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2. weather
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ADVANCES IN ATMOSPHERIC SCIENCES, VOL. 32, APRIL 2015, 515–527
Statistical Analysis of Thunderstorms on the Eastern Tibetan Plateau Based on
Modified Thunderstorm Indices
YOU Wei, ZANG Zengliang∗, PAN Xiaobin, ZHANG Lifeng, and LI Yi
Institute of Meteorology and Oceanography, PLA University of Science and Technology, Nanjing 211101
(Received 11 March 2014; revised 24 June 2014; accepted 24 July 2014)
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 SICCL ), 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 SICCL index.
Key words: thunderstorm, Tibetan Plateau, modified parameters, skill score
Citation: You, W., Z. L. Zang, X. B. Pan, L. F. Zhang, and Y. Li, 2015: Statistical analysis of thunderstorms on the eastern
Tibetan Plateau based on modified thunderstorm indices. Adv. Atmos. Sci., 32(4), 515–527, doi: 10.1007/s00376-014-4039-x.
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; Meißner 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: (1) instability over
a layer of sufficient depth; (2) a moist layer at low levels;
and (3) 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
∗
Corresponding author: ZANG Zengliang
Email: [email protected]
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
© Institute of Atmospheric Physics/Chinese Academy of Sciences, and Science Press and Springer-Verlag Berlin Heidelberg 2015
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THUNDERSTORMS ON THE QINGHAI-TIBET PLATEAU
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 (SICCL ; 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 SICCL
index cannot reflect the characteristics of convective weather
1000
39N
37N
1500
2000
2500 2000
1500
35N
33N
31N
Tuotuohe
Yushu
Nagqu
Lhasa 2500
1500
2000
1000 2500
2500
1500 20001000 2000
27N
78E 81E 84E 87E 90E 93E 96E 99E 102E 105E
29N
3000 3500 4000 4500 5000 5500
Fig. 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.
VOLUME 32
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).
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).
2.1. Definition of a thunderstorm
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
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YOU ET AL.
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.
2.2. Calculation and analysis schemes
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 Ts and dewpoint temperature Td with Ts and Td 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.
Ts and Td of the surface at 1400 LST were used instead of Ts
and Td of the surface at 0800 LST.
2.3. Modification of the stability parameters
Analysis of the difference in average temperature sounding, average humidity sounding, average depression of dewTable 1. Number of days with and without thunderstorms at different stations on the Tibetan Plateau during a 5-yr period (2006–10)
from June to August.
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 SICCL 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.
2.4. Stability parameters of the skill score and determination of the threshold
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 3a shows the difference in mean temperature on
thunderstorm and non-thunderstorm days in the four regions
Table 2. Contingency table used to verify predictions.
Forecast
Station
Elevation Thunderstorm Non-thunderstorm Missing
(units: m)
day
day
data
Nagqu
Lhasa
Tuotuohe
Yushu
4508
3650
4535
3682
257
194
88
112
198
235
357
332
8
31
15
16
Yes
No
a
Correct event forecast
c
False alarms
b
Surprise events
d
Non-events
Observation
Yes
No
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Table 3. Skill scores and their equations (a, b, c and d determined from Table 2).
Skill score
Code
Probability of detection
POD
False alarm ratio
FAR
Critical success index
CSI
True skill statistic
TSS
Heidke skill score
HSS
a
a+b
c
FAR =
a+c
a
CSI =
a+b+c
c
a
−
TSS =
a+b c+d
2(ad − bc)
HSS =
(a + b)(b + d) + (a + c)(c + d)
POD =
(a)
Pressure[ hPa]
100
150
200
250
300
350
400
450
500
550
surface
−80
Equation
Nagqu
Lhasa
Yushu
Tuotuohe
−60
−40
−20
temperature[ºC]
0
200
(b)
Pressure[ hPa]
250
300
350
400
450
500
550
surface
20
200
250
Pressure[ hPa]
20
Nagqu
Lhasa
Yushu
Tuotuohe
40
60
humidity[100%]
80
(c)
300
350
400
450
500
550
Nagqu
Lhasa
Yushu
Tuotuohe
surface
346 348 350 352 354 356 358 360
pesedo−equivalent potential temperature[K]
Fig. 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.
