Lightning Prediction in the Tehran Region Using the WRF Model With Multiple Physical Parameterizations and an Ensemble Approach

Abstract

This study aims to predict the lightning (thunderstorm) potential in the Tehran region using data from meteorological synoptic stations and the Earth Networks Total Lightning Network (ENTLN). We employed the Weather Research and Forecasting (WRF) model to simulate lightning, focusing on the innermost domain, which spans between 34.5 and 36.5°N, and between 49.5 and 53.25°E. The initial and boundary conditions for the WRF model were derived from the Global Forecast System data set, with a spatial resolution of 0.5°. We analyzed 10 significant lightning events from 2015 to 2022, primarily focusing on the spring season. Lightning simulations were conducted using the WRF model with seven different physical schemes and the Lightning Potential Index. The results indicate that the WRF model, particularly when utilizing the Morrison, WDM6, and NSSL‐2 schemes, effectively simulates lightning regions. However, some underestimation was observed, notably in the southwestern portion of the study area. Comparisons with ENTLN data showed that configurations 1 and 2, using WSM6 and Goddard schemes, achieved the highest Probability of Detection, Critical Success Index, and higher Success Rates for actual lightning events. The uncertainty in lightning simulation and the model's sensitivity to physical parameterization highlight the importance of using an ensemble approach in the WRF model. By averaging outputs from different configurations in the ensemble, a more optimal result, closer to observed data, can be achieved. Based on these findings, we recommend the ensemble method as the most reliable approach for more accurate lightning simulations in future studies.

Introduction

Lightning from thunderstorms is a well-known and significant threat to human life. Some studies suggest that global annual fatalities due to lightning could exceed 20,000 (e.g., Holle, 2016). In addition to the loss of life, lightning also causes substantial damage in various industries, including agriculture—resulting in farm animal fatalities—and in the power generation and transmission sectors (Holle et al., 2005; Zhang et al., 2011). Given its potential for widespread impact, providing accurate and timely lightning forecasts is essential for mitigating these risks and supporting national economic stability and development (Guan et al., 2020).

Numerical weather prediction (NWP) models employ two primary approaches for lightning forecasting. The first is based on cloud electrification physics, incorporating prognostic equations for hydrometeor charge density to predict total cloud charge and electric field evolution (Fierro et al., 2013). The second approach utilizes dynamic, thermodynamic, and microphysical parameters within NWP models to identify lightning-related activity (Gharaylou et al., 2019; Huang et al., 2015; Saleh et al., 2023; Wang et al., 2010; Yair et al., 2010). These methods complement each other, enhancing the accuracy and reliability of lightning predictions.

Several physics-based tools have been developed to improve lightning forecasting. McCaul et al. (2009) introduced the Lightning Forecasting Algorithm (LFA), which transforms selected proxy fields from convective-allowing models into time-dependent, two-dimensional lightning density fields. Key indicators used in the LFA include upward graupel flux (GFX) and total vertical ice integral (VII). Subsequent assessments of LFA's sensitivity to microphysical schemes and boundary layer configurations found varied performance across different ensemble members and geographic regions (McCaul et al., 2020; Prasad et al., 2024). These studies emphasize the importance of optimizing forecasting techniques for improved reliability.

In addition to diagnostic tools like the LFA, explicit lightning prediction schemes have also been evaluated. Dafis et al. (2018) assessed a computationally efficient method for predicting lightning activity using simulated flash origin density (FOD) fields. The simulated lightning fields showed good agreement with observed data, although predictions of lightning activity over the sea were generally less accurate. The study found that lightning events over the sea near Greece, which primarily occur during the colder months, were poorly predicted. This indicates that seasonal variations significantly influence the accuracy of lightning forecasts. Furthermore, lightning forecasting using the Weather Research and Forecasting (WRF) model coupled with electrification and discharge schemes (ELEC package) tends to perform better during warmer months, highlighting the seasonal variation in forecasting accuracy. Meanwhile, Rabbani et al. (2022) demonstrated the effectiveness of combining diagnostic tools and explicit electric field simulations to improve prediction reliability. They used the Lightning Potential Index (LPI), which incorporates graupel and local ice content, alongside explicit electric field forecasts generated by the WRF model incorporating the ELEC package, to analyze five lightning events that occurred between 2 April 2019, and 20 May 2021. Their qualitative analysis revealed a strong agreement between observations and WRF model simulations, particularly in identifying the regions where lightning activity first developed.

The LPI-based forecasts also demonstrated excellent performance in predicting lightning events. These findings emphasize the effectiveness of combining diagnostic tools and explicit prediction schemes to enhance lightning forecasting. The LPI has also been widely used for lightning forecasting, with studies showing its advantages over alternatives such as the Electric POTential (POT) index (Gharaylou et al., 2019) and other thermodynamic-based metrics including LTI and CAPE × P (Saleh et al., 2023).

Several microphysics parameterization schemes have demonstrated strong performance in predicting lightning when used in models like the WRF model. Among them, double-moment schemes, such as the Morrison scheme, are particularly effective in forecasting lightning activity, especially in regions prone to severe convective storms (Babuňková Uhlířová et al., 2022; Mondal et al., 2024). By employing the ensemble method with the WRF model and its parameterization techniques, more accurate lightning predictions can be achieved (Kumar et al., 2022; Prasad et al., 2024). Ensemble approaches are particularly useful for addressing uncertainties in predictions and enhancing accuracy across varying conditions. In this regard, Prasad et al. (2024) compared the lightning forecast accuracy of the NCMRWF regional ensemble prediction system and its deterministic counterpart. They found that ensemble forecasts outperform deterministic ones in skill scores, error reduction, and event discrimination, justifying the computational effort for lightning predictions with high spatial variability.

Building on these findings, this research focuses on predicting lightning events using the WRF regional model with customized physical parameterization and validating the predictions through widely applied statistical indices. Due to the limited research conducted in this field within the study area, further investigation is essential. Moreover, ensemble-based lightning prediction studies have not yet been performed for this region. This study addresses these gaps to advance the understanding of lightning activity and refine prediction methods specifically for the Tehran region.

