1. Introduction
Lightning is considered as one of the most spectacular weather phenomena and all‐pervasive atmospheric hazards across the globe (Shearman and Ojala 1999; Cooray et al. 2007; Singh and Singh 2015). Over the Indian subcontinent, the lightning flashes associated with severe thunderstorms mostly occurred during the pre-monsoon and post-monsoon season due to favorable atmospheric conditions, such as strong solar heating of land surface and convergence of dry and wet air masses, among other several reasons (Manohar and Kesarkar 2004; Kandalgaonkar et al. 2005). There is a threat to human life and other livestock during thunderstorm seasons due to wind/gust, lightning strikes, hail and flash floods. A study based on past 32 years of data suggests that the overall fatality rate is about 0.25 per million population per year in India only due to lightning strikes (Singh and Singh 2015). Recently, Mahapatra et al. (2018) reported that 40% of the extreme weather event related accidental deaths (e.g., cold wave, extreme precipitation, heat wave, lightning, and tropical cyclone) in India during 2001–14, are caused by lightning alone. They also demonstrated that deaths due to extreme precipitation and tropical cyclones declined over time, whereas deaths caused by lightning strikes have been increasing. Therefore, there is a need for systematic thunderstorms and lightning flash predictions and preparedness over the Indian subcontinent.
Most of the lightning studies available over Indian region (e.g., Kandalgaonkar et al. 2005; Ranalkar and Chaudhari 2009; Pawar et al. 2012) are based on satellite datasets like Optical Transient Detector (OTD) and Lightning Imaging Sensor (LIS) from the Tropical Rainfall Measuring Mission (TRMM). These studies have mostly investigated spatiotemporal variability of lightning over the Indian region with nonlinear positive relationships between lightning flash density and latitude, observed in the pre-monsoon and monsoon seasons whereas a bimodal variation is observed in the post-monsoon season (Kandalgaonkar et al. 2005). Manohar and Kesarkar (2004) have done a comprehensive study on the climatology of thunderstorm activity over the Indian region and its relation with rainy days. They have reported dominant thunderstorms in pre-monsoon season with occasional rainfall and vice versa in monsoon season. Ranalkar and Chaudhari (2009) investigated seasonal variation of lightning events in the context of synoptic systems. Other studies have investigated the thermodynamical aspects during the lightning activity (e.g., Ramesh Kumar and Kamra 2012; Murugavel et al. 2014). Pawar et al. (2012) studied the effect of CAPE on lightning activity and noticed a systematic increase in lightning over central India with increase in CAPE. Tyagi (2007) studied thunderstorm climatology over India based on 450 observatories and reported the annual frequency of thunderstorms as 100–120 days.
Apart from the climatology studies of lightning over India (Kandalgaonkar et al. 2005; Pawar et al. 2012; Murugavel et al. 2014), forecasting of lightning research has come a long way with better understanding of charge separation mechanism and thunder cloud electrical structure (Kamra 1970; Mason 1988; Brooks and Saunders 1994; Berdeklis and List 2001; Pawar and Kamra 2004, 2009; Saunders 2008). The advances in understanding the cloud processes and storm electrification (Price and Rind 1992, hereafter PR92; Price and Rind 1993, 1994; Barthe and Pinty 2007; Barthe et al. 2010; Barth et al. 2012), and the availability of observations, made it possible to develop a mechanism for lightning forecast using dynamical model. Until recent past, over India, empirical relations were established with the predictors such as CAPE and other thermodynamic stability parameters which can be used as predictors for thunderstorms (Mukhopadhyay et al. 2003; Chaudhari et al. 2010; Tyagi et al. 2011).
Previous modeling research have studied numerical models and their sensitivity to different microphysical schemes and are tested for thunderstorms over India by several researchers (e.g., Rajeevan et al. 2010; Litta et al. 2012; Halder and Mukhopadhyay 2016). Madhulatha et al. (2013) also suggested that continuous measurement of temperature and humidity might be helpful to produce skillful prediction of lightning/thunderstorm. Statistical relations were established using past observed data based on binary logistic regression technique (Rajeevan et al. 2012). Ghosh et al. (1999) and Dasgupta and De (2007) also developed binary logistic regression models and examined the significant meteorological parameters for predicting short-term prediction of pre-monsoon convective events (e.g., thunderstorms) over Kolkata (India) using statistical methods. Yair et al. (2010) developed a lightning potential index (LPI), which is calculated in the charge separation region of clouds between 0° and −20°C, which is favorable for noninductive collisional charge separation due to intense updraft (Latham et al. 2004).
In recent times, the lightning prediction from numerical models has gathered a lot of interest because of its promising results. Lightning parameterizations have been developed and introduced in regional and global models based on studies from Price and Rind (1992, 1993, 1994). The parameterization is based on relating the convective cloud top height and the prevailing updrafts and the ratio between cloud to ground and cloud to cloud lightning flashes from observations. Many studies established the fact that the lightning flash rate is directly proportional to the vertical updrafts (Rutledge et al. 1992; Deierling and Petersen 2008). Relationship between lightning and hydrometeors is established through the lower mixed phase region of convective clouds, which ultimately produces heavy rainfall at the surface (Goodman et al. 1988; Williams 1989; Carey and Rutledge 1996; Petersen et al. 1996). A couple of studies have shown that microphysical properties including graupel have a significant effect on the lightning activity in convective clouds (Lund et al. 2009; Guo et al. 2016; Chang et al. 2020). Positive correlations between rainfall and lightning initiation are noted (Lal and Pawar 2009). The predictive capabilities of lightning by regional models have been addressed by many studies (e.g., Müller et al. 2016; Politi et al. 2018; Igri et al. 2018). Wong et al. (2013) tested the flash rate parameterization and scaling dependency and concluded that for PR92 proper cloud top adjustment should be made to match expected 20-dBZ reflectivity. Giannaros et al. (2015) evaluated the performance of lightning forecasting system in Europe by implementing a modified version of PR92. The evaluation of the modeling system was conducted on a Boolean decision basis and the verification scores were computed. Dafis et al. (2018), implemented an explicit electrification and lightning parameterization scheme and evaluated against the diagnostic schemes using statistical neighborhood methods. Wang et al. (2018) evaluated the lightning forecast based on PR92 and also on data assimilation. He concluded that PR92 could simulate proper forecast pattern with weaker magnitude forecast. Recently for the first time over India, the authors in their initial study qualitatively evaluated and analyzed lightning flash simulation from various lightning parameterization schemes and compared them with observations (Mohan et al. 2021). This work attempts to propose a better modeling framework for lightning prediction and forecast over Indian region with multiple lightning parameterization schemes in the WRF Model.
Here, we especially address the skill of the different model configurations in forecasting of lightning flash count. For the same, we have carried out numerical experiments with the WRF Model and evaluated the skills of lightning flash simulations from different microphysical schemes. Furthermore, we have attempted to verify the rainfall prediction skill with lightning prediction. The detailed statistical analysis of the model results will provide greater confidence for using the dynamical system for the real-time operational purpose, for which the real-time skill is also evaluated. This study is arranged as follows: section 2 deals with the model configuration and observed data used. Section 3 discusses the verification methods. Results and discussions are presented in section 4. A summary and conclusions are stated in section 5.
2. Model configuration and data
In the current study the Advanced Research version of the WRF Model (ARW) version 3.8.1 is used to simulate the lightning events. This modeling system is developed by National Center for Atmospheric Research (NCAR). It is a fully compressible, nonhydrostatic system of equations with complete Coriolis and curvature terms. Model equations are in the mass-based terrain following sigma coordinate system and solved on an Arakawa-C grid. The Runge–Kutta third-order time integration technique is used for model integration. The detailed description of the model can be found in Skamarock et al. (2008). The initial area of study is over the state of Maharashtra, which is situated in the western part of India (Fig. 1a). The domain of operational lighting prediction system over India is shown in Fig. 1c.
