Relationship between radar reflectivity thresholds and very low frequency/low frequency total lightning for thunderstorm identification

Abstract

To improve our knowledge of the spatio‐temporal correspondence between radar reflectivity and VLF/LF total lightning data, this paper proposes indexes to quantify the horizontal distribution and temporal evolution characteristics between radar composite reflectivity images and total lightning density map, lightning clusters and radar cells with different radar reflectivity thresholds (30, 35, 40, 45 and 50 dBZ), respectively. It is found that the number of radar grid cells with radar reflectivity over 30 dBZ is ten times the number of lightning grid cells. At the identification stage, the lightning activity regions in a radar cell account for less than 30% using thresholds of 30, 35 and 40 dBZ, respectively, and the radar cell has more than one lightning cluster, which means that the mesoscale convective systems typically have more than one draft, and drafts are only small part of the convection. The majority of the centroid deviations is less than 10 km, indicating that there are some shifts between electrically active regions and convective regions. Results suggest that VLF/LF total lightning data are consistent with radar data and total lightning data can be used individually on a smaller spatio‐temporal scale than radar data.

INTRODUCTION

Thunderstorms are deep moist convections across the world and are characterised by related features of lightning activity and convective precipitation [1]. The locations of mesoscale convective systems (MCSs) present similarity with the distribution of lightning [2, 3], and the spatio-temporal correspondence between the radar reflectivity and total lightning activity of thunderstorms play a fundamental role in lightning warning studies and assessments of the risks from lightning.

The relationship between lightning activity and convective activity is usually focused. Radar is widely used in weather forecasting, but total lightning monitoring is lacking. The weather radars map the precipitation using reflectivity factor Z (the product of the number of drops per m³ and the average sixth power of their diameter expressed in mm) [4–6], while lightning location systems based on electromagnetic field location technology provide real-time impulses of intra-cloud (IC) pulses and cloud-to-ground (CG) strokes [7], which refers to total lightning [8]. Proctor [9] reported that 66% of lightning flashes began within the 20-dBZ contours while 27% occurred near the high-reflectivity cores. Lund [10] took altitude into account and most lightning happened in the 3–6 km or 7–10 km altitude range, near the 35-dBZ contour in the convective line. The lightning flashes propagated in space with lower reflectivity, whose distribution was slightly different from flash initiations [11]. Then, lightning flashes were divided into stratiform lightning flashes and convective lightning flashes. Wang concluded that the stratiform lightning flash began near the bright band area and had a linear relationship with the maximum reflectivity within the lightning extension areas [12]. The predictor was the 35-dBZ at the height of the −10°C isotherm to forecast the onset of CG flashes [13, 14].

Radar reflectivity based on physical values is the approach to identifying storms [15], and many centroid-based tracking algorithms have been proposed to analyse the spatiotemporal characteristics of thunderstorms [16–21]. Then, some tracking methods based on radar data are introduced to characterise the movement of lightning activity [22, 23]. The Warning Decision Support System–Integrated Information software is combined with the ZEUS (named after the Greek god of lightning) network to nowcast the severe thunderstorms, where the probability of detection was between 0.46 for 30 min and 0.25 for 120 min [24]. Cheng et al. [25] of our team used an eight-connectivity method to identify electrically active areas and analysed the duration, area, velocity and direction of eight thunderstorms in the Pearl River Delta region.

After the two trajectory algorithms were described individually, the spatio-temporal correspondence between radar data and lightning data was reported [26, 27]. The trajectories of radar and lightning are consistent and the positive lightning can be used as a warning of tornadoes [28]. Meyer et al. [20] introduced the tracking and monitoring of electrically charged cells (ec-TRAM) from the Cb-TRAM algorithm (Cumulonimbus Tracking And Monitoring) [29], and analysed the spatial distribution of lightning clusters and radar cells. It was found that 73% of ec-TRAM cells consist of exactly one radar and one lightning cell. It is well recognised that the lightning was closely related to updraft [30–32] and most the of IC and CG flashes were in the maturity stage. The CG flash rate was proportional to the rain rates [33, 34] and correlated with the precipitation ice mass flux from 7 to 11 km above 0.7 in the three stages [34]. Liu et al. [35] came to a conclusion that composite reflectivity above 45-dBZ corresponds to the lightning data cell and Strauss et al. [36] found that electrically active cells deviate from convective precipitation by several pixels.

