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Statistical Analysis of Thunderstorms on the Eastern Tibetan Plateau Based on Modified Thunderstorm Indices


doi: 10.1007/s00376-014-4039-x

  • The Tibetan Plateau, with an average altitude above 4000 m, is the highest and largest plateau in the world. The frequency of thunderstorms in this region is extremely high. Many indices are used in operational forecasting to assess the stability of the atmosphere and predict the probability of severe thunderstorm development. One of the disadvantages of many of these indices is that they are mainly based on observations from plains. However, considering the Plateau's high elevation, most convective parameters cannot be applied directly, or their application is ineffective. The pre-convective environment on thunderstorm days in this region is investigated based on sounding data obtained throughout a five-year period (2006-10). Thunderstorms occur over the Tibetan Plateau under conditions that differ strikingly from those in plains. On this basis, stability indices, such as the Showalter index (including SI and SI CCL), and the K index are improved to better assess the thunderstorm environments on the Plateau. Verification parameters, such as the true-skill statistic (TSS) and Heidke skill score (HSS), are adopted to evaluate the optimal thresholds and relative forecast skill for each modified index. Lastly, the modified indices are verified with a two-year independent dataset (2011-12), showing satisfactory results for the modified indices. For determining whether or not a thunderstorm day is likely to occur, we recommend the modified SI CCL index.
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Manuscript received: 11 March 2014
Manuscript revised: 24 June 2014
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Statistical Analysis of Thunderstorms on the Eastern Tibetan Plateau Based on Modified Thunderstorm Indices

  • 1. Institute of Meteorology and Oceanography, PLA University of Science and Technology, Nanjing 211101

Abstract: The Tibetan Plateau, with an average altitude above 4000 m, is the highest and largest plateau in the world. The frequency of thunderstorms in this region is extremely high. Many indices are used in operational forecasting to assess the stability of the atmosphere and predict the probability of severe thunderstorm development. One of the disadvantages of many of these indices is that they are mainly based on observations from plains. However, considering the Plateau's high elevation, most convective parameters cannot be applied directly, or their application is ineffective. The pre-convective environment on thunderstorm days in this region is investigated based on sounding data obtained throughout a five-year period (2006-10). Thunderstorms occur over the Tibetan Plateau under conditions that differ strikingly from those in plains. On this basis, stability indices, such as the Showalter index (including SI and SI CCL), and the K index are improved to better assess the thunderstorm environments on the Plateau. Verification parameters, such as the true-skill statistic (TSS) and Heidke skill score (HSS), are adopted to evaluate the optimal thresholds and relative forecast skill for each modified index. Lastly, the modified indices are verified with a two-year independent dataset (2011-12), showing satisfactory results for the modified indices. For determining whether or not a thunderstorm day is likely to occur, we recommend the modified SI CCL index.

1. Introduction
  • Thunderstorm forecasting is one of the most difficult issues in weather forecasting. Forecasting accuracy has improved greatly with the development of numerical weather prediction (NWP) models; however, forecasts of the type, intensity, occurrence time and location of strong convection are often inaccurate (Anquetin et al., 2005; Mei\ssner et al., 2007). Convective parameters are important tools utilized to forecast, monitor and analyze potential severe convective weather. Many meteorologists have pointed out that convection requires three basic conditions: (2) instability over a layer of sufficient depth; (3) a moist layer at low levels; and (4) a mechanism (i.e., lift) that triggers the convection (Doswell III, 1987; Johns and Doswell III, 1992). Meteorologists have presented many different thermodynamic and kinetic parameters that meet all or some of these requirements to forecast the possibility of thunderstorms by studying pre-convective sounding data or data from NWP models (Showalter, 1953; Galway, 1956; Jefferson, 1963; Schulz, 1989; Davis and Johns, 1993; Lee and Passner, 1993; Brooks et al., 1994; Doswell III and Rasmussen, 1994; Fuelberg and Biggar, 1994; Huntrieser et al., 1997; Rasmussen and Blanchard, 1998; Thompson et al., 2003; Rasmussen, 2003; Groenemeijer, 2005; Manzato, 2005; Finch and Bikos, 2010; Chaudhuri et al., 2013).

