1 Introduction

Thunderstorm (TS) is one of the severe weather events that cause loss of life and property. This phenomenon, which occur a spatial scale from a few meters to several kilometers, can cause excessive rainfall, lightning, severe wind gust, hail, and even tornadoes in the affected regions (Saha et al., 2014; Umakanth et al., 2020). Understanding the formation mechanisms, severities, and predictabilities of TSs is of interest to many sectors and decision makers. The aviation sector is at the top of the sectors dealing with TSs because lead to accidents and incidents in the aviation operations (Islam & van Amstel, 2018; Koutavarapu et al., 2021; Özdemir & Deniz, 2016; Yavuz et al., 2020, 2022a). Studies in the literature have identified three basic requirements for TS formation: (1) instability in the atmosphere, (2) sufficient moisture at lower tropospheric levels, and (3) lifting mechanisms (such as convection, frontal lifting, convergence) (Arora et al., 2023; Bennett et al., 2006; Kunz et al., 2020; Trapp, 2013). Additionally, the necessity of vertical wind shear has been recognized as a fourth requirement (Dennis & Kumjian, 2017; Özdemir, 2021). Numerous studies in the literature have investigated the temporal distribution of TSs and the environmental conditions under which they occur. Krocak and Brooks (2020) examined intraday variations of severe TSs in the United States and found that intraday differences were limited. Taszarek et al. (2019) studied the climatology of TSs in the European Region, noting that the highest numbers of TSs occurred in July and August in northern latitudes, and May and June in southern latitudes. They also found that TSs were most commonly observed between April and May in Turkey. Kahraman and Markowski (2014) stated that tornadoes generally occur in the afternoon and early evening hours in Turkey. Studies conducted in the South Asia (Ahmed et al., 2019) and China (Chen et al., 2013; Ma et al., 2021; Tian et al., 2015) have also shown that TSs are most frequent during the warm season (May–September). It was also found that the highest number of observations in TS-induced hail events peaked in May and June (Kahraman et al., 2016).

Many studies have been conducted for different regions around the world to estimate the occurrence of TSs. For nowcasting and forecasting applications, mostly radar-satellite products (e.g., Bonelli & Marcacci, 2008; Dung et al., 2022; Wilson & Mueller, 1993; Wilson et al., 1998; Yavuz, 2023; Yavuz et al., 2020), numerical weather prediction models (e.g., Huang et al., 2022; Mazzarella et al., 2022; Müller et al., 2022), statistical methods (e.g., Guo et al., 2022; Leinonen et al., 2022; Schmeits et al., 2005), lightning observations (e.g., Bonelli & Marcacci, 2008; Haklander & Delden, 2003; Kohn et al., 2011; Mondal et al., 2022), and sounding observations (e.g., Bondyopadhyay & Mohapatra, 2022; Madhulatha et al., 2013; Tyagi et al., 2011, 2022) were used. Wilson and Mueller (1993) stated that the most important problem encountered in nowcasting of TSs is knowing the initiation and development stages of the storm. It has also been stated that understanding the boundary layer thermodynamic changes has an important role in the formation of TSs. To investigate these conditions, case studies and climatological analyzes have been carried out at various airports worldwide (Drozdov et al., 2013; Ryley et al., 2020; Taszarek et al., 2020; Yavuz et al., 2020). Pandit et al. (2023) found that TSs at 12 airports in India occur mostly between at 1200–1400 UTC. This phenomenon is attributed to the atmospheric boundary layer being characterized by turbulent kinetic energy, turbulent momentum, sensible and latent heat fluxes, and vertical wind shear. These conditions contain important dynamic and thermodynamic processes for the formation and development of TSs (Karan, 2007). Sudden changes in wind speed and direction, which are frequently observed during TS events, cause pilots to lose control, especially during take-off and landing (Tafferner et al., 2010). In some studies conducted for the European Region, it was determined that the wind gust values were 80 knots and above in the presence of TSs (Punkka et al., 2006; Taszarek et al., 2019). Short-duration excessive rainfalls, hail events, and icing have also been included in the literature as important meteorological phenomena affecting aviation activities during TSs (Ma et al., 2021; Yang et al., 2018).

