Zusammenfassung
Dieser Beitrag präsentiert Ergebnisse aus elektromagnetischen Feldberechnungen unter Verwendung der FDTD-Methode (Finite-Differenzen-Methode im Zeitbereich). Konkret wurde die Ausbreitung eines elektromagnetischen Felds simuliert, welches mit einer bestimmten, messtechnisch erfassten Blitzentladung (sog. „Event“) am Gaisberg-Sendeturm (Salzburg, Österreich) in Verbindung steht. Digitale Geländemodelldaten der realen Ausbreitungspfade vom Gaisberg zu sieben Sensoren des Blitzortungsnetzwerks ALDIS wurden zur Initialisierung der FDTD-Simulationsdomäne verwendet. Um den Blitzkanal zu modellieren, wurde das MTLE-Modell (Modified Transmission Line Model with Exponential Decay) angenommen und der an der Turmspitze, also am Fußpunkt des Blitzkanals, gemessene Blitzstrom als Feldquelle in der Simulation verwendet. Damit wurden die elektromagnetischen Felder entlang der verschiedenen Pfade simuliert und die resultierende Maximalfeldstärke des magnetischen (H‑)Felds an den Sensorstandorten mit der tatsächlich gemessen Feldstärke der ALDIS-Sensoren verglichen. Die Ergebnisse der 3D-FDTD-Feldberechnungen korrelieren gut mit den tatsächlich registrierten Sensor-Messwerten zum gegebenen Event, während die zylindrisch-symmetrische 2D-FDTD-Simulation nicht für alle Ausbreitungspfade in der Lage ist, die gemessenen Feldwerte zu reproduzieren. Der Grund liegt in der komplexen Struktur des alpinen Geländes und den damit verbundenen Reflexionen und Beugungsphänomenen in Tälern und an Bergkämmen. Des Weiteren konnte anhand eines Sets von Sensor-Messwerten von 54 Events verifiziert werden, dass der Einschlag auf der Spitze eines Bergs im Gegensatz zu einem Einschlag auf ebenem Boden zu erhöhten gemessenen Feldwerten führen kann. Dies folgt aus der speziellen Bergtopographie vom Einschlagspunkt in die gegebene Ausbreitungsrichtung. Im Allgemeinen führt stark unebenes Gelände, wie es etwa im alpinen Raum vorliegt, zu einer Dämpfung des Felds entlang des Ausbreitungspfads.
Abstract
In this paper, the results of electromagnetic field computations using the finite-difference time-domain (FDTD) method are presented. Specifically, the propagation of an electromagnetic field caused by a lightning event on the Gaisberg mountain (Salzburg, Austria) was simulated. To initialize the FDTD simulation domain, digital elevation model (DEM) data of the real propagation paths from the Gaisberg to seven different sensors of the lightning detection network ALDIS were used. To model the lightning channel, the MTLE (modified transmission line model with exponential decay) was applied, and the lightning current measured at the top of the tower, that is, at the base of the lightning channel, was used as the current source in the simulation. This way, the electromagnetic fields were simulated for the different propagation paths, and the resulting peak values of the magnetic (H) fields at the ALDIS sensor locations were compared with the values actually measured by the ALDIS sensors. The results of the 3D FDTD computations correlate well with the values actually recorded by the sensors for a given event, while the cylindrical symmetrical 2D FDTD simulation is not capable of reproducing the values measured. This can be explained by the fact that the complex terrain of the Alpine region with its reflections and diffraction phenomena in valleys and on mountain ridges cannot be represented accurately in 2D FDTD simulations. Furthermore, by using a set of sensor values from 54 (normalized) events, we were able to verify that a strike on top of a mountain can lead to higher values compared to a strike on flat terrain. This is due to the specific topography from the strike point in the given direction of propagation. In general, rough terrain like the Austrian Alps has an attenuating effect on the propagating electromagnetic fields.