    Thunderstorm parameters describe the potential of thunderstorms. However, the referred threshold values are not definite and may vary when applied in different regions and to different types of thunderstorms. For example, (Huntrieser et al., 1997) and (Haklander and Van Delden, 2003) calculated the statistic of parameter thresholds and the critical success index (CSI) of different thunderstorms in the Switzerland and Netherlands. The results showed that convective available potential energy (CAPE) had the highest CSI score in the Netherlands and that the total totals (TT) (Peppler and Lamb, 1989) achieved highest values in Switzerland. They also found that the threshold values of a parameter differ greatly. (Rasmussen and Blanchard, 1998) analyzed the relationships between thunderstorms and various parameters based on CAPE above zero from over 6000 sounding datasets in the United States. They found that the parameter of lift condensation level (LCL) achieved the highest skill score for forecasting thunderstorms, with an optimum value of 800 m. Similar statistical studies on the relationship between different convective parameters and strong convective weather have been conducted, for example, by (Doswell III and Schultz, 2006), (Brooks, 2009), (Kunz, 2007), (Groenemeijer and van Delden, 2007), (Wagner et al., 2008), (Dalla Fontana, 2008), (Gottlieb and Wysocki, 2009), (Yamane et al., 2010), (Grams et al., 2012), and (Thompson et al., 2012). In China, Many interesting studies out with a focus on convective weather have also been carried out (Hu et al., 2010a; Xu and Zipser, 2010; Li et al., 2004a; Gao et al., 2005; Qin et al., 2006; Wang and L\"u, 2007; Li et al., 2008; He et al., 2011; Yu et al., 2011; Yu et al., 2012; Sun and Tao, 2012; Fan and Yu, 2013; Zheng et al., 2013).

    The Tibetan Plateau, the world's highest plateau, has an average altitude of over 4000 m (see Fig. 1). Its unique terrain conditions distinguish it from plains and general mountains in terms of weather characteristics. The heating effect of the plateau functions directly in the middle troposphere, especially during summer (Ye and Gao, 1989); this phenomenon indicates the location of the strong convective zone. Statistics show that the Tibetan Plateau is a place that experiences one of the highest frequencies of thunderstorms and lightning in China, and even worldwide (Ye and Gao, 1989; Jiang and Fan, 2002; Zhang et al., 2003; Qie et al., 2004; You et al., 2012).

    Many thunderstorm parameters are designed based on observations from plains (altitude: <1000 m). Thus, most convective indices are difficult to calculate or apply to the Tibetan Plateau because most parts of it are higher than 700 hPa. For instance, the calculation of the K index (see appendix) requires a temperature and dew point of 850 and 700 hPa; thus, this index cannot be computed in most parts of the Plateau. Although several indices can be calculated directly, the high altitude of the Plateau affects the representation of the physical mechanism of these indices. For example, the modified Showalter index (SI CCL; see appendix), which reveals the difference between the temperature (in °C) at 500 hPa when a parcel of air is adiabatically uplifted from the convective condensation level, and the actual environmental temperature at 500 hPa, indicates the difference between low-level warm/moist air and cold/dry air in the middle troposphere. However, in the Plateau region, the calculated SI CCL index cannot reflect the characteristics of convective weather because the initial lift height of the air parcel is close to 500 hPa (e.g., the elevation of Nagqu Station is approximately 590 hPa) and the difference is particularly small. Research on the applicability of convective indices in the Tibetan Plateau remains limited due to the sparse data availability. Moreover, soundings are normally implemented in the early morning (0800 LST; LST = UTC + 8) and evening (2000 LST) because they need to keep pace with world time (0000 UTC and 1200 UTC).

    Figure 1.  Topographic view and distribution of sounding stations over the Tibetan Plateau. The black squares represent radiosonde stations; white circles represent surface stations; shading represents elevations higher than 3000 m.

    The pre-convective environment on thunderstorm days is analyzed in this study based on limited sounding and ground observational data, the aim being to modify traditional stability parameters and render them applicable to the Tibetan Plateau. Section 2 describes the data and methods used in this research. The characteristics of the pre-convective environment on thunderstorm days in this region are analyzed in section 3. Commonly used convective indices, such as the Showalter index (SI) and K index, are also modified. Section 4 provides the forecast skill calculations for each modified parameter. An independent dataset is adopted in section 5 to evaluate the modified stability parameters. Finally, section 6 provides a summary and discussion of the findings.

2. Data and methodology
  • Continuous sounding data were obtained from four stations——Lhasa, Nagqu, Tuotuohe and Yushu (shown in Fig. 1) ——and from 44 manmade surface observations on the Tibetan Plateau. Each surface observation includes a code approved by the World Meteorological Organization. One hundred different present and past weather types were assigned two-digit numbers (00 to 99). The following numbers indicate the occurrence of thunderstorms: 17, 29, and 91 to 99. Data from the sounding stations and surface observations were provided by the National Meteorological Center. These data include surface observation data obtained eight times a day (0200, 0500, 0800, 1100, 1400, 1700, 2000, and 2300 LST) and sounding data obtained twice a day (0800 and 2000 LST) during a five-year period (June to August from 2006 to 2010).

