# A Year-Long Total Lightning Forecast over Italy with a Dynamic Lightning Scheme and WRF

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## Abstract

**:**

## 1. Introduction

## 2. Data and Methods

#### 2.1. WRF Model

#### 2.2. The Dynamic Lightning Scheme and LINET Data

^{−1}kg

^{−1}). The electric potential is computed for positive, negative, and intracloud lightning. Negative flashes originate from the lower part of the cloud, positive flashes originate from the upper part of the cloud, and intracloud flashes originate everywhere in the cloud. These assumptions are consistent with the tripolar charge model of Williams [73], but more complex electric structures can be present inside the clouds [73].

^{−4}C; L75, in which the charge transferred in 1 s is 0.75 × 10

^{−4}C; and L100, in which the charge transferred in 1 s is 1.0 × 10

^{−4}C. The three settings were used to simulate all 162 cases considered in this work.

^{9}J for positive strokes and 1 × 10

^{9}J for intracloud and negative strokes), it is converted into electrical energy by lightning strokes (cloud-to-ground or intracloud), immediately dissipating the energy and reducing the electric potential magnitude at that grid point. The same thresholds as Lynn et al. [72] are used. The sum of positive, negative, and intracloud lightning is considered for comparison with observed strokes.

#### 2.3. Case Studies

## 3. Results

#### 3.1. Example of Predicted Fields

^{2}for the verifications area, i.e., the number of strokes observed/forecasted in a day in each WRF grid cell in the verification area). This was a well predicted event. Observations (Figure 3d) shows intense electrical activity with about 204,000 strokes recorded for the day. The total number of strokes is underestimated by L50, slightly overestimated by L75, and quite overestimated by L100.

#### 3.2. Comparison among L50, L75, and L100 Configurations and Upscaling of the Model Output

#### 3.3. Performance in Different Seasons and Comparison between the Forecast over Land and over Sea

_{o}/2, where f

_{o}is the probability of occurrence of the forecasted event. We consider the event as having at least 1 stroke in a grid cell per day for the L75 configuration of the lightning scheme. The probability of occurrence of the forecast event f

_{o}is about 1% in winter and spring, and 2% in summer and fall. These probabilities were estimated considering the number of grid cells in which strokes were observed over the total number of grid cells.

_{o}for different seasons and the result of Lynn [52], a 0.5 threshold was used to determine the scale of usefulness of the forecast.

^{2}) larger than the meteorological alert areas used by the Civil Protection Department.

#### 3.4. Sensitivity to the Microphysical Scheme

^{−4}C, so the impact of changing the microphysical scheme can be quantified by comparing WSM6 and L75 forecasts.

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

Observed | Observed | ||

YES | NO | ||

Forecast | YES | a | b |

Forecast | NO | c | d |

_{r}is the probability of a correct forecast by chance when the yes/no forecast occurrence is independent from the observation. The frequency bias (FBIAS; range (0, +∞), where 1 is the perfect score, i.e., when no misses and false alarms occur) is the ratio of the number of yes forecasts of the event and the observed number of yes events. The probability of detection (POD; range (0, 1), where 1 is the perfect score and 0 is the worst value) is the proportion of correct forecasts over the total number of observed events. The threat score (TS; range (0, 1), where 1 is the perfect score and 0 is the worst score) is the number of correct forecasts of the event divided by the total number of occasions on which the event was observed and/or forecast. The equitable threat score (ETS; range (−1/3, 1), where 1 is the perfect score and 0 is a useless forecast) is the proportion of correct forecasts corrected for the probability of a correct forecast by chance, where the occurrence/non-occurrence of the event is independent from its observation.

_{x}and N

_{y}are the number of grid points in the x and y directions (635 in both directions in this paper). Fractions are generated for different spatial scales by changing the value of n, which can be any odd value up to 2N − 1, where N is the number of points along the longest side of the domain. In the statistics of this paper, n varies from 3 to 43, corresponding to spatial scales from 9 to 129 km. The FSS score is summed over all grid points in the domain, and it is defined such that the perfect (no) skill forecast has an FSS equal to 1 (0).

_{(n),i,j}is the resultant field of observed fractions for a square of length n obtained from the binary field I

_{o}and M

_{(n),i,j}is the resultant field of forecast fractions for a square of length n obtained from the binary field I

_{M}. Specifically, I

_{o}(I

_{M}) is 1 if the observed (forecast) lightning density per grid cell is above a threshold value, and I

_{o}(I

_{M}) is 0 if the observed (forecast) lightning density per grid cell is below this threshold. The corresponding formulae are as follows:

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**Figure 1.**WRF domain and verification area (domain around Italy). Locations cited in the text are also shown.