The main objective of this paper is to compare the horizontal and temporal correspondence between radar reflectivity and very low frequency/low frequency (VLF/LF) total lightning data in thunderstorms rather than individual flash. Then, the correspondence of total lightning clusters based on the combinatorial eight-connectivity method and radar cells with different thresholds are systematically analysed to find the reflectivity threshold for total lightning activity. Indexes are proposed to quantify the horizontal distribution and temporal evolution between radar composite reflectivity images and total lightning density maps, as well as lightning clusters and radar cells with different thresholds in this paper. Two selected thunderstorms are used to present the statistical results.

The organisation of the paper is as follows: Section 2 gives an introduction of study area, data, the identification methods of lightning clusters and radar cells and indexes of images and identification results. Two cases are presented in Section 3, and Section 4 discusses the differences between the two datasets. Section 5 presents conclusions.

METHOD AND DATA

Radar data

The meteorological radar Z9200 (23.00°N, 113.355°E) is located in Guangzhou, in the south of China (Figure 1), at 180 m above sea level. The S-band Doppler radar is operated by the Chinese Meteorological Administration. It has a range of 230 km and covers the Pearl River Delta region [35]. The radar performs a dedicated reflectivity scan at nine elevations (0.5°, 1.5°, 2.4°, 3.4°, 4.3°, 6.0°, 9.9°, 14.6° and 19.5°) every 6 min and the spatial resolution is 1 km [37]. The original radar reflectivity data in spherical coordinates are transformed into Cartesian coordinates with a horizontal resolution of 0.01° longitude × 0.01° latitude (approximately 1.1 km × 1.1 km) [37] and the radar composite reflectivity is used in this paper.

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Total lightning data

The total lightning data are provided by the Foshan Total Lightning Location System (FTLLS) [8], which has nine stations in Figure 1. FTLLS adopts the time of arrival (TOA) method based on the LF/VLF band to locate positions of IC pulses and CG strokes [38, 39], which are referred to lightning events in the following part. The study region covers the Pearl River Delta, from latitude 21° to 25°N and longitude 111° to 115°E. The temporal and spatial resolutions of lightning density maps are consistent with radar images, using time interval of 6 min and 0.01° grid cell.

Identification methodology

Identification of radar cell

The radar composite reflectivity image is a picture of grid cells with reflectivity values, and the identification method of the radar cell is shown in Figure 2a. The contiguous region above the pre-set threshold is identified as a storm [17] and it is defined as a radar cell [20] in the following parts. According to whether it includes adjacent grid cells on the diagonal in the continuous region, it can be divided into the four-connectivity method and the eight-connectivity method. The four-connectivity method is that grid cells adjacent to each other by sides are clustered into a radar cell [17], while the eight connectivity method is grid cells adjacent to each other with sides and corners. The values of grid cells above 30-dBZ are extracted from the radar reflectivity image in Figure 2a1. We use the eight-connectivity method to identify radar cells in Figure 2a2. When the value of the grid cell exceeding the threshold is defined as the central grid cell, its eight adjacent grid cells are searched. If the values of adjacent grid cells exceed the threshold, they are considered as new central grid cells until no more grid cells exceeding the threshold are found. The reflectivity thresholds of radar cells are set to 30 [16], 35 [17], 40 [19], 45 and 50-dBZ to form 30-dBZ radar cell, 35-dBZ radar cell, 40-dBZ radar cell, 45-dBZ radar cell and 50-dBZ radar cell in Figure 2a3, respectively. The minimum area of the 30-dBZ radar cell is eight grid cells. The radar cell centroid is calculated by averaging the grid cell coordinates weighted by the reflectivity value, and the radar cell is outlined by a convex polygon. The radar cell centroid (x_rc, y_rc) is calculated by Equations (1) and (2): 1 $${x}_{\text{rc}}=\frac{\sum\limits _{i=1}^{N}{x}_{i}{Z}_{i}}{\sum\limits _{i=1}^{N}{Z}_{i}}$$ 2 $${y}_{\text{rc}}=\frac{\sum\limits _{i=1}^{N}{y}_{i}{Z}_{i}}{\sum\limits _{i=1}^{N}{Z}_{i}}$$ where (x_i, y_i) is the coordinate of the radar cell i, Z_i is the value of reflectivity in the grid cell and N is the number of grid cells in a single radar cell.

