill scores (CSI, POD, FAR, TSS, and S) were derived, but only the values of the TSS were considered to verify the success of the thunderstorm prediction. A guidance value had to be determined for every decision variable to receive the single components A, B, C, and D (Fig. 2). That value was found at the point where TSS reached a maximum. This optimized guidance value divided the dataset into two groups. One group contained the values larger than the determined value. This means for an index like the K index, which ideally increases with increasing thunderstorm activity, that thunderstorms were predicted as long as the guidance value was exceeded. In contrast, if the values were smaller than the determined value, no thunderstorms were predicted. For an index like the Showalter index, which ideally decreases with increasing thunderstorm activity, the conditions were reversed.
In Table 2 five skill scores for 16 stability indices are shown for the prediction of nonthundery and thundery days, respectively. For the decision at 0000 UTC, whether a thundery day will be expected or not, the use of the original Showalter index (850 hPa) showed the highest TSS skill score. The guidance value for SI850 was determined to be 1.8°C (Table 2). In this case thunderstorms were predicted as long as this value was not exceeded. At 1200 UTC the highest TSS skill score for the same prediction was reached by using the SWEAT index with the guidance value >60 (no dimension).
The decision at 0000 UTC, whether a day with isolated or widespread thunderstorms will be expected, was most successful by using the stability indices SILCL (<−0.5°C) or SLI (<1.4°C), see Table 3. At 1200 UTC the indices DCI (>20.3°C) and CAPECCL (>500 J kg−1) showed the best results.
In addition to the stability the wind shear belongs to the most important parameters for the prediction of thunderstorms (important for the thunderstorm organization). On days with forthcoming thunderstorm activity, weak wind shear was present at 0000 UTC in the layer between 3 and 6 km (TSS = 0.21). In contrast, strong wind shear was apparent at 1200 UTC in the layer between the surface and 3 km (TSS = 0.26).
b. Probability distributions
In Fig. 4a the probability distribution for the best stability index at 0000 UTC, namely SI850 (see Table 2), is shown for nonthundery and thundery days, respectively. The interval of each class is 0.1°C. The probability distributions were slightly smoothed to ignore isolated zero values in frequency. The guidance temperature value, where the two distributions coincide (dashed line), is given in the legend of the figure. Most important is the size of the area that is not jointly covered. For SI850 this area reached 30%. In comparison the probability distribution of the KO index is shown in Fig. 4b (the rest of the stability indices are not shown because of the lack of space). It is obvious that the success by using this index was remarkably smaller than for SI850. The area, where the two distributions do not overlap, is only 19%.
The best results were achieved by using the 1200 UTC stability indices instead of the 0000 UTC ones. This result is reasonable, given the temporal proximity of the 1200 UTC sounding to diurnal convection initiation. In Fig. 5a the probability distribution of SI850 at noon is shown. In this case the nonoverlapping area increased to 48%. The best stability index at noon UTC (Table 2b) is the SWEAT index. In Fig. 5b the probability distribution of this index is presented. This index shows an even greater nonoverlapping area of 53% in comparison to SI850. No probability distributions were calculated for the categories with isolated and widespread thunderstorm days because of the small number of data.
c. Mean temperature soundings and hodographs
The comparison of the three mean temperature soundings for no, isolated, and widespread thunderstorm days shows a strong correlation between the instability and the forthcoming thunderstorm activity. On average no CAPECCL (0 J kg−1) was available on days without thunderstorms, neither at 0000 nor as well as at 1200 UTC. Days with isolated thunderstorms showed an average CAPECCL of 210 J kg−1 at 0000 and 400 J kg−1 at 1200 UTC. In comparison the days with widespread thunderstorms showed an average CAPECCL of 1150 J kg−1 at 0000 and 1060 J kg−1 at 1200 UTC.
