Feasibility of forecasting convective rain by diagnosing intracloud lightning jumps

This study conducted a comparison of the data quality of Earth Networks (EN) and Taiwan Power Company’s Total Lightning Detection System (TLDS) and evaluated the feasibility of using intracloud (IC) lightning to issue convective rain warnings. The results indicate uncertainties in the TLDS positioning of IC lightning. When forecasting convective rain on the basis of IC lightning jumps using EN data, the mean prefigurance and postagreement scores were 0.8 and 0.67, respectively, which were more favourable than the respective TLDS scores of 0.65 and 0.47. In regions with high TLDS positioning uncertainties, the use of EN data increased the number of prefigurance and postagreement hits in each analysis zone and raised the prefigurance and postagreement scores to 0.3 and 0.5, respectively. This indicates that analyses using EN data can reduce the risk of missed convective rain warnings when diagnosing IC jumps and can reduce the false alarm rate. In this study, IC jumps preceded convective rains by a maximum of 27.5–39.3 min on average in all analysis zones across Taiwan. The results suggest that diagnosing IC jumps to forecast convective rain is feasible, but until the uncertainties in the positioning of IC lightning using TLDSs have been remedied, EN data are the more suitable diagnostic choice.


Introduction
Taiwan is situated under the East Asian monsoon subsystem and receives as much as 2500 mm of rainfall on average from May to September (Chen and Chen 2003;Chen et al. 2007;Wang et al. 2008;Chen et al. 2014;Chen et al. 2016;Chen et al. 2017;Wu et al. 2021).The number of short-duration heavy precipitation cases in Taiwan continues to increase (Chen and Lu 2007).In the face of increasing short-term extreme rainfall, the Taiwan Central Weather Bureau has added "1-h/3-h rainfall of 40 mm/100 mm or more" to the short-duration heavy rainfall standard in 2020.Afternoon thunderstorms (ATs) and accompanying convective rain account for a large proportion of short-duration heavy rainfall up to 30% during summer monsoons (Wu et al. 2016) and up to 75% of the rainfall in the north of Taiwan (Chen et al. 2014(Chen et al. , 2016;;Tan et al. 2022), and is one of the major causes for flooding and landslides.
Because of the local circulation and the thermal effect from the sun's rays during the day, the windward slopes of western Taiwan and neighbouring regions are conducive to the occurrence of thunderstorms (Lin and Kuo 1996;Kuo and Wu 2019;Miao and Yang 2020) and extreme rainfall events.For example, on June 4, 2021, the daily rainfall in Taiwan exceeded 200-300 mm (Chen et al. 2022).During warm season, afternoon (12:00 p.m. to 9:00 p.m., local time) thunderstorms vary considerably across regions in terms of rainfall occurrence time, duration, occurrence of a strong echo and maximum rainfall (Lin et al. 2011); these differences increase the difficulty of forecasting thunderstorms.
There is a dense distribution of military and civilian airports in western Taiwan and hence frequent takeoffs and landings.High impact weather associated with thunderstorms, such as heavy rainfall, low visibility, low cloud curtains, slippery runways, cloud-to-ground lightning, lowaltitude wind shear, strong gusts, poses great risk to aviation (Cao et al. 2014(Cao et al. , 2018;;Chen et al. 2020;O'Connor and 59 Page 2 of 13 Kearney 2018; Tan et al. 2022).Faced with potential hazards from thunderstorms, airport weather forecasting operations typically rely on weather radars to detect potential hazards from thunderstorms.However, for rapid evolving thunderstorms, the time discontinuity and delay of radar echo are often the main contributors to cause the decision hesitancy, to determine where a weather hazard exceeds flight operation standards.The forecasting of thunderstorms requires the development and application of other early warning systems in addition to model forecasting and radar echo detection.
Lightning jumps (i.e.sudden surges in lightning frequencies) have been used as a forecast indicator for thunderstorms for several decades (Williams et al. 1999;Gatlin and Goodman 2010;Schultz et al. 2011Schultz et al. , 2016)).The monitoring of lightning jumps can reveal abnormally high surges in lightning frequencies and signal the critical time when a thunderstorm enters the developing stage.These diagnoses can provide early warnings for hails, tornadoes, strong surface winds and other severe weather events that occur during the mature stage of a thunderstorm (Schultz et al. 2009;Darden et al. 2010;Farnell and Rigo 2020).When lightning frequency changes reach the jump threshold, the lifetime of the thunderstorm is extended, and the vertically integrated liquid water and maximum estimated size of hail increase markedly (Chronis et al. 2015).