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Identification of total lightning cluster

For total lightning data, the temporal and spatial parameters of total lightning density maps are consistent with those of the radar images. Due to the random distribution of total lightning data, we use the combinatorial eight-connectivity method to form lightning clusters [40].

Lightning events are scattered into geographical grid cells in a single time interval to form the total lightning density map and its grid cell map in Figure 2b1. The eight-connectivity method is applied to identify the primary lightning clusters in Figure 2b2 and the minimum area of clusters is three grid cells. The formation of the final lightning cluster depends on the gap between the primary clusters determined by the application scale. Since the span of the transmission line in power systems is usually less than 500 m, the distance of five spans is about 2.5 km and the area of a circle with a radius of 2.5 km is 19.63 km². The median area with two grid cells between primary lightning clusters is 16.94 km². The area values of the two are equivalent. Then, when the number of grid cells between lightning clusters increases, it has a great impact on the number of lightning clusters, the proportion of area and the utilisation rate of lightning events [38]. The spatial parameter of the distance between lightning clusters is set to the two grid cells in this paper. It means that a grid cell in a cluster is in the two-grid-cell range of a grid cell in another cluster and they form the final lightning cluster in Figure 2b3. Convex polygons also fit the final lightning clusters. The centroid and area of the convex polygon are the centroid and area of the lightning cluster, respectively.

Indexes of images and identification results

To compare the spatio-temporal correspondence between radar data and the VLF/LF total lightning data, the following indexes are used to quantify the correlation of images and the identification results, respectively. The indexes for radar reflectivity and total lightning data are presented in the following parts.

Indexes of radar composite reflectivity images and radar cells

In the radar composite reflectivity image and the total lightning density map at the same moment, the number of grid cells for lightning data and radar data are counted, respectively, and the index is the percentage of grid cells in an image at the time interval of 6 min. The percentage of radar grid cells in a radar composite reflectivity is the percentage of the number of radar grid cells with lightning data in the region where the radar grid cell value exceeds a pre-set threshold. All radar grid cells with values greater than 30-dBZ in the radar composite reflectivity image are called the 30-dBZ regions. In the same way, the 35, 40, 45 and 50-dBZ regions are defined. Regions with different thresholds are outlined and overlapping regions with lightning events and radar data are coloured in Figure 3a. The percentage of lightning grid cells in a radar composite reflectivity image is calculated by Equation (3): 3 $${P}_{\text{rg}}=\frac{{N}_{\text{rl}}}{{N}_{\text{rt}}}\times 100\%$$ where N_rl is the number of radar grid cells with lightning data in the region where the values of radar grid cells exceed a pre-set threshold and N_rt is the number of radar grid cells in the image at the time interval of 6 min whose values exceed pre-set thresholds (30, 35, 40, 45 and 50-dBZ).

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In the identification stage, lightning clusters and radar cells are outlined in Figure 3c and the spatio-temporal relationship between lightning clusters and radar cells is concerned. The number of lightning clusters in a radar cell is counted. Two lightning clusters are located within a 30-dBZ radar cell while there is only one lightning cluster in the 35-dBZ radar cell, 40-dBZ radar cell, 45-dBZ radar cell and 50-dBZ radar cell in Figure 3d, respectively. Then, the coverage rate of each radar cell is the percentage of lightning grid cells in a radar cell. The brown grid cells are the overlapping area of lightning clusters and radar cells, and there are nine, seven, five, two and one grid cells with lightning events in the 35, 40, 45 and 50-dBZ radar cell, respectively. The radar cell area is the area of grid cells that exceed the threshold and the radar cell is outlined by the fitted convex polygon. The radar cell area and coverage rate P_rc are calculated by Equations (4) and (5): 4 $${S}_{\text{rad}}={N}_{\text{rad}}\times {S}_{\mathrm{g}}$$ 5 $${P}_{\text{rc}}=\frac{{S}_{\mathrm{o}}}{{S}_{\text{rad}}}\times 100\%$$ where N_rad is the number of radar grid cells in a single radar cell; S_g is the area of a grid cell; S_o is the overlapping area of the lightning cluster and the radar cell; S_rad is the area of the radar cell of different thresholds (30, 35, 40, 45 and 50-dBZ).