The differences in the instability appear more pronounced if the differences between the three mean temperature soundings are determined (Figs. 6a–d). The most significant temperature differences were generally obtained in the layer between 1.5 and 2 km (∼850 hPa). In this layer the mean 0000 UTC sounding from the days with isolated thunderstorms was approximately 3°C warmer (Fig. 6a) than for the days without thunderstorms. The same comparison for days with widespread thunderstorms showed an approximately 6°C warmer layer (Fig. 6b). At 1200 UTC this warm layer also appeared at the surface (Fig. 6c). In general the positive temperature difference reduced markedly in the layer between 2 and 5 km (∼500 hPa). Above 5 km no large temperature differences were obtained in comparison to the days without thunderstorms. Obviously, on thundery days an especially strong conditionally unstable layer is present between 850 and 500 hPa.
In Figs. 6a–d the differences between the mean dewpoint depression (T–Td) soundings are also presented. The reason for showing the dewpoint depression (T–Td) instead of the dewpoint (Td) is that the dewpoint depression is well correlated with the relative humidity in a temperature range typical for summertime conditions. The most striking differences between the mean dewpoint depression soundings occur in the layer between 3 and 4 km (600–700 hPa). On thundery days this layer was especially humid (small dewpoint depression) in comparison to the conditions on nonthundery days. This results in an especially strong difference between the two mean dewpoint depression soundings in this layer as shown in Figs. 6a–d. For instance the dewpoint depression was approximately 7°C lower at 1200 UTC on thundery days (Figs. 6c and 6d). This reservoir of humid air about 1000 m above the condensation level seems to be very important for the further development of strong thunderstorms.
The comparison of mean hodographs shows marked differences for the three thunderstorm categories (Fig. 7). The distinct low-level jet at 3 km on thundery days is remarkable (Figs. 7b and 7c), and the southwesterly or westerly winds dominated through the whole troposphere. On the contrary, no pronounced low-level jet was present on nonthundery days (Fig. 7a), and the mean wind direction veered to the west or northwest above 3 km. The southwesterly or westerly winds are important for the advection of warm and humid air from the Mediterranean region (Huntrieser et al. 1994a), and the pronounced low-level jet influences the organization of the thunderstorms. The unstable layer between 850 and 500 hPa over northern Switzerland on thundery days develops when warm air in the lower layer is transported from the Mediterranean region by southwesterly winds (mostly in the warm sector of a low) and colder air is advected in higher levels from the approaching trough from the west.
For a more detailed investigation of the differences between the hodographs, the wind vectors were divided into their components u and v. The v component (north–south) is the most important component for the initiation of thunderstorms. On forthcoming thundery days a strongly increasing southerly wind component was observed through the lowest 3 km (Fig. 8). In the layer above (3–6 km) the influence of the southern component decreased clearly. However, in the upper troposphere the southern component increased again. The mean vertical wind profiles showed very similar conditions on days with isolated and widespread thunderstorms. On the contrary, the days without thunderstorm activity showed that the northern component was more dominating. A light southerly component was visible only in the layer between 2 and 3 km.
The second wind component u (east–west) showed no such striking differences as obtained for the v component. However, on thundery days an especially strong increase of westerly winds in the lowest layer (surface–3 km) was also observed for this component. In the midlayer (3–6 km) the increase with height was minor. In contrast the days without thunderstorms showed a regular increasing westerly wind component through the lowest 6 km.
The above-mentioned differences indicate which levels (for temperature, relative humidity, and wind shear) correlate best with the development of thunderstorms in Switzerland. The same levels are also used for the calculation of the indices with the best results (see section 4a and the appendix) as the original Showalter index (includes T850 and T500), the SWEAT index (contains T850–T500 and wind shear between 850 and 500 hPa), and the K index (contains T850–T500 and T700–Td700).
d. Discussion of the results
The results of our study have shown that stability indices are important thunderstorm predictors. The best index to use at 0000 UTC for the prediction of a nonthundery or thundery day is the original Showalter index (SI850). At 1200 UTC the best results are obtained with the combined SWEAT index closely followed by the original Showalter index (SI850). The CAPECCL and DCI belong to the most successful parameters whether isolated or widespread thunderstorms are expected.
