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In this section, the thunderstorm tracking and the lightning forecasting algorithms are described in five basic steps. To explain the methodology, we assumed some parameters, as shown in Fig 2. At the instant time TO2 that is equal to TF1, the assumptions are: (i) Cell A is at X02 and cell B is at XF1. (ii) Cell B started from X01 at time TO1 further back than cell A. (iii) In the next step after time TF1, the corresponding positions of cell A and cell B will be XN2 and XN1, respectively. (iv) The ellipse is the forecasted cell over XN at the time TN that is the same as TN1 or TN2. Based on the nature of these assumptions, the tracking and forecasting details will be given in the following subsections.
Figure 2. Two different cells are identified to be A and B as denoted by the dark gray polygons in the observation area. The tracked path of the thunderstorm X01 shows the initial location of cell B at time TO1, and the XF1 arrowhead shows the current location of the cell B centroid at time TF1. Cell A and cell B are forecasted in the mutual direction at XN and the thunderstorm at TF1 and T02 is divided into two different cells with their centroids moving toward TN1 and TN2. The TN is the final time at position XN that could be mutually identified from cell A and cell B and called a merged cell. The proposed position after a considerable time TN shows the predicted position of the cell.
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The lightning pulses (lightning radiation sources) obtained by BLNET are converted into a density map in real-time. In the cell identification process; first, the area of observation is converted to grids with the size of 4 km by 4 km. The total numbers of pulses located in each grid are counted in 10-minute intervals, which are updated every two minutes according to the latest observations. The 10-minute selection could vary for different networks based on the available data sets. However, the 2-minute update is fixed to observe the sudden changes earlier and to reduce the blackout time. It is assumed that if the total number of pulses occurring in the grids exceeds a certain threshold then those grids are considered active. Here, we considered the threshold to be five, which is an arbitrary number and is dependent on the performance of a particular network. By the observation of BLNET, more than 400 pulses could be located for a single flash (Srivastava et al., 2019; Yuan et al., 2020). During the initial stage of development, we overlapped radar and lightning data to choose the grid size and found that most grids of cells exceed the threshold. Although few of the cells have less than five pulses, and sometimes even one or two pulses, that did not overlap with the radar, we assume that there could be detection errors in the lightning location system. Excluding those grids below the threshold, the confidence of the density map is enhanced. Thenceforth, all the active grids were used to obtain the boundaries of thunderstorm cells using the neighborhood technique. The neighborhood technique suggests that all grids connected in any of the eight directions are from the same cell (Gonzalez et al., 2004). An example is shown in Fig. 2; all the active grids marked in gray are divided into two cells. These cells are denoted as cell A and cell B, and their boundaries are identified, which are symbolized by black polygons. To facilitate easy understanding of the pictures and in the interest of being user-friendly, the density map will not be shown in the results section.
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As the identified boundaries of thunderstorm cells are not precise enough for tracking, we smooth the boundaries by using the moving average method. Two different approaches were considered in locating the centroid of the cell for tracking the thunderstorm path. The first approach took each active grid with a number of pulses below a given threshold (a threshold value of 25 was considered for the cases consider in this paper, the selection of threshold depends on the performance of the lightning location network). By doing this, the centroid is directly acquired from the mean of the obtained points from the polygon boundaries. In the second approach, for a cell of grids with their numbers of pulses larger than that of the threshold pulses, the grid with the highest number of pulses was considered the centroid of that particular cell. The obtained centroid is considered as the initial position of the cell, thereafter, the same procedure is used to identify the following positions in a 2-minute interval. The 10-minute density maps with cell identification were updated every two minutes by following the new observations, as explained in the previous section. Based on these centroids, the direction and displacement of a thunderstorm were obtained.
Here we took the centroid position at (
$ {x}_{n},{y}_{n}) $ and the previous centroid position at ($ {x}_{n-1},{y}_{n-1}) $ . Then the displacement and direction of a thunderstorm are obtained using Eqs. (1a) and (1b):In Fig. 2, the path of a thunderstorm is shown in black arrows. Here, TO1 represents the initial time at the starting location of the thunderstorm, and TF1 shows the present position of the identified cell.