Although lightning jump algorithms were originally used in the tracking and warning of severe weather phenomena, such as hails and tornadoes, these algorithms have also been applied to non-severe convective systems (Ramis et al.1997;Pineda et al. 2011;Koutroulis et al. 2012;Iordanidou et al. 2016;Wu et al. 2017Wu et al. , 2018;;Basarab et al. 2015;Tippett and Koshak 2018;Takahashi 1978).Algorithms that diagnose lightning jump use the length of the lightning frequency sampling period, mean values and the definition of an abnormal surge in their calculations; each of these can be processed through multiple processing approaches and can be applied as effective warning indicators through maximising the probability of detection (POD) and minimising the false alarm rate (FAR) (Gatlin and Goodman 2010).An investigation of 6 thunderstorm days-each day comprising multiple thunderstorms-in northern Alabama and southern Tennessee in the United States in the springs of 2002 and 2003 revealed that lightning jumps preceded severe weather by an average of 22 min; the optimal POD was 0.9, and the lowest FAR was of 0.34 (Gatlin and Goodman 2010).
Generally, intracloud (IC) lightning is most active during the early development stage of a thunderstorm (Lang and Rutledge 2002), whereas cloud-to-ground (CG) lightning occurs only after the main core of the thunderstorm cell has decreased in altitude.Therefore, IC lightning tends to peak earlier in terms of frequency and occurs in greater quantities compared with CG lightning.Consequently, in severe weather (Schultz et al. 2011) or airport CG lightning (Holle et al. 2016) warnings, diagnosing total lightning jump, including both IC and CG lightning, is more advantageous than diagnosing CG lightning jump alone (Tai et al. 2017;Wang and Liao 2006).In ocean storm cases, the locations of high IC density and sudden heavy rainfall demonstrate clear upstream and downstream relationships (Wang and Liao 2006).
The lightning jump data of Total Lightning Detection System (TLDS) from Taiwan Power Company (Taipower) has been used as a forecast indicator for thunderstorms for recent decades (Lin 1999;Hong 2002;Wang and Liao 2006;Chen and Hong 2015;Tai et al. 2008Tai et al. , 2015Tai et al. , 2017;;Yeh et al. 2017).Tai et al. (2015) analysed three cases and indicated that IC lightning develops earlier and in greater quantities than CG lightning during a thunderstorm.They also found using TLDS data, to diagnose the features of rapid increase in IC frequency during afternoon thunderstorms, hailstorms and typhoon rainbands, can assist in predicting sudden and heavy rainfall, hail, and harsh flight conditions; IC jump was observed to precede sudden and heavy rain at a single rainfall station by 40 min.Tai et al. (2017) analysed the IC jump during the afternoon period from May to October 2015 and determined that the mean IC quantity plus twice the standard deviation is the optimal IC jump threshold.Furthermore, the mean value of the postagreement hit rate exceeded 0.61, with the maximum value approaching 0.87, indicating the usefulness of diagnosing IC jumps for the early warning of convective rain in Taiwan.
There is a spatial correlation between lightning of TLDS, radar echo and rainfall (Tai et al. 2015(Tai et al. , 2017)).However, in areas with frequent convective rains in southwestern Taiwan, only 27-52% of convective rain events have IC jumps within the preceding 50 min (Tai et al. 2017).The low percentage of thunderstorms detection in southwestern Taiwan may be a consequence of uncertainties in IC positioning in the TLDS.
Compared to TLDS which has been used in Taiwan for recent decades, the Total Lightning Network of Earth Networks (EN) system was first applied to Taiwan in 2017 and EN lightning data have not been used to study lightning jump before.Recently short-duration heavy precipitation has been paid more attention in Taiwan; thus, the prediction method of short-time heavy rain with lightning jump needs further study.The selection of suitable lightning data and lightning jump algorithm to predict thunderstorms and intense rainfall is an important issue.If the EN system has fewer uncertainties regarding IC positioning, the use of EN data to diagnose and issue early warnings for convective rains may be more beneficial.As such, IC jumps may have considerable application on research and development of early warning system for high aviation risks relating to thunderstorms.
The EN system and TLDS were the two commonly used lightning detection systems in Taiwan, the two major goals of this study were (1) to evaluate the feasibility of using IC jumps in the advance warning of convective rains during the mature stage of a thunderstorm and (2) to compare the data quality of the EN system and TLDS and their performances on heavy rain warning as the lightning jump is used as an indicator.This paper is organised as follows: Sect. 2 introduces the research method and the definitions of convective rain, lightning jump, prefigurance and postagreement.The research results are presented in Sect.3, which details the difference in data quality between the EN system and TLDS, and the strengths and weaknesses of EN and TLDS data in diagnosing IC jumps, and issuing thunderstorm warnings according to the prefigurance and postagreement scores.Section 4 provides some concluding remarks and suggestions regarding the feasibility of using lightning data in thunderstorm warnings.