Indexes of total lightning density maps and total lightning clusters

For total lightning data, the same indexes are used to quantify the spatio-temporal characteristics of lightning density maps and lightning clusters, and the number of lightning grid cells is calculated. The percentage of grid cells in a lightning density map is the percentage of the number of radar grid cells exceeding 0-dBZ in the lightning grid cells. Lightning regions are marked as the number of lightning events in grid cells and overlapping regions are coloured in Figure 3b. The percentage of radar grid cells in a lightning density map is calculated by Equation (6): 6 $${P}_{\mathrm{lg}}=\frac{{N}_{\text{lr}}}{{N}_{\text{lt}}}\times 100\%$$ where N_lr is the number of lightning grid cells whose values exceed 0-dBZ; N_lt is the number of grid cells with lightning events in the time interval of 6-min lightning density map. t represents the time interval. The number of radar cells with intersecting areas in a lightning cluster is counted, and the coverage rate of each lightning cluster is the percentage of grid cells whose values exceed 0-dBZ in a lightning cluster. LC₁ has an overlapping area with the 30, 35, 40, 45 and 50-dBZ radar cells, and it has one radar cell in five subplots of Figure 3d. There are two grid cells in the overlapping area of LC₂ and the 30-dBZ radar cell, but LC₂ has no radar cells in the rest of the subplots of Figure 3d. Similarly, the lightning cluster is also fitted by the convex polygon and the area of the lightning cluster is the area of the fitted convex polygon. The lightning cluster area and coverage rate are calculated by Equations (7) and (8): 7 $${S}_{\text{li}}={N}_{\text{li}}\times {S}_{\mathrm{g}}$$ 8 $${P}_{\text{lc}}=\frac{{S}_{\mathrm{o}}}{{S}_{\text{li}}}\times 100\%$$ where N_li is the number of grid cells in a lightning cluster; S_li is the area of the lightning cluster.

The spatial distance between lightning cluster centroid and radar cell centroid is named the centroid deviation. If there is an overlapping area between the lightning cluster and the radar cell, the centroid deviation is the distance between the two centroids in Figure 3d. The centroid deviation D_C between the lightning cluster and the radar cell with different thresholds is calculated by Equation (9): 9 $${D}_{\mathrm{C}}=\sqrt{{\left({x}_{\text{Cr}}-{x}_{\text{Cl}}\right)}^{2}+{\left({y}_{\text{Cr}}-{y}_{\text{Cl}}\right)}^{2}}$$ where (x_Cr, y_Cr) and (x_Cl, y_Cl) are the centroid positions of radar cell and lightning cluster, respectively. The evaluation indexes are shown in Table 1.

TABLE 1 Definition of evaluation indexes.

Parameter	Definition
Prg	The percentage of lightning grid cells in a radar composite reflectivity image
Prc	The radar cell coverage rate
Nrl	The number of lightning clusters in a radar cell
Plg	The percentage of radar grid cells in a lightning density map
Plc	The lightning cluster coverage rate
Nlr	The number of radar cells in a lightning cluster
DC	The centroid deviation between lightning cluster and radar cell

RESULTS

The proposed approach of identification method was used to outline lightning clusters and radar cells with different thresholds, and indexes were applied to test the spatio-temporal relationship between lightning clusters and radar cells in the two selected thunderstorms. Two cases of thunderstorms are selected in the Pearl River Delta and the details of the two cases are shown in Table 2.

TABLE 2 List of thunderstorms based on radar data and lightning data used in this analysis.

Case	Start time (UTC)	End time (UTC)	Lightning events (IC and CG)
T20140516	16 May 2014 00:30	17 May 2014 14:00	583,975
T20140708	8 July 2014 02:42	8 July 2014 13:24	126,547

Case study of T20140516

Spatio-temporal correspondence of images

The first case occurred from 00:30 UTC (Coordinated Universal Time) on 16 May 2014 to 14:00 UTC on 17 May 2014, which was a passing thunderstorm and lasted 37.5 h. The distribution of radar grid cells changes flat in Figure 4a, which shows an upward trend before 09:24 UTC on 17 May 2014 and a downward trend thereafter. The peak values are 77,589 at 08:30 UTC on 16 May 2014 and 111,649 at 09:24 UTC on 17 May 2014, respectively. The distribution of lightning grid cells is divided into four parts with maximum values of 3005, 2850, 2506 and 4929 at 08:36 UTC, 17:48 UTC, 22:24 UTC 16 May 2014 and 10:54 UTC 17 May 2014 in Figure 4b, respectively. The number of radar grid cells is about two orders of magnitude larger than the number of lightning grid cells. The percentage of radar grid cells with reflectivity values above 30-dBZ ranges from 60.3% to 97.3% while more than 42.5% of grid cells have one Lightning event.