  • The thunderstorms that occur on the Tibetan Plateau during daytime (0800 and 2000 LST) account for over 90% of the total number of thunderstorms; most of them occur between 1400 and 2000 LST. Records show that only four thunderstorms occurred in Nagqu before 1400 LST during 2006-10; only one occurred in Lhasa; and none occurred at the other two stations. Thus, this study focuses on thunderstorms that occurred in the afternoon.

    A thunderstorm day was defined as a day upon which at least one thunderstorm report was recorded (no double counting) in the data from the surface observation and adjacent stations between 1400 and 2000 LST (radius <150 km, as shown in Fig. 1). When a surface observation station was within the range of two sounding stations (e.g., the surface observation stations in Lhasa and Nagqu), the method of (Rasmussen and Blanchard, 1998) in selecting "proximity soundings" was implemented. The method was designed to find a reasonably nearby sounding that was in the "inflow sector" of the event and reduce the likelihood that the sounding had been contaminated by convection. If more than one sounding satisfied the inflow and range criteria, for simplicity the sounding with the largest CAPE was chosen as being "representative" of the event.

    A non-thunderstorm day was defined as a day upon which no thunderstorm reports were recorded in the data from the surface observation and adjacent stations between 1400 and 2000 LST. Incorrect or incomplete data were excluded (i.e., soundings with incomplete wind or humidity data were rejected) based on the above definition of thunderstorms. The number of thunderstorm and non-thunderstorm days in each region is shown in Table 1.

  • The differences in the pre-convective environments on thunderstorm and non-thunderstorm days were discussed based on temperature and humidity. The profile characteristics of the averages of temperature, specific humidity, depression of the dew point, and potential pseudo-equivalent temperature on thunderstorm and non-thunderstorm days on the Tibetan Plateau were analyzed. Vertical sounding was conducted on the ground at 500, 400, 300, 250, 200, 150 and 100 hPa. Logarithmic linear interpolation was applied at every 10 hPa in the generation of the vertical profile chart, and sounding data at 0800 LST were used in the calculation.

    (Turcotte and Vigeneux, 1987) modified the surface layer of sounding and replaced surface temperature T s and dew-point temperature T d with T s and T d in the outbreak of convection in the CAPE calculation. Considering that a thunderstorm is a short-term and small-scale system, data obtained from an approaching thunderstorm are representative. A similar modification in the calculation of the parameters associated with the surface elements was implemented in this study. T s and T d of the surface at 1400 LST were used instead of T s and T d of the surface at 0800 LST.

  • Analysis of the difference in average temperature sounding, average humidity sounding, average depression of dew-point temperature sounding, and average pseudo-equivalent potential temperature sounding on the Tibetan Plateau on thunderstorm and non-thunderstorm days indicates that the vertical structure of the atmosphere above the Plateau is different from that above plains (see section 3). The improvement of the K, SI and SI CCL indices is elaborated in section 4 based on the pre-convective environmental elements profile on thunderstorm days on the Plateau to determine the weather on the Plateau on thunderstorm days.

  • Skill scores and an appropriate index threshold are critical in determining the index forecast accuracy. The appropriateness of the threshold relies on the score rules. Categorical verification is an objective method employed to assess the forecast skills of various indices and to determine a suitable threshold. The target dataset in this study was inputted into a 2×2 contingency table (Table 2) and divided into four parts (a, b, c and d) based on the observation (yes/no) and forecast events (yes/no). This method is widely used in weather forecast evaluation (Huntrieser et al., 1997; Kunz, 2007). The threshold index value of the classified data was determined with the commonly used five-skill scoring method. Frequently used skill scores, such as CSI, POD, FAR, TSS and HSS were calculated in this study (see Table 3 for the skill score algorithm); however, only the TSS score was used to determine the value of the threshold, and in the verification process, given that each index was assigned a threshold value that provides the best TSS (Gottlieb and Wysocki, 2009). In addition, these skill sores are most commonly used and quite easy to understand.

3. Environmental characteristics and meteorological factors of thunderstorms
  • In general the mean temperature reduces markedly throughout the entire layer on thunderstorm days, but especially in the layer between 250 and 100 hPa (Fig. 2a), and a large value arear of humidity is observed in the lower layer of the atmosphere (Fig. 2b). The vertical profile of mean pseudo-potential temperature shows that there is an unstable layer between 500 and 400 hPa on thunderstorm days over four stations (Fig. 2c).