The unique climate of Tehran, characterized by its semi-arid conditions and mountainous terrain, plays a significant role in the region's lightning and thunderstorm activity. Seasonal variations, particularly during spring and early summer, bring increased atmospheric instability due to surface heating and moisture influx from surrounding areas, leading to heightened thunderstorm and lightning occurrences (Khorshiddoust et al., 2017). Accurately forecasting these events in Tehran is crucial for reducing weather-related risks and enhancing safety, and supporting sectors like agriculture, infrastructure, and energy, which are vulnerable to severe weather phenomena.

Data and Methodology

Data and Study Area

We used data from Iran's meteorological synoptic stations, METAR (METeorological Aerodrome Report) records, and the Earth Networks Total Lightning Network (ENTLN) to identify and select lightning events in the Tehran region, which is situated between 34.5 and 36.5°N and 49.5 and 53.25°E. This area corresponds to the innermost domain for lightning simulation in the WRF model, as depicted in Figure 1. The initial and boundary conditions for the WRF model were derived from the Global Forecast System (GFS) data, which has a spatial resolution of 0.5°. The GFS data provides a general yet relatively accurate representation of atmospheric conditions, making it suitable for use as both initial and boundary conditions for the regional WRF model. The 0.5° resolution corresponds to a distance of approximately 55 km and is updated every 6 hr. These data are crucial for simulating atmospheric processes at various scales, including those associated with the formation and development of lightning.

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The meteorological station data includes measurements of key atmospheric variables such as temperature, humidity, air pressure, wind speed, direction, and current weather data. These stations include Abali, Chitgar, Damavand, Doshantapeh, Firuzkuh, Imam Khomeini International Airport, Lavasan, Shahriar, Geophysics, Mehrabad Airport, Shemiran, and Varamin. These variables have been continuously recorded at hourly or three-hourly intervals, and were used to assess the prevailing weather conditions during lightning events. Given the sensitivity of lightning prediction to the physical parameterization employed (McCaul et al., 2020), we also analyzed an ensemble of WRF simulations. The validation of the model outputs was conducted using lightning data from the ENTLN.

ENTLN, a global lightning detection system, uses over 1,600 sensors to detect both in-cloud and cloud-to-ground lightning. It uses GPS-based time-of-arrival detection and advanced algorithms to classify lightning. With ongoing enhancements, the ENTLN offers timing, location, and peak current data with high accuracy: classification accuracy exceeding 95%, detection efficiency up to 95%, stroke classification accuracy of 94% for natural lightning, a median location error of 215m, and a median peak current estimation error of 15%. This data set includes the time and exact locations of recorded lightning events, which enabled us to pinpoint the locations of lightning strikes and compare them with local meteorological data.

Methodology

Lightning Event Selection in the Tehran Region

An analysis of the current weather data provided by the Meteorological Organization of Iran indicates that thunderstorm or lightning occurrences were documented on 1,451 days during spring and summer from 2015 to 2022. These observations include the following synoptic codes: 13 (lightning visible, no thunder heard), 17 (thunderstorm, but no precipitation at the time of the observation), 18 (squalls at or within the sight of the station), 29 (thunderstorm with or without precipitation), 91–94 (thunderstorm during the preceding hour but not at the time of the observation), and 95–99 (thunderstorm at the time of the observation). We selected significant lightning events from these records during 2015–2022, focusing specifically on the spring season. This choice was made due to the substantial differences in the dynamical and thermodynamical mechanisms driving convective clouds and atmospheric systems across different seasons. Spring, characterized by strong surface heating and associated atmospheric instability, creates an ideal environment for the development of thunderstorms and intense lightning activity. These seasonal differences increase the likelihood of stronger and more severe lightning events compared to other times of the year.

Using ENTLN data, we identified 10 major lightning events in the Tehran region. These events, listed in Table 1, occurred on 29 April 2017; 5 May 2017; 22 May 2018; 1 April 2019; 6 April 2019; 10 May 2019; 9 April 2020; 23 April 2020; 25 May 2021; and 1 May 2022. These events are referred to as Cases 1 through 10, respectively. The highest number of lightning strikes occurred on 25 May 2021, with 6,459 strikes, reflecting significant lightning activity on that day. The second-highest number was recorded on 1 April 2019, with 5515 strikes. The fewest strikes were recorded on 29 April 2017, with just 929 strikes.

Table 1 Total Number of Lightning Strikes Recorded by ENTLN and Peak Activity Hours for the Innermost Domain of the WRF Model and the K-Index (KI) for 10 Thunderstorm Events in Tehran Based on the Analysis of the Wyoming Skew-T at 12:00 UTC

Events	Case study	Peak lightning activity period	Total number of lightning strikes in a day	KI
Case 1	29 April 2017	12–24 UTC	929	34
Case 2	5 May 2017	10–15 UTC	1,959	33.9
Case 3	22 May 2018	9–15 UTC	1,344	32.3
Case 4	1 April 2019	14–22 UTC	5,515	35.9
Case 5	6 April 2019	11–17 UTC	2,473	28.9
Case 6	10 May 2019	8–22 UTC	2,590	26.7
Case 7	9 April 2020	18–24 UTC	1,370	20
Case 8	23 April 2020	9–21 UTC	1,415	35.9
Case 9	25 May 2021	12–24 UTC	6,459	30.5
Case 10	1 May 2022	11–16 UTC	1,517	30.1

The longest peak activity duration occurred on 10 May 2019, with a sustained period of 14 hr, from 0800 UTC to 2200 UTC. In contrast, the shortest peak durations, lasting 5 hr, were observed on 1 May 2022, and 5 May 2017. Table 1 also reveals that days with higher lightning counts typically had longer peak activity periods (12 hr or more), indicating that sustained lightning activity on these days contributed to the overall higher number of lightning strikes.

In our study, the type of thunderstorms for all case studies was determined using METAR records and satellite water vapor images, and all case studies were classified as frontal thunderstorms. Frontal thunderstorms are typically characterized by advancing cold fronts, resulting in organized convection along frontal boundaries due to dynamic and thermodynamic interactions (Wallace & Hobbs, 2006).