Besides the stability indices, the vertical wind shear and the relative humidity show a marked correlation to the development of thunderstorms. On days with forthcoming thunderstorm activity the wind shear in the layer between 3 and 6 km is weak at 0000 UTC. On the contrary, strong wind shear between the surface and 3 km (low-level jet) is present at 1200 UTC. The analysis of the relative humidity (dewpoint depression used) revealed for thundery days a drier layer in 850 hPa at 0000 UTC and a more humid layer in 700 hPa at 1200 UTC than for nonthundery days.
The results of the present study show several similarities to the ones from Florida published recently by Fuelberg and Biggar (1994), who received the best results with the stability index SLI. As a whole, their results were not as good as those presented for Switzerland. For instance, the separation of mean values, skill scores, and probability distributions for the different thunderstorm categories no convection/weak convection/strong convection was less successful as in the present study. Fuelberg and Biggar obtained the following mean values and standard deviations for SLI [°C]: strong convection, −6.5 ± 1.8; weak convection, −5.2 ± 2.1; and no convection, −3.7 ± 3.0. For Switzerland the corresponding values are widespread and severe: thunderstorms, −4.1 ± 2.6; isolated thunderstorms, −1.6 ± 2.5; and no thunderstorms, 2.2 ± 3.5. The reasons for the better results in Switzerland are unknown. Perhaps the different definition of the thunderstorm days has an influence, or the better results were achieved because of the larger dataset. Fuelberg and Biggar (1994) also found large differences in the wind direction on days with and without convection. In Florida, strong convection was always coupled with southwesterly winds. In contrast, the north to northwesterly winds were dominant on days with no convection. A humid layer between 700 and 500 hPa was also observed.
The mean vertical wind profiles (u and v components), as described in section 4c for Switzerland, show similarities to the profiles presented by Brown (1993, Fig. 4) for days with supercell thunderstorms in the United States. The only striking difference is the height of the low-level jet. In Switzerland the maximum of this jet is observed at 3 km (∼700 hPa), probably influenced by the Alps. In comparison Brown (1993) detected this jet maximum at 1.5-km height (∼850 hPa) for the United States (see also Houze et al. 1993; Maddox 1976).
5. New thunderstorm indices
a. Development of the indices
The guidance value for the occurrence of thunderstorms was determined to be <5.1 (no dimension). In the contingency table presented in Table 4 the thunderstorm prediction under the application of the new SWISS00 index part b was compared to the results by applying the original Showalter index part a. The new SWISS00 index (TSS = 0.374) barely showed better results in comparison to the original Showalter index (TSS = 0.350). The application of the new SWISS00 index resulted in 73% correctly predicted cases, 13% missed cases, and 14% cases with false alarms (Table 4b).
However, the thunderstorm prediction can be improved at 0000 UTC if the current synoptic situation is considered. Thunderstorms can also be expected under certain circumstances if the SWISS00 index or the original Showalter index exceed the guidance value. The requirement is that a cold front is expected to pass through Switzerland during the second half of the day (1200–2400 UTC). In addition, the weather situation (geostrophic wind direction) is not allowed to include a northern wind component. These days are characterized by a strong diurnal change in stability caused by the approach of a cold front (advection of warm and cold air in different heights). The additional synoptic criteria improved the correct prediction by applying the SWISS00 index by about 3% as shown in Table 4d. The TSS value increased from 0.374 to 0.501, which means 76% of the cases are correctly predicted, 8% are missed cases, and 16% are false alarm cases. The reduction of the missed cases from 13% to 8% by adding the synoptic situation to the SWISS00 index is remarkable. By applying the original Showalter index combined with the synoptic situation, the TSS value increased from 0.350 to 0.480, which means 74% of the cases are correctly predicted, 9% are missed cases, and 17% are false alarm cases (Table 4c). The improvement by using the synoptic criteria to the SWISS00 index is more successful than the one of the original Showalter index.