Literatur
Norton KA (1941) The calculation of ground-wave field intensity over a finitely conducting spherical earth. Proc IRE 29(12):623–639. https://doi.org/10.1109/JRPROC.1941.233636
Wait JR (1970) Electromagnetic waves in stratified media. Elsevier
Wait JR, Murphy A (1957) Influence of a ridge on the low-frequency ground wave. J Res Natl Bur Stand 58:1–5
Wait JR, Murphy A (1958) Further studies of the influence of a ridge on the low-frequency ground wave. J Res Natl Bur Stand 61(1):57–60
Cooray V, Fernando M, Sørensen TS, Götschl T, Pedersen A (2000) Propagation of lightning generated transient electromagnetic fields over finitely conducting ground. J Atmos Sol Terr Phys 62(7):583–600. https://doi.org/10.1016/S1364-6826(00)00008-0
Ming Y, Cooray V (1994) Electromagnetic radiation fields generated by lightning return strokes over a stratified ground
Delfino F, Procopio R, Rossi M (2008) Lightning return stroke current radiation in presence of a conducting ground: 1. Theory and numerical evaluation of the electromagnetic fields. J Geophys Res Atmos 113(D5):D5110. https://doi.org/10.1029/2007JD008553
Delfino F, Procopio R, Rossi M, Rachidi F, Nucci CA (2008) Lightning return stroke current radiation in presence of a conducting ground: 2. Validity assessment of simplified approaches. J Geophys Res Atmos 113(D5):D5111. https://doi.org/10.1029/2007JD008567
Ming Y, Cooray V (1992) Propagation effects caused by a rough ocean surface on the electromagnetic fields generated by lightning return strokes
Bardo EA, Cummins KL, Brooks WA (2004) Lightning current parameters derived from lightning location systems: what can we measure? In: 18th International Lightning Detection Conference (ILDC), Bd. 39, S 1–13
Cummins KL, Cramer JA, Brooks AA (2005) On the effect of land: Sea and other earth surface discontinuities on LLS-inferred lightning parameters, In: VIII International Symposium on Lightning Protection, 21–25 Nov 2005.
Yee K (1966) Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media. IEEE Trans Antennas Propag 14(3):302–307
Taflove A, Hagness SC (2005) Computational electrodynamics: the finite-difference time-domain method, 3. Aufl. Artech house, Norwood
Baba Y, Rakov VA (2016) Electromagnetic computation methods for lightning surge protection studies. IEEE, Wiley
Baba Y, Rakov VA (2020) Lightning-induced effects in electrical and telecommunication systems. Institution of Engineering and Technology
Kohlmann H, Schulz W (2021) Comparison of 3‑D and 2‑D cylindrical symmetry FDTD simulation results of a lightning strike to Gaisberg with ALDIS sensor measurements. IEEE Trans Electromagn Compat. https://doi.org/10.1109/TEMC.2021.3073787
Kohlmann H (2020) FDTD simulation of lightning electromagnetic fields—an approach with the software package MEEP. TU Wien
Hou W, Azadifar M, Rubinstein M, Zhang Q, Rachidi F (2020) An efficient FDTD method to calculate lightning electromagnetic fields over irregular terrain adopting the moving computational domain technique. IEEE Trans Electromagn Compat 62(3):976–980. https://doi.org/10.1109/TEMC.2019.2917282
Soto EA, Perez E, Herrera-Murcia JG (2014) Electromagnetic field due to lightning striking on top of a cone-shaped mountain using the FDTD. Electromagn Compat IEEE Trans 56(5):1112–1120. https://doi.org/10.1109/TEMC.2014.2301138
Li D et al (2016) On lightning electromagnetic field propagation along an irregular terrain. IEEE Trans Electromagn Compat 58(1):161–171. https://doi.org/10.1109/TEMC.2015.2483018