Saleh et al. (2023) demonstrated that LPI performs better in predicting lightning for thunderstorms with relatively strong convection, as determined by stability indices like the K-index. Considering this, we analyzed whether the intensity of convection impacts the accuracy of lightning prediction within the frontal thunderstorm cases studied.

Table 1 also presents the K-Index (KI) for selected study cases. KI is an effective measure for assessing the likelihood and intensity of convection. It is calculated based on temperatures at the 850, 700, and 500 hPa levels, as well as dew points at the 850 and 700 hPa levels. Specifically, the temperature difference between the 850 and 500 hPa levels, the dew point at 850 hPa, and the difference between temperature and dew point at 700 hPa are often used to indicate instability, moisture levels, and saturation (George, 1960). Higher KI values, resulting from larger temperature differences between 850 and 500 hPa or greater moisture at 700 hPa, signify a greater potential for convection (Sturtevant, 1995). Thunderstorm probabilities vary with KI, ranging from very low when KI is below 20 to a high likelihood of widespread activity when KI exceeds 35 (Sturtevant, 1995). The examination of the KI values reveals a moderately convective environment at 12:00 UTC for Cases 1–10, while Cases 4 and 8 exhibit a severely convective environment (as shown in Table 1).

Simulation Domain and WRF Configuration

Figure 1 illustrates the simulation domain, consisting of three nested domains with spatial resolutions of 27, 9, and 3 km. This multi-domain setup allows for a more refined study of the region and enhances prediction accuracy at finer scales. Given the crucial role of microphysical schemes in lightning prediction, this study employs seven configurations with different microphysical schemes, as detailed in Table 2. These configurations incorporate various approaches to simulating cloud microphysical processes, which are crucial for accurately modeling lightning formation and distribution.

Table 2 Configuration Used in the WRF Model Execution

	1	WSM6 (Hong & Lim, 2006)
Microphysical schemes	2	Goddard (Tao et al., 2016)
3	Thompson (Thompson et al., 2008)
4	Milbrandt–Yau (Milbrandt & Yau, 2005)
5	Morrison (Morrison et al., 2009)
6	WDM6 (Lim & Hong, 2010)
7	NSSL-2 (Mansell et al., 2010)
Longwave radiation scheme		RRTM (Mlawer et al., 1997)
Shortwave radiation scheme		Dudhia (Dudhia, 1989)
Surface layer scheme		Revised MM5 (Jiménez et al., 2012)
Surface layer scheme		Unified Noah (Tewari et al., 2004)
Boundary-layer scheme		YSU (Hong et al., 2006)
Convective scheme		Kain–Fritsch (Kain, 2004)

For these simulations, the primary focus was on two-moment microphysical schemes (Milbrandt–Yau, Morrison, WDM6, NSSL-2). Previous studies (e.g., Babuňková Uhlířová et al., 2022; Gharaylou et al., 2020; Mondal et al., 2023, 2024; Vani et al., 2022) suggest that two-moment schemes enhance the prediction of the LPI. These schemes offer a more detailed representation of cloud processes and lightning distribution, as they predict both the size and number of particles independently, leading to a more accurate depiction of particle size distributions. Consequently, two-moment schemes generally outperform single-moment schemes in predicting atmospheric phenomena like precipitation and lightning.

In contrast, single-moment schemes predict only one variable, typically the mixing ratio, which, while simpler, does not capture the complexity of cloud processes as effectively. As a result, single-moment schemes are less suitable for simulating detailed atmospheric dynamics, particularly when accurate predictions of lightning, heavy precipitation, and cloud particle distributions are essential. Additional microphysical schemes were selected based on previous lightning simulation studies conducted in the region (Gharaylou et al., 2020; Saleh et al., 2023).

Lightning Forecasting and Probabilistic Predictions

The Ensemble Prediction System (EPS) is a weather forecasting technique that involves running multiple simulations with small variations in initial conditions or using different models known as single and multi-model approaches (Bowler et al., 2008; Prasad et al., 2024; Tracton & Kalnay, 1993). In ensemble prediction systems (EPSs) based on a single model, the probability distribution function reflects forecast uncertainty, which depends on the synoptic situation. In contrast, multi-model ensembles derive their characteristics from the unique attributes of individual models (Prasad et al., 2024).

The primary goal of EPS is to quantify uncertainties in weather predictions, as numerical weather models are highly sensitive to initial conditions, where even small changes can lead to significantly different outcomes. Over time, the accuracy of these predictions can degrade substantially (Lorenz, 1963). Because EPS captures these uncertainties, it has become an essential tool in meteorological forecasting. Leith (1974) demonstrated that ensemble prediction could notably improve forecasting accuracy, particularly when ensemble members are properly designed to reflect uncertainties in the system's initial states. Leith's findings showed that ensemble forecasting could outperform single deterministic predictions because slight variations in initial conditions often produce divergent results. This underscores the critical importance of understanding and accounting for uncertainties in weather predictions, as they can heavily influence the model's outputs.

Probabilistic forecasting, which is grounded in ensemble forecasting principles, is especially valuable because it provides a distribution of possible outcomes rather than relying on a single deterministic forecast. This approach enables a more accurate estimation of the likelihood of various scenarios, which is crucial for modeling complex atmospheric phenomena such as thunderstorms and lightning due to the atmosphere's inherently nonlinear and chaotic nature.

In lightning ensemble forecasting, multiple prediction models, including the WRF model, are used to simulate weather conditions, with indices like the LPI computed to assess lightning probabilities. These indices are then applied in ensemble simulations to provide a comprehensive view of the likelihood of lightning occurrence. This study utilizes a single-model ensemble approach with the WRF model, employing the LPI to evaluate lightning likelihoods. It is important to mention that the LPI is a direct output of the WRF model.