The basic objective of the study being statistical evaluation of model performance, the availability of observations is of prime importance. There is a Lightning Detection Network (LDN) over India, which is established by Indian Institute of Tropical Meteorology (IITM). Initially over 17 Earth Network lightning sensors were installed over Maharashtra, due to which for the initial study, lightning events over this region are studied for validation. From 2019, a total of 70 lightning sensors were installed all over India. These sensors have a wider detection frequency range from 1 Hz to 12 MHz, which allows greater lightning detection. Lower frequencies are used to detect cloud to ground (CG) activity and higher frequencies for in-cloud lightning (IC). The detection efficiency over the region is 90% for CG lightning flashes and 50% for IC flashes. Lightning strokes emit pulses of electromagnetic energy that are received by the lightning detection antennas. The sensor processes the pulses using time-of-arrival methodology and transmits waveform. With the availability of observed lightning data over the state, this region is chosen for the model evaluation. The 5-yr (2014–18) climatology of total lightning over Maharashtra from LDN is presented in Fig. 1b for reference. The pulse data are gridded and presented at model resolution of 1 and 3 km (for real-time forecast validation mentioned later) for comparison. The climatology shows maximum lightning activity over the western part and central part of Maharashtra. A total of 16 thunderstorm cases with widespread lightning during pre-monsoon seasons of the years from 2016 to 2018 are considered. For real-time forecast validation of lightning during five pre-monsoon months, the lightning data from 70 LDN sensors installed all over India, is gridded to 3-km resolution to match the model resolution (mentioned later).
The model is configured with four nested domains of horizontal grid spacing of 27, 9, 3, and 1 km each, with innermost domain over Maharashtra (Fig. 1a). The model is simulated for 24 h based on the 0000 UTC initial condition of the preceding day of lightning event and is vertically integrated up to 50 hPa with 45 vertical levels. It is integrated with a time step of 72 s for all domains to call the lightning parameterization. The model setup in detail, with the selected parameterization schemes chosen for this study, are presented in Table 1. Since cloud microphysical properties play an important role in understanding the thundercloud properties, each case is simulated with four different microphysical options (WSM6, Thompson, Morrison, and WDM6), to understand the different types of hydrometeors and complex interactions between them, which in turn impact the buoyancy and convective fluxes. The sensitivity of cloud microphysics in predicting convective storms and precipitation has been addressed by many researchers (McCumber et al. 1991; Reisner et al. 1998; Gilmore et al. 2004; Liu and Moncrieff 2007). The WSM6 is a 6-class single-moment scheme with graupel and combined snow/graupel fall speed wherein the ice number is a function of ice content (Hong et al. 2004, 2006). The Thompson scheme is a partial double moment microphysics scheme with ice phase and mixed phase processes (Thompson et al. 2004, 2008). The Morrison scheme is also a double moment scheme with all hydrometeors except for cloud water. The mass mixing ratio and number concentration are also predicted (Morrison et al. 2009). The WDM6 is similar to WSM6 but with double moment for warm rain processes and enables us to investigate the cloud condensation nuclei and number concentrations of cloud and rain (Hong et al. 2004). The existing lightning parameterization which is based on cloud top defined by the radar reflectivity factor threshold of 20 dBZ (PR92) is chosen (Price and Rind 1992) for the initial analysis based on our previous study (Mohan et al. 2021), which is also used for the real-time weather forecasting in WRF over Greece (Giannaros et al. 2015). It is also important to note that Giannaros et al. (2015) highlighted two case studies and suggested to look into more variables for realistic lightning prediction, though there is an uncertainty. They also highlighted the necessity of proper representation of convection and clearly related the false prediction of lightning due to falsely predicted convection. Truthfully, they also mentioned that the results over Greece could be different for a different region, which strongly depends upon the convection and horizontal grid spacing (Giannaros et al. (2015). In this scheme the lightning generated from cloud systems over land and ocean are differentiated by considering different formulations for flash rate, since the cloud dynamics are different. The other physics options are presented in Table 1: viz., Grell–Devenyi for cumulus scheme (Grell and Dévényi 2002), Yonsei University scheme (Hong et al. 2006) for PBL (Gangopadhyay et al. 2019), new version of Rapid Radiative Transfer Model (RRTMG) for shortwave and longwave radiation scheme (Iacono et al. 2008), the revised MM5 Monin–Obukhov scheme (Jiménez et al. 2012) for surface layer scheme, and the unified Noah land surface model (Tewari et al. 2004) for land surface.
Model configuration and lightning events selected for study.
The model is initialized with the NCEP FNL Operational Global Analysis 6-hourly data with resolution of 1° × 1°. The sea surface temperature (SST) boundary conditions are provided from NOAA/NCEP real-time global sea surface temperature analysis (http://polar.ncep.noaa.gov/sst/rtg_high_res/) with a resolution of 0.5° × 0.5°. Daily accumulated rainfall from TRMM Multisatellite Precipitation Analysis (TMPA) (3B42v7) is also used in this present study (Huffman et al. 2010, 2007) for the validation of model simulated rainfall. The model simulated rainfall from the innermost domains is regridded to the observational resolution of 0.25° × 0.25° and compared.
For the validation of real-time lightning forecast, the everyday forecast for five pre-monsoon months of 2019 (April and May) and 2020 (March, April, and May) are considered over India. The above mentioned physics are used in real-time lightning prediction system with Morrison microphysical scheme. The model is configured with single domain at 3-km resolution covering all Indian region (Fig. 1c) and is initialized with the IITM-developed GFST1534 (∼12.5 km, Global Forecast System). It is integrated with a time step of 15 s (Table 1).
3. Methodology
The analysis is performed in terms of spatial agreement, fractional skill score (FSS), diurnal correlation and objective evaluation is carried out in terms of different skill scores, viz., probability of detection (POD), hit rate (HR), false alarm ratio (FAR), probability of false alarm detection (POFD), and the critical success index (CSI; also called the threat score) and Heidke skill score (HSS). The receiver operating characteristic (ROC), which is used to determine the skill of model in differentiating between event/occurrence and nonevent/nonoccurrence, is also calculated.
a. Spatial agreement
b. Fractional skill score (FSS)
c. Correlation
d. Objective evaluation
The lightning flash is evaluated in terms of occurrence/no occurrence in the grid box. Once the days are classified as lightning or no lightning for both the observations and forecast, contingency tables are prepared (Wilks 2011). A contingency table identifies the four possible combinations of forecasts (lightning/no lightning) and observations (lightning/no lightning) and is called the joint distribution. The combinations are “events hit” (A), where an event is forecast to occur and does occur; “misses” (B), where an event is forecast not to occur but does occur; “false alarm” (C), where an event is forecast to occur but does not occur; and “no event hits” (D), where an event is forecast not to occur and does not occur (Table 2). The model’s skill in forecasting lightning and rainfall is measured from statistics (usually called skill scores), that are computed from the elements in the contingency table (Hogan and Mason 2012, and references therein).
2 × 2 contingency table.
Skill scores used to evaluate the lightning events. Variables A, B, C, and D are defined in Table 2; Total = A + B + C + D, CF = A + D, and E = [(A + C) (A + B) + (C + D) (B + D)]/Total.