The guidance value for the occurrence of thunderstorms was determined to be <0.6 (no dimension). In Table 5 the new SWISS12 index is compared to the SWEAT index and the surface lifted index. The results show that the application of the new SWISS12 index (TSS = 0.587) is better than the SWEAT index (TSS = 0.548) but significantly better than the SLI (TSS = 0.479) alone. Under the application of the SWISS12 index, 78% of the cases are correctly predicted, only 5% are missed cases, and 17% are false alarm cases (Table 5c). This is an even better result than that obtained at 0000 UTC (Table 4). The low number of missed cases is especially striking. No improvement of the SWISS12 index was reached by considering the present synoptic situation (especially cold front passages). The SWISS12 index is probably a better indicator for the diurnal preconvective situation than a 0000 UTC index.
The probability distributions were calculated for the SWISS indices, confirming the results from the skill score TSS, which show that the new SWISS indices reached the highest scores. For the SWISS00 index the nonoverlapping area of the two distributions on thundery and nonthundery days increases to 35% (original Showalter index 30%). The SWISS12 index shows similar improvements. The nonoverlapping area increases from 53% (SWEAT index) to 57% (SWISS12 index).
For the decision, between an isolated and widespread thunderstorm day, no suitable combined thunderstorm index was found at 0000 UTC, probably because of the small dataset. Instead it is suggested to use the CAPECCL only (TSS = 0.480) with the guidance value >650 J kg−1 for widespread thunderstorms or the DCI (TSS = 0.505) with the guidance value >17.3°C. The verification of these two indices is presented in Table 6. A correct prediction with the application of CAPECCL is reached in 74% of the cases, only 3% are missed, and 23% are false alarm cases.
The CS index (TSS = 0.515) is similar to the energy–helicity index presented by Hart and Korotky (1991). The guidance value of the CS index exceeded > 2700 [J kg−1 m s−1 (6 km)−1] for the prediction of widespread thunderstorms. The contingency table (not presented here) showed that the application of the CS index resulted in 72% correct predictions, 3% missed cases, and 25% false alarm cases.
b. Verification of the indices
The next step is to examine how useful these indices are in comparison to the traditional indices presented in the appendix. For this verification an independent dataset is used [“cross validation”; Mosteller and Tukey (1977)] including the summer months from May to August 1990, 1992, and 1993 (no data were available for 1991). The original dataset contains 369 days, whereby on 70 days no representative or complete soundings are available (section 3a). The remaining days are divided into 198 days without thunderstorms and 101 days with thunderstorms. The thunderstorm days are further divided into 82 days with isolated thunderstorms and 19 days with widespread and severe thunderstorms. The same calculations as presented in section 3c are carried out.
The most useful stability indices at 0000 UTC for the prediction of days with or without thunderstorms by considering the TSS skill score are (see Table 7a) KO (0.392), SILCL (0.366), TT (0.362), SI850 (0.327), and SWEAT (0.327). In comparison the SWISS00 index shows the best result with TSS = 0.411. The guidance values derived from the original dataset (May–August 1985–89) were used. Table 8 shows the improvements for the test dataset by using SWISS00 index combined with the synoptic situation (TSS = 0.543) instead of the best traditional index (SI850). The percentage of missed forecasts decreases from 14% to 5%, and the ratio of the correct predictions increases from 69% to 75%. In comparison the improvements by using the original Showalter index (SI850) combined with the synoptic situation (TSS = 0.381) are not that successful: the percentage of missed forecasts decreases from 14% to 11%, and the ratio of the correct predictions increases from 69% to 70%.