LPI: A Tool for Predicting Lightning Events

LPI is a key parameter for lightning prediction and is also useful for improving forecasts of convective storms and heavy precipitation (Yair et al., 2010). This index quantifies the potential for charge generation and separation within a cloud and it is expressed by the following equation: 1 $$\text{LPI}=1/V\iiint \varepsilon {w}^{2}dx\,dy\,dz$$ where V represents the volume of air in the layer between 0°C and −20°C, and is the vertical wind component (w) in m s⁻¹. The integral is computed over the cloud volume, from the freezing level (measured in kilometers above the ground) to the height of the −20°C isotherm. ɛ is a dimensionless quantity, ranging from 0 to 1, and is defined as: 2 $$\varepsilon =\sqrt{{2Q}_{i}{Q}_{l}}/\left({Q}_{i}+{Q}_{l}\right)$$ where Q_l is the mass mixing ratio of liquid water, and Q_i is the mass mixing ratio of ice, both expressed in kg kg⁻¹. The ice mass mixing ratio, Q_i, is calculated as: 3 $${Q}_{i}={q}_{g}\,\left[\left(\sqrt{{q}_{s}{q}_{g}}/\left({q}_{s}{+q}_{g}\right)\right)+\left(\sqrt{{q}_{i}{q}_{g}}/\left({q}_{i}{+q}_{g}\right)\right)\right]$$ where q_g, q_s, and q_i represent the mass mixing ratios for graupel, snow, and ice in the cloud, respectively, in units of kg kg⁻¹.

Validation of Lightning Simulations

To assess the performance of ensemble and probabilistic lightning forecasts, several evaluation metrics are employed, including Probability of Detection (POD), Critical Success Index (CSI), Success Rate (SR), and Bias. These metrics are defined as follows:

• POD (Probability of Detection): This index measures the model's ability to correctly identify actual events, such as lightning. It is calculated as the ratio of correctly predicted events to the total number of real events: 4 $$\text{POD}=\frac{H}{H+M}$$ where H represents the number of times the model correctly predicted lightning, and M is the number of instances where the model failed to predict lightning, even though it actually occurred. The closer this index is to 1, the better the model's ability to detect lightning events.

• CSI (Critical Success Index): This index evaluates the model's ability to predict lightning events while considering both false positives and false negatives. CSI values range from 0 to 1, with 1 indicating a perfect forecast: 5 $$\text{CSI}=\frac{H}{H+M+F}$$ where F is the number of times the model predicted lightning but it did not actually occur (false positive). The CSI provides a comprehensive measure of the model's accuracy in forecasting actual events.

• SR (Success Rate): This index represents the ratio of correct lightning predictions to the total number of predictions (both correct and incorrect): 6 $$\text{SR}=\frac{H}{H+F}$$ The closer this index is to 1, the better the model is at accurately predicting lightning events.

• Bias: This index measures the model's tendency to overestimate or underestimate lightning occurrences. It is calculated as:

7 $$\text{bias}=\frac{H+F}{H+M}$$

Overall, the POD index evaluates the model's ability to accurately identify all true lightning events. The CSI provides an overall measure of forecast accuracy by considering both false positives and false negatives. The SR focuses on the ratio of successful lightning predictions, helping to minimize false errors. The bias index identifies whether the model tends to overpredict or underpredict lightning events relative to actual occurrences. Each of these indices is essential for assessing the performance of lightning simulations with the WRF model, helping to highlight the model's strengths and areas for improvement. For example, a model with a high POD but also a high bias may detect many lightning events but overpredict the number of occurrences, necessitating adjustments to improve prediction accuracy.

Furthermore, to quantitatively analyze the results, the simulated LPI from the innermost domain of WRF simulations using seven microphysics schemes is compared with the ENTLN data across all case studies. This analysis utilizes a Taylor diagram (Taylor, 2001). A Taylor diagram is a graphical tool used to summarize and compare the performance of different models or configurations by illustrating their correlation, standard deviation, and root mean square error (RMSE) in relation to observed data.

Results

Comparison of Simulated Lightning Events With ENTLN Data for 10 Case Studies

To evaluate the performance of the WRF model across seven different microphysics configurations (Table 2), we compare the model's predictions with lightning data from the ENTLN for the 10 case studies listed in Table 1. ENTLN primarily tracks high-energy lightning strikes, so a threshold of 5 J kg⁻¹ was used to align the LPI output from the WRF model with the ENTLN data. This threshold, as recommended by Dementyeva et al. (2015) and Babuňková Uhlířová et al. (2022), serves as a criterion for various parameterization schemes to predict the occurrence of lightning flashes. It optimizes prediction accuracy by focusing on stronger lightning events and excluding weaker, less significant strikes. The actual lightning event locations from ENTLN are represented as black dots on the maps for each case study, while the simulated lightning areas from the WRF model, for each microphysics configuration, are shown in colored regions indicating the potential for lightning.

Case Study Summaries:

• 29 April 2017 (Figure  2): The analysis of the ENTLN data shows that lightning mainly occurred in the western and central parts of the study area, suggesting strong convective activity in these regions. Among the WRF configurations, Configurations 5, 6, and 7 provided better agreement with the observed ENTLN data, indicating that more complex two-component microphysics schemes performed better in simulating convection-driven lightning.

• 5 May 2017 (Figure  3): The analysis of the ENTLN data indicates a lightning cluster along the northeastern-southwestern axis of the region. The WRF simulations, however, failed to reproduce the spatial distribution accurately, with the predicted areas being smaller than observed.

• 22 May 2018 (Figure  4): The analysis of the ENTLN data shows extensive lightning activity, particularly in the central regions of Tehran and Alborz provinces. However, the WRF model, across all configurations, predicted smaller areas of lightning and failed to capture some of the active regions observed in the ENTLN data.

• 1 April 2019 (Figure  5): This event, the second strongest among the 10 case studies, shows a large cluster of lightning in the elevated regions of Tehran and Alborz provinces. The simulated lightning matched well with the ENTLN data, with Configurations 4 and 7 performing particularly well in capturing the southwestern distribution of lightning.