Data source
In this study, lightning and rainfall data from April to June 2018 were extracted from the following sources for analysis: (i) EN data were acquired from the company of WeatherRisk Explore.(ii) TLDS data were downloaded from the Government Open Data Platform (https:// data.gov.tw/ datas et/ 9712).(iii) Nationwide 10-min accumulated precipitation data were obtained from the National Science and Technology Center for Disaster Reduction.
The electromagnetic band detected using the EN system has a frequency range of 1 Hz-12 MHz (Thompson et al. 2014), whereas the TLDS band ranged from 1 kHz to 1 GHz (Wang and Liao 2006).The major difference between the two systems is how they record IC lightning; TLDS acts as a source of data within a two-dimensional space, whereas the EN system provides a combination of three-dimensional (including height, which was not used in this study) flash data (the company of WeatherRisk Explore did not specify the algorithms used).

Analytical methods
Lightning jumps can precede severe weather by up to 37 min (Gatlin and Goodman 2010).Surges in IC frequency can precede heavy and sudden rainfall by 40 min (Tai et al. 2015).Regarding the time required for diagnosis before lightning jumps reach the threshold, the duration for observing the correlation between the recorded lightning and subsequent rainfall was set in this study to be 1 h, which was determined to be sufficient for encompassing all lightning activity during the developing stage of the thunderstorm and the heavy and sudden rainfall that may occur during the mature stage.At rainfall stations, thunderstorms with rainfall may arrive from any direction.Assuming that a thunderstorm can travel 36 km/h, with the rainfall station as the centre, a 72 × 72 km 2 range was set as the target zone for analysis, which acts as the spatial area for diagnosing the correlations between lightning jumps and convective rains.
Taiwan's Central Mountain Range spans the entire island from north-northeast to south-southwest.In the present study, the Central Mountain Range was divided into northern, north-central, central, and southern sections (Fig. 1a).Taiwan has over 900 rainfall stations, most of which are on the western side of the mountain range (Fig. 1b, grey points).
In other words, this study comprised over 900 analysis zones for the analysis of the correlation between IC jumps and convective rains.The definitions of convective rains, IC jumps, prefigurance and postagreement are provided as follows.
(a) Definition of convective rain When any rainfall station in the analysis zone measures 10-min rainfall equal to or greater than 10 mm, a convective rain event (R) was determined to have occurred in that analysis zone.For example, on June 14, 2015, afternoon thunderstorms were active across the western slopes of the Central Mountain Range, and during the 10-min timespan from 06:40 to 06:50 UTC, in the analysis zone centred on rainfall station C0AG90 (Fig. 1b, red point), 12 stations recorded 10-min precipitation exceeding 10 mm; consequently, a convective rain event was determined to have occurred in this analysis zone at 06:50 UTC on June 14, 2015.During the same timeframe, although multiple rainfall stations in the analysis zone centred on rainfall station C0O810 (Fig. 1b, blue point) measured rainfall, none of these stations accumulated 10 mm of precipitation; as such, this analysis zone was determined to have had no convective rain event at 06:50 UTC on June 14, 2015.