    Figure 2.  (a) Mean temperature soundings, (b) mean humidity vertical profiles, and (c) mean pseudo-potential temperature vertical profiles for days with thunderstorms during 2006-10.

    Figure 3.  Difference between the (a) mean temperature soundings, (b) mean specific humidity vertical profiles, (c) mean dew-point depression vertical profiles, and (d) mean pseudo-potential temperature vertical profiles for days with and without thunderstorms during 2006-10 (average value on thunderstorm days minus that on non-thunderstorm days).

    Figure 3a shows the difference in mean temperature on thunderstorm and non-thunderstorm days in the four regions of the Tibetan Plateau (the average profile of thunderstorm days minus that of non-thunderstorm days). The temperature difference is most obvious at 500 to 400 hPa (approximately 5800 to 7600 m). The maximum mean temperature difference at Tuotuohe, Yushu and Nagqu is at 500 hPa, and the mean temperature on thunderstorm days is 1°C higher than that on non-thunderstorm days. The temperature difference is slightly smaller at Lhasa, with the maximum value at 400 hPa. The negative temperature difference at the top of the boundary layer at Lhasa could be attributable to the air from differing thermodynamic characteristics entrained through the top of the height of the boundary layer (Hu et al., 2010b). The mean temperature difference in the four regions decreases to a negative value above 200 hPa, with the maximum negative value found at the top of the pressure range shown, i.e. at 100 hPa, except for Yushu where it is 150 hPa. The lower layer of the troposphere on the plains during thunderstorm days is usually warmer (e.g., around 850 hPa) than on non-thunderstorm days, whereas no large temperature differences are found above the higher layer (e.g. 500 hPa) in comparison to the days without thunderstorms. The conditions between 850 and 500 hPa are unstable on thunderstorm days (Huntrieser et al., 1997). However, on the Tibetan Plateau, the most positive temperature differences are obtained in the layer between 500 and 400 hPa, whereas the negative temperature differences are presented above 250 hPa, near the tropopause height (Fig. 3a). The conditionally unstable layer is obtained above 500 hPa (Fig 2c). This conditional instability is mainly caused by the high temperature in the middle troposphere, with no strong low temperature near the top of the troposphere. A significant temperature reduction at 100 hPa is observed at Nagqu, Tuotuohe and Lhasa, possibly attributable to the convective activities on thunderstorm days increasing the tropopause height. The temperature at Yushu increases between 150 and 100 hPa, probably because of the low altitude of Yushu and its location on the eastern border of the Plateau. Yushu's tropopause height (150 hPa) is smaller than that of the other three stations. Apart from thunderstorms, other impacting factors, such as the plateau vortex and torrent and the ozone jet, also affect the change in the height of the tropopause (Zou et al., 1989; Chakrabarty et al., 2000). Thus, the temperature changes are more complicated above 200 hPa. The same situation on the surface and at 500 hPa (Fig. 3a) is observed at Yushu and Tuotuohe. The average temperature on thunderstorm days is 1°C higher than that on non-thunderstorm days. However, the mean surface temperature at Lhasa and Nagqu on "thundery" days exhibit no strong difference when compared with the mean surface temperature on non-thundery days. The thunderstorm pseudo-potential temperature profiles (Fig. 2c) at Nagqu, Yushu and Tuotuohe indicate that the weather conditions in the near-surface level lower than 500 hPa is stable on thunderstorm days and that thunderstorms may be cause by an unstable layer above 500 hPa.

    Another condition that causes thunderstorms is the presence of sufficient moisture in the lower atmospheric layer. Prior studies have reported that a large value arear of humidity on plains or in low-altitude regions on thunderstorm days is found at 600 to 700 hPa (George, 1960; Huntrieser et al., 1997). The differences in the mean specific humidity soundings of the four regions are presented in Fig. 3b. The highest layer of the profile reaches 200 hPa only, considering that no humidity observations were obtained above 200 hPa. The humidity throughout the entire layer on thunderstorm days is higher than that on non-thunderstorm days; the difference reaches its maximum at 500 hPa (in addition to the maximum difference at ground level in Lhasa). Between 500 and 250 hPa, the difference in average specific humidity decreases rapidly with height and approaches 0 at 250 hPa. Figure 3c shows that the differences in the mean depression of the dew point (T-T d) soundings are in the negative area. The dew point on thunderstorm days is strikingly higher than on non-thunderstorm days because the temperature on thunderstorm days is higher than on non-thunderstorm days, and the depression of the dew point difference is lower in the former. The most striking differences between the mean dew point depression soundings are at 300 hPa, indicating that air is most likely to condense on thunderstorm days in this layer. Overall, the humidity of the entire layer on thunderstorm days is higher than that on non-thunderstorms days. The zone of high humidity on thunderstorm days is presented at approximately 500 hPa, and the layer within which condensation is likely to occur is at approximately 300 hPa.