• 6 April 2019 (Figure  6): The analysis of the ENTLN data reveals high lightning density in the western and central areas. Simulations in Configurations 2, 3, and 5 showed better agreement with the observed data in the central and northwestern regions.

• 10 May 2019 (Figure  7): Lightning streaks were observed along the northeastern-southwestern axis. While most configurations captured the general lightning areas, Configurations 1 and 6 overpredicted lightning in the central parts of the region.

• 9 April 2020 (Figure  8): The analysis of the ENTLN data indicated a concentration of lightning in the western and southwestern areas. The simulated lightning in all configurations was weaker in the southwest compared to other regions.

• 23 April 2020 (Figure  9): Lightning was observed along two axes from the northwest to the southeast. Configurations 1, 2, and 6 performed better in capturing lightning in the southern regions of the study area.

• 25 May 2021 (Figure  10): As the strongest lightning event among the 10 case studies, the analysis of ENTLN data revealed a high density of lightning along a northwest-southeast axis, particularly in the western part of the study area. Configurations 1, 2, 3, and 7 produced patterns similar to the ENTLN data, though the simulated lightning was slightly shifted westward.

• 1 May 2022 (Figure  11): The analysis of the ENTLN data indicates concentrated lightning in the western part of the region. All seven simulations predicted the lightning extent well, with strong alignment between model predictions and observed data.

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Overall Comparison Results of Simulated Lightning Events

Overall, the WRF model, using different microphysics configurations, was successful in simulating the spatial distribution of lightning for the various case studies. However, the extent and concentration of lightning were sometimes over- or under-predicted. The results reveal distinct trends across the case studies. Lightning activity was frequently concentrated in elevated regions, such as Tehran and Alborz provinces, emphasizing the role of topography in lightning activity (Khorshiddoust et al., 2017). Configurations utilizing the Morrison, WDM6, and NSSL-2 schemes (configurations 5, 6, and 7) demonstrated better performance, consistent with the observations of Chen and Liu (2024) and Mondal et al. (2023). Chen and Liu (2024) highlighted the effectiveness of the Morrison and WDM6 schemes in the WRF model for simulating convective precipitation, potentially related to lightning prediction. Similarly, Mondal et al. (2023) emphasized the notable efficiency of the NSSL-2 scheme in detecting lightning events. The results also indicate an underestimation of weaker convection, as observed on 22 May 2018, and 9 April 2020, similar to findings reported by Saleh et al. (2023) in the same study region.

Validation of Simulated Lightning Events

To validate the results of lightning simulations using the WRF model for each of the 10 study days across all 7 configurations and the ensemble, several performance indices were employed: POD, CSI, SR, and Bias. Each configuration was evaluated on a day-by-day basis at 10-min intervals, with a final overall summary of the model's performance for each configuration.

For assessing whether lightning events were predicted or missed in the study area (the innermost lightning simulation domain of the WRF model), and excluding the initial spin-up time (which is considered to be 12 hr), the LPI in the study area was averaged every 10 min. A lightning event was predicted if the LPI exceeded 5 J kg⁻¹; otherwise, it was considered a non-event. Using this threshold to predict or classify lightning events over a 10-min period, the simulation results were validated against the ENTLN data. The results of this validation are presented in Figure 12 and Table 3.

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Table 3 Prediction Skill Scores for 7 Configurations in Lightning Simulations Using the WRF Model Across 10 Case Studies