At 1200 UTC the best results for the traditional indices are obtained for SI850 (TSS = 0.516), SLI (0.492), and SILCL (0.452), numbers given in Table 7b. Again, the new SWISS12 index delivers the best results (TSS = 0.555) from all compared indices. From the numbers in Table 9 the improvements by using the new SWISS12 index instead of the SWEAT index (best index 1985–89) or SI850 (best index 1990–93) can be clearly seen. The ratio of the missed cases decreases from 16% to 8%, and the ratio of the correct predictions increases from 76% to 78% by using the new SWISS12 index instead of the SWEAT index.
In addition to the TSS skill score, the calculation of the probability distributions shows the best results for the new combined indices. At 0000 UTC the nonoverlapping area of one distribution reaches 42% by using the SWISS00 index (here without synoptic). At 1200 UTC the same area for the SWISS12 index reaches 56%. The nonoverlapping area is on average ∼5% greater than the one of the best traditional index.
As mentioned in section 5a the best thunderstorm index at 0000 UTC for the distinction of isolated or widespread thunderstorm days is the CAPECCL. The verification shows that 70% of the cases are correctly predicted, 9% are missed, and 21% are false alarm cases (TSS = 0.270). For the same prediction at 1200 UTC the best results are obtained with the new combined CS index (TSS = 0.461) in comparison to the best classic index CAPECCL (TSS = 0.343). The correct prediction increases from 76% to 79%, and the missed cases decrease from 9% to 7% (Table 10).
This verification on an independent test dataset confirms that the new indices give the best results for the thunderstorm prediction. In Table 11 the most important indices and their guidance values are summarized for different thunderstorm classes and times as well as the improvement (in percent) compared to the best traditional index.
6. Summary and conclusions
The prediction of thunderstorms (if, where, and when thunderstorms will occur) is one of the most difficult tasks for a weather forecaster. This paper presents some suggestions on how the thunderstorm prediction in Switzerland north of the Alps can be improved with rather simple methods.
The best traditional index to be used at 0000 UTC for the forecast of a nonthundery or a thundery day is the original Showalter index (SI850) and at 1200 UTC it is the SWEAT index. The CAPECCL is the most successful parameter at midnight as well as at 1200 UTC for the decision, whether isolated or widespread thunderstorms are expected. The comparison of the mean temperature soundings and hodographs from Payerne for the three thunderstorm categories (no/isolated/widespread) show that the strength of the wind shear and the amount of relative humidity also correlate well with the occurrence of thunderstorms.
The most important parameters like stability, wind shear, and relative humidity are combined in new thunderstorm indices specially adjusted to the conditions in northern Switzerland called SWISS indices. SWISS stands for combined stability and wind shear index for thunderstorms in Switzerland. The SWISS indices are used for the decision of whether a thunderstorm day is to be expected or not. The SWISS00 index (calculated from the 0000 UTC radiosounding) contains the original Showalter index, the wind shear between 3 and 6 km, and the dewpoint depression at 600 hPa. All of these parameters are smallest on days with thunderstorms. The thunderstorm prediction can be improved if the current synoptic situation (cold front passage) is considered. At 1200 UTC, the surface lifted index combined with the wind shear between the surface and 3 km and the dewpoint depression at 650 hPa shows the best results (SWISS12 index). The wind shear is particularly large on days with thunderstorms (low-level jet). In contrast, the other two parameters are particularly small. For the decision of whether a day with isolated or widespread thunderstorms is expected, the best parameter is a combination of CAPECCL and the wind shear in the lowest 6 km. This new parameter is called the “CS index.”
All of the traditional and newly created indices used for the thunderstorm prediction were verified on an independent dataset containing 3 yr. The results are satisfactory. The new indices especially designed for northern Switzerland are the best for the prediction of no, isolated, or widespread thunderstorms.