(b) Process of diagonising IC lightning jumps
Looking at the accumulated number of IC lightning flashes in intervals of 5 min within the analysis zones, the timeframe from t0 to t10 contained six moving intervals, t0-t5, t1-t6… t5-t10.The 5-min accumulated IC counts during these six intervals were expressed as SR1 to SR6.When SR1 through SR5 were not zero, the IC jump diagnostic process was initiated, and, at t9, the mean value (SRmean) of SR1 to SR5 and standard deviation (σ) were calculated.If SR6 at t10 is calculated to be greater than (SRmean + ασ), then the IC quantity at t10 was determined to have reached the IC jump 59 Page 4 of 13 threshold (Fig. 2); here, α is a variable.This algorithmic process lasts 10 min, and the diagnostic results are updated once per min, providing real-time lightning data.
For severe weather warnings, such as hails, tornadoes and strong gusts, Schultz et al. (2009) suggested that the calculation of lightning jump should be started after the lightning rate reaches a threshold; moreover, calculations are typically initiated using greater lightning rate and may be combined with the σ-level (or α value) to demonstrate changes in the intensities of the updraft volume and graupel mass in the thunderstorm (Schultz et al. 2015).
Since the main severe weather concern is heavy rainfall in Taiwan, our focus in this study is on short-duration convective rainfall.Therefore, the lightning jumps are diagnosed without the use of a threshold of lightning rate as in Schultz et al. (2015) to obtain larger numbers of lightning jumps.
This study adopted five 5-min moving intervals for calculating the accumulated IC lightning.The condition for initiating calculations was an IC quantity in each moving interval that was not zero, and the calculations included the moving average and an α value of 2. These variables can be adjusted.It means that the diagnosis of lightning jump is in progress all the time.If SR1-SR5 were all not zero, the comparison of SR6 and (SRmean + ασ) was performed at t10, otherwise the time was shifted forward by 1 min to t11 and new SR1-SR5 were calculated.
(c) Definitions of prefigurance and postagreement Because a convective rain event (R) is known to have occurred at t0, the prefigurance of the analysis zone was based on whether an IC jump was detected during the Fig. 2 The IC jump diagnostic process, in which t0 to t10 was the timeframe for diagnosing one IC jump.From t5 to t10, the IC quantities over the previous 5 min (SR 1 -SR 6 ) were calculated each min, and the SR 1 -SR 5 mean (SR mean ) and standard deviation (σ) were calculated at t9.The determination of whether SR 6 was greater than (SR mean + ασ) occurred at t10 timeframe t50 to t0 on the basis of the IC record of the 1 h from t60 to t0 (Fig. 3a).From t60 onwards, the earliest that an identifiable IC jump could occur was at t50, and an IC jump may occur at 51 time points from then until t0.However, these 51 time points are based on the prerequisite condition that a convective rain event (R) occurs at t0; in other words, even if the IC jump threshold was exceeded more than once between t50 and t0, this is regarded as only one prefigurance hit (i.e. one IC jump prior to the convective rain event).If no IC jump occurred between t50 and t0, then a miss was recorded.During the analysis interval, the prefigurance hit was divided by the number of convective rain events to yield the prefigurance score of the analysis zone.
The postagreement of the analysis zone was based on whether a convective rain event occurred within 50 min after an IC jump according to the 1-h time series of IC quantities (Fig. 3b).The IC records were analysed starting from t60, and an IC jump that occurs between t50 and t41 may be the preceding indicator of up to six possible convective rain events (i.e.R1-R6) that may occur at t50, t40, t30, t20, t10 and t0.However, even if more than one convective rain event occurred between t50 and t0, these events were only counted as one postagreement hit (i.e.convective rain that occurs when the IC jump threshold has been met).The absence of a convective rain event after the IC jump threshold was met was recorded as a false alarm.During the specified timeframe, the number of postagreement hits was divided by the number of IC jumps to obtain the postagreement score of the analysis zone, whereas the number of false alarms was divided by the number of IC jumps to obtain the FAR.The higher the postagreement score was, the lower the FAR was.