Li D et al (2016) Analysis of lightning electromagnetic field propagation in mountainous terrain and its effects on ToA-based lightning location systems. J Geophys Res Atmos 121(2):895–911. https://doi.org/10.1002/2015JD024234
Li D et al (2019) The propagation effects of lightning electromagnetic fields over mountainous terrain in the earth-ionosphere waveguide. J Geophys Res Atmos 124(24):14198–14219. https://doi.org/10.1029/2018JD030014
Li D, Rubinstein M, Rachidi F, Diendorfer G, Schulz W, Lu G (2017) Location accuracy evaluation of ToA-based lightning location systems over mountainous terrain. J Geophys Res Atmos 122(21):11,711–760,775. https://doi.org/10.1002/2017JD027520
Hou W, Azadifar M, Rubinstein M, Rachidi F, Zhang Q (2020) On the propagation of lightning-radiated electromagnetic fields across a mountain. IEEE Trans Electromagn Compat. https://doi.org/10.1109/TEMC.2019.2947095
Oskooi A, Roundy D, Ibanescu M, Bermel P, Joannopoulos JD, Johnson SG (2010) Meep: a flexible free-software package for electromagnetic simulations by the FDTD method. Comput Phys Commun 181(3):687–702. https://doi.org/10.1016/j.cpc.2009.11.008
(2021) MEEP documentation. https://meep.readthedocs.io. Zugegriffen: 5. Juli 2021
(2021) MEEP Github repository. https://github.com/NanoComp/meep. Zugegriffen: 5. Juli 2021
Nucci CA, Mazzetti G, Rachidi F, Ianoz MV (1988) On lightning return stroke models for „LEMP“ calculations
Rachidi F et al (2001) Current and electromagnetic field associated with lightning-return strokes to tall towers. Electromagn Compat IEEE Trans 43(3):356–367. https://doi.org/10.1109/15.942607
Courant R, Friedrichs K, Lewy H (1928) Über die partiellen Differenzengleichungen der mathematischen Physik. Math Ann 100(1):32–74. https://doi.org/10.1007/BF01448839
ITU Radiocommunication Assembly (1999) World atlas of ground conductivities. ITU Radiocommunication Assembly
Kohlmann H, Schulz W, Rachidi F (2021) Evaluation of site errors in LLS magnetic direction finding caused by large hills using the 3D-FDTD technique. Earth Space Sci. https://doi.org/10.1029/2021ea001914
Schulz W, Diendorfer G, Pedeboy S, Poelman D (2016) The European lightning location system EUCLID—Part 1: Performance analysis and validation. Nat Hazards Earth Syst Sci 16(2):595–605. https://doi.org/10.5194/nhess-16-595-2016
Heidler F, Paul C (2021) Field enhancement by lightning strikes to tall tower versus lightning strikes to flat ground. IEEE Trans Electromagn Compat 63(2):550–557. https://doi.org/10.1109/TEMC.2020.3021202
Schulz W, Diendorfer G (2004) Lightning peak currents measured on tall towers and measured with lightning location systems. In: 18th International Lightning Detection Conference (ILDC), Bd. 51, S 1–5
Schulz W, Diendorfer G (2002) Amplitude site error of magnetic direction finder. In: 26th International Conference on Lightning Protection (ICLP) 09.2002, S 4–7
Author information
Authors and Affiliations
Corresponding author
Additional information
Hinweis des Verlags
Der Verlag bleibt in Hinblick auf geografische Zuordnungen und Gebietsbezeichnungen in veröffentlichten Karten und Institutsadressen neutral.
Rights and permissions
About this article
Cite this article
Kohlmann, H., Schulz, W. & Pichler, H. Simulation elektromagnetischer Felder durch Folge eines Blitzeinschlags auf dem Gaisberg und der anschließende Vergleich der Ergebnisse mit Messungen der ALDIS-Blitzortungssensoren. Elektrotech. Inftech. 139, 335–343 (2022). https://doi.org/10.1007/s00502-022-01028-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00502-022-01028-x