Hence, here the model skill score is calculated from the 2 × 2 contingency table (Table 2), which shows the frequency of “yes” and “no” forecast and occurrences. Based on the contingency table, different skill scores predicting the efficiency of the model are calculated with the formula given in Table 3.
Spatial agreement and standard deviation for all the lightning events.
e. Receiver operating characteristic (ROC) curve
The ROC is a representation of the skill of forecasting system in which the hit rate and false alarm rate are compared. It is used to evaluate the quality of probability of forecast (Kharin and Zwiers 2003). The area under the curve (AUC) represents the model skill with value ranging from 0 (indicating false alarm) to 1 (indicating hits). For this study, the AUC is calculated for the ROC curve between POD and POFD.
4. Results and discussion
A total of 16 lightning events that occurred during pre-monsoon season over Maharashtra were selected for the present study (Table 1). For spatial analysis only few cases were presented here, for rest of the evaluation all the cases were tabulated and presented. The results presented in sections 4a–4f are from the innermost domain covering Maharashtra with a resolution of 1 km.
a. Spatial analysis
The spatial lightning distribution as simulated from the model shows similar activity for all the four microphysics, when compared to observation. Spatial lightning distribution for one event is shown in Fig. 2. For most of the events, there is a widespread lightning activity all over the domain, wherein for certain cases the lightning activity is observed as isolated patches at different locations. Though the performance of the model with all four microphysics does seem similar, they tend to overestimate in the lightning activity in terms of the region of extent with a visible spatial shift in many cases. Since the peak activity occurred between 0900 and 1200 UTC, the spatial pattern of maximum reflectivity in different ranges during this 3-h interval for the same event with all four microphysics is shown in Fig. 3. There are fairly high reflectivity values in regions (e.g., north of 20) where the total lightning counts are not very large. And that the model forecasts has convection there, but clearly predicted too much lightning.
(a) The domain setup with innermost domain over Maharashtra. (b) The climatology of total lightning flash density (flashes per km2) over Maharashtra from LDN from 2014 to 2018. (c) The domain setup for operational lightning forecast.
Citation: Weather and Forecasting 37, 5; 10.1175/WAF-D-21-0080.1
(a) The domain setup with innermost domain over Maharashtra. (b) The climatology of total lightning flash density (flashes per km2) over Maharashtra from LDN from 2014 to 2018. (c) The domain setup for operational lightning forecast.
Citation: Weather and Forecasting 37, 5; 10.1175/WAF-D-21-0080.1
(a) The domain setup with innermost domain over Maharashtra. (b) The climatology of total lightning flash density (flashes per km2) over Maharashtra from LDN from 2014 to 2018. (c) The domain setup for operational lightning forecast.
Citation: Weather and Forecasting 37, 5; 10.1175/WAF-D-21-0080.1
The 24-h accumulated spatial lightning flash count over innermost domain (1 km) on 29 Feb 2016 with (a) WSM6, (b) Thompson, (c) Morrison, (d) WDM6, and (e) observation from LDN.
Citation: Weather and Forecasting 37, 5; 10.1175/WAF-D-21-0080.1
The 24-h accumulated spatial lightning flash count over innermost domain (1 km) on 29 Feb 2016 with (a) WSM6, (b) Thompson, (c) Morrison, (d) WDM6, and (e) observation from LDN.
Citation: Weather and Forecasting 37, 5; 10.1175/WAF-D-21-0080.1
The 24-h accumulated spatial lightning flash count over innermost domain (1 km) on 29 Feb 2016 with (a) WSM6, (b) Thompson, (c) Morrison, (d) WDM6, and (e) observation from LDN.
Citation: Weather and Forecasting 37, 5; 10.1175/WAF-D-21-0080.1
Spatial distribution of maximum reflectivity during the time of peak lightning activity (0900–1200 UTC) over innermost domain on 29 Feb 2016 with (a) WSM6, (b) Thompson, (c) Morrison, and (d) WDM6.
Citation: Weather and Forecasting 37, 5; 10.1175/WAF-D-21-0080.1
Spatial distribution of maximum reflectivity during the time of peak lightning activity (0900–1200 UTC) over innermost domain on 29 Feb 2016 with (a) WSM6, (b) Thompson, (c) Morrison, and (d) WDM6.
Citation: Weather and Forecasting 37, 5; 10.1175/WAF-D-21-0080.1
Spatial distribution of maximum reflectivity during the time of peak lightning activity (0900–1200 UTC) over innermost domain on 29 Feb 2016 with (a) WSM6, (b) Thompson, (c) Morrison, and (d) WDM6.
Citation: Weather and Forecasting 37, 5; 10.1175/WAF-D-21-0080.1
To quantify the above findings, the spatial agreement at 1-km grid over the 24-h period has been carried out (discussed in section 3a). All the four schemes showed a very good agreement for all cases with minimum agreement at 0.52 and maximum agreement at 0.95. The lightning product from Thompson microphysics scheme shows that an average of 0.81 of the model grid boxes match with the observation (Table 4). The ensemble of multiple microphysics schemes shows 0.74 of spatial agreement, which exhibits the positive performance of the model in simulating the lightning. The average standard deviation among the microphysics is ±4–5. This large deviation may be attributed to the limitation in model to represent the microphysical processes of thunderstorms with difference in nature and the composite hydrometeors.
Diurnal correlation of lightning flash count for all the lightning events.
b. Diurnal variation
Given the complexity of spatiotemporal prediction of lightning, in the previous section the spatial distribution is analyzed. The diurnal variation of lightning flash counts over the whole domain is presented in Figs. 4 and 5. For most cases, it is observed that the time of mature stage of the event has been very rightly captured, though there is an overestimation in the flash count. For some cases there is a delay in the time of convective activity initiation, against the observed, that may be due to the model spinup time that it takes for initializing. Even for cases where there is observed activity at two different times (afternoon and late evening), the model was able to capture. The diurnal correlation of the lightning flash counts is calculated and tabulated in Table 5. Both Thompson and WSM6 show a correlation of 0.76, which indicate a high temporal accuracy of the simulated events. The ensemble mean correlation from all the microphysics is 0.72.
Diurnal variation of lightning flash count for eight different events over the innermost domain (date of event mentioned above each graph).
Citation: Weather and Forecasting 37, 5; 10.1175/WAF-D-21-0080.1
Diurnal variation of lightning flash count for eight different events over the innermost domain (date of event mentioned above each graph).
Citation: Weather and Forecasting 37, 5; 10.1175/WAF-D-21-0080.1
Diurnal variation of lightning flash count for eight different events over the innermost domain (date of event mentioned above each graph).
Citation: Weather and Forecasting 37, 5; 10.1175/WAF-D-21-0080.1
As in Fig. 4, but different thunderstorm cases. Diurnal variation of lightning flash count for the remaining eight lightning events over the innermost domain (date of event mentioned above each graph).
Citation: Weather and Forecasting 37, 5; 10.1175/WAF-D-21-0080.1
As in Fig. 4, but different thunderstorm cases. Diurnal variation of lightning flash count for the remaining eight lightning events over the innermost domain (date of event mentioned above each graph).
Citation: Weather and Forecasting 37, 5; 10.1175/WAF-D-21-0080.1
As in Fig. 4, but different thunderstorm cases. Diurnal variation of lightning flash count for the remaining eight lightning events over the innermost domain (date of event mentioned above each graph).