Density distribution of the EN and TLDS data
The differences in quality between the EN system and TLDS were qualitatively analysed through the spatial distribution of lightning density.The analysis involved the sectioning of the island of Taiwan (approximately 21-26° N, 118-123° E) into 500 × 500 spatial units under the 0.01° E × 0.01° N resolution.The raw positioning records of IC and CG lightning during the period of April to June 2018 were then sorted into corresponding spatial units according to their latitude and longitude, and the cumulative quantities were then calculated.
The density distributions demonstrated the following characteristics: (i) The high-density IC and CG spatial distributions in the EN data were consistent and mostly on the western slopes parallel to the Central Mountain Range (Fig. 4a, b).(ii) IC and CG distribution consistency was not observed in the TLDS data (Fig. 4c, d).In the northern section of the Central Mountain Range, IC lightning was not distributed parallel to the mountains, and west of the southern section is an IC lightning blind strip.Furthermore, radial IC lightning distribution centres were present in both the southwest and southeast (Fig. 4c).(iii) EN data outperformed TLDS data in CG detection efficiency (Fig. 4b, d).(iv) EN data included IC data in China's Fujian Province and the surrounding sea areas (Fig. 4a, upper left).

Prefigurance and postagreement of correlation between lightning and convective rain
The analysis results presented in Sect.3.1.indicate that the EN system's lightning positioning was more accurate than that of the TLDS (Fig. 4a).IC positioning using the TLDS indicated uncertainties within the data, whether in the form of detection blind zones, radial distributions, or the absence of distributions parallel to the Central Mountain Range.This section presents an analysis of each afternoon throughout April to June 2018 (IC data began from 03:00 UTC, and rainfall data from before 12:50 UTC were used; these data represented are hereafter referred to as 'the analysis duration'), which was conducted on the basis of the definitions provided in Sect.2.2. and a comparison of the lightning and rainfall prefigurance and postagreement scores.The purpose of the analysis was to quantify the differences in data quality between the two systems and to evaluate the strengths and weaknesses of applying these two systems to convective rain warnings.

(a) Prefigurance
Less convective rain events per analysis zone (Fig. 5) occurred on the western slopes in the northern section of the Central Mountain Range compared with the other regions, Because the occurrence times of convective rain events in each analysis zone were known, a review of EN time series data up to 1 h prior to each rainfall event was performed to detect whether the IC jump threshold was met and could reveal the number of prefigurance hits in the EN data.The results indicated that the spatial distribution of the prefigurance hits (Fig. 6) was highly similar to that of the convective rain events (Fig. 5); furthermore, the prefigurance score for each analysis zone was generally favourable, with most exceeding 0.75 and some exceeding 0.875 (Fig. 6b).These scores indicated that most of the convective rain events during the analysis duration were closely related to the highly active IC lightning prior to rainfall.
A review of the TLDS time series data up to 1 h prior to each rainfall event was conducted to determine the number of prefigurance hits in the TLDS data.The TLDS prefigurance hits were more numerous along the western slopes of the central section of the Central Mountain Range and the northern section, which are hot zones for convective rains; however, the TLDS IC data included a detection blind zone, radial distributions, and a lack of distributions parallel to the Central Mountain Range (Fig. 4c).Even though some ICs may be missing or wrongly positioned, ICs outside the blind strip will still be counted because the range of analysis zone is larger than that of the blind strip.These data characteristics may have led to discrepancies between the TLDS and EN data in terms of the cumulative IC quantity within the same analysis zone during the same time interval, which would have both affected the number of times the IC jump threshold was reached and altered the spatial distribution of the scores.Consequently, compared with the diagnostic results obtained using EN data (Fig. 6a, b), because of the fewer prefigurance hits, the rainfall hot zones along the western slopes of the southern section of the Central Mountain Range had visibly lower prefigurance scores, which were between 0.25 and 0.5, whereas the western slopes of the central section of the Central Mountain Range-also a rainfall hot zone-contained a narrower region in which the prefigurance score was at least 0.75.One other rainfall hot zone, located in the northern section of the Central Mountain Range, presented a slightly lower prefigurance score (Fig. 7a, b).