    Pseudo-equivalent potential temperature sounding can reflect the convective stability of moist air. Figure 3d shows the differences in the average pseudo-equivalent potential temperature on thunderstorm and non-thunderstorm days. The mean pseudo-equivalent potential temperature on thunderstorm days is higher than that on non-thunderstorm days. The maximum value is at 500 hPa, which indicates that the air mass above 500 hPa is wet and potentially unstable (Fig. 2c).

    Figure 4.  Difference between the (a) mean surface temperature, (b) mean surface dew-point, and (c) mean surface wet-bulb temperature during 0800-2000 LST for days with and without thunderstorms (average value on thunderstorm days minus that on non-thunderstorm days).

    Figure 4 shows the change in surface mean, mean dew point, and mean wet-bulb temperatures on thunderstorm and non-thunderstorm days from 0800 and 2000 LST (the average value on thunderstorm days minus that on non-thunderstorm days). The average temperature difference gradually decreases with time (Fig. 4a). The difference between 1700 and 2000 LST is negative and particularly small, which indicates that the temperature after thunderstorms is usually low. The average dew point temperature differences are positive and increase with time (Fig. 4b). The difference between 1700 and 2000 LST is greater than that in the other time periods because of precipitation after a thunderstorm. Figure 4c shows the difference curve of the average wet-bulb temperature (T W). The maximum value occurs at 1400 LST, indicating that the surface has high temperature and humidity just before a thunderstorm.

4. Improvement of the stability parameters and skill score
  • 4.1.1 Modified SI index

    \begin{equation} \label{eq1} {\rm SI}_{\rm M}=T_{\rm e250}-T_{500\hbox{-}250} . \end{equation}

    The original SI index indicates the stability between the lower layer at 850 hPa and the middle layer at 500 hPa of the troposphere (refer to appendix). Equation (2) expresses the difference between the observed temperature at 250 hPa (T e250) and the temperature (T500-250) of an air parcel after being lifted pseudo-adiabatically to 250 hPa from 500 hPa. The smaller the SI M the greater the possibility of thunderstorms. The SI index reflects the difference between the warm humid layer below and the dry cold layer above. On the Tibetan Plateau, the warmest and wettest lower layer is located at 500 hPa on thunderstorm days, as determined by comparing with no thunderstorm days (Fig. 3); the coldest dry upper layer is above 250 hPa. Tests were conducted at 100, 150, 200 and 250 hPa and the initial lifting point of the air parcel was fixed at 500 hPa to determine the height of the dry, cold upper layer (Fig. 3a). The results show that among the four sites, SI M at the 250 hPa upper layer achieves the best forecasting effect because the temperature lapse rate below 250 hPa is relatively large and decreases with a relatively complex change above 250 hPa. This decrease could be caused by the elevated height of the troposphere; however, other factors may also affect the changes in tropopause height. Therefore, the lifting end point of the air parcel on the upper layer was fixed at 250 hPa.

    4.1.2 Modified SI CCL index

    \begin{equation} \label{eq2} {\rm SI}_{\rm MCCL}=T_{\rm e250}-T_{{\rm CCL}\hbox{-}250} . \end{equation}

    The definition of the original SI CCL is shown in the appendix. The thermal effects cause the air parcel on the ground to be lifted freely to the condensation level, where the surface mixing ratio line intersects with the temperature curve (Saucier, 1955). The condensation level is also the height at which a parcel of air, when heated sufficiently from below, rises and becomes saturated. A high surface humidity indicates a low CCL height, and a lower SI MCCL is conducive to thunderstorm occurrence. T e250 in Eq. (3) represents the actual environmental temperature at 250 hPa. T CCL-250 is the 250 hPa temperature of a parcel lifted moist-adiabatically from its convective condensation level (CCL). The modified SI MCCL on the Tibetan Plateau reflects the stability between the surface and the height of 250 hPa before thunderstorms. The surface humidity at 0800, 1100 and 1400 LST is considered in this study. The surface humidity at 1400 LST is the best, which is consistent with the increasing surface humidity before thunderstorms as shown in Fig. 4b (the data at and after 1700 LST have no forecast significance).