Citation: Weather and Forecasting 37, 5; 10.1175/WAF-D-21-0080.1
Area under curve (AUC) for lightning from ROC analysis from experiments with different microphysics calculated over 50 × 50 km2 and 10 × 10 km2 grid boxes.
c. Fractions skill score (FSS)
Combined model skill for all 16 cases is presented in terms of FSS (Roberts and Lean 2008) with different thresholds at neighborhoods from 25 to 250 km2 (Fig. 6a). The results suggest that forecast with 0.2 threshold yields slightly better result at 50- and 75-km neighborhood scales, though the scales are large for forecast application. With the increase in threshold there is no significant dispersion observed. The variation of FSS with time at different radial distances with threshold of 0.2 and 1 show higher skill at 1200 UTC, which is the time of peak activity for all the cases and thereafter reduce with increase in forecast hour (Figs. 6b,c). This 3-hourly FSS is below the useful threshold of 0.5, which is not encouraging, but higher FSS values for larger radii above 150 km, computed 3-hourly, is obtained, which is not presented here as it is not necessarily relevant in assessing the skill given the larger scale. This might be due to the fact that there is an over estimation in modeled lightning flashes as reported in all the cases with temporal shift in few cases. So this must have accounted for lower FSS value, whereas for 24 h, the shift might have been nullified. Similar result is reported by Blaylock and Horel (2020) over certain stations.
Fractional skill score (FSS) calculated (a) with different thresholds at different spatial resolutions averaged over a 24-h period, (b) with a 0.2 lightning threshold, and (c) with a 1 lightning threshold.
Citation: Weather and Forecasting 37, 5; 10.1175/WAF-D-21-0080.1
Fractional skill score (FSS) calculated (a) with different thresholds at different spatial resolutions averaged over a 24-h period, (b) with a 0.2 lightning threshold, and (c) with a 1 lightning threshold.
Citation: Weather and Forecasting 37, 5; 10.1175/WAF-D-21-0080.1
Fractional skill score (FSS) calculated (a) with different thresholds at different spatial resolutions averaged over a 24-h period, (b) with a 0.2 lightning threshold, and (c) with a 1 lightning threshold.
Citation: Weather and Forecasting 37, 5; 10.1175/WAF-D-21-0080.1
d. Objective evaluation
The model skill score in simulating the lightning flashes in every 50 × 50 km2 and 10 × 10 km2 grid box is calculated (Figs. 7a,b) from the innermost domain of 1 km. The grid to grid existence of lightning for all 16 cases is considered for this analysis, making the sample size of around 6264 for 10 km and 238 for 50 km for each case. The results show a fairly good POD of 0.84 (0.76) and FAR of 0.27 (0.51) for 50 km (10 km). The HR, POFD, CSI, and HSS for 50 km (10 km) is 0.73 (0.68), 0.44 (0.36), 0.63 (0.41), and 0.40 (0.33), respectively. It is noted that the performances of all the microphysics schemes in terms of skill score are in very good agreement with each other. The results represent the average skill score for all the selected events. The evolution of skill during the total duration of activity from 0900 to 1800 UTC shows that during the development of the event at 0900 UTC the POD is relatively low with higher FAR compared to other time intervals (Fig. 7c). The POD for rest time intervals is almost same (0.78) but the FAR is less during the time of peak activity (0.4) and increased at the dissipating time of 1800 UTC (0.69). The hit rate of 0.67 is almost constant for all time intervals. The CSI and HSS is less during convective activity initiation and high at time of peak activity and reduce thereafter.
Lightning skill scores calculated from experiments with different microphysics schemes over a region of (a) 50 × 50 km2 and (b) 10 × 10 km2 from the 1-km domain and (c) 3-hourly skill score over 50 × 50 km2 region.
Citation: Weather and Forecasting 37, 5; 10.1175/WAF-D-21-0080.1
Lightning skill scores calculated from experiments with different microphysics schemes over a region of (a) 50 × 50 km2 and (b) 10 × 10 km2 from the 1-km domain and (c) 3-hourly skill score over 50 × 50 km2 region.
Citation: Weather and Forecasting 37, 5; 10.1175/WAF-D-21-0080.1
Lightning skill scores calculated from experiments with different microphysics schemes over a region of (a) 50 × 50 km2 and (b) 10 × 10 km2 from the 1-km domain and (c) 3-hourly skill score over 50 × 50 km2 region.
Citation: Weather and Forecasting 37, 5; 10.1175/WAF-D-21-0080.1
We have also compared the POD and FAR calculated from reflectivity based PR92 lightning parameterization with the widely used diagnostic schemes by McCaul et al. (2009, hereafter MC09) at different time intervals. The skill analysis shows the lesser POD in all the 16 cases used in this study (figure not shown) with MC09. The average POD and FAR over a 50 × 50 km2 grid region are 0.29 and 0.62, respectively. MC09 parameterization might be good for the convection over other regions, but the skill (POD) is less and FAR is more as compared to PR92 over Indian subcontinent.
e. Receiver operating characteristic (ROC) curve
The ROC curve has been plotted for all 16 cases and for different microphysics (Fig. 8a). This also has been carried out for every 50 × 50 km2 and 10 × 10 km2 grids (not shown in figure), to study the skill of model. The area under the ROC curve gives the AUC score. An AUC score of greater than 0.5 (50% chance) is considered as skillful in forecasting. The average AUC for 50 km with WSM6 is 0.79 and for rest all three microphysics it is 0.77. The boxplot for AUC with different microphysics show the minimum, maximum and mean AUC for all the 16 cases (Fig. 8b). The AUC calculated over 10-km grid boxes for WSM6 is 0.71 and Morrison is 0.70. The AUC for both Thompson and WDM6 is similar with a score of 0.69 (Table 6). Each AUC values indicate an acceptable level of skillfulness (where “acceptable” is implied as greater than 0.5). There are spread for all 16 events from minimum to maximum AUC for each microphysical scheme and all depict the acceptable level of sinfulness. Overall it is observed that the AUC with different microphysics is almost similar, which indicates that there is no much difference in performance.
f. Skill of rainfall
Several analyses and studies on thunderstorm electrification process show that the charge centers in a thunderstorm are collocated with precipitation in regions of specific temperature and that the rapid electrical development is associated with the development of precipitation in the cloud (Saunders 2008). Based on this, the skill of model in simulating precipitation is also carried out so that it indirectly implies the skill in prediction of lightning. Similar to the lightning distribution, the rainfall distribution from model simulations are comparable with a similar envelope of the observed rainfall from TRMM 3B42, but with an over estimation by all microphysics and different patterns within. The model skill score in predicting rainfall is also carried out similar to lightning (Fig. 9a). An average POD of 0.81 and FAR of 0.51 is noted, which is closer to the skill scores of model in predicting lightning. The HR, POFD, CSI, and HSS with rainfall are 0.72, 0.33, 0.43, and 0.38, respectively. This skill is comparable with studies like Müller et al. (2016) which also reported similar skill in rainfall forecast.
(a) ROC curve for all microphysics averaged over all 16 events for a region of 50 × 50 km2. (b) Boxplot of AUC calculated with different microphysics, indicating the minimum, maximum, and mean AUC.
Citation: Weather and Forecasting 37, 5; 10.1175/WAF-D-21-0080.1
(a) ROC curve for all microphysics averaged over all 16 events for a region of 50 × 50 km2. (b) Boxplot of AUC calculated with different microphysics, indicating the minimum, maximum, and mean AUC.
Citation: Weather and Forecasting 37, 5; 10.1175/WAF-D-21-0080.1
(a) ROC curve for all microphysics averaged over all 16 events for a region of 50 × 50 km2. (b) Boxplot of AUC calculated with different microphysics, indicating the minimum, maximum, and mean AUC.
Citation: Weather and Forecasting 37, 5; 10.1175/WAF-D-21-0080.1
(a) Rainfall skill score over 24-h period from all experiments with different microphysics over a region of 50 × 50 km2. (b) Scatterplot of POD of rainfall and lightning with best fit line over a region of 50 × 50 km2 for all the events.