Reference(s)
Donaldson et al. (1975)
Donaldson et al. (1975)
Donaldson et al. (1975)
Hanssen and Kuipers (1965);
Doswell III and Flueck (1989)
Brier and Allen (1952)
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
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Nagqu
Nagqu
Lhasa
Lhasa
Yushu
Yushu
Tuotuohe
Tuotuohe
Nagqu
Nagqu
Lhasa
Lhasa
Yushu
Yushu
Tuotuohe
Tuotuohe
Nagqu
Nagqu
Lhasa
Lhasa
Yushu
Yushu
Tuotuohe
Tuotuohe
Nagqu
Nagqu
Lhasa
Lhasa
Yushu
Yushu
Tuotuohe
Tuotuohe
Fig. 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).
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 − Td ) 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 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
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THUNDERSTORMS ON THE QINGHAI-TIBET PLATEAU
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ing that the surface has high temperature and humidity just
before a thunderstorm.
4. Improvement of the stability parameters
and skill score
4.1. Definitions of the modified stability indices
4.1.1. Modified SI index
SIM = Te250 − T500-250 .
(1)
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 (1) expresses the difference between the observed temperature at 250 hPa (Te250 ) and
the temperature (T500-250 ) of an air parcel after being lifted
pseudo-adiabatically to 250 hPa from 500 hPa. The smaller
the SIM 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, SIM
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 SICCL index
SIMCCL = Te250 − TCCL-250 .
Fig. 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).
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 (TW ). The maximum value occurs at 1400 LST, indicat-
(2)
The definition of the original SICCL 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 SIMCCL is conducive to thunderstorm occurrence. Te250 in Eq. (2) represents the actual
environmental temperature at 250 hPa. TCCL-250 is the 250
hPa temperature of a parcel lifted moist-adiabatically from its
convective condensation level (CCL). The modified SIMCCL
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
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YOU ET AL.
1700 LST have no forecast significance).
4.1.3. Modified SIMS index
SIMS = Te250 − Ts-250 .
(3)
The definition of the SIMS index is similar to that of the SIM
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 (Te250 ) and the temperature
(Ts-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 SIMS . The smaller the
SIMS the greater the possibility of thunderstorms.
4.1.4. Modified K index
KM = (T500 − T250 ) + Td500 − 0.3(T − Td )300 .
(4)
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 − Td ) at 700 hPa. (T500 − T250 ) in Eq. (4) is the
temperature difference between 500 and 250 hPa; it indicates
the temperature lapse rate between the two layers. Td500 is
the dew-point temperature at 500 hPa; it shows the humidity
conditions of the low level. (T − Td )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 KM
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. Td 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 KM index modified in Eq. (4) is
therefore expressed by these three levels.
4.1.5. Modified K index considering surface temperature
KMS = T500 − T250 + 2Tds − 0.3(T − Td )300 .
(5)
Similar to the KM index, the first and third terms in Eq. (5)
represent the temperature lapse rates between 500 and 250
hPa and the degree of air saturation at 300 hPa. Tds 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 KMS 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
521
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.
4.2. Skill score of the stability index
A statistical analysis of thunderstorm and nonthunderstorm 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 nonthunderstorm 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.
Typically, the smaller the overlapping part between the
thunderstorm and non-thunderstorm boxes, the better the diagnosis effect. The overlapping part of the SIMCCL and KMS
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 KM and CAPE
indices, a thunderstorm is likely to occur. In contrast, if the
index value is less than the threshold value in the SIM , SIMLCL
and SIMCCL 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: SIMCCL , KMS , KM , SIM and
CAPE. Among these indices, SIMCCL 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 KM , which reaches a POD of
0.891, followed by SIMCCL , which reaches the POD to 0.852.
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THUNDERSTORMS ON THE QINGHAI-TIBET PLATEAU
VOLUME 32
Fig. 5. Box plots of (a) SIM , (b) SIMCCL , (c) SIMS , (d) KM , (e) KMS , 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 6 1.5×
(interquartile range) above the third quartile. Red plus signs are outliers.