    4.1.3 Modified SI MS index

    \begin{equation} \label{eq3} {\rm SI}_{\rm MS}=T_{\rm e250}-T_{{\rm s}\hbox{-}250} . \end{equation}

    The definition of the SI MS index is similar to that of the SI M index except that the initial uplifting level of the air parcel is on the surface and is expressed by the difference between the observed temperature at 250 hPa (T e250) and the temperature (T s-250) of an air parcel after being lifted pseudo-adiabatically to 250 hPa from the surface. The initial lift temperature and dew point are the surface temperature and the surface dew point at 1400 LST. High temperature and humidity in the lower atmosphere generate a small SI MS. The smaller the SI MS the greater the possibility of thunderstorms.

    4.1.4 Modified K index

    \begin{equation} \label{eq4} K_{\rm M}=(T_{500}-T_{250})+T_{\rm d500}-0.3(T-T_{\rm d})_{300} . \end{equation}

    The formula of the original K index is shown in the appendix. The K index increases with the decrease in static stability between 850 and 500 hPa, the increase in moisture at 850 hPa, and the increase in the degree of saturation of the middle layer (T-T d) at 700 hPa. (T500-T250) in Eq. (5) is the temperature difference between 500 and 250 hPa; it indicates the temperature lapse rate between the two layers. T d500 is the dew-point temperature at 500 hPa; it shows the humidity conditions of the low level. (T-T d)300 is the depression of the dew point at 300 hPa (showing the degree of saturation of the layer), and 0.3 is an empirical coefficient employed to make the relative contributions consistent. The higher the K M value the more likely thunderstorms are to occur. The atmosphere is unstable between 500 and 250 hPa on thunderstorm days over the Tibetan Plateau (high temperature lapse rate); humidity at 500 hPa is usually the highest, i.e. T d is relatively large. Moreover, the depression of the dew point at 300 hPa is small. Thus, the three points of division (850, 500 and 700 hPa) of the K index on plains change to 500, 250 and 300 hPa in plateau areas. The K M index modified in Eq. (5) is therefore expressed by these three levels.

    4.1.5 Modified K index considering surface temperature

    \begin{equation} \label{eq5} K_{\rm MS}=T_{500}-T_{250}+2T_{\rm ds}-0.3(T-T_{\rm d})_{300} . \end{equation}

    Similar to the K M index, the first and third terms in Eq. (6) represent the temperature lapse rates between 500 and 250 hPa and the degree of air saturation at 300 hPa. T ds is the dew-point temperature of the surface at 1400 LST. Figure 3b shows that before thunderstorms, the average dew-point temperature of the surface at 1400 LST is strikingly higher than that at 0800 LST. The empirical coefficients are 2 and 0.3. A large K MS value indicates a high possibility of thunderstorm occurrence.

    4.1.6 CAPE

    In the CAPE calculation (see appendix), the low-layer temperature and the dew point take the value of surface temperature and surface dew point at 1400 LST, respectively. The greater the CAPE is, the higher the degree of instability of the atmosphere and the greater the possibility of thunderstorm occurrence. The unstable energy of the Tibetan Plateau must be smaller than that of plains in CAPE calculations given the large initial uplifting height that results in the high altitude on Plateau.

  • A statistical analysis of thunderstorm and non-thunderstorm events from June to August between 2006 and 2010 was conducted with the six indices mentioned above. Figure 5 shows the boxplots of the six indices on thunderstorm and non-thunderstorm days at Nagqu. The smaller the range of the whisker and the box, the smaller the dispersion of the parameter value. The figure shows that, barring CAPE, the thickness of the box on the thunderstorm side and the epitaxial whisker are smaller than those on the non-thunderstorm side, hence the small dispersion of the index value of the thunderstorm events, which indicates that these indices can suitably reflect the common features of thunderstorm events. However, for non-thunderstorm events, a large dispersion of the index value indicates that these indices cannot properly reflect the characteristics of non-thunderstorm events.

    Figure 5.  Box plots of (a) SI M, (b) SI MCCL, (c) SI MS, (d) K M, (e) K MS, and (f) CAPE for sampled days with (left) and days without (right) thunderstorms. The blue box extends from the 25th percentile to the 75th percentile (interquartile range), and the red line is the median value. The lower error bar extends to the smallest data value that is ≥1.5× (interquartile range) below the first quartile, and the upper error bar extends to the largest data value that is ≤1.5× (interquartile range) above the third quartile. Red plus signs are outliers.

