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This study investigates lightning at tall objects and evaluates the risk of upward lightning (UL) over the eastern Alps and its surrounding areas. While uncommon, UL poses a threat, especially to wind turbines, as the long-duration current of UL can cause significant damage. Current risk assessment methods overlook the impact of meteorological conditions, potentially underestimating UL risks. Therefore, this study employs random forests, a machine learning technique, to analyze the relationship between UL measured at Gaisberg Tower (Austria) and $35$ larger-scale meteorological variables. Of these, the larger-scale upward velocity, wind speed and direction at 10 meters and cloud physics variables contribute most information. The random forests predict the risk of UL across the study area at a 1 km$^2$ resolution. Strong near-surface winds combined with upward deflection by elevated terrain increase UL risk. The diurnal cycle of the UL risk as well as high-risk areas shift seasonally. They are concentrated north/northeast of the Alps in winter due to prevailing northerly winds, and expanding southward, impacting northern Italy in the transitional and summer months. The model performs best in winter, with the highest predicted UL risk coinciding with observed peaks in measured lightning at tall objects. The highest concentration is north of the Alps, where most wind turbines are located, leading to an increase in overall lightning activity. Comprehensive meteorological information is essential for UL risk assessment, as lightning densities are a poor indicator of lightning at tall objects.

Upward lightning (UL) has become an increasingly important threat to wind turbines as ever more of them are being installed for renewably producing electricity. The taller the wind turbine the higher the risk that the type of lightning striking the man-made structure is UL. UL can be much more destructive than downward lightning due to its long lasting initial continuous current leading to a large charge transfer within the lightning discharge process. Current standards for the risk assessment of lightning at wind turbines mainly take the summer lightning activity into account, which is inferred from LLS. Ground truth lightning current measurements reveal that less than 50% of UL might be detected by lightning location systems (LLS). This leads to a large underestimation of the proportion of LLS-non-detectable UL at wind turbines, which is the dominant lightning type in the cold season. This study aims to assess the risk of LLS-detectable and LLS-non-detectable UL at wind turbines using direct UL measurements at the Gaisberg Tower (Austria) and S\"antis Tower (Switzerland). Direct UL observations are linked to meteorological reanalysis data and joined by random forests, a powerful machine learning technique. The meteorological drivers for the non-/occurrence of LLS-detectable and LLS-non-detectable UL, respectively, are found from the random forest models trained at the towers and have large predictive skill on independent data. In a second step the results from the tower-trained models are extended to a larger study domain (Central and Northern Germany). The tower-trained models for LLS-detectable lightning is independently verified at wind turbine locations in that domain and found to reliably diagnose that type of UL. Risk maps based on case study events show that high diagnosed probabilities in the study domain coincide with actual UL events., Comment: 24 pages, 8 figures

Upward lightning is much rarer than downward lightning and requires tall ($100+$~m) structures to initiate. It may be either triggered by other lightning discharges or completely self-initiated. While conventional lightning location systems reliably detect downward lightning, they miss a specific flash type of upward lightning that consists only of a continuous current. Globally, only few specially instrumented towers can detect this flash type. The proliferation of wind turbines in combination with large damage from upward lightning necessitates an improved understanding under which conditions the self-initiated and the undetected subtype of upward lightning occur. To find larger-scale meteorological conditions favorable for self-initiated and undetectable upward lightning, this study uses a random forest machine learning model. It combines direct measurements at the specially instrumented tower at Gaisberg mountain in Austria with explanatory variables from larger-scale atmospheric reanalysis data (ERA5). Atmospheric variables reliably explain whether upward lightning is self-initiated by the tower or triggered by other lightning discharges. The most important variable is the height of the $-10~^\circ$C isotherm above the tall structure: the closer it is the higher is the probability of self-initiated upward lightning. Two-meter temperature and the amount of CAPE are also important. For the occurrence of upward lightning undetectable by lightning location systems, this study finds a strong relationship to the absence of lightning in the vicinity.

Compared here are the calculated fields of the Traveling Current Source (TCS), Modified Transmission Line (MTL), and the Diendorfer-Uman (DU) models with a channel base current assumed in Nucci et al. on the one hand and with the channel base current assumed in Diendorfer and Uman on the other hand. The characteristics of the field wave shapes are shown to be very sensitive to the channel base current, especially the field zero crossing at 100 km for the TCS and DU models, and the magnetic hump after the initial peak at close range for the TCS models. Also, the DU model is theoretically extended to include any arbitrarily varying return stroke speed with height. A brief discussion is presented on the effects of an exponentially decreasing speed with height on the calculated fields for the TCS, MTL, and DU models.