Citation: Weather and Forecasting 37, 5; 10.1175/WAF-D-21-0080.1
(a) Rainfall skill score over 24-h period from all experiments with different microphysics over a region of 50 × 50 km2. (b) Scatterplot of POD of rainfall and lightning with best fit line over a region of 50 × 50 km2 for all the events.
Citation: Weather and Forecasting 37, 5; 10.1175/WAF-D-21-0080.1
(a) Rainfall skill score over 24-h period from all experiments with different microphysics over a region of 50 × 50 km2. (b) Scatterplot of POD of rainfall and lightning with best fit line over a region of 50 × 50 km2 for all the events.
Citation: Weather and Forecasting 37, 5; 10.1175/WAF-D-21-0080.1
Further, we investigate how the accuracy in lightning forecast corresponds to accuracy in rainfall. To do so, the correlation coefficient is calculated for the POD of rainfall and lightning (for 50 × 50 km2 grid box, Fig. 9b). This shows the correlation of the (POD) rainfall and lightning for all the 16 events. It is important to note that almost all the points lie in between >0.55 and <0.95, and correlation is significant at the 0.95 variance level. It is also noted that there is a linear relationship between rainfall and lightning POD. Therefore, it can be pointed out that the accuracy in forecasting the probability of lightning did correspond to rainfall forecast in terms of location of occurrence with an overestimation in the amount.
g. Real-time lightning forecast
After the initial analysis, presently, the above model configuration along with the Morrison microphysics scheme with a domain of resolution of 3 km is used to simulate lightning events over the entire Indian region, in order to reduce computational time for the daily operational forecast. For illustration, forecasts of two widespread lightning events on 15 April 2020 and 24 May 2020 are presented in Fig. 10, in comparison with observations. We notice that the location and pattern of lightning event could be well simulated, but the extent of the activity is spread around compared to observations. The lightning activity simulated over the oceanic regions cannot be validated due to nonavailability of observational data. The observed lightning data stands valid over Indian region due to the location accuracy of the sensors.
Spatial distribution of lightning flashes for two different cases: 15 Apr 2020 and 24 May 2020 from (a),(c) model real-time forecasting system and (b),(d) corresponding lightning observation.
Citation: Weather and Forecasting 37, 5; 10.1175/WAF-D-21-0080.1
Spatial distribution of lightning flashes for two different cases: 15 Apr 2020 and 24 May 2020 from (a),(c) model real-time forecasting system and (b),(d) corresponding lightning observation.
Citation: Weather and Forecasting 37, 5; 10.1175/WAF-D-21-0080.1
Spatial distribution of lightning flashes for two different cases: 15 Apr 2020 and 24 May 2020 from (a),(c) model real-time forecasting system and (b),(d) corresponding lightning observation.
Citation: Weather and Forecasting 37, 5; 10.1175/WAF-D-21-0080.1
All the five months showed a decent spatial agreement with minimum of 0.63 (63%) for the month of May 2020 and maximum agreement of 0.81 (81%) in March 2020. Overall, the number of grid boxes (at 3-km resolution) that match spatially is approximately 72% for the duration of five pre-monsoon months. The model skill score shows an average POD of 0.90, FAR of 0.64, hit rate of 0.57, and POFD of 0.50 over the whole region for all months (plots not shown). The spatial distribution of POD and FAR calculated grid to grid is presented in Fig. 11 at the peak time of activity of 1200 UTC. The higher false alarm may be due to the spatial and temporal shift and over estimation of lightning flashes with higher bias in some regions. Such higher false alarms and spatial over estimation were reported in others studies also (Giannaros et al. 2015), where PR92 was used. But as reported in our first part of this study (Mohan et al. 2021), the WRF could model the convective structures as observed from the reflectivity, lightning, and cloud hydrometeors. The over estimation of lightning flash count is linked with an overprediction of convective intensity and storm top.
(top) POD and (bottom) FAR from operational forecasting system for the months (a),(f) April 2019; (b),(g) May 2019; (c),(h) March 2020; (d),(i) April 2020; and (e),(j) May 2020.
Citation: Weather and Forecasting 37, 5; 10.1175/WAF-D-21-0080.1
(top) POD and (bottom) FAR from operational forecasting system for the months (a),(f) April 2019; (b),(g) May 2019; (c),(h) March 2020; (d),(i) April 2020; and (e),(j) May 2020.
Citation: Weather and Forecasting 37, 5; 10.1175/WAF-D-21-0080.1
(top) POD and (bottom) FAR from operational forecasting system for the months (a),(f) April 2019; (b),(g) May 2019; (c),(h) March 2020; (d),(i) April 2020; and (e),(j) May 2020.
Citation: Weather and Forecasting 37, 5; 10.1175/WAF-D-21-0080.1
Although presently for real-time operational forecast simulation, we have used Morrison microphysics (MP) scheme, but the results of the skill analysis from 16 thunderstorm cases with different MP schemes depict that there are not many differences among various MP schemes.
5. Summary and conclusions
The quantitative assessment of model performance in simulating lightning flash count is carried out. This study is a part of the project with an objective of developing a regional modeling system for the accurate prediction of lightning in real time. The model has been stabilized and configured to our region of interest. A total of 16 lightning cases were identified and simulated with that model set up, with four different microphysical schemes. The spatial analysis of lightning flash counts for all the cases show that the model is able to capture the pattern of occurrence with some over estimation. The maximum reflectivity in the region of lightning occurrence indicates the simulation of convection. The spatial agreement of lightning showed a very positive result with maximum agreement of 0.95 calculated over 50-km grid region for all the 16 cases over 24-h forecast period. Out of the four microphysics chosen, simulations with Thompson have shown an agreement of 0.81. The ensemble spatial agreement is 0.74, which encourages the use of ensemble approach with which the uncertainty introduced by all sub grid parameterizations is represented. There is a considerable variation in standard deviation observed which may be attributed to the diversity of thunderstorm cases chosen which have different physical properties. To estimate the temporal skill in predicting lightning, the diurnal correlation is calculated, which is 0.72 for all the microphysics. Few cases showed a temporal lag in the initiation stage, which is due to the model spinup time. The FSS with 0.2 threshold yields better skill at 50-km scale and the skill is the highest at 1200 UTC which is peak time of activity. The objective evaluation is carried out based on the contingency table. The POD, FAR, HR, POFD, CSI, and HSS are 0.76, 0.51, 0.68, 0.36, 0.41, and 0.33, respectively, with a location accuracy of 10 km. The ROC curve shows average area under curve to be 0.79 with WSM6 and 0.77 for all the cases at 50-km range and for 10-km area, the AUC is 0.71 (WSM6), 0.70 (Morrison), and 0.69 (Thompson and WDM6). Also the skill score from 3-km domain has an average POD of 0.88 which is fairly good but with a higher FAR 0.66. The relation between precipitation and lightning is re-established by comparing the predicted rainfall and lightning. The accuracy in forecasting the POD of lightning did correspond to accuracy in forecasting rainfall.
ROC curves, correlation, skill scores, spatial agreement were used to evaluate the accuracy and usefulness of the forecasts. Forecast probabilities are most reliable with a spatial area of 50 km2 boxes (which is at the district level). The positive results led us to operationally forecast the lightning all over India in real time for the pre-monsoon 2019 and 2020, with confidence at district level. A decent spatial agreement ranging from 0.63 (63%) to 0.81 (81%) is obtained from the real-time lightning forecast. The skill of the system is encouraging with POD of 0.90 and FAR of 0.64.