Case study	Configuration	H	F	M	N	POD	SR	bias	CSI	Case study	H	F	M	N	POD	SR	Bias	CSI
Case 1	Config.1	27	3	23	92	0.54	0.9	0.6	0.51	Case 6	66	9	16	54	0.8	0.88	0.91	0.72
Config.2	39	4	11	91	0.78	0.91	0.86	0.72	63	24	19	39	0.76	0.72	1.06	0.59
Config.3	16	3	34	92	0.32	0.84	0.38	0.3	62	36	20	27	0.75	0.63	1.19	0.52
Config.4	12	3	38	92	0.24	0.8	0.3	0.23	66	36	16	27	0.8	0.64	1.24	0.56
Config.5	18	4	32	91	0.82	0.82	0.44	0.33	66	33	16	30	0.8	0.66	1.2	0.57
Config.6	23	1	27	94	0.96	0.96	0.48	0.45	66	13	16	50	0.8	0.83	0.96	0.69
Config.7	29	3	21	92	0.91	0.91	0.64	0.55	66	45	16	18	0.8	0.59	1.35	0.52
Ensemble	14	2	36	93	0.32	0.86	0.26	0.27	62	18	20	45	0.75	0.77	0.97	0.62
Case 2	Config.1	42	18	48	37	0.47	0.7	0.67	0.39	Case 7	52	22	19	52	0.73	0.7	1.04	0.56
Config.2	43	21	47	34	0.48	0.67	0.71	0.39	51	30	20	44	0.72	0.63	1.14	0.5
Config.3	37	15	53	40	0.41	0.71	0.58	0.35	30	34	41	40	0.42	0.47	0.9	0.29
Config.4	36	12	54	43	0.4	0.75	0.53	0.35	53	43	18	31	0.75	0.55	1.35	0.46
Config.5	38	15	52	40	0.42	0.72	0.59	0.36	32	31	39	43	0.45	0.51	0.89	0.31
Config.6	42	22	48	33	0.47	0.66	0.71	0.38	45	26	26	48	0.63	0.63	1	0.46
Config.7	40	15	50	40	0.44	0.72	0.61	0.38	46	52	25	22	0.65	0.47	1.38	0.37
Ensemble	39	15	51	40	0.43	0.72	0.6	0.37	38	27	33	47	0.54	0.58	0.92	0.39
Case 3	Config.1	34	3	12	96	0.74	0.92	0.8	0.69	Case 8	55	47	6	37	0.9	0.54	1.67	0.51
Config.2	35	3	11	96	0.76	0.92	0.83	0.71	48	48	5	36	0.92	0.54	1.7	0.51
Config.3	38	7	8	92	0.83	0.84	0.98	0.72	37	37	11	47	0.82	0.57	1.43	0.51
Config.4	31	0	15	99	0.67	1	0.67	0.67	47	47	11	37	0.82	0.52	1.59	0.46
Config.5	34	2	12	97	0.74	0.94	0.78	0.71	41	41	12	43	0.8	0.54	1.48	0.48
Config.6	28	1	18	98	0.61	0.97	0.63	0.6	41	41	6	43	0.9	0.57	1.57	0.54
Config.7	31	3	15	96	0.67	0.91	0.74	0.63	65	65	3	19	0.95	0.47	2.02	0.46
Ensemble	32	1	14	98	0.7	0.97	0.72	0.68	41	41	10	43	0.84	0.55	1.51	0.5
Case 4	Config.1	87	35	7	16	0.93	0.71	1.3	0.67	Case 9	80	3	36	26	0.69	0.96	0.72	0.67
Config.2	65	37	29	14	0.69	0.64	1.09	0.5	88	2	28	27	0.76	0.98	0.78	0.75
Config.3	85	40	9	11	0.9	0.68	1.33	0.63	84	1	32	28	0.72	0.99	0.73	0.72
Config.4	90	50	4	1	0.96	0.64	1.49	0.63	69	0	47	29	0.59	1	0.59	0.59
Config.5	72	36	22	15	0.77	0.67	1.15	0.55	76	2	40	27	0.66	0.97	0.67	0.64
Config.6	78	36	16	15	0.83	0.68	1.21	0.6	73	5	43	24	0.63	0.94	0.67	0.6
Config.7	91	51	3	0	0.97	0.64	1.51	0.63	76	3	40	26	0.66	0.96	0.68	0.64
Ensemble	39	39	16	12	0.83	0.67	1.24	0.59	74	1	42	28	0.64	0.99	0.65	0.63
Case 5	Config.1	41	28	2	74	0.95	0.59	1.6	0.58	Case 10	43	31	2	69	0.96	0.58	1.64	0.57
Config.2	41	26	2	76	0.95	0.61	1.56	0.59	43	48	2	52	0.96	0.47	2.02	0.46
Config.3	40	17	3	85	0.93	0.7	1.33	0.67	38	56	7	44	0.84	0.4	2.08	0.38
Config.4	41	56	2	46	0.95	0.42	2.26	0.41	34	56	11	44	0.76	0.38	2	0.34
Config.5	40	18	3	84	0.93	0.69	1.35	0.66	40	53	5	47	0.89	0.43	2.06	0.41
Config.6	41	35	2	67	0.95	0.54	1.77	0.53	41	46	4	54	0.91	0.47	1.93	0.45
Config.7	42	68	1	34	0.98	0.38	2.56	0.38	43	45	2	55	0.96	0.49	1.96	0.48
Ensemble	41	15	2	87	0.95	0.73	1.3	0.71	38	51	7	49	0.84	0.43	1.98	0.4

In this table:

• H represents the number of times the model correctly predicted lightning (true positives).

• M represents the number of times the model failed to predict lightning, but it actually occurred (false negatives).

• F represents the number of times the model predicted lightning, but it did not occur (false positives).

• N represents the number of times lightning did not occur, and the model did not predict it either (true negatives).

The terms “positive” and “negative” refer to actual lightning occurrences or non-occurrences, respectively.

$1:$

Case

29 April 2017 (Figure 12a and Table 3)

The best performance for detecting lightning events in this case study is observed in configuration 2, followed by configurations 7 and 1. Configuration 4 shows the lowest POD. Additionally, configurations 6, 7, 2, and 1 demonstrate higher SR, indicating fewer false positives. In all 7 configurations, the model predicted fewer lightning events than actually occurred on this day. Configuration 2 has the bias value closest to 1. Furthermore, configurations 2, 7, and 1 achieve the highest CSI, suggesting fewer misdiagnoses and false detections.

$2:$

Case

5 May 2017 (Figure 12b and Table 3)

In this case, detection performance is generally low across all configurations, with the highest POD values from configuration 2 and the lowest from configuration 4. The range of changes in POD is narrow, from 0.48 to 0.4. Configuration 4, with the highest SR, has the fewest false positives. All configurations predicted fewer lightning events than actually occurred. Configurations 2 and 6 have the bias values closest to 1. All configurations show similar CSI values, but configurations 1 and 2 stand out with the highest CSI, indicating fewer misdiagnoses and false detections.

$3:$

Case

22 May 2018 (Figure 12c and Table 3)

Configuration 3 achieves the highest POD (0.83), demonstrating good performance in identifying real lightning events. Configurations 2 and 5 follow closely with values of 0.76 and 0.74, respectively. In contrast, configuration 6 has the lowest POD (0.61), indicating weaker performance. Configuration 4 shows the best SR, meaning all of its positive predictions were correct. Configuration 3, with a bias value of 0.98, is closest to an ideal prediction, as the number of positive predictions is nearly equal to the actual positive events. In all configurations, the model predicted fewer lightning events than actually occurred. Configuration 3 has the highest CSI, followed by configurations 2 and 5.

$4:$

Case

1 April 2019 (Figure 12d and Table 3)

Configurations 7 and 4 show the highest POD, indicating a better ability to identify actual lightning events. Configuration 2, with a POD of 0.69, has the lowest detection probability, suggesting poorer performance. All configurations show similar SR values, with configuration 1 having the highest SR (0.71). In this case, all configurations show positive bias, meaning they over-predicted lightning events. Configuration 2, with a bias of 1.09, is closest to ideal, while configuration 7 has the highest positive bias (1.51). Configuration 1, with an SR of 0.67, has the highest CSI, indicating good performance in accurately predicting lightning events.