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Over the course of the lifecycle, it is commonly observed that it could merge into a strong extensive convective system, or split into smaller cells, which might go on to be identified as more than one cell. The single-cell, multi-cell, and squall lines are the usual classifications of thunderstorms, and splitting or merging could happen more than once with a multi-cell or in a squall line. A single cell indicates that no merging or splitting occurred in the system. The merging process considered in this article is simulated by converting two or more adjoining cells into a single cell considering the mutual direction of all the convective cells. This direction is obtained using Eq. (2) and an example is shown in Fig. 2.
Here, TNi (where i indicates the number of the cell) shows the position of each cell, and TN is the average position. The merging process usually happens between the developing and mature stages of a thunderstorm. Conversely, splitting is a process in which a single cell or squall line divides into multi-cells. To obtain this, we consider the discontinuity due to voided grids in the primary cell to split the primary cell into multi cells. The splitting process may occur during any stage of thunderstorm development. Consequently, during the process of splitting and merging, this algorithm tracks the direction of a thunderstorm instead of a single cell.
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Based on the above section, updated direction and displacement of thunderstorm cells are determined, and the possible forecast positions of the cells can then be acquired. The algorithm now considers only the first 10 minutes as the initial condition, which is updated every two minutes, and the direction and displacement are determined for each new position. The 2-minute interval was selected to avoid the sudden changes in the possible moving direction that results due to a higher sampling rate. Here, the displacement of the thunderstorm is obtained via Eq. (3).
where C represents the displacement at every updated instance, j represents the forecast instance, and
$ {I}_{i} $ represents the displacement and direction at the ith instance.In Eq. (3), the averaging is performed to improve the accuracy of the thunderstorm movement in case of a sudden increase in total lightning at any grid. Further, it also reduces the errors from a large pulse density which can accompany long-duration flashes. As shown in Fig. 2, XF1 is the present position and XN is the forecasted position of the thunderstorm. The new position of the cell needs to be determined in the time needed to issue a lightning warning in the AOC. Another benefit of the 2-minute sampling output would also allow for the lightning data to be fed into a severe weather warning algorithm, which is beyond the scope of this work.
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Based on the thunderstorm tracking methodology, the thunderstorm is nowcasted at the AOC at various lead times. The performances of the forecasting methods are evaluated in terms of the probability of detection (POD), the false alarm rate (FAR), and the critical success index (CSI), as shown in Table 1. In this work, we propose that a warning would be generated if any cell reaches the AOC (the gray-colored square in Fig. 3), within the expected time. The warning system is tested based on the available data and the warning capability is discussed according to the POD and FAR. The criteria for testing the algorithm included the number of hits determined correctly (Hits), false alarms (False), and missed cases (Misses). The “Hits” are defined when the current observed position overlaps with the corresponding previous forecast position. The “False” is defined when none of the current observed positions overlap with the corresponding previous forecasted positions. The “Miss” is defined when the current observed positions are available but none of them correspond with the previous forecast positions. The evaluations of the forecasting methods are done based on the above rules and are shown in Fig. 3, which can be formulated as:
Forecast lead time (min) POD FAR CSI 5 91.0 2.1 89.3 15 80.0 21.8 65.4 30 62.8 33.3 47.8 Table 1. The success rate of nowcasting in the selected area of concern (AOC). The total number of selected cases is 1159.
Figure 3. Three different categories have been classified as a predictor: the dark shading shows the present cell, and an ellipse shows a predicted cell. If any grid of the forecasted cell overlaps with the identified cell, it is a hits case; if none of the grids overlapped with, then it is false, and if it is identified but not a forecast, then it is a miss case.
Forecast lead time (min) | POD | FAR | CSI |
5 | 91.0 | 2.1 | 89.3 |
15 | 80.0 | 21.8 | 65.4 |
30 | 62.8 | 33.3 | 47.8 |