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 KMS (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 KMS ,
SIM and SIMCCL exceed 0.4. The index with the highest TSS
score at Yushu is SIMCCL (Table 7), whose TSS score reaches
0.448. The scores of KM 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
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YOU ET AL.
Table 4. Comparison of five skill scores for the six modified indices
used for the prediction of non-thundery/thundery days at Nagqu.
Stability
index
Limit
CSI
POD
FAR
HSS
TSS
SIM
SIMCCL
SIMS
KM
KMS
CAPE
<4.0
<−0.5
<−1.0
>22.5
>31.7
>565
0.576
0.631
0.568
0.614
0.613
0.537
0.794
0.852
0.767
0.891
0.825
0.731
0.322
0.291
0.314
0.336
0.295
0.333
0.307
0.406
0.313
0.322
0.381
0.256
0.300
0.393
0.307
0.305
0.371
0.252
Table 5. Comparison of five skill scores for the six modified indices
used for the prediction of non-thundery/thundery days at Lhasa.
Stability
index
Limit
CSI
POD
FAR
HSS
TSS
SIM
SIMCCL
SIMS
KM
KMS
CAPE
<4.2
<−1.2
<0.4
>24.0
>33.5
>700
0.510
0.481
0.503
0.519
0.524
0.416
0.856
0.706
0.904
0.856
0.807
0.649
0.442
0.397
0.469
0.431
0.401
0.464
0.303
0.333
0.256
0.325
0.368
0.182
0.320
0.339
0.275
0.342
0.381
0.186
Table 6. Comparison of five skill scores for the six modified indices
used for the prediction of non-thundery/thundery days at Tuotuohe.
Stability
index
Limit
CSI
POD
FAR
HSS
TSS
SIM
SIMCCL
SIMS
KM
KMS
CAPE
<4.3
<0.0
<0.1
>22.5
>32.5
>622
0.327
0.324
0.295
0.295
0.354
0.295
0.761
0.750
0.810
0.807
0.852
0.727
0.634
0.635
0.683
0.683
0.621
0.668
0.308
0.303
0.238
0.240
0.342
0.252
0.430
0.421
0.378
0.381
0.500
0.366
Table 7. Comparison of five skill scores for the six modified indices
used for the prediction of non-thundery/thundery days at Yushu.
Stability
index
Limit
CSI
POD
FAR
HSS
TSS
SIM
SIMCCL
SIMS
KM
KMS
CAPE
<4.8
<−1.2
<−0.1
>25.4
>41.2
>625
0.323
0.392
0.373
0.315
0.323
0.344
0.732
0.795
0.786
0.684
0.679
0.696
0.634
0.564
0.585
0.632
0.608
0.595
0.229
0.352
0.318
0.221
0.260
0.282
0.304
0.448
0.412
0.283
0.323
0.350
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
SIMCCL and KMS , 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 SIM (0.427) and KMS (0.392). CAPE has the lowest score.
The overall TSS score of each index T Tuotuohe is relatively
high, among which SIMCCL and SIM score higher than 0.4.
The indices with the highest scores are SIMCCL (0.442) and
SIMS (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 SIMCCL . 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 SIMCCL
and KMS ) 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
Table 8. Number of days with and without thunderstorms at different stations on the Tibetan Plateau during a 2-yr period (2011–12)
from June to August.
Station
Thunderstorm days
Non-thunderstorm days
Nagqu
Lhasa
Tuotuohe
Yushu
103
88
43
39
76
85
135
126
524
THUNDERSTORMS ON THE QINGHAI-TIBET PLATEAU
Table 9. Modified indices with optimal thresholds and different skill
scores for the thunderstorm prediction verified against independent
data at Nagqu between 2011 and 2012.
Stability
index
Limit
CSI
POD
FAR
HSS
TSS
SIM
SIMCCL
SIMS
KM
KMS
CAPE
<4.0
<−0.5
<−1.0
>22.5
>31.7
>565
0.573
0.660
0.574
0.571
0.625
0.514
0.796
0.903
0.757
0.816
0.825
0.699
0.328
0.290
0.291
0.343
0.279
0.339
0.272
0.417
0.327
0.262
0.396
0.214
0.263
0.396
0.323
0.251
0.385
0.212
Table 10. Modified indices with optimal thresholds and different
skill scores for the thunderstorm prediction verified against independent data at Lhasa between 2011 and 2012.