It is very important to know the thermodynamic structure of the atmosphere for predicting the TSs. For this reason, atmospheric stability indices (thermodynamic indices) and parameters have been used to analyze TSs in many studies. These indices and parameters provide important information about the stability of the atmosphere at that moment. However, it is widely recognized that each index and parameter does not show the same performance in all regions and atmospheric conditions. Showalter (1953) developed an index (Showalter Index—SI) to forecast thunderstorms and non-severe convective showers. He revealed the measure of the stability of the atmosphere by determining the threshold values for the dimensionless results of this index. Threshold values for these indices have been adjusted for various regions in many studies (David & Smith, 1971; Ellrod & Field, 1984). Similarly, many indices and parameters have been presented in the literature for forecasting TSs, severe TSs, and tornadoes. The K-Index (KI) was developed by George (1960) to forecast non-severe TSs similarly to the SI. The Lifted Index—LI (Galway, 1956), Totals Totals Index—TTI (Miller, 1967), and Severe Weather Threat Index—SWEAT (Bidner, 1970) were developed to forecast severe TSs and tornadoes. Modifications in these indices were made for different regions (Charba, 1977; Peppler & Lamb, 1989), and the threshold values have been adjusted temporally and spatially (Miller et al., 1972; Prosser & Foster, 1966; Sadowski & Rieck, 1977). The Convective Available Potential Energy (CAPE), Convective Inhibition (CIN), and Bulk Richardson Number (BRN) are atmospheric parameters that offer insights into atmospheric convection and wind shear conditions (Lucas et al., 1994; Weisman & Klemp, 1982; Yavuz et al., 2022b; Zhang, 2003). There are numerous studies in the literature that have utilized these indices for different regions. Wu et al. (2024) calculated CAPE, CIN, KI, and LI using data from 120 radiosonde stations across China. Spatially varying index results were obtained for pre-storm, storm onset, and post-storm periods in the analyses conducted for the warm season. In a study by Sahu et al. (2024) focusing on Northeastern India, frequency analyses of thunderstorms during the pre-monsoon season found that thermodynamic index values varied based on the topography. Rafati et al. (2024) found a correlation between mesoscale convective systems (MCSs) and high CAPE values in their investigation of MCS structures in southwestern Iran.

There are many studies in the literature in which TS analyzes were made for megacity Istanbul. In these studies, case analyzes (Baltaci et al., 2019; Özdemir, 2021; Toker et al., 2021; Yavuz et al., 2020) and climatological analyzes (Kahraman et al., 2020; Özdemir et al., 2017; Tanriover et al., 2015; Yavuz et al., 2022a) were performed. However, there is no study on the prediction of TSs with atmospheric stability parameters and thermodynamic indices. In this study, first, a temporal analysis of TSs in Istanbul for the 22-year period (2001–2022) was performed. The TS events were identified using aviation reports of Istanbul Sabiha Gokcen International Airport, and a total of 703 TS events were identified. Then, the thermodynamic indices and stability parameters were analyzed for both TS and non-TS events. The stability of the atmosphere in TS and non-TS events was demonstrated using five thermodynamic indices (SI, LI, SWEAT, KI, TTI) and three atmospheric parameters (CAPE, CIN, BRN). Event-based and seasonal analyzes were conducted for each of the indices-parameters, and performance analyzes were carried out for the threshold values in the literature. The success ratio of each index and parameter was first tested by using multiple skill scores. Then, various modifications were applied to the threshold values, and efforts were made to determine the appropriate threshold values. In conclusion, recommendations for threshold values for each index and parameter are presented. Detailed information about the study area, data sets, TS events, thermodynamic indices, atmospheric stability parameters, and skill scores are given in Sect. 2. All analyzes results are given in Sect. 3. Conclusions and discussions in line with the results are given in Sect. 4.

2 Data and Methodology

2.1 Study Area

Istanbul is a megacity located in the northwest of Turkey. The city, which has a bosphorus that connects the Asian and European continents, has coasts to the Marmara Sea in the south and the Black Sea in the north. The effects of the Black Sea climate are observed in the northern part of the city and the Mediterranean climate prevails in the south (Yavuz et al., 2022c). There are three airports in the city, two on the European continent and one on the Asian continent. Istanbul Sabiha Gokcen International Airport is located on the Asian part of the city. Istanbul Kartal radiosonde station is the only station in the city and is located on the Asian part. Both the airport and the radiosonde station are situated at nearly sea level. The location information of the city, airport and radiosonde station is given in Fig. 1.