The next step in predicting thunderstorms is to decide more exactly where and when thunderstorms will actually occur. A first attempt in this direction was presented by Huntrieser (1995). In this study a method was developed for the estimation of the regional stability in Switzerland. Temperature and dewpoint values from the ANETZ stations below 1000 m and the temperature value at 500 hPa from the sounding in Payerne were used to calculate the surface lifted index. The spatial distribution of this index was drawn. It became apparent that these fields were not easy to interpret. In addition to stability, the topography plays a crucial role for the initiation of thunderstorms in a mountainous country like Switzerland. Furthermore, the depth of the moist layer, convergence, and the vertical wind shear control the initiation of thunderstorms. Unfortunately, it is not possible at present to determine these quantities on a regional scale. In the future, it is planned to consider the new SWISS index for operational thunderstorm forecasting and for studies in mesoscale numerical prediction models.
Acknowledgments
The authors are grateful to Prof. R. Steinacker from the Institute of Meteorology and Geophysics (University Vienna) for allowing duplication of the orographical map of the alpine region, as presented in Fig. 1, and to W. Henrich from the Institute of Atmospheric Science (ETH Zürich) for modifying this map as desired. Many thanks also to the data providers: Swiss Meteorological Institute and the Swiss Hail Insurance Company. We would like to thank Frank Mair for a thorough and careful reading of the manuscript.
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APPENDIX
Summary of Parameters
(See page 124.)
Fig. 1. Topographic view over the European alpine region with Switzerland (bold border) in the left center surrounded by France, Germany, Austria, and Italy. Two major mountain chains range over Switzerland: the Jura Mountains in the northwest and the Alps in the south. The bold dotted line with the arrows indicates the test area used in this study: the northern part of Switzerland. The only radiosonde site in Switzerland (Payerne) is marked with a balloon.
Citation: Weather and Forecasting 12, 1; 10.1175/1520-0434(1997)012<0108:COTAND>2.0.CO;2
Fig. 1. Topographic view over the European alpine region with Switzerland (bold border) in the left center surrounded by France, Germany, Austria, and Italy. Two major mountain chains range over Switzerland: the Jura Mountains in the northwest and the Alps in the south. The bold dotted line with the arrows indicates the test area used in this study: the northern part of Switzerland. The only radiosonde site in Switzerland (Payerne) is marked with a balloon.
Citation: Weather and Forecasting 12, 1; 10.1175/1520-0434(1997)012<0108:COTAND>2.0.CO;2
Fig. 1. Topographic view over the European alpine region with Switzerland (bold border) in the left center surrounded by France, Germany, Austria, and Italy. Two major mountain chains range over Switzerland: the Jura Mountains in the northwest and the Alps in the south. The bold dotted line with the arrows indicates the test area used in this study: the northern part of Switzerland. The only radiosonde site in Switzerland (Payerne) is marked with a balloon.
Citation: Weather and Forecasting 12, 1; 10.1175/1520-0434(1997)012<0108:COTAND>2.0.CO;2
Fig. 2. Contingency table used to verify predictions (after Hofmann 1974).
Citation: Weather and Forecasting 12, 1; 10.1175/1520-0434(1997)012<0108:COTAND>2.0.CO;2
Fig. 2. Contingency table used to verify predictions (after Hofmann 1974).
Citation: Weather and Forecasting 12, 1; 10.1175/1520-0434(1997)012<0108:COTAND>2.0.CO;2
Fig. 2. Contingency table used to verify predictions (after Hofmann 1974).
Citation: Weather and Forecasting 12, 1; 10.1175/1520-0434(1997)012<0108:COTAND>2.0.CO;2
Fig. 3. Probability distributions of the decision variable x indicating the occurrence (f0)/nonoccurrence (f1) of a predictand. The value xG marks the threshold to separate the two probability distributions. The size of the shaded area corresponds to the efficiency of the decision variable x.
Citation: Weather and Forecasting 12, 1; 10.1175/1520-0434(1997)012<0108:COTAND>2.0.CO;2
Fig. 3. Probability distributions of the decision variable x indicating the occurrence (f0)/nonoccurrence (f1) of a predictand. The value xG marks the threshold to separate the two probability distributions. The size of the shaded area corresponds to the efficiency of the decision variable x.