$5:$

Case

6 April 2019 (Figure 12e and Table 3)

Configuration 7, with a POD of 0.98, demonstrates the best performance in detecting real lightning events. The remaining configurations show similar POD values. The ensemble shows an SR of 0.73, followed by configuration 3 with an SR of 0.7, indicating high success in identifying actual lightning events with fewer false positives. However, configuration 7 has the lowest SR (0.38), showing a high number of false positives. Configuration 7 also has the highest bias value (2.56), suggesting that it over-predicts lightning events. The ensemble and configuration 5, with biases of 1.3 and 1.35, respectively, exhibit lower biases and have reached a better balance between predictions and actual events. The ensemble and configurations 3 and 5 have the highest CSI, showing better overall performance in predicting lightning events. Configuration 7, with a CSI of 0.38, shows the lowest CSI, highlighting its relative weakness in accurate prediction compared to other configurations. The ensemble and configurations 3 and 5 perform the best in this case study based on POD, SR, bias, and CSI. Although configuration 7 has the highest POD, it requires improvement due to its higher bias and false detections.

$6:$

Case

10 May 2019 (Figure 12f and Table 3)

All configurations have similar POD values greater than 0.75, showing a good ability to identify real lightning events. Configurations 1 and 6 have the highest SR, indicating better alignment between predictions and actual lightning occurrences. Configurations 3, 4, and 7 show lower SR values compared to the others. Configuration 7, with a bias of 1.35, shows the highest positive bias, predicting more events than actually occurred. In contrast, configurations 6 and 1, with biases of 0.96 and 0.91, respectively, show more balanced biases. In terms of CSI, configurations 1 and 6 show the highest values (0.72 and 0.69, respectively), indicating high accuracy in predicting lightning events, while configurations 3 and 7, with CSI values of 0.52, have lower prediction accuracy.

$7:$

Case

9 April 2020 (Figure 12g and Table 3)

Configurations 1, 2, 4, 6, and 7 show high detection probabilities, indicating a good ability to identify actual lightning events. Configurations 3 and 5 have lower POD values (0.42 and 0.45), suggesting poorer detection. Configurations 1, 2, and 6 have the best SR, while configurations 3 and 7 show the lowest SR (0.47). Configurations 4 and 7 have the highest positive bias, suggesting an overestimation of lightning events, which may lead to more false detections. Configuration 6, with a bias of 1.0, is the most balanced between predictions and actual lightning events. Overall, configurations 1 and 2 perform best in terms of CSI, while configurations 3 and 5 show weaker performance in this regard.

In this case study, configurations 1 and 2 outperform the others across most indices. These configurations show good detection ability (POD) with higher accuracy (CSI) and maintain a relatively balanced ratio between true positives and false negatives. Configurations 3 and 5 exhibit the weakest performance. Although configurations 4 and 7 have high detection probabilities, they produce a significant number of false detections due to a strong positive bias, leading to overprediction of lightning events.

$8:$

Case

23 April 2020 (Figure 12h and Table 3)

Configuration 7 has the highest POD, showing a strong ability to correctly predict actual lightning events. The other configurations also exhibit a good POD (above 0.80). Configuration 3, with an SR of 0.57, has the highest SR, indicating it performs well in reducing false positive predictions. Configuration 7, with an SR of 0.47, has the lowest SR. The ensemble has an SR of 0.55, and configuration 3, with an SR of 0.57, shows the best performance in reducing false positives. Configuration 7, with a bias of 2.02, has the highest bias, indicating over-prediction. Configurations 3, 5, and the ensemble have lower bias values, indicating a better balance between predicted and actual lightning events. Configuration 6 has the highest CSI, reflecting better accuracy in predicting lightning events, while configurations 4 and 7 have the lowest CSI values.

$9:$

Case

25 May 2021 (Figure 12i and Table 3)

Configuration 2 has the highest POD (0.76), indicating it is the most accurate in identifying real lightning events. Configuration 4 has the lowest POD (0.59), missing some actual lightning events. The SR is highest for configurations 3, 4, and the ensemble, showing good accuracy in reducing false positives. Configuration 2 has the best bias value (0.78) and the highest CSI value (0.75), indicating a good balance between predicting lightning events and reducing false positives.

$10:$

Case

1 May 2022 (Figure 12j and Table 3)

All configurations have acceptable POD values, with configurations 1, 2, and 7 showing the highest POD (0.96), while configuration 4 has the lowest (0.76). The SR ranges from 0.38 to 0.58, indicating moderate to lower accuracy. Configuration 1 has the lowest bias (1.64), suggesting a better prediction balance. Configuration 1 also has the highest CSI, reflecting better accuracy in predicting lightning events.

Overall Validation Results of Simulated Lightning Events

Overall, configurations 1 and 2 demonstrated higher POD values than the other configurations, indicating a better ability to detect actual lightning events. However, this trend was not consistent across all study days, as certain cases (e.g., case study 4) presented exceptions. The SR index, which reflects the ability of models to detect lightning events accurately while minimizing false positives, showed that configurations 1 and 4 performed well in reducing false positives. This outcome is consistent with observations by Mondal et al. (2023), who highlighted the ability of advanced microphysics schemes to reduce false positives through improved hydrometeor representation.

Bias varied considerably across different case studies and configurations. In four cases, configurations overestimated the occurrence of lightning events, while in four other cases, they underestimated them. Configuration 2 consistently exhibited lower bias compared to the others, suggesting that it strikes a better balance between predicted and actual lightning events.

The CSI, which emphasizes the model's ability to predict significant and rare events (excluding true negatives), indicated that configurations 1 and 2 performed better across the majority of case studies.

Overall, configurations 1 and 2, which employed the WSM6 and Goddard microphysics schemes respectively, were the top performers in terms of POD, CSI, and SR, making them the most accurate and reliable configurations for simulating lightning events. Mohan et al. (2024) demonstrated that the WSM6 and Goddard schemes forecasted more intense updraft velocities in the upper troposphere, reflecting the simulation of a stronger convective system. As noted by Yair et al. (2010), updrafts are incorporated into the calculation of the LPI, primarily contributing in the production of hydrometeors. These, along with liquid water content, are critical factors in the generation of lightning flashes, as highlighted by Saunders et al. (1991). Some configurations, while exhibiting the highest detection probabilities, still need improvement due to their high bias and frequent false positives. The ensemble approach also provided a valuable average performance, combining the strengths of all configurations, as noted by Prasad et al. (2024).