(b) Postagreement
Diagnosis using EN data revealed that analysis zones with the greatest number of IC jumps were distributed across two areas, namely the northern section and the western slopes of the central section of the Central Mountain Range (Fig. 8a).These were determined to be hot zones where thunderstorms frequently develop rapidly during the analysis duration.Analysis zones with fewer IC jumps were located in the western slopes of the north-central section of the Central Mountain Range, resulting in a discontinuous spatial distribution of high numbers of IC jumps, similar to that of the convective rain events (Fig. 5).The highest number of postagreement hits were located in the western slopes of the central section of the Central Mountain Range, followed by those located in the western slopes of the southern section and the northern section.Except for the southernmost area of Taiwan which has no airport in service, the fewest postagreement hits were in the western slopes of the northcentral section (Fig. 8b).Except for those on the western slopes of the north-central section of the Central Mountain Range, each analysis zone had postagreement scores higher than 0.625, with the highest score of approximately 0.875 (Fig. 8c).These results indicate that when a thunderstorm intensifies rapidly and the lightning frequency increases and reaches the IC jump threshold, the likelihood of convective rainfall within the same analysis zone becomes relatively high.Thus, through tracking IC time series data within the EN system, correlations can be drawn between lightning activity during the developing stage and convective rain during the mature stage of thunderstorms.
In northern Taiwan, the IC lightning in the TLDS data-both on flatlands in the northern section of the Central Mountain Range-did not exhibit any distributions parallel to the Central Mountain Range and is inconsistent with the distributions of the CG lightning and hot zones for the convective rainfall in the TLDS data.Despite the quantity of IC jumps (Fig. 9a), the IC lightning was not clearly correlated with convective rain.Consequently, the IC postagreement hits and scores (Fig. 9b, c) were lower for the TLDS data than for the EN data (Fig. 8b, c).A band-shaped blind zone was present in the western slopes of the southern section of the Central Mountain Range amongst the IC distributions based on the TLDS data (Fig. 4c), resulting in a drastic 25-75% reduction in the Fig. 7 Spatial distribution of prefigurance a hits and b scores based on TLDS data when the time of the convective rain event is known number of IC jump events and postagreement hits (Fig. 9a,  b) compared with those based on the EN data (figure not provided).For example, in the analysis zone centred on station C0O810 (Fig. 1b, blue point, blue frame), the number of IC jumps diagnosed using the EN and TLDS data were 752 and 508; respectively, the postagreement hits were 601 and 204, respectively.The lower postagreement score for TLDS is due to the fact that the postagreement hits are only 204, which is much lower than 601.The existence of the blind zone shows that there should be two kinds of TLDS IC position uncertainty: missing positioning or wrong positioning.Missing positioning may reduce the number of IC jumps, whilst wrong positioning may induce IC jumps to show up in the analysis zone that is unrelated to convective rainfall events.This indicates that the blind zone in the TLDS detection of IC lightning affected the diagnosis of IC jumps, lowering the postagreement score of the analysis zone; the postagreement scores were 0.8 and 0.4 for the EN and TLDS data, respectively.That is to say, the false alarm rate (FAR) of EN is 0.2, which is much lower than 0.6 of TLDS.However, analysis zones in part of the southern section had favourable postagreement performances (Fig. 9c), indicating that, despite the uncertainties in TLDSs IC positioning and the drastically reduced likelihood of diagnosing IC jumps, when the threshold was met, the likelihood of convective rain occurring in the analysis zone remained relatively high.Furthermore, on the western slopes of the central section of the Central Mountain Range, despite the radial distributions of IC lightning nearby (Fig. 4c), the number of IC jump events and postagreement hits (Fig. 9a, b) were 3-25% lower than those diagnosed using the EN data (figure not provided); the postagreement score (Fig. 9c) was only slightly lower than that based on the EN data.The mean prefigurance scores were 0.80 and 0.67 for the EN system and TLDS, respectively.The EN system outperformed the TLDS in the overwhelming majority of the analysis zones (Fig. 10a).Along the western side of the southern section of the Central Mountain Range, the presence of a hot zone of convective rain during the analysis duration and the location of a blind zone in the TLDS IC lightning detection lowered the TLDS score.Using the EN data raised the prefigurance score from 0.3 to 0.5 and obviously lowered the risk of missed convective rain warnings through the diagnosis of IC jumps.Even on the western side of the north-central section of the Central Mountain Range, use of the EN data raised the prefigurance score from 0.1 to 0.3.This indicated that, compared with the TLDS data, use of the EN IC lightning data demonstrated the suitability of the diagnostic process illustrated in this study.
The mean postagreement scores were 0.65 and 0.47 for the EN system and TLDS, respectively.The EN system outperformed the TLDS in the overwhelming majority of analysis zones (Fig. 10b).In the northern section of the Central Mountain Range, the spatial distribution of IC and CG lightning in the TLDS data is inconsistent with the convection rain hot zones.Using the EN data, the postagreement score for that region rose from 0.1 to 0.5, and, in turn, the FAR for the convective rain warnings based on IC jumps declined.Furthermore, on the western side of the southern section of the Central Mountain Range, the use of the EN IC data not only enhanced the likelihood of diagnosing IC jumps but also increased the postagreement score from 0.3 to nearly 0.5, lowering the FAR caused by the IC blind zone considerably.On the west side of the north-central section of the Central Mountain Range, where convective rains were less common, the use of the EN data reduced the FAR from 0.1 to 0.3.These results indicate that using EN data is more effective than using TLDS data when diagnosing IC jumps to forecast convective rain.

