Sferics and Tweeks
Prepared by Ryan Said and Morris Cohen
Stanford University, Stanford, CA
IHY Workshop on
Advancing VLF through the Global
AWESOME Network
1
Lightning
•
Different types of lightning: +CG, -CG, IC
•
Current forms a large electric field antenna, radiating radio waves
•
Large component in VLF range
2
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
Tweek Atmospheric
Ionospheric reflections
Modal cutoff
4
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
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
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
Tweek Atmospheric
•
•
•
•
Many Ionospheric reflections visible
Ray model: individual impulses
Modal model: summation of modes
Many modal cutoff frequencies visible
Ionospheric reflections
Modal cutoff
8
Tweek Atmospheric
z
x
y
Ray Hops
Ground Wave
1st mode cutoff
9
Long-Range Sferic
Slow Tail
•
•
•
•
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
Dispersion
Slow Tail
10
Long-Range Sferic
•
•
•
Time-domain: short impulse (top panel)
Frequency-domain: smooth, mostly single mode (bottom panel)
Minimum attenuation near 13 kHz
11
Lightning characteristics
+ ++ + + +
+ + + ++
+
+ + +
+
+
+
- - - - - - -
-
+ ++ + + +
+ ++ ++ +
+
+ +
-
+
-
Return stroke
peak current
(i.e., kA)
+ ++ + + +
+ +
Total charge moment
(I.e., C•km)
+ +
12
Sferic Characteristics
• VLF peak
– Mostly TM Modes
– 8-12 kHz peak
energy
• ELF peak
VLF Peak
ELF “Tail”
– Delayed
– TEM mode
– Associated with
sprites
– <1kHz energy
13
Peak Current
+ ++ + + +
+ + + ++
+
+ + +
+
+
+
- - - - - - - - -
 Peak current is
proportional to VLF
peak for a given
propagation path
Return stroke
peak current
(i.e., kA)
+ ++ + + +
+ +
VLF
Peak
14
Total Charge Moment
-
+ ++ + + +
+ ++ ++ +
+
+ +
-
+
-
 Total ELF energy is
proportional to total
charge transfer
 ELF energy attenuates
more in Earth-ionosphere
waveguide
Total charge moment
(I.e., C•km)
+ +
ELF Energy
Reising [1998]
15
Determining Azimuth
NS
Incident wave S
Wood and Inan [2002]
Φ
EW
Band of frequencies: use a
weighted average
Single Frequency:
NS ~ S*cos(Φ)
EW ~ S*sin(Φ)


fu
fl
 EW ( f ) 
 | NS ( f ) |2  | EW ( f ) |2 df
tan 1 
 NS ( f ) 
fu
2
2
|
NS
(
f
)
|

|
EW
(
f
)
|
df

fl
If same constant of
proportionality:
EW/NS = tan(Φ)
Φ = tan-1(EW/NS)
16
Determining Azimuth cont’d
Short
FFT
Calculated azimuth
For each frequency, compare
magnitude from NS and EW antenna to
calculate azimuth, then average over
frequency:
kf 

 EW ( s ) 
kf
kf
f N tan 1  kfNs  | NS ( Ns ) |2  | EW ( Ns ) |2
k l
 NS ( ) 
fs
N 


fu N
fu N
fs
fs

k
fl N
fs
| NS (
kfs 2
kf
) |  | EW ( s ) |2
N
N
17
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
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
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