Figure 1
figure 1

Study area

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2.2 Data and Determination of TS Events

The study period spanned 22-year from 2001 to 2022. In the determination of this period, the availability of aviation reports was taken as a basis. Istanbul Sabiha Gokcen International Airport became operational in 2001. Therefore, access to aviation reports published by the airport was available from this year. There are many reports published by airports. Among these, the Meteorological Aerodrome Report (METAR) is typically issued hourly at national airports and half-hourly at international airports. The Special Meteorological Aerodrome Report (SPECI) is published in case of occurrence of situations that adversely affect aviation activities between two METARs (Özdemir et al., 2016). In this study, the METARs and SPECIs published by Sabiha Gokcen International Airport were analyzed. Almost all of the reports (98% of the reports) within the period were published in full and made available to users (IOWA, 2023). In these reports, there is a lot of information such as air temperature (T), dew point temperature (Td), relative humidity (RH), wind speed (Ws), wind direction (Wd), and present weather code (PWC). These reports were used to determine TS events. When determining TS events, all TS types (e.g., TS, TSRA, TSSN, TSSNRA, VCTS, TSQLS, TSGR, TSGRRA, TSSHRA) were extracted from the aviation reports. For a TS event, the presence of any type of TS in both reports was sought, and was determined as a single event based on its presence in the reports within the following three hours. If two TS observations are given more than three hours apart, even on the same day, this is determined as two separate TS events. As a result of the analyzes, a total of 703 TS events have been identified over a 22-year period.

After the TS events were determined, the sounding data of Istanbul Kartal Radiosonde station were obtained from the University of Wyoming Atmospheric Sciences website within the scope of the period (University of Wyoming, 2023). Sounding observations are made twice a day at 0000 UTC and 1200 UTC. For this reason, all sounding observations were analyzed, and then analyzes were carried out for TS events based on the sounding observation closest to the event hours. For instance; when the event occurs at 0500 UTC, the 0000 UTC sounding is considered; when it occurs at 0700 UTC, the 1200 UTC sounding is considered; and finally, when it occurs at 2000 UTC, the sounding data from the following day's 0000 UTC is examined. Due to the chaotic nature of the atmosphere, the temporal scale is particularly important in such events. Therefore, the approach is not simply to rely on the sounding closest to the event hour, but also to consider the principle that the selection should capture atmospheric conditions most representative of the event period, even if it entails a combination of pre-event and post-event stability assessments. This justification ensures that the analysis encompasses the relevant atmospheric dynamics influencing the event. Only 10 of the TS events had no sounding observations available. Therefore, all analyzes were performed for 693 of the 703 TS events.