Citation: Weather and Forecasting 12, 1; 10.1175/1520-0434(1997)012<0108:COTAND>2.0.CO;2
Fig. 3. Probability distributions of the decision variable x indicating the occurrence (f0)/nonoccurrence (f1) of a predictand. The value xG marks the threshold to separate the two probability distributions. The size of the shaded area corresponds to the efficiency of the decision variable x.
Citation: Weather and Forecasting 12, 1; 10.1175/1520-0434(1997)012<0108:COTAND>2.0.CO;2
Fig. 4. The relative frequency distribution of (a) the original Showalter index and (b) the KO index at 0000 UTC.
Citation: Weather and Forecasting 12, 1; 10.1175/1520-0434(1997)012<0108:COTAND>2.0.CO;2
Fig. 4. The relative frequency distribution of (a) the original Showalter index and (b) the KO index at 0000 UTC.
Citation: Weather and Forecasting 12, 1; 10.1175/1520-0434(1997)012<0108:COTAND>2.0.CO;2
Fig. 4. The relative frequency distribution of (a) the original Showalter index and (b) the KO index at 0000 UTC.
Citation: Weather and Forecasting 12, 1; 10.1175/1520-0434(1997)012<0108:COTAND>2.0.CO;2
Fig. 5. The relative frequency distribution of (a) the original Showalter index and (b) the SWEAT index at 1200 UTC.
Citation: Weather and Forecasting 12, 1; 10.1175/1520-0434(1997)012<0108:COTAND>2.0.CO;2
Fig. 5. The relative frequency distribution of (a) the original Showalter index and (b) the SWEAT index at 1200 UTC.
Citation: Weather and Forecasting 12, 1; 10.1175/1520-0434(1997)012<0108:COTAND>2.0.CO;2
Fig. 5. The relative frequency distribution of (a) the original Showalter index and (b) the SWEAT index at 1200 UTC.
Citation: Weather and Forecasting 12, 1; 10.1175/1520-0434(1997)012<0108:COTAND>2.0.CO;2
Fig. 6. Difference between the mean temperature soundings (temperature and dewpoint depression) (a) on days with isolated thunderstorms and days without thunderstorms at 0000 UTC (b) on days with widespread thunderstorms and days without thunderstorms at 0000 UTC, (c) on days with isolated thunderstorms and days without thunderstorms at 1200 UTC and (d) on days with widespread thunderstorms and days without thunderstorms at 1200 UTC.
Citation: Weather and Forecasting 12, 1; 10.1175/1520-0434(1997)012<0108:COTAND>2.0.CO;2
Fig. 6. Difference between the mean temperature soundings (temperature and dewpoint depression) (a) on days with isolated thunderstorms and days without thunderstorms at 0000 UTC (b) on days with widespread thunderstorms and days without thunderstorms at 0000 UTC, (c) on days with isolated thunderstorms and days without thunderstorms at 1200 UTC and (d) on days with widespread thunderstorms and days without thunderstorms at 1200 UTC.
Citation: Weather and Forecasting 12, 1; 10.1175/1520-0434(1997)012<0108:COTAND>2.0.CO;2
Fig. 6. Difference between the mean temperature soundings (temperature and dewpoint depression) (a) on days with isolated thunderstorms and days without thunderstorms at 0000 UTC (b) on days with widespread thunderstorms and days without thunderstorms at 0000 UTC, (c) on days with isolated thunderstorms and days without thunderstorms at 1200 UTC and (d) on days with widespread thunderstorms and days without thunderstorms at 1200 UTC.
Citation: Weather and Forecasting 12, 1; 10.1175/1520-0434(1997)012<0108:COTAND>2.0.CO;2
Fig. 7. Comparison between the mean 0000 UTC hodographs for no/isolated/widespread thunderstorm days (first * = 1 km, last * = 11 km).