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The results of overlapping grid cells in lightning density maps and radar composite reflectivity images are presented in Figure 5 and the grid cell distribution in the overlapping area is shown in Figure 5b. For grid cells of lightning data, the number of grid cells containing a Lightning event is 219,810, accounting for about 79.0% and 94.2% of the lightning grid cells have reflectivity in Figure 5a. The distribution of the radar grid cell's reflectivity averaged over five intervals is described in Figure 5c. The number of radar grid cells increases sharply and peaks around the interval of 20 to 25-dBZ, followed by a steady decline to higher values. About 33.8% of the values exceed 30-dBZ in the thunderstorm. However, only 9.8% of radar grid cells have lightning events, of which 83.4% have values above 30-dBZ. It is found that if the number of lightning events in the grid cell is higher, the reflectivity value is greater in Figure 5b.

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Spatio-temporal correspondence between lightning clusters and radar cells

At the step of identification, lightning clusters and radar cells with different thresholds (30, 35, 40, 45 and 50-dBZ) are identified every 6 min, respectively, and an example is depicted in Figure 6. The spatio-temporal relationship between lightning clusters and radar cells are shown in Figure 7 and the first column is the result of radar cells.

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The distribution between the coverage rate of radar cells with different thresholds and the number of lightning clusters in the overlapping area is presented in Figure 7a. It is found that the majority of radar cells do not contain any lightning cluster in Figure 7b–f. About 7.5% of 30-dBZ radar cells have lightning clusters while 3.6% include two or more lightning clusters. The number of radar cells containing lightning clusters increases from 7.5% to 20.8% with increasing the threshold while the number of them consisting of two or more clusters presents an opposite trend, decreasing from 3.6% to 1.2%. When the coverage rate of radar cells is greater than zero, the coverage rate of radar cells is depicted in Figure 8a. The peaks of coverage rate are around the interval of 0%–10% except for 50-dBZ radar cells, followed by a sharp decline to higher values. Although the number of radar cells with low coverage rate increases with the threshold increase, their percentage decreases, accounting for 72.2%, 62.1%, 48.8% and 33.1%, respectively. As for the 50-dBZ radar cell, the coverage rate is mainly evenly distributed below 40% and the number is about 350.

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Results of lightning clusters are presented in the second column of Figure 7 and the distribution between the coverage rate of lightning clusters and the number of radar cells with different thresholds in the overlapping area is depicted in Figure 7g. It is found that 85.6%, 75.9% and 64.6% of the lightning clusters overlap 30-dBZ radar cells, 35-dBZ radar cells and 40-dBZ radar cells in Figure 7h–j, respectively. The vast majority of lightning clusters have overlapping areas with one radar cell, accounting for 84.9%, 73.7% and 59.7%, respectively, while less than 3% of lightning clusters consist of two or more radar cells.

More than 48% of lightning clusters do not overlap 45-dBZ radar cells and 50-dBZ radar cells in Figure 7k–l. The number of lightning clusters shows an upward trend when the coverage rate between lightning clusters and radar cells of the 30, 35 and 40-dBZ increases from 0% to 100% in Figure 8b, respectively. The majority of lightning clusters are completely covered, accounting for 62.4%, 44.3% and 25.6%, respectively, because the area of radar cells is large enough to cover lightning clusters. The number of lightning clusters stabilised at approximately 330 using the threshold of 45-dBZ while the number of clusters shows a downward trend with coverage rate using 50-dBZ, and 65.6% have a coverage rate lower than 30%.