    Typically, the smaller the overlapping part between the thunderstorm and non-thunderstorm boxes, the better the diagnosis effect. The overlapping part of the SI MCCL and K MS boxplots is relatively small (Figs. 5b and e), whereas that of the CAPE index boxplots is large (Fig. 5f). Specifically, the overlapping part of the thunderstorm and non-thunderstorm boxplots (500 and 800 J kg-1) in CAPE occupies 51.3% of the thickness of a thunderstorm box and 56.5% of that of a non-thunderstorm box. Thus, determining whether a thunderstorm will occur based on the critical threshold value is difficult.

    The modified stability parameter has a certain denotative meaning in thunderstorm forecasting. The modified stability parameter is assessed with the five types of skill scores in the following paragraphs. The method employed to determine the threshold values has already been described in section 2.3. The threshold value of each stability parameter can be obtained through TSS optimal scoring. If the index value is greater than the threshold value in the K M and CAPE indices, a thunderstorm is likely to occur. In contrast, if the index value is less than the threshold value in the SI M, SI MLCL and SI MCCL indices, a thunderstorm is likely to occur. Table 3 shows the five types of skill scores on thunderstorm and non-thunderstorm days, as well as the threshold values of the different stability indices. The average value of TSS is 0.320. The most appropriate indices for the prediction of thunderstorms in descending order are: SI MCCL, K MS, K M, SI M and CAPE. Among these indices, SI MCCL has the highest TSS score (0.393). The index with a relatively low TSS score is CAPE. The descending order of HSS scores of the indices is similar to that of TSS, but with relatively large differences in POD. The highest index is K M, which reaches a POD of 0.891, followed by SI MCCL, which reaches the POD to 0.852. Figures 5d and b show that this ranking was obtained because the thickness of the box of the two indices in the thunderstorm event is thinner than that in the non-thunderstorm event. Therefore, the possibility of determining a threshold value that can evaluate the POD is definitely high.

    The modified index was then calculated and analyzed statistically with the same method employed at Lhasa, Tuotuohe and Yushu. Tables 5-7 show the five types of skill scores on thunderstorm and non-thunderstorm days and the forecasting threshold values of each index. Among the indices, the one with the highest TSS forecasting score at Lhasa is K MS (Table 5). The CAPE index achieves a minimum score of 0.186. The TSS score of each index at Tuotuohe is higher than that in the other regions (Table 6), among which the TSS scores of K MS, SI M and SI MCCL exceed 0.4. The index with the highest TSS score at Yushu is SI MCCL (Table 7), whose TSS score reaches 0.448. The scores of K M are relatively low. The TSS scores of the remaining indices exceed 0.3.

    The average TSS value of the six indices in Tables 4-7 is 0.321, 0.307, 0.413 and 0.353, respectively. The TSS scores of the indices are generally high at Tuotuohe Station. The vertical profiles of the environmental elements (Fig. 3) show that the differences in environmental factors during thunder-storm and non-thunderstorm days are most obvious at Tuotuohe, and that the modified index is based on the characteristics of the environmental factors on thunderstorm days. Therefore, the thunderstorm forecast accuracy of the modified index at Tuotuohe is better than that in the other regions.

    Except for the relatively low TSS scores of CAPE at Yushu and Lhasa, CAPE obtains scores above 0.35 at Yushu and Tuotuohe because the temperature difference between thunderstorm and non-thunderstorm days at Tuotuohe and Yushu is large and the temperature difference at Lhasa and Nagqu is small (Figs. 3a and 4a). In particular, the average temperature of the surface layer at Lhasa on thunderstorm days is smaller than that on non-thunderstorm days. The CAPE calculation is extremely sensitive to the elevation temperature on the lower layer, thereby making the CAPE thunderstorm forecast less effective in these two regions.

5. Verification of the modified stability indices based on an independent dataset
  • Five-year data on thunderstorm and non-thunderstorm days were employed to conduct a statistical analysis for the modified stability indices. The various thresholds of the stability indices were determined. The summers of 2011 and 2012 were utilized as the independent dataset for forecast verification of the six stability indices, and the definition and index calculation of thunderstorm days were made identical to those of the previous days. Table 8 shows the number of thunderstorm and non-thunderstorm days in the summers of 2011 and 2012 in each region. Tables 9-12 provide the skill score comparison of thunderstorm forecasts for the various stability indices. The indices with high TSS scores at Nagqu are SI$_{\rm MCCL}$ and $K_{\rm MS}$, whose scores are 0.396 and 0.385, respectively; these indices indicate whether or not a thunderstorm is likely to occur. At Lhasa, the indices with a high TSS score are SI$_{\rm M}$ (0.427) and $K_{\rm MS}$ (0.392). CAPE has the lowest score. The overall TSS score of each index T Tuotuohe is relatively high, among which SI$_{\rm MCCL}$ and SI$_{\rm M}$ score higher than 0.4. The indices with the highest scores are SI$_{\rm MCCL}$ (0.442) and SI$_{\rm MS}$ (0.399).