Citation: Weather and Forecasting 12, 1; 10.1175/1520-0434(1997)012<0108:COTAND>2.0.CO;2
Fig. 7. Comparison between the mean 0000 UTC hodographs for no/isolated/widespread thunderstorm days (first * = 1 km, last * = 11 km).
Citation: Weather and Forecasting 12, 1; 10.1175/1520-0434(1997)012<0108:COTAND>2.0.CO;2
Fig. 7. Comparison between the mean 0000 UTC hodographs for no/isolated/widespread thunderstorm days (first * = 1 km, last * = 11 km).
Citation: Weather and Forecasting 12, 1; 10.1175/1520-0434(1997)012<0108:COTAND>2.0.CO;2
Comparison between the mean 0000 UTC vertical windprofiles (v component) for no/isolated/widespread thunderstorm days.
Citation: Weather and Forecasting 12, 1; 10.1175/1520-0434(1997)012<0108:COTAND>2.0.CO;2
Comparison between the mean 0000 UTC vertical windprofiles (v component) for no/isolated/widespread thunderstorm days.
Citation: Weather and Forecasting 12, 1; 10.1175/1520-0434(1997)012<0108:COTAND>2.0.CO;2
Comparison between the mean 0000 UTC vertical windprofiles (v component) for no/isolated/widespread thunderstorm days.
Citation: Weather and Forecasting 12, 1; 10.1175/1520-0434(1997)012<0108:COTAND>2.0.CO;2
Table A1. Summary of thermodynamic and kinematic parameters used: T is temperature (°C), Td is dewpoint temperature (°C), Θ is potential temperature (K), Θe is equivalent potential temperature (K), ρ is density (kg m−3), g is the acceleration of gravity (m s−2), z is height (m), H is height of an indicated pressure level (decameter), ν is wind speed (m s−1), and S is vertical wind shear between two indicated levels (s−1). Subscripted numbers indicate constant pressure levels.
Table A1 (Continued)
overview of the most frequently used skill scores.
Comparison of five skill scores for 16 stability indices used for the prediction nonthundery/thundery days at (a) 0000 UTC and (b) 1200 UTC. Bold values indicate the 5 stability indices with the highest skill scores.
Comparison of five skill scores for 16 stability indices used for the prediction isolated/widespread thunderstorms at (a) 0000 UTC and (b) 1200 UTC. Bold values indicate the 5 stability indices with the highest skill scores.
Verification of thunderstorm predictions under application of (a) the original Showalter index, (b) the new SWISS00 index, (c) the original Showalter index combined with synoptic information, and (d) the new SWISS00 index combined with synoptic information at 0000 UTC.
Verification of thunderstorm predictions under application of (a) the surface lifted index, (b) the SWEAT index, and (c) the new SWISS12 index at 1200 UTC.
Verification of thunderstorm predictions under application of (a) the CAPECCL and (b) the deep convective index at 0000 UTC.
Comparison of five skill scores for 16 traditional stability indices and the newly developed SWISS index (test dataset) used for the prediction nonthundery/thundery days at (a) 0000 UTC and (b) 1200 UTC. Bold values indicate the 5 stability indices with the highest skill scores.
Verification of thunderstorm predictions under application of (a) the original Showalter index, (b) the new SWISS00 index, (c) the original Showalter index combined with synoptic information, and (d) the new SWISS00 index combined with synoptic information at 0000 UTC for the test dataset.
Verification of thunderstorm predictions under application of (a) the SWEAT index, (b) the original Showalter index, and (c) the new SWISS12 index at 1200 UTC for the test dataset.
Verification of thunderstorm predictions under application of (a) the CAPECCL and (b) the CS index at 1200 UTC for the test dataset.
The most successful Swiss thunderstorm indices and the improvements in comparison to the best traditional indices for the test dataset.