2.3 Atmospheric Stability Parameters and Thermodynamic Indices

There are many thermodynamic indices and atmospheric parameters used to determine the stability of the atmosphere. Some of these are used to predict non-severe convective precipitations (Busuioc et al., 2016; Queralt et al., 2007; Umakanth et al., 2020), thunderstorms (Arora et al., 2023; Koutavarapu et al., 2022; Sahu et al., 2020; Umakanth et al., 2021), severe thunderstorms (Farnell & Llasat, 2013; Koutavarapu et al., 2021; Kunz, 2007), and tornadoes (Tajbakhsh et al., 2012). The SI is an index used to predict non-severe convective rainfall and thunderstorms. It was developed for forecasting TSs in the southwest United States. It measures the instability of the atmosphere of the layer between 850 and 500 hPa levels. The index is generally a function of these two atmospheric levels. It also predicts the latent instability of this layer. The LI is a modified version of the SI used to predict severe TSs. Similar to the SI, it was developed to estimate the latent instability of the layer. The SWEAT was developed to predict severe TSs, just like the LI. In the first developed version of the index, there is no wind shear term. In the second version, wind parameters between 850 and 500 hPa levels were added to the equation. The SWEAT is also used to identify severe and non-severe TSs. The KI is a combination of moisture content at 850–700 hPa levels and temperature at 850–500 hPa levels. It is the indirect measure of the vertical development of the moist layer. It is used to predict TSs that occur in weak wind conditions in the absence of frontal or cyclonic effects. The TTI is an index consisting of two components, vertical totals (VT) and cross totals (CT). The VT indicates the temperature difference between 850 and 500 hPa levels, while CT indicates the dew point temperature difference between 850 and 500 hPa levels. The TTI, which is used to detect potentially severe weather events, can offer overestimation in the forecast of convective weather events. The CAPE is a measure of atmospheric convection. The vertical profile of the atmosphere is calculated throughout. The CIN is the negative part of the CAPE. The high values of the CAPE are an indicator of atmospheric instability, while the low values of the CIN are an indicator of atmospheric instability. The BRN is directly related to the CAPE and gives the relationship between the wind shear vector and the CAPE. Just like the CAPE, the instability of the atmosphere is expected to be severe at high values. The threshold values and formulas of the thermodynamic indices and atmospheric stability parameters used in this study are given in Table 1. The value ranges provided here for each index and parameter are the intervals determined for the regions where the referenced studies were conducted. However, these values are generally accepted worldwide as averages.

Table 1 Threshold values and formulas of thermodynamic indices and atmospheric stability parameters
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2.4 Skill Scores

In this study, skill scores were used to evaluate the performance of thermodynamic indices and atmospheric stability parameters. These methods have been preferred for estimating the stability of the atmosphere in many studies similar to this study (Arora et al., 2023; Sahu et al., 2020; Tyagi et al., 2011). In order to calculate the skill scores, it is necessary to classify the actual TS event observations and the estimation results obtained from the indices and parameters. In this context, Table 2 provides information on the parameters to be used in skill score calculations for classifying actual TS event observations and estimation results obtained from the indices and parameters.

Table 2 Contingency table
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The skill scores and calculation methods used in this study are given in Table 3. Here are some parameters that are not included in Table 2. Where \(N = A + B + C + D\), total number of events, \(E = \left[ {\left( {A + C} \right)\left( {A + B} \right) + \left( {C + D} \right)\left( {B + D} \right)} \right]/N\), expected number of correct forecast by chance. The POD is the measure by which TS events can be detected. It is the proportion of cases in which real events are correctly detected through indices and parameters. The FAR is the ratio of cases where the TS event estimates are made but there is no actual TS. The MR is the proportion of cases in which TS events occur but cannot be predicted. The CSI, HSS, and TSS are methods that statistically reveal the relationship between the predictions and the observations. The high rates of these three methods are an indication of high consistency.

Table 3 Information about skill scores
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3 Results

3.1 Frequency and Duration of the TS Events

In this section, intraday, monthly and annual frequencies of TS events are examined. In addition, the average event duration was revealed by considering the start and end times of each event. Over the 22-year period, the annual average of TS events was 32, with the highest occurrence of 62 events recorded in 2018 (Fig. 2a). The highest monthly observation rate (69%) was recorded during the warm seasons from May to September. The highest number of observations seasonally was observed in summer (43%), autumn (27%), spring (22%), and winter (8%), respectively (Fig. 2b). In the literature, it has been stated that TSs are more observed especially at the beginning of the summer and autumn seasons (Ma et al., 2021; Tian et al., 2015). In studies conducted for Istanbul for different periods, it was found that the highest number of TS observations occurred in June and September. It was also stated that there was no annual trend in these studies for Istanbul (Özdemir et al., 2017; Yavuz et al., 2022a). The temporal analyzes results in this study are also consistent with both the general literature and the results of the studies conducted for the city in different periods. The duration of TS events has mostly ranged from several minutes to a few hours (0–3 h). 70% of the events lasted in the range of 0–3 h (Fig. 2c). Considering the lifetimes of meso-scale systems, this result is in line with expectations. It has been revealed in many studies in the literature that TS events mostly occur in the afternoon and evening hours (Karan, 2007; Kahraman et al., 2016; Pandit et al., 2023; Yavuz et al., 2022a). In this study, it was found that only 16% of the events occurred at night (0000–0600 UTC), and 61% of them occurred in the time period from sunrise to sunset. 21% of the events occurred from sunset to nightfall (Fig. 2d). The most important reason for this is that turbulent eddy packets are still present in the residual layer after sunset.