**Figure 2.**(

**a**) Total number of observed strokes in different seasons for all days (yellow) and the 162 cases studied (grey); (

**b**) the hourly distribution of the strokes shown in (

**a**).

**Figure 3.**Strokes density field (number of strokes in 9 km

^{2}) for 3 October 2020 calculated with a charge transfer setting of (

**a**) L50, (

**b**) L75, (

**c**) L100 for the lightning scheme; (

**d**) LINET strokes density. The total number of strokes is shown in the figure title of each panel. The dots represent the daily rate, i.e., the number of strokes accumulated for the whole day in the model grid cells (3 km horizontal resolution). LINET daily data are remapped onto the model grid. Gray dots are smaller than other dots to avoid a large superposition of the dots.

**Figure 4.**Total number of strokes simulated (L50, L75, L100) and observed (OBS) for each season and for the year. The number of cases considered are shown in Table 1.

**Figure 5.**The upscaling of the model output. The green cell has a horizontal resolution of 12 km as a result of applying an upscale factor of 4. The 3 km WRF grid is shown in blue.

**Figure 6.**Performance diagram for grid cells of (

**a**) 6 km and (

**b**) 24 km. L50 is represented by a diamond, L75 is represented by a circle, and L100 by a square. Red symbols are used for 1 stroke per grid cell per day, green symbols for 10 strokes per grid cell per day, and magenta symbols for 30 strokes per grid cell per day. Grey lines indicate FBIAS with values in grey, and blue lines indicate the TS with values in blue.

**Figure 7.**Fraction skill score for different scales for x from 9 to 129 km in 6 km increments. The FSS refers to the L75 configuration and the event forecast is 1 stroke per grid cell.

**Figure 8.**Taylor diagram for the 162 cases studied and each configuration of the DLS. The number of 48 km grid cells classified as sea and land is 44,712 and 34,930, respectively. The cells containing an equal amount of WRF 3 km grid cells labelled as land or sea were discarded from the analysis. L50S is the result for L50 over the sea, L50L is the results for L50 over the land; L75S is the result for L75 over the sea, L75L is the result for L75 over the land; L100S is the result for L100 over the sea, L100L is the result for L100 over the land.

**Figure 9.**(

**a**) FBIAS, (

**b**) POD, (

**c**) FAR, and (

**d**) ETS for different lightning thresholds (x-axis) for L75 (blue curves) and the same charge configuration using the WSM6 microphysical scheme (red curves). Scores are shown for 24 km grid cells.

SEASON | Number of Days |
---|---|

SUMMER | 69 |

FALL | 46 |

WINTER | 18 |

SPRING | 29 |

**Table 2.**Number of strokes simulated with the different charge transfer settings by the DLS (columns L50, L75, and L100) and observed by LINET (column OBS) for each season and for the whole year. The second number in each cell of the L50, L75, and L100 columns shows the correlation coefficient for the daily simulated and observed number of strokes for each season and for the whole year. The number of pairs used for each correlation are those from Table 1: 29 in spring, 69 in summer, 46 in fall, 19 in winter, 162 for the whole year.

SEASON/YEAR | L50 | L75 | L100 | OBS |
---|---|---|---|---|

SPRING | 352,397; 0.64 | 647,563; 0.66 | 968,901; 0.66 | 494,678 |

SUMMER | 3,630,810; 0.76 | 5,954,415; 0.77 | 8337,,408; 0.77 | 7,140,804 |

FALL | 2,314,092; 0.76 | 3,861,155; 0.78 | 5,491,026; 0.77 | 3,528,789 |

WINTER | 521,886; 0.87 | 1,021,174; 0.85 | 1,574,974; 0.84 | 332,347 |

YEAR | 6,819,185; 0.77 | 11,484,307; 0.77 | 16,372,309; 0.77 | 11,496,618 |

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## Share and Cite

**MDPI and ACS Style**

Federico, S.; Torcasio, R.C.; Lagasio, M.; Lynn, B.H.; Puca, S.; Dietrich, S.
A Year-Long Total Lightning Forecast over Italy with a Dynamic Lightning Scheme and WRF. *Remote Sens.* **2022**, *14*, 3244.
https://doi.org/10.3390/rs14143244

**AMA Style**

Federico S, Torcasio RC, Lagasio M, Lynn BH, Puca S, Dietrich S.
A Year-Long Total Lightning Forecast over Italy with a Dynamic Lightning Scheme and WRF. *Remote Sensing*. 2022; 14(14):3244.
https://doi.org/10.3390/rs14143244

**Chicago/Turabian Style**

Federico, Stefano, Rosa Claudia Torcasio, Martina Lagasio, Barry H. Lynn, Silvia Puca, and Stefano Dietrich.
2022. "A Year-Long Total Lightning Forecast over Italy with a Dynamic Lightning Scheme and WRF" *Remote Sensing* 14, no. 14: 3244.
https://doi.org/10.3390/rs14143244