Figure 9 presents the percentage of centroid deviations between lightning clusters and radar cells, and the peak of centroid deviation is around the interval of 0–10 km, followed by a sharp decline to higher values. The centroid deviation of the five thresholds from 0 to 10 km accounts for 24.2%, 37.6%, 57.6%, 73.0% and 86.8%, respectively. It is found that as the radar threshold increases, the percentage of centroid deviations of short distance increases sharply. About 25.9% of the centroid deviation is greater than 50 km between 30-dBZ radar cells and lightning clusters, while less than 10% of centroid deviation is greater than 50 km using thresholds of 35, 40, 45 and 50-dBZ, respectively. The area of lightning clusters and radar cells with different thresholds are illustrated in Figure 10. The median area of lightning clusters is 13.3 km² while the median areas of radar cells of the five radar thresholds are 36.3, 35.1, 18.2, 13.3 and 6.1 km², respectively. The median area of lightning clusters is approximately the same as that of 45-dBZ radar cells.

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Case study of T20140708

This case belonged to a locally generated thunderstorm and occurred at 02:42 UTC on 8 July 2014, lasting 10.8 h. The number of radar gird cells goes up and then remains stable, with a maximum of 111,1641 at 12:42 UTC in Figure 11a while the number of lightning grid cells has two peaks appearing at 05:54 UTC and 10:06 UTC in Figure 11b, respectively. The percentage of radar cells containing lightning clusters increases with the thresholds from 10.6% to 21.7%, but the number of radar cells with two or more lightning clusters shows a downward trend in Table 3. However, the majority of lightning clusters have one radar cell in the overlapping area and the percentage of lightning clusters with radar cells decreases with the increase of the radar threshold from 85.7% to 39.8%. The percentage of lightning clusters with two or more radar cells in the overlapping area grows from 1.0% to 6.8% in Table 4.

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TABLE 3 Statistical results of the number of lightning clusters contained in a radar cell on 8 July 2014.

Threshold (dBZ)	Number of radar cells	Radar cells with one lightning clusters	Percentage (%)	Radar cells with more than one lightning clusters	Percentage (%)	Median area (km2)
30	7267	489	6.7	286	3.9	39.9
35	6947	593	8.5	293	4.2	36.3
40	7749	721	9.3	263	3.4	19.4
45	6078	861	14.2	197	3.2	14.5
50	5085	99	19.6	106	2.1	8.5

TABLE 4 Statistical results of the number of radar cells overlapped in a lightning cluster on 8 July 2014.

Threshold (dBZ)	Number of lightning clusters	Lightning clusters with one radar cells	Percentage (%)	Lightning clusters with more than one radar cells	Percentage (%)	Median area (km2)
30	2073	1756	84.7	21	1.0	15.7
35	1613	77.8	29	1.4
40	1391	67.1	84	4.1
45	1094	52.8	140	6.8
50	718	34.7	106	5.1

The coverage of radar cells is presented in Figure 12a. More than 55% of radar cells have less than 30% coverage while the coverage of lightning clusters is concentrated in the interval greater than 80% using thresholds of 30, 35, 40 and 45-dBZ in Figure 12b, respectively. The coverage rate between 50-dBZ radar cells and lightning clusters peaks around the interval of 20%–30%. The peaks of centroid deviations are within 10 km, accounting for 40.0%, 53.7%, 65.0%, 75.4% and 86.8% in Figure 12c, respectively, and the median area difference between the 45-dBZ radar cell and the cluster is only 1.2 km².

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DISCUSSION

The weather radar maps the convective activity using reflectivity factor Z, which is the product of the number of drops per m³ and the average sixth power of their diameter expressed in mm. As its beam sweeps through the thunderstorm, the weather radar reflects water, ice condensate, and ionised lightning channels, which cannot directly distinguish between lightning activity and convective activity. The FTLLS adopts the TOA method based on the LF/VLF band to locate real-time positions of IC pulses and CG strokes. Due to the lack of quantitative analysis on the relationship between lightning activity and convective activity [36], this paper aims to quantify the horizontal distribution and temporal evolution characteristics between radar composite reflectivity images and total lightning density map, lightning clusters and radar cells with different radar reflectivity thresholds, respectively.