Figure 2
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Analyzes of a annual, b monthly, c lifetime, and d onset hours of TS events

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3.2 Distributions of Thermodynamic Indices and Atmospheric Parameter Values in TS Events

Atmospheric instability plays a major role in the occurrence of TSs. Some sounding parameters and indices used to reveal the stability of the atmosphere. These are important in understanding the formation, development, and distribution phases of TSs. In this section, five thermodynamic indices and three atmospheric stability parameters were analyzed for the days when TS events were present. In the examinations carried out during the period, analyzes of these indices and parameters were performed according to the closest sounding observation where TS events occurred. The average values of the SI, LI, SWEAT, KI, and TTI were 1.9, 0.0, 159.4, 27.7, and 48.4, respectively. The average values of the CAPE, CIN, and BRN were 331.4, − 63.9, and 55.9, respectively (Fig. 3). Arora et al. (2023) investigated TS and non-TS days for six cities in India and found that the TTI on TS days ranged between 37.1 to 57.0, and the KI ranged between 22.1 and 44.0. Tyagi et al. (2011) analyzed TS days in Kolkata, India, and stated that the SWEAT should be greater than 180.0, the TTI greater than 46.0, the KI greater than 24.0, the CAPE greater than 1000.0, the BRN greater than 41, and the LI should be less than − 3.0. Bondyopadhyay and Mohapatra (2022) found that TS activities were observed when the CAPE values were greater than 1359.0 for the city of Patna, India, and the CAPE values were greater than 203.0 for the city of Bhuvaneswar. In the same study, it was found that other thermodynamic indices and stability parameters for different cities also varied on a wide scale. As a result, the threshold values in the literature for both thermodynamic indices and stability parameters need to be modified regionally and temporally.

Figure 3
figure 3

Distributions of the thermodynamic indices (SI, LI, SWEAT, KI, TTI) and stability parameters (CAPE, CIN, BRN) in TS events

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3.3 Comparison of Indices and Parameters in TS and Non-TS Events

This study conducted analyses of thermodynamic indices and stability parameters for both TS and non-TS events over the 22-year period. High values of some of the indices and parameters (e.g., SWEAT, KI, TTI, CAPE, BRN) and low values of some (e.g., SI, LI, CIN) are directly proportional to the occurrence of TS and severe TS. There are threshold values for these indices and parameters in the literature (Table 1), but these values can be modified in different regions and temporal scales. In general, the expected situation is that the values of indices and parameters that should be high in TS events are higher than non-TS events, on the other hand, those that should be low are lower. As a result of analyzes for five indices and three parameters, the average of SI values was 5.0 less in TS events than in non-TS events. Similarly, the average of the LI values was 6.0 less and the average of the CIN values was 39.5 less. The average values for SWEAT, KI, TTI, CAPE, and BRN were 67.3, 17.4, 7.8, 288.6, and 53.1 higher in TS events than in non-TS events, respectively (Fig. 4).

Figure 4
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Value ranges of the indices and parameters in TS and non-TS events

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3.4 Seasonal Distributions of Index and Parameter Values in TS Events

The stability of the atmosphere varies sub-daily, daily, monthly, and seasonally. Accordingly, thermodynamic indices and parameters obtained from sounding observations also receive different values. In this section, the seasonal distributions of the indices and parameters that have been analyzed in the previous sections are analyzed. First, the distributions of the values taken by the indices and parameters, which are the measure of the instability of the atmosphere of their increasing values, are given in Fig. 5. Then, the distributions of the values taken by the indices and parameters, which are the measures of the instability of the atmosphere of the decreasing values, are given in Fig. 6.