The improvements of lightning forecast can be attributed through multiple approaches: (i) increasing horizontal resolution of the model, (ii) multiphysics ensemble technique, (iii) improve initialization through better data assimilation (particularly reflectivity and lightning), (iv) improving through proper threshold of reflectivity and IC/CG ratio based on observation, (v) improvement the formation of cloud ice in the microphysical parameterization scheme, (vi) modifying rain drop size distribution, and (vii) incorporating proper cloud–aerosol interaction in numerical model. Based on the overall analysis carried out, we are further working on accurate location specific forecast by trying to modify the cloud top height in model based on observations. We would like to extend our analysis by assimilation of lightning into the convective forecast and others which improves the intensity and the location of the storm. We would further like to extend our analysis to modify the cloud top height in model based on observations and improving model physics to further improve the forecast.
Acknowledgments.
IITM is funded by the Ministry of Earth Sciences, government of India. Authors are thankful to the team of HPCS, IITM (Aaditya and Pratyush) for their kind support. The observed data provided by the Lighting Detection Network team, IITM, are acknowledged. We duly acknowledge NASA for the precipitation data used, which are freely accessible (https://disc.gsfc.nasa.gov/datasets/TRMM_3B42_Daily_7). We are grateful to three anonymous reviewers for their constructive suggestions to improve the quality of the manuscript.
Data availability statement.
The data used in this study are archived in HPCS and are available at the FTP link: ftp://103.251.184.52.
REFERENCES
Barth, M. C., J. Lee, A. Hodzic, G. Pfister, W. C. Skamarock, J. Worden, J. Wong, and D. Noone, 2012: Thunderstorms and upper troposphere chemistry during the early stages of the 2006 North American Monsoon. Atmos. Chem. Phys., 12, 11 003–11 026, https://doi.org/10.5194/acp-12-11003-2012.
Barthe, C., and J. P. Pinty, 2007: Simulation of electrified storms with comparison of the charge structure and lightning efficiency. J. Geophys. Res., 112, D19204, https://doi.org/10.1029/2006JD008241.
Barthe, C., W. Deierling, and M. C. Barth, 2010: Estimation of total lightning from various storm parameters: A cloud-resolving model study. J. Geophys. Res., 115, D24202, https://doi.org/10.1029/2010JD014405.
Berdeklis, P., and R. List, 2001: The ice crystal-graupel collision charging mechanism of thunderstorm electrification. J. Atmos. Sci., 58, 2751–2770, https://doi.org/10.1175/1520-0469(2001)058<2751:TICGCC>2.0.CO;2.
Blaylock, B. K., and J. D. Horel, 2020: Comparison of lightning forecasts from the High-Resolution Rapid Refresh model to Geostationary Lightning Mapper observations. Wea. Forecasting, 35, 401–416, https://doi.org/10.1175/WAF-D-19-0141.1.
Boccippio, D. J., K. L. Cummins, H. J. Christian, and S. J. Goodman, 2001: Combined satellite- and surface-based estimation of the intracloud–cloud-to-ground lightning ratio over the continental United States. Mon. Wea. Rev., 129, 108–122, https://doi.org/10.1175/1520-0493(2001)129<0108:CSASBE>2.0.CO;2.
Brooks, I. M., and C. P. R. Saunders, 1994: An experimental investigation of the inductive mechanism of thunderstorm electrification. J. Geophys. Res., 99, 10 627–10 632, https://doi.org/10.1029/93JD01574.
Carey, L. D., and S. A. Rutledge, 1996: A multiparameter radar case study of the microphysical and kinematic evolution of a lightning producing storm. Meteor. Atmos. Phys., 59, 33–64, https://doi.org/10.1007/BF01032000.
Chang, J., J. Gu, F. Ji, F. Chang, and H. Sayit, 2020: Relationship between microphysical properties of convective clouds and lightning activity in a typical thunderstorm in Sichuan basin. Pol. J. Environ. Stud., 30, 571–583, https://doi.org/10.15244/pjoes/123291.
Chaudhari, H. S., G. K. Sawaisarje, M. R. Ranalkar, and P. N. Sen, 2010: Thunderstorms over a tropical Indian station, Minicoy: Role of vertical wind shear. J. Earth Syst. Sci., 119, 603–615, https://doi.org/10.1007/s12040-010-0044-3.
Cooray, V., V. Rakov, and N. Theethayi, 2007: The lightning striking distance—Revisited. J. Electrost., 65, 296–306, https://doi.org/10.1016/j.elstat.2006.09.008.
Dafis, S., A. Fierro, T. M. Giannaros, V. Kotroni, K. Lagouvardos, and E. Mansell, 2018: Performance evaluation of an explicit lightning forecasting system. J. Geophys. Res. Atmos, 123, 5130–5148, https://doi.org/10.1029/2017JD027930.
Dasgupta, S., and U. K. De, 2007: Binary logistic regression models for short term prediction of premonsoon convective developments over Kolkata (India). Int. J. Climatol., 27, 831–836, https://doi.org/10.1002/joc.1449.
Deierling, W., and W. A. Petersen, 2008: Total lightning activity as an indicator of updraft characteristics. J. Geophys. Res., 113, D16210, https://doi.org/10.1029/2007JD009598.
Gangopadhyay, A., R. Kanase, G. Mohan, M. Halder, M. Deshpande, P. Mukhopadhyay, and J. Srinivasan, 2019: Use of a weather forecast model to identify suitable sites for new wind power plants in Karnataka. Curr. Sci., 117, 1347–1353, https://doi.org/10.18520/cs/v117/i8/1345-1347.
Ghosh, S., P. K. Sen, and U. K. De, 1999: Identification of significant parameters for the prediction of pre-monsoon thunderstorms at Calcutta, India. Int. J. Climatol., 19, 673–681, https://doi.org/10.1002/(SICI)1097-0088(199905)19:6<673::AID-JOC384>3.0.CO;2-O.
Giannaros, T. M., V. Kotroni, and K. Lagouvardos, 2015: Predicting lightning activity in Greece with the Weather Research and Forecasting (WRF) model. Atmos. Res., 156, 1–13, https://doi.org/10.1016/j.atmosres.2014.12.009.
Gilmore, M. S., J. M. Straka, and E. N. Rasmussen, 2004: Precipitation and evolution sensitivity in simulated deep convective storms: Comparisons between liquid-only and simple ice and liquid phase microphysics. Mon. Wea. Rev., 132, 1897–1916, https://doi.org/10.1175/1520-0493(2004)132<1897:PAESIS>2.0.CO;2.
Goodman, S. J., D. E. Buechler, P. D. Wright, and W. D. Rust, 1988: Lightning and precipitation history of a microburst‐producing storm. Geophys. Res. Lett., 15, 1185–1188, https://doi.org/10.1029/GL015i011p01185.
Grell, G. A., and D. Dévényi, 2002: A generalized approach to parameterizing convection combining ensemble and data assimilation techniques. Geophys. Res. Lett., 29, 1693, https://doi.org/10.1029/2002GL015311.
Guo, F. X., G. Y. Lu, X. Wu, H. L. Wang, Z. P. Liu, M. Bao, and Y. W. Li, 2016: Occurrence conditions of positive cloud-to-ground flashes in severe thunderstorms. Sci. China Earth Sci., 59, 1401–1413, https://doi.org/10.1007/s11430-016-5279-7.
Halder, M., and P. Mukhopadhyay, 2016: Microphysical processes and hydrometeor distributions associated with thunderstorms over India: WRF (cloud-resolving) simulations and validations using TRMM. Nat. Hazards, 83, 1125–1155, https://doi.org/10.1007/s11069-016-2365-2.