Performance Evaluation of Configurations Using Taylor Diagram Analysis

The Taylor diagram analysis reveals the performance of different configurations across the cases. In Case 1 (Figure 13a), the second configuration has the highest correlation (0.85) and lowest error, aligning best with observations. Case 2 (Figure 13b) shows similar correlation and RMSE for all configurations, with the fourth having the lowest standard deviation. In Case 3 (Figure 13c), the first and sixth configurations show the highest correlation, the fourth has the lowest standard deviation, and the first demonstrates the lowest RMSE. Case 4 (Figure 13d) indicates low correlation across all configurations, with configurations 1, 4, and 7 having the lowest RMSE, and configurations 4 and 7 showing the lowest standard deviation. For Case 5 (Figure 13e), configurations 3 and 5 exhibit the highest correlation, the sixth has the lowest RMSE, and the fourth has the lowest standard deviation. In Case 6 (Figure 13f), configurations 1 and 6 achieve both the highest correlation and the lowest RMSE, while the fourth maintains the lowest standard deviation. Case 7 (Figure 13g) highlights configurations 1 and 4 as having the highest correlation and lowest RMSE, with configuration 4 also displaying the lowest standard deviation. For Case 8 (Figure 13h), configuration 3 demonstrates the highest correlation and lowest RMSE, while the fourth shows the lowest standard deviation. Similarly, in Case 9 (Figure 13i), configuration 3 achieves the highest correlation and lowest RMSE, while configuration 4 again has the lowest standard deviation. Finally, in Case 10 (Figure 13j), configuration 1 shows the highest correlation and lowest RMSE, with configuration 4 continuing to demonstrate the lowest standard deviation. Overall, the optimal configuration cannot be definitively determined, as its performance varies across cases, making it highly dependent based on the criteria being emphasized.

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Conclusions

This study aimed to predict lightning events in the Tehran region using data from Iranian meteorological stations and the ENTLN data. The study area, which spans from 34.5°N to 36.5°N and from 49.5°E to 53.25°E, was selected as the innermost domain for the WRF model. The model's initial and boundary conditions were derived from the GFS data set, with a spatial resolution of 0.5°. The focus was on the spring season, characterized by intense surface heating and atmospheric instability, which provides favorable conditions for thunderstorm development and strong lightning activity. Ten thunderstorm events from April and May in recent years were selected for analysis.

Using the WRF model's physics, lightning occurrences were predicted based on the LPI as the primary indicator. Given the sensitivity of lightning prediction to microphysical schemes, various parameterizations were applied during the simulations. The results were evaluated by comparing the model's outputs with the ENTLN data to assess their accuracy and reliability.

The WRF model, with various microphysics configurations, successfully simulated the spatial distribution of lightning across the case studies, though it occasionally over- or under-predicted lightning extent and intensity. In most cases, the lightning area predictions were reasonably accurate, although some regions, particularly in the southwestern part of the study area, showed underprediction. Configurations 5, 6, and 7 (Morrison, WDM6, and NSSL-2) performed best, consistent with findings by Chen and Liu (2024) and Mondal et al. (2023), while weaker convection was underestimated, consistent with observations by Saleh et al. (2023). The results also demonstrated that the WRF model performed reasonably well in predicting strong lightning events, particularly when evaluated against the ENTLN data, which provided reliable measurements of actual occurrences. Notably, a strong correlation was observed between the total number of lightning strikes and the duration of peak activity, with the most intense lightning activity occurring during afternoon and evening hours.

Validation using the POD, SR, CSI, and bias indices revealed that configurations 1 and 2, using the WSM6 and Goddard microphysics schemes, performed the best in detecting actual lightning events, capturing the highest number of occurrences. Mohan et al. (2024) highlighted the ability of these microphysics schemes to simulate stronger convective systems with intense upper troposphere updrafts, which are key to hydrometeor formation and lightning generation, as supported by Yair et al. (2010) and Saunders et al. (1991).

The configurations were assessed based on their alignment with actual ENTLN data and statistical metrics, including correlation, standard deviation, and RMSE. This analysis revealed that identifying the optimal configuration is challenging as its performance varies across different cases, relying heavily on the specific criteria and priorities being considered.

This study also demonstrates that the performance of different WRF configurations varies significantly, highlighting the inherent challenges and uncertainties in accurately predicting lightning. Consistent with findings by McCaul et al. (2009) and Babuňková Uhlířová et al. (2022), no single configuration excelled across all cases, emphasizing the value of ensemble approaches that combine multiple configurations. Such methods leverage the strengths of various setups, leading to more reliable and accurate predictions.

The findings have practical applications, especially in improving lightning forecasts for regions prone to storms. These advancements can support early warning systems and disaster management, helping to protect lives and property. The study also highlights the importance of analyzing each day's results and using several evaluation methods to identify the best configurations for different weather conditions. However, this research also uncovered some limitations, such as underestimating weaker thunderstorms and varying performance across case studies. Future work should focus on exploring improved ensemble forecasting methods to address these issues. Using advanced techniques like data assimilation and refining model physics could improve accuracy. Additionally, incorporating high-resolution satellite and radar data would offer deeper insights into lightning behavior, further improving predictions.

In conclusion, this study makes a significant contribution to lightning prediction, providing a strong basis for future studies. By emphasizing the role of microphysics schemes and ensemble approaches, it paves the way to better storm forecasting in Tehran and similar areas. These findings not only advance scientific understanding but also provide practical tools to mitigate the risks of lightning and protect communities.

Acknowledgments

The authors would like to thank the support team at Earth Networks (), for providing the lightning data.

Conflict of Interest

The authors declare no conflicts of interest relevant to this study.

Data Availability Statement

The Grid Analysis and Display System (GrADS) and Python scripts and the output data from simulations that we used in this study have been shared at (Khansalari and Gharaylou (2024)). We also obtained the ENTLN data from the support team at Earth Networks (), the global forecast system (GFS) data from , and the present weather phenomenon from the Meteorological Organization of Iran from .

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