    Combining the historical and independent datasets, the best modified indices to be used for the forecast of a thundery day on the Tibetan Plateau is SI$_{\rm MCCL}$. This index is relatively stable and can be used as the optimal discriminant index on the Tibetan Plateau for thunderstorm forecasting. The optimal index that distinguishes thunderstorm days shows that the thunderstorm forecast results of the calculation requiring the surface temperature or the dew-point index (such as SI$_{\rm MCCL}$ and $K_{\rm MS}$) are good. This finding reveals the importance of observational data on approaching thunderstorms for the diagnosis of the occurrence of thunderstorms. If sounding data on approaching thunderstorms are available, the capability of the modified index to identify thunderstorms can be enhanced.

6. Summary and conclusions
  • This paper focuses on the systematic study of modifications to thunderstorm indices for the Tibetan Plateau. The SI, SI MCCL and K indices have been redefined according to the special characteristics of the environment on the Plateau, where thunderstorms occur frequently. The aforementioned three indices have been assessed and compared based on the composite forecasting skill scores of historical samples. The modified stability indices are suitable for thunderstorm forecasting on the Tibetan Plateau. Finally, trial forecasts were conducted with thunderstorm and non-thunderstorm days from June to August 2011 and 2012 as independent samples. POD, FAR, CSI, TSS and HSS were calculated to evaluate the forecasting accuracy rates and to assess the thunderstorm forecast accuracy of each stability index.

    This study is the first to comprehensively examine the improvement of convection indices on the Tibetan Plateau. The modified indices can significantly increase the thunderstorm forecast accuracy in high-elevation locations, such as Nagqu, Lhasa, Tuotuohe and Yushu. The highest TSS skill scores of the independent samples reach 0.396 (SI MCCL index, Nagqu), 0.438 (SI M index, Lhasa), 0.502 (SI M index, Yushu), and 0.442 (SI MCCL index, Tuotuohe). Overall, SI MCCL is the optimal index for thunderstorm forecasting on the Tibetan Plateau. It should be noted that the indices proposed in this study involve thermodynamic parameters, most of which are calculated based on temperature and humidity. Several studies have shown that the atmospheric heat source on the Tibetan Plateau has a strong positive correlation with the number of thunderstorm days and that the correlation coefficient reaches 0.86 (Zhu et al., 2012). Thus, the frequent occurrence of thunderstorms on the Plateau is probably due to thermodynamic factors instead of dynamic factors. We also attempted to calculate the wind shear value based on different height levels, the convective inhibition (CIN), the most-unstable (MU) CAPE, and the mean-layer (ML) CAPE (Craven et al., 2002). These indices on thunderstorm days are not strikingly different from those on non-thunderstorm days (data not shown). In particular, the values of unstable energy parameters such as MLCAPE are mostly zero. However, whether dynamic and unstable energy parameters can be used for second judgments based on thermodynamic parameters requires further research.

    Unfortunately, the strength and types of thunderstorms are not classified in this study. The environmental characteristics of different types of thunderstorms may differ, and some types of thunderstorms may be affected by dynamic factors. In addition, the sounding stations selected herein represent the environmental characteristics at approximately 150 km within 12 h (0800 and 2000 LST) due to the exceptionally sparse distribution of the soundings and ground stations on the Tibetan Plateau. However, under certain conditions, the sounding stations do not represent the atmospheric environment within the scope and timing, such as squall lines and several relatively small-scale weather systems. Thus, some thunderstorms and other small-scale convective systems are not recorded or monitored. In addition, convective weather mainly occurs in the afternoon and before midnight; thus, sounding in the morning cannot diagnose afternoon thunderstorms very well, and sounding in the evening can only diagnose thunderstorms that occur at night. Such is the case in the entire East Asian region. Therefore, the application of rawinsonde sounding data in convective weather is generally inadequate in these areas. Moreover, the surface observations were made every 3 h, and the time rate was relatively rough. If observational data, such as ground and sounding data, as well as unconventional observational data (radar, satellite, lightning location data), can be further enriched with a high resolution, the accuracy of thunderstorm forecasting based on the modified indices may be enhanced.

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