Hogan, R. J., and I. B. Mason, 2012: Deterministic forecasts of binary events. Forecast Verification: A Practitioner’s Guide in Atmospheric Science, I. T. Jolliffe and D. B. Stephenson, Eds., Wiley, 31–59, https://doi.org/10.1002/9781119960003.ch3.
Hong, S. Y., J. Dudhia, and S. H. Chen, 2004: A revised approach to ice microphysical processes for the bulk parameterization of clouds and precipitation. Mon. Wea. Rev., 132, 103–120, https://doi.org/10.1175/1520-0493(2004)132<0103:ARATIM>2.0.CO;2.
Hong, S. Y., Y. Noh, and J. Dudhia, 2006: A new vertical diffusion package with an explicit treatment of entrainment processes. Mon. Wea. Rev., 134, 2318–2341, https://doi.org/10.1175/MWR3199.1.
Huffman, G. J., and Coauthors, 2007: The TRMM Multisatellite Precipitation Analysis (TMPA): Quasi-global, multiyear, combined-sensor precipitation estimates at fine scales. J. Hydrometeor., 8, 38–55, https://doi.org/10.1175/JHM560.1.
Huffman, G. J., R. F. Adler, D. T. Bolvin, and E. J. Nelkin, 2010: The TRMM Multi-satellite Precipitation Analysis (TMPA). Satellite Rainfall Applications for Surface Hydrology. M. Gebremichael and F. Hossain, Eds., Springer, https://doi.org/10.1007/978-90-481-2915-7_1.
Iacono, M. J., J. S. Delamere, E. J. Mlawer, M. W. Shephard, S. A. Clough, and W. D. Collins, 2008: Radiative forcing by long-lived greenhouse gases: Calculations with the AER radiative transfer models. J. Geophys. Res., 113, D13103, https://doi.org/10.1029/2008JD009944.
Igri, P. M., R. S. Tanessong, D. A. Vondou, J. Panda, A. Garba, F. K. Mkankam, and A. Kamga, 2018: Assessing the performance of WRF model in predicting high-impact weather conditions over Central and Western Africa: An ensemble-based approach. Nat. Hazards, 93, 1565–1587, https://doi.org/10.1007/s11069-018-3368-y.
Jiménez, P. A., J. Dudhia, J. F. González-Rouco, J. Navarro, J. P. Montávez, and E. García-Bustamante, 2012: A revised scheme for the WRF surface layer formulation. Mon. Wea. Rev., 140, 898–918, https://doi.org/10.1175/MWR-D-11-00056.1.
Kamra, A. K., 1970: Effect of electric field on charge separation by the falling precipitation mechanism in thunderclouds. J. Atmos. Sci., 27, 1182–1185, https://doi.org/10.1175/1520-0469(1970)027<1182:EOEFOC>2.0.CO;2.
Kandalgaonkar, S. S., M. I. R. Tinmaker, J. R. Kulkarni, A. Nath, M. K. Kulkarni, and H. K. Trimbake, 2005: Spatio-temporal variability of lightning activity over the Indian region. J. Geophys. Res., 110, D11108, https://doi.org/10.1029/2004JD005631.
Kharin, V. V., and F. W. Zwiers, 2003: On the ROC score of probability forecasts. J. Climate, 16, 4145–4150, https://doi.org/10.1175/1520-0442(2003)016<4145:OTRSOP>2.0.CO;2.
Lal, D. M., and S. D. Pawar, 2009: Relationship between rainfall and lightning over central Indian region in monsoon and premonsoon seasons. Atmos. Res., 92, 402–410, https://doi.org/10.1016/j.atmosres.2008.12.009.
Latham, J., A. M. Blyth, H. J. Christian, W. Deierling, and A. M. Gadian, 2004: Determination of precipitation rates and yields from lightning measurements. J. Hydrol., 288, 13–19, https://doi.org/10.1016/j.jhydrol.2003.11.009.
Litta, A. J., U. C. Mohanty, and S. M. Idicula, 2012: The diagnosis of severe thunderstorms with high-resolution WRF model. J. Earth Syst. Sci., 121, 297–316, https://doi.org/10.1007/s12040-012-0165-y.
Liu, C., and M. W. Moncrieff, 2007: Sensitivity of cloud-resolving simulations of warm-season convection to cloud microphysics parameterizations. Mon. Wea. Rev., 135, 2854–2868, https://doi.org/10.1175/MWR3437.1.
Lund, N. R., D. R. Macgorman, T. J. Schuur, M. I. Biggerstaff, and W. D. Rust, 2009: Relationships between lightning location and polarimetric radar signatures in a small mesoscale convective system. Mon. Wea. Rev., 137, 4151–4170, https://doi.org/10.1175/2009MWR2860.1.
Madhulatha, A., M. Rajeevan, M. Venkat Ratnam, J. Bhate, and C. V. Naidu, 2013: Nowcasting severe convective activity over southeast India using ground-based microwave radiometer observations. J. Geophys. Res. Atmos., 118, 1–13, https://doi.org/10.1029/2012JD018174.
Mahapatra, B., M. Walia, and N. Saggurti, 2018: Extreme weather events induced deaths in India 2001–2014: Trends and differentials by region, sex and age group. Wea. Climate Extremes, 21, 110–116, https://doi.org/10.1016/j.wace.2018.08.001.
Manohar, G. K., and A. P. Kesarkar, 2004: Climatology of thunderstorm activity over the Indian region: II. Spatial distribution. Mausam, 55, 31–40, https://doi.org/10.54302/mausam.v55i1.854.
Mason, J., 1988: The generation of electric charges and fields in thunderstorms. Proc. Roy. Soc., 415A, 303–315, https://doi.org/10.1098/rspa.1988.0015.
McCaul, E. W., S. J. Goodman, K. M. LaCasse, and D. J. Cecil, 2009: Forecasting lightning threat using cloud-resolving model simulations. Wea. Forecasting, 24, 709–729, https://doi.org/10.1175/2008WAF2222152.1.
McCumber, M., W.-K. Tao, J. Simpson, and R. Penc, 1991: Comparison of ice-phase microphysical parameterization schemes using numerical simulations of tropical convection. J. Appl. Meteor., 30, 985–1004, https://doi.org/10.1175/1520-0450-30.7.985.
Mohan, G. M., and Coauthors, 2021: Evaluating different lightning parameterization schemes to simulate lightning flash counts over Maharashtra, India. Atmos. Res., 255, 105532, https://doi.org/10.1016/j.atmosres.2021.105532.
Morrison, H., G. Thompson, and V. Tatarskii, 2009: Impact of cloud microphysics on the development of trailing stratiform precipitation in a simulated squall line: Comparison of one- and two-moment schemes. Mon. Wea. Rev., 137, 991–1007, https://doi.org/10.1175/2008MWR2556.1.
Mukhopadhyay, P., J. Sanjay, and S. S. Singh, 2003: Objective forecast of thundery/nonthundery days using conventional indices over three northeast Indian stations. Mausam, 4, 867–880.
Müller, O. V., M. A. Lovino, and E. H. Berbery, 2016: Evaluation of WRF Model forecasts and their use for hydroclimate monitoring over Southern South America. Wea. Forecasting, 31, 1001–1017, https://doi.org/10.1175/WAF-D-15-0130.1.
Murugavel, P., S. D. Pawar, and V. Gopalakrishan, 2014: Climatology of lightning over Indian region and its relationship with convective available potential energy. Int. J. Climatol., 34, 3179–3187, https://doi.org/10.1002/joc.3901.