Lead time of IC jump warnings to convective rain
According to the definition of postagreement in this study (Fig. 3b), when two or more rainfall events occurred amongst possible rain events R1 through R6, only one postagreement hit was counted for the IC jump at t50.However, the lead time for these rainfall events may be (0 + n × 10) min, in which n has a value between 0 and 5.In other words, the actual lead time may be as short as 0 min (the convective rain occurred at the same time that the IC jump threshold was met) or as long as 50 min.An IC jump that occurred between t49 and t1 may have a lead time of 1-49 min.If only one rainfall event occurred amongst R1 and R6, the minimum lead time was the same as the maximum lead time.
According to these principles, the diagnosis of IC lightning using the EN data could reveal the mean minimum and mean maximum lead times of all postagreement hits for any analysis zone.For example, in the analysis zone centred on rainfall station C0AG90 (Fig. 1b, red point, red square), an analysis of all postagreement hit events revealed that the mean minimum and mean maximum lead times were 13.3 and 34.9 min, respectively; the analysis zone centred on rainfall station C0O810 (Fig. 1b, blue point, blue square) had mean minimum and mean maximum lead times of 11.6 and 34.7 min, respectively.Amongst all the analysis zones across Taiwan, excluding the open sea, the minimum lead times ranged from 9.1 to 19.4 min, and the maximum lead times ranged from 27.5 to 37.8 min (Fig. 11).