Figure 5
figure 5

Seasonal variations of the SWEAT, KI, TTI, CAPE, and BRN values

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Figure 6
figure 6

As in Fig. 5 for the SI, LI, and CIN values

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Unlike the KI, TTI, CAPE and BRN, the SWEAT received its highest average value (172.3) in winter. It was followed by fall (162.0) and summer (154.3). The KI received its highest average value in summer (29.8) and lowest in winter (21.9). The TTI received its highest average value in spring (50.0) and lowest in summer. The CAPE and BRN received their highest average values by a wide margin in summer (546.1, 61.1, respectively) and their lowest values in winter (32.1, 0.9, respectively) (Fig. 5). The SI, LI, and CIN received their lowest average values in summer (1.0, -1.8, -70.7, respectively) and highest average values in winter (3.7, 3.2, -25, respectively) (Fig. 6). In general, the thermodynamic indices can get the highest (lowest) values on average in different seasons; on the other hand, all three atmospheric stability parameters showed similar structure in all seasons.

3.5 Skill Scores in Forecasting TS Events

In the forecasting of TS events, the performance of each thermodynamic index and atmospheric stability parameter was discussed separately. In this direction, first, a general evaluation was made for each index and parameter in TS events (Table 4), and then a seasonal evaluation was carried out (Table 5). The threshold values given in the literature sometimes lead to overestimation and sometimes underestimation. The ideal state required for each index and parameter is when the POD, CSI, HSS, and TSS values are high and the FAR and MR values are low. High POD values are a measure of the success of predicting events. But the fact that the POD value alone is high (or the MR value is low) does not make sense if the FAR values are also high. For example; the POD value for the KI was 0.93 and the FAR value was 0.82 (Table 4). This means that the threshold value is located slightly below the ideal states. Both values represent the highest values among all indices and parameters. On the other hand, the CSI and HSS received the lowest values for the KI. Therefore, the forecast success for this threshold value remained low in terms of the KI. The POD value for the CAPE is the lowest among other indices and parameters. However, the FAR value is also the lowest. On the other hand, the HSS value got the highest value. The main problem with the CAPE is the low predictability of events. Thanks to the improvements to be made in the threshold value by considering other skill scores, the POD, CSI, HSS, and TSS can be increased. As a result, it is very difficult to examine skill scores and conclude that this is the best among indices and parameters. In order to make a better estimation here, the skill scores in Table 4 must be in high harmony with each other. Similar processes were also carried out seasonally in order to better present this harmony and evaluate the performances in case the events were experienced more/less (Table 5).

Table 4 Skill scores for atmospheric stability indices and parameters
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Table 5 The seasonal skill scores for the atmospheric stability indices and parameters
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In the seasonal examinations conducted with the skill scores, the POD values reached the highest values in almost all of the indices and parameters (except the TTI) in the summer season. Accordingly, the lowest MR values were seen in the summer season. The main reason for this is that TS events were mostly observed in summer. In this season, where more events were observed, the rate of detecting more events also increased. The CSI, HSS, and TSS scores all had their lowest values in winter. This situation is directly proportional to the observation of TS events in the least number of winter season. The SI had the highest values in all of the POD, CSI, HSS, and TSS scores in summer. The SWEAT showed similar results as the LI. Therefore, the threshold value put forward in the literature gives the best results in the summer season. There is no similar situation as in the SI for the LI, KI, and TTI. The skill scores did not show a common seasonal trend. The atmospheric stability parameters CAPE and BRN had the highest values of all of the POD, CSI, HSS, and TSS scores in summer, just like the LI. On the other hand, these two parameters failed in all scores in winter. On the other hand, the CIN took different skill score values for each season (Table 5). As a result, the seasonal skill scores for each index and parameter revealed different results. While the success of the skill scores increased when TS events were observed frequently, the opposite situation occurred when TS events were observed the least.