Pawar, S. D., and A. K. Kamra, 2004: Evolution of lightning and the possible initiation/triggering of lightning discharges by the lower positive charge center in an isolated thundercloud in the tropics. J. Geophys. Res., 109, D02205, https://doi.org/10.1029/2003JD003735.
Pawar, S. D., and A. K. Kamra, 2009: Maxwell current density characteristics below isolated thunderstorms in tropics. J. Geophys. Res., 114, D04208, https://doi.org/10.1029/2008JD010348.
Pawar, S. D., D. M. Lal, and P. Murugavel, 2012: Lightning characteristics over Central India during Indian summer monsoon. Atmos. Res., 106, 44–49, https://doi.org/10.1016/j.atmosres.2011.11.007.
Petersen, W. A., S. A. Rutledge, and R. E. Orville, 1996: Cloud-to-ground lightning observations from TOGA COARE: Selected results and lightning location algorithms. Mon. Wea. Rev., 124, 602–620, https://doi.org/10.1175/1520-0493(1996)124<0602:CTGLOF>2.0.CO;2.
Politi, N., P. T. Nastos, A. Sfetsos, D. Vlachogiannis, and N. R. Dalezios, 2018: Evaluation of the AWR-WRF model configuration at high resolution over the domain of Greece. Atmos. Res., 208, 229–245, https://doi.org/10.1016/j.atmosres.2017.10.019.
Price, C., and D. Rind, 1992: A simple lightning parameterization for calculating global lightning distributions. J. Geophys. Res., 97, 9919–9933, https://doi.org/10.1029/92JD00719.
Price, C., and D. Rind, 1993: What determines the cloud‐to‐ground lightning fraction in thunderstorms? Geophys. Res. Lett., 20, 463–466, https://doi.org/10.1029/93GL00226.
Price, C., and D. Rind, 1994: Modeling global lightning distributions in a general circulation model. Mon. Wea. Rev., 122, 1930–1939, https://doi.org/10.1175/1520-0493(1994)122<1930:MGLDIA>2.0.CO;2.
Rajeevan, M., A. Kesarkar, S. B. Thampi, T. N. Rao, B. Radhakrishna, and M. Rajasekhar, 2010: Sensitivity of WRF cloud microphysics to simulations of a severe thunderstorm event over Southeast India. Ann. Geophys., 28, 603–619, https://doi.org/10.5194/angeo-28-603-2010.
Rajeevan, M., A. Madhulatha, M. Rajasekhar, J. Bhate, A. Kesarkar, and B. V. Appa Rao, 2012: Development of a perfect prognosis probabilistic model for prediction of lightning over south-east India. J. Earth Syst. Sci., 121, 355–371, https://doi.org/10.1007/s12040-012-0173-y.
Ramesh Kumar, P., and A. K. Kamra, 2012: The spatiotemporal variability of lightning activity in the Himalayan foothills. J. Geophys. Res., 117, D24201, https://doi.org/10.1029/2012JD018246.
Ranalkar, M. R., and H. S. Chaudhari, 2009: Seasonal variation of lightning activity over the Indian subcontinent. Meteor. Atmos. Phys., 104, 125–134, https://doi.org/10.1007/s00703-009-0026-7.
Reisner, J., R. M. Rasmussen, and R. T. Bruintjes, 1998: Explicit forecasting of supercooled liquid water in winter storms using the MM5 mesoscale model. Quart. J. Roy. Meteor. Soc., 124, 1071–1107, https://doi.org/10.1002/qj.49712454804.
Roberts, N. M., and H. W. Lean, 2008: Scale-selective verification of rainfall accumulations from high-resolution forecasts of convective events. Mon. Wea. Rev., 136, 78–97, https://doi.org/10.1175/2007MWR2123.1.
Rutledge, S. A., E. R. Williams, and T. D. Keenan, 1992: The Down Under Doppler and Electricity Experiment (DUNDEE): Overview and preliminary results. Bull. Amer. Meteor. Soc., 73, 3–16, https://doi.org/10.1175/1520-0477(1992)073<0003:TDUDAE>2.0.CO;2.
Saunders, C., 2008: Charge separation mechanisms in clouds. Space Sci. Rev., 137, 335–353, https://doi.org/10.1007/s11214-008-9345-0.
Shearman, K. M., and C. F. Ojala, 1999: Some causes for lightning data inaccuracies: The case of Michigan. Bull. Amer. Meteor. Soc., 80, 1883–1891, https://doi.org/10.1175/1520-0477(1999)080<1883:SCFLDI>2.0.CO;2.
Singh, O., and J. Singh, 2015: Lightning fatalities over India: 1979-2011. Meteor. Appl., 22, 770–778, https://doi.org/10.1002/met.1520.
Skamarock, W. C., and Coauthors, 2008: A description of the Advanced Research WRF version 3. NCAR Tech. Note NCAR/TN-475+STR, 113 pp. https://doi.org/10.5065/D68S4MVH.
Tewari, M., and Coauthors, 2004: Implementation and verification of the unified Noah land surface model in the WRF model. 20th Conf. on Weather Analysis and Forecasting/16th Conf. on Numerical Weather Prediction, Seattle, WA, Amer. Meteor. Soc., 14.2a, https://ams.confex.com/ams/84Annual/techprogram/paper_69061.htm.
Thompson, G., R. M. Rasmussen, and K. Manning, 2004: Explicit forecasts of winter precipitation using an improved bulk microphysics scheme. Part I: Description and sensitivity analysis. Mon. Wea. Rev., 132, 519–542, https://doi.org/10.1175/1520-0493(2004)132<0519:EFOWPU>2.0.CO;2.
Thompson, G., P. R. Field, R. M. Rasmussen, and W. D. Hall, 2008: Explicit forecasts of winter precipitation using an improved bulk microphysics scheme. Part II: Implementation of a new snow parameterization. Mon. Wea. Rev., 136, 5095–5115, https://doi.org/10.1175/2008MWR2387.1.
Tyagi, A., 2007: Thunderstorm climatology over Indian region. Mausam, 2, 189–212, https://doi.org/10.54302/mausam.v58i2.1204.
Tyagi, B., V. Naresh Krishna, and A. N. V. Satyanarayana, 2011: Study of thermodynamic indices in forecasting pre-monsoon thunderstorms over Kolkata during STORM pilot phase 2006–2008. Nat. Hazards, 56, 681–698, https://doi.org/10.1007/s11069-010-9582-x.
Wang, Y., Y. Yang, and S. Jin, 2018: Evaluation of lightning forecasting based on one lightning parameterization scheme and two diagnostic methods. Atmosphere, 9, 99, https://doi.org/10.3390/atmos9030099.
Wilks, D. S., Ed., 2011: Statistical forecasting. Statistical Methods in the Atmospheric Sciences, 3rd ed. Elsevier, 215–300.
Williams, E. R., 1989: The tripole structure of thunderstorms. J. Geophys. Res., 94, 13 151–13 167, https://doi.org/10.1029/JD094iD11p13151.
Wong, J., M. C. Barth, and D. Noone, 2013: Evaluating a lightning parameterization based on cloud-top height for mesoscale numerical model simulations. Geosci. Model Dev., 6, 429–443, https://doi.org/10.5194/gmd-6-429-2013.
Yair, Y., B. Lynn, C. Price, V. Kotroni, K. Lagouvardos, E. Morin, A. Mugnai, and M. Del Carmen Llasat, 2010: Predicting the potential for lightning activity in Mediterranean storms based on the Weather Research and Forecasting (WRF) model dynamic and microphysical fields. J. Geophys. Res., 115, D04205, https://doi.org/10.1029/2008JD010868.