Stability
index
Limit
CSI
POD
FAR
HSS
TSS
SIM
SIMCCL
SIMS
KM
KMS
CAPE
<4.2
<−1.2
<0.4
>24.0
>33.5
>700
0.597
0.573
0.551
0.525
0.567
0.456
0.902
0.866
0.927
0.756
0.829
0.674
0.362
0.372
0.424
0.367
0.358
0.415
0.415
0.378
0.278
0.340
0.389
0.157
0.427
0.383
0.283
0.342
0.392
0.156
Table 11. Modified indices with optimal thresholds and different
skill scores for the thunderstorm prediction verified against independent data at Tuotuohe between 2011 and 2012.
Stability
index
Limit
CSI
POD
FAR
HSS
TSS
SIM
SIMCCL
SIMS
KM
KMS
CAPE
<4.3
<0.0
<0.1
>22.5
>32.5
>622
0.423
0.370
0.354
0.322
0.347
0.301
0.767
0.767
0.814
0.651
0.767
0.651
0.507
0.577
0.611
0.611
0.607
0.641
0.426
0.334
0.291
0.268
0.289
0.220
0.502
0.422
0.394
0.330
0.378
0.281
Table 12. Modified indices with optimal thresholds and different
skill scores for the thunderstorm prediction verified against independent data at Yushu between 2011 and 2012.
Stability
index
Limit
CSI
POD
FAR
HSS
TSS
SIM
SIMCCL
SIMS
KM
KMS
CAPE
<4.8
<−1.2
<−0.1
>25.4
>41.2
>625
0.313
0.377
0.355
0.325
0.291
0.333
0.769
0.744
0.692
0.634
0.590
0.641
0.655
0.567
0.578
0.600
0.635
0.590
0.222
0.354
0.326
0.275
0.225
0.297
0.317
0.442
0.399
0.329
0.272
0.355
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
VOLUME 32
SI, SIMCCL 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 (SIMCCL index, Nagqu),
0.438 (SIM index, Lhasa), 0.502 (SIM index, Yushu), and
0.442 (SIMCCL index, Tuotuohe). Overall, SIMCCL 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 diag-
APRIL 2015
YOU ET AL.
nose 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.
Acknowledgements. The surface and sounding data were provided by the National Meteorological Center, China Meteorological
Administration. This research was supported by the National Natural Science Foundation of China (Grant Nos. 41275128, 41375063
and 41206163) and the Chengdu Institute of Plateau Meteorology
Foundation.
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APPENDIX
Traditional sounding indices
Showalter index (SI)
SI = Te500 − T850-500 .
This index is defined as the difference between the observed
temperature at 500 hPa (Te500 ) and the temperature (T850-500 )
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YOU ET AL.
of an air parcel after it has been lifted pseudo-adiabatically to
500 hPa from 850 hPa (Showalter, 1953).
Modified Showalter index (SICCL )
SICCL = Te500 − TCCL-500 .
TCCL-500 in the above equation is the 500 hPa temperature of a
parcel lifted moist-adiabatically from its modified convective
condensation level (Huntrieser et al., 1997).
K index (K)
K = (Te850 − Te500 ) + Td850 − (Te700 − Td700) .
Te850 in the above equation is the environmental temperature
at 850 hPa (similar to Te500 and Te700 ), and Td850 is the dewpoint temperature at 850 hPa (similar to Td700 ). This index increases with the decrease in static stability between 850 and
527
500 hPa, the increase in moisture at 850 hPa, and the increase
in relative humidity at 700 hPa (George, 1960).
CAPE
Z ZEL Tvp − Tve
dz .
CAPE = g
Tve
ZLFC
ZLFC in the above equation denotes the free convection level,
which is the height at which the difference between the air
parcel temperature and the ambient temperature shifts from
negative to positive; ZEL is the equilibrium level, which refers
to the height at which the difference between the air parcel
temperature and the ambient temperature shifts from positive
to negative. Tvp is the potential temperature of a parcel lifted
dry adiabatically from the surface to its condensation level
and moist adiabatically thereafter. Tve is the potential temperature of the environment.