Conclusion
This study first conducted a comparison of the spatial distribution of IC and CG densities according to lightning data spanning April to June 2018 from the EN system and TLDS databases.The results indicated that on the western side of the Central Mountain Range, where multiple major airports are located, the TLDS detection of IC lightning contained a blind zone, and the IC distributions were radial or not parallel to the mountain range.These distribution characteristics evoke uncertainties in the TLDS positioning of IC lightning.
Then based on IC lightning data from afternoons within the same timeframe, over 900 analysis zones (each 72 × 72 km 2 ) were reduced to zones that demonstrated convective rain, which was defined in this study as one or more rainfall station recordings of at least 10 mm of rainfall for 10 min.The IC jump threshold was the moving average of the IC frequency over five 5-min intervals plus twice the standard deviation.The correlation between meeting the IC jump threshold and convective rain that occurred within the next 50 min was then analysed.The results revealed that convective rain warnings based on IC jumps diagnosed using the EN data had a mean prefigurance score of 0.8 and a mean postagreement score of 0.65; the mean scores using the TLDS data were 0.67 and 0.47, respectively.The EN data were more effective than the TLDS data throughout all the analysis zones, that is, convective rain warnings based on the diagnosis of IC jumps using the EN data had lower miss rates and FARs than those based on the TLDS data.Therefore, this study suggests that until the uncertainties in the TLDS positioning of IC lightning have been addressed, diagnosing IC jumps to forecast convective rain that follows thunderstorms is more feasible using EN data.Furthermore, on the basis of definitions and calculations used in this study, IC jumps preceded convective rains by a maximum of 27.5-39.3min on average in all analysis zones across Taiwan.
Adverse aviation conditions that accompany thunderstorms, such as CG lightning, slippery runways, low cloud ceilings, low visibility, wind shear and turbulence, are closely associated with heavy and sudden rainfall (Tai et al. 2015).From the perspective of issuing weather alerts, improving the forecasting of heavy and sudden rains during thunderstorm seasons can assist in maintaining aviation safety.The spatial and temporal scales affected by convective rains are correlated with thunderstorm intensity.Adjusting the number of 10 mm (10 min) −1 rainfall stations assists in determining the correlations of rainfall with thunderstorm development and intensity, enabling the classification of the scope of the spatial impact of convective rain, the alteration of IC frequencies during SR1 through SR5, and the simultaneous diagnosis of σ-level time series data; as such, this correlation warrants further analysis in future studies.Moreover, the results of this study clearly indicate differences in data quality between the two lightning detection systems, suggesting possible flaws in the TLDS.Enhancing data quality may strengthen the security of the Taipower power grid as well as diversify the data applications relating to lightning in Taiwan.

Fig. 1
Fig. 1 Nationwide a altitude and b distribution of rainfall stations (grey points).The isolines in a represent altitudes of 200, 1000 and 3000 m marked by grey, blue and dark grey shades; N, NC, C and S represent the northern, north-central, central and southern sections of the Central Mountain Range.In b, the red and blue points and squares indicate rainfall stations C0AG90 and C0O810, respectively, and their corresponding analysis zones.The x-axis and y-axis are the longitude and latitude, respectively

Fig. 3
Fig. 3 The definitions of a prefigurance and b postagreement.R represents one convective rain event, and J represents an IC jump event.H represents the prefigurance or postagreement hit

Fig. 4
Fig. 4 Frequency distributions from April to June 2018: EN a IC data and b CG data; TLDS c IC data and d CG data

Fig. 5 Fig. 6
Fig. 5 Spatial distribution of afternoon convective rain events in each analysis zone (April-June 2018)

Fig. 8 Fig. 9
Fig. 8 Spatial distribution of a number of IC jumps, b postagreement hits and c postagreement scores based on EN data and rainfall data (c) Difference between the EN system and TLDS The different performances of both detection systems in forecasting convective rainfall based on IC lightning are indicated by the mathematical differences in their prefigurance and postagreement scores (EN-TLDS).

Fig. 10
Fig. 10 Spatial distribution of differences between EN and TLDS scores: a prefigurance scores and b postagreement scores

Fig. 11
Fig. 11 Spatial distribution of a mean minimum and b mean maximum lead times (min)