3.6 Skill Scores in Modificated Threshold Values

The threshold values for the thermodynamic indices and stability parameters, which are set forth in the literature, need to be modified in order to predict TS events for Istanbul. In the general and seasonal analyzes, the necessity of this modification has emerged with many skill scores. In this respect, it is very important to determine the threshold values that can be used not only seasonally but also for all times. In this study, it has been tried to determine the most appropriate threshold values by making various increases and decreases in the threshold values for each index and parameter (Table 6). In these analyzes, evaluations were made on the basis of the skill scores. The threshold values for each index and parameter in the literature are given in Table 1. In this context, analyzes were carried out based on the most ideal condition that reveals the instability of the atmosphere among the threshold values in the literature. In this section, each index and parameter has been reduced and increased at various rates according to the threshold values in the literature, and the different results have emerged. 10% increase/decrease has been applied for all threshold values. Changes made to 20% and above for both increase and decrease have reduced skill score achievements. For this reason, 10% and 20% increases were applied first, then 10% and 20% reduces were applied. Increase and decrease have different meanings for each index and parameter. For example, the values below the threshold for the SI, LI, and CIN and above the threshold for the SWEAT, KI, TTI, CAPE, and BRN indicate an increased probability of TS events. Therefore, increase (decrease) here means decreasing (increasing) the current threshold value for the SI, LI, and CIN, and increasing (decreasing) the current threshold value for the SWEAT, KI, TTI, CAPE, and BRN (Table 6).

Table 6 The skill scores in modified threshold values
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As a result of the increase/decrease applied for the threshold values set forth in the literature (Galway, 1956; George, 1960; Miller et al., 1972; Peppler & Lamb, 1989; Showalter, 1953; Weisman & Klemp, 1982; Ye et al., 1998; Zhang, 2003), the most appropriate threshold values for each index and parameter are given in Table 7. As a result of the analyzes made for the BRN, a significant level of consistency in skill scores could not be achieved in threshold value increases/decreases. For this reason, it would be appropriate to use the threshold value available in the literature for the BRN.

Table 7 The threshold values in the literature and proposed
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The skill scores according to the proposed threshold values are given in Table 8. Since the threshold value for the BRN was kept the same as in the literature, there was no change in the scores. Improvement in the range of 2–9% in the CSI, 2–15% in the HSS, and 1–10% in the TSS (only 4% reduction in the TTI) with the threshold value offered for each index and parameter has taken place. Although the POD values are mostly on a downward trend, similar or even higher decreases in the FAR values have occurred. Therefore, although the rate of correct detection decreases, the rate of incorrect detection decreases at least as much.

Table 8 The skill scores for proposed thresholds
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4 Discussion and Conclusions

Thermodynamic indices and atmospheric stability parameters are used to predict non-severe convective showers, TSs, severe TSs, and tornadoes. However, the consistency of these forecasts with a single index or parameter is not high. In addition, the threshold values revealed as a result of the analyzes made at different times for certain regions in the literature need to be revised temporally and spatially. In this study, first, temporal analyzes of TS events for Istanbul was performed for many years. Then, thermodynamic indices and stability parameters were analyzed at various temporal scales and their variations in TS and non-TS events were determined. Through various skill scores, the success of the threshold values in the literature for Istanbul was tested. Finally, new threshold values have been proposed for the megacity by making modifications on the threshold values. The prominent results of the study are as follows:

  • No significant trend was observed on an annual basis throughout the study period, but it was determined that 69% of TS events occurred during the warm season (May–September). TS events were mostly observed in the afternoon and evening hours as expected. But their duration mostly (%93) lasted on the order of a few hours (0–3 h).

  • Thermodynamic indices and stability parameters were found to have significant differences in TS events compared to non-TS events. However, threshold values could not be met even in the presence of TS events for some indices and parameters. This is due to the temporal and spatial differences of the threshold values.

  • The indices showed the most successful forecasts mostly in the summer season (The POD value ranges between 0.58 and 0.97; the CSI value ranges between 0.22 and 0.37; and the TSS value varies between 0.32 and 0.57). The main reason for this is that the highest numbers of TS events are in this season. In addition, the CAPE and BRN exhibited the highest success rates during the summer season compared to other seasons, making them favorable parameters for predicting summer season TS events.. However, in the winter season, both CAPE and BRN had almost no success in predicting TS events.

  • Large differences were observed in the seasonal skill scores of the indices and parameters for the current threshold values in the literature. Of the indices and parameters, the best predictions were mostly in the summer and the worst predictions were in the winter.

  • Following the skill score analyzes for the threshold values available in the literature, modifications were made for each index and parameter. As a result of these modifications, success of up to 15% has been achieved in all indices and parameters skill values except the BRN. According to CSI, the success rate for SI is 15%; for LI, it is 8%; for SWEAT, it is 5%; for KI, it is 12%; for TTI, it is 10%; for CAPE, it is 8%; and for CIN, it is 7%.