According to the statistical results of the two cases above, the number of radar grid cells with reflectivity above 0-dBZ is about 100 times the number of lightning grid cells, while the number of radar grid cells exceeding 30-dBZ is an order of magnitude larger than that of lightning grid cells. More than 90% of the lightning grid cells have values of radar reflectivity while less than 10% of the radar grid cells have lightning events. Most lightning events occur in the region with high radar reflectivity, which is in accordance with Zhou's conclusion [26]. The duration of lightning activity is shorter than that of a thunderstorm in Figures 4 and 10. Zheng et al. reported that CGs are mainly located in the updraft region [34], and Stolzenburg et al. found that a typical electrical structure exists around updrafts in MCS [31]. Thunderstorms with updrafts may produce many small ice particles (ice crystals, snow, etc.) and numerous charged ice crystals in the updraft are lifted and these charges generate lightning at high levels [11, 12]. Most lightning activity is recorded when thunderstorms are mature [33], which is why lightning activity is shorter than that of thunderstorms. According to the model of the MCS, updrafts are only a small part of the convective region and the conclusion is consistent with statistical results [41].

For identification results, about 10% of 30-dBZ radar cells have lightning clusters, and more than half contain a lightning cluster, which is slightly lower than Meyer's conclusion [20]. On average, each radar cell has 2.1 lightning clusters, which is consistent with about 2.4 lightning clusters per radar cell at the time interval of 5 min [20]. That means that MCS usually has more than one updraft [32]. The median area of 30-dBZ radar cells is less than 40 km², which is 10 km² smaller than that of Germany's 33-dBZ radar cells. The median area of lightning clusters in Meyer's paper is about 3 times that of this paper, because Meyer discarded track duration below 35 min [20].

The median area of the lightning clusters is closest to the median area of the 45-dBZ radar cell and the coverage rate distribution of lightning clusters is relatively even. The coverage rate between lightning clusters and 50-dBZ radar cells is concentrated at lower values. Srivastava et al. [35] reported that composite reflectivity larger than 45-dBZ corresponds to a lightning cell, which is similar to the results in Figure 6. According to the model of the MCSs, the reflectivity core is a new cell development with peak reflectivity above 50-dBZ and convective updraft is typically ahead of the intense and developing core in the convective region of MCS [31, 32]. Strauss verified some spatial shifts between electrically active regions and convective activity [36]. The index of centroid deviation can quantitatively evaluate the distance. The centroid deviations of the 45-dBZ radar cells and the 50-dBZ radar cells are mostly less than 10 km and decrease with increasing thresholds in Figures 9 and 12c.

CONCLUSIONS

This paper introduces indexes to quantify the horizontal and temporal correspondence between radar composite reflectivity images and total lightning density maps, respectively. Two different types of cases are used as examples to present statistical results. As far as the image level is concerned, there are differences in the applicable scales of the two datasets. It is found that the number of radar grid cells with reflectivity above 0-dBZ is about 100 times the number of lightning grid cells, while the number of radar grid cells exceeding 30-dBZ is an order of magnitude larger than that of lightning grid cells. More than 90% of the lightning grid cells have radar values, while less than 10% of the radar grid cells have lightning events. On the other hand, the duration of lightning activity is shorter than that of thunderstorm.

The paper also systematically analyses the spatio-temporal relationship of identification results of the two datasets and proposes indexes to quantify the horizontal distribution and temporal evolution characteristics between lightning clusters and radar cells with different thresholds (30, 35, 40, 45 and 50-dBZ), respectively. It is found that the median area of the lightning clusters is closest to the median area of the 45-dBZ radar cell. The centroid deviations of 45-dBZ radar cells and 50-dBZ radar cells are mostly less than 10 km.

The horizontal and temporal correspondence between radar reflectivity and total lightning data helps us learn the complex interrelations between lightning and convective activity. Based on the results above, total lightning data provide a more accurate temporal and spatial scale of thunderstorms than radar data. Total lightning data can be individually regarded as a reliable tool for identifying, tracking and nowcasting thunderstorms in the field of lightning activity, such as lightning warning systems.

ACKNOWLEDGEMENTS

The work was supported by the Fundamental Research Funds for the Central Universities (Grant No. 2042023kf0183), the National Natural Science Foundation of China (Grant Nos. 52177154 and 51807144).

CONFLICT OF INTEREST STATEMENT

The authors declare no conflicts of interest.

DATA AVAILABILITY STATEMENT

The data that support the findings of this study are available on request from the corresponding author. The data are not publicly available due to privacy or ethical restrictions.

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