1. 1 Sferics and Tweeks Prepared by Ryan Said and Morris Cohen Stanford University, Stanford, CA IHY Workshop on Advancing VLF through the Global AWESOME Network

2. 2 Lightning Different types of lightning: +CG, -CG, IC Current forms a large electric field antenna, radiating radio waves Large component in VLF range 2

3. 3 Sferic in Earth-Ionosphere Waveguide Shape of sferics, tweeks vary by ionosphere and ground profile Tweeks more common at night, where ionosphere reflects more energy (lower electron collision rate at higher altitude) 3

4. 4 Tweek Atmospheric Modal cutoff Ionospheric reflections 4

5. 5 Ray Model Ionosphere enables long-range propagation of emitted radio pulse Guided radio pulse called a “Radio Atmospheric,” or “Sferic” Sferic with many visible reflections forms a “Tweek Atmospheric” Hop arrival times related to ionospheric reflection height Arrive later during nighttime (higher and stronger reflection at night than during day) See [Nagano 2007] for dependence of arrival time with height 5

6. 6 Modal Model Modal analysis: each mode dictates waveguide velocity, attenuation rate Discrete modes are functions of frequency, boundary reflections Solve by requiring phase consistency between: F1, F3 Each mode has a cutoff frequency fc Below this frequency, attenuation is very high Nighttime ionosphere: fc ~ 1.8 kHz for the first mode (m=1) Based on actual ionospheric profiles, can calculate high attenuation below 5 kHz 6

7. 7 TE and TM Modes Sferic consists of a combination of TE (Transverse Electric) and TM (Transverse Magnetic) modes Vertical lightning channel preferentially excites TM modes Horizontal loop antennas measure Hy (from TM) and Hx (from TE) Tweeks contain more Hx than early part of sferics 7

8. 8 Tweek Atmospheric Many Ionospheric reflections visible Ray model: individual impulses Modal model: summation of modes Many modal cutoff frequencies visible Modal cutoff Ionospheric reflections 8

9. 9 Tweek Atmospheric 1 st mode cutoff Ground Wave Ray Hops 9 z y x

10. 10 Long-Range Sferic High attenuation below 5 kHz (especially during daytime) No tweeks at long range: too much attenuation “Slow Tail” from QTEM mode Waveguide dispersion: Lower frequencies travel slower than higher frequencies Lower frequency components seen to arrive later Slow Tail Dispersion 10

11. 11 Long-Range Sferic Time-domain: short impulse (top panel) Frequency-domain: smooth, mostly single mode (bottom panel) Minimum attenuation near 13 kHz 11

12. 12 Lightning characteristics + + + + + + + + + + + + + + + + + + - - - - - - - - - - -- - + + + + + + + + Return stroke peak current (i.e., kA) + + + + + + + + + + + + + + ++ - - - - - + + Total charge moment (I.e., Ckm)

13. 13 Sferic Characteristics VLF peak –Mostly TM Modes –8-12 kHz peak energy ELF peak –Delayed –TEM mode –Associated with sprites –<1kHz energy VLF PeakELF “Tail”

14. 14 Peak Current + + + + + + + + + + + + + + + + + + - - - - - - - - - - -- - + + + + + + + + Return stroke peak current (i.e., kA)  Peak current is proportional to VLF peak for a given propagation path VLF Peak

15. 15 Total Charge Moment  Total ELF energy is proportional to total charge transfer  ELF energy attenuates more in Earth-ionosphere waveguide ELF Energy + + + + + + + + + + + + + + ++ - - - - - + + Total charge moment (I.e., Ckm) Reising [1998]

16. 16 Determining Azimuth Single Frequency: EW NS Incident wave S Φ NS ~ S*cos(Φ) EW ~ S*sin(Φ) If same constant of proportionality: EW/NS = tan(Φ) Φ = tan -1 (EW/NS) Band of frequencies: use a weighted average Wood and Inan [2002]

17. 17 Determining Azimuth cont’d For each frequency, compare magnitude from NS and EW antenna to calculate azimuth, then average over frequency: Short FFT Calculated azimuth

18. 18 Future Work Use methods in previous references to monitor ionosphere during various conditions (night/day, summer/winter, low- /mid-/high-latitude) –As a side effect, can monitor strike locations (especially when Tweeks are visible, see [Nagano 2007]) 18

19. 19 References: Theoretical and Background Budden, K. G., “The wave-guide mode theory of wave propagation” Logos Press, 1961 –Overview of theoretical framework for waveguide propagation Budden, K. G. “The Propagation of Radio Waves” Cambridge University Press, 1985 –Detailed methodologies for calculating electromagnetic propagation characteristics Galejs, J. “Terrestrial propagation of long electromagnetic waves” Pergamon Press New York, 1972 –Calculation of earth-ionosphere waveguide propagation Rakov, V. A. & Uman, M. A. “Lightning - Physics and Effects” Cambridge University Press, 2003, 698 –Overview of the lightning strike, including models for electromagnetic radiation from lightning (little emphasis on waveguide propagation) Uman, M. A. “The Lightning Discharge” Dover Publications, Inc., 2001 –Overview of lightning processes 19

20. 20 References: Calculations Wait, J. R. & Spies, K. P. “Characteristics of the Earth-Ionosphere Waveguide for VLF Radio Waves” National Bureau of Standards, 1964 –Numerical evaluation of waveguide propagation based on assumed ionospheric profiles Nagano, I.; Yagitani, S.; Ozaki, M.; Nakamura, Y. & Miyamura, K. “Estimation of lightning location from single station observations of sferics” Electronics and Communications in Japan, 2007, 90, 22-29 –Calculation of propagation distance and ionospheric height based on tweek measurements Ohya, H. et al., “Using tweek atmospherics to measure the response of the low-middle latitude D-region ionosphere to a magnetic storm,” Journal of Atmospheric and Solar-Terrestrial Physics, 2006, 697-709 –Ionospheric diagnostics based on tweek measurements 20