Modeling and Subionospheric VLF
perturbations caused by direct and indirect
effects of lightning
Prepared by Benjamin Cotts
Stanford University, Stanford, CA
IHY Workshop on
Advancing VLF through the Global AWESOME
Network
Overview
• Ionospheric Perturbations
– Modeling & Data Challenges
• Recovery Time
– E.g. LEP Events
• Onset delay/Onset duration
– Dependencies
• Early VLF Events
(Physical Mechanism)
– E.g. LEP Event
– E.g. Early VLF Event
2
Problems Subionospheric
VLF Observations
1. LEP Events: GLOBAL ELECTRON LOSS RATE
2. Early VLF Events CAUSATIVE MECHANISM
a) When – time of year?
a)
b)
Season
Solar Cycle
b) Where –
a)
b)
geographic location?
Location relative to transmitter or receiver
c) Storm type – Lightning Characteristics?
d) …
3
The Radiation Belts
• Particles are trapped in the Earth’s magnetic field
–
–
–
–
Gyrate around magnetic field lines
Mirror between hemispheres
Drift around earth (drift current)
Scattered particles ‘precipitate’ into the atmosphere
4
Whistler Waves
Source: [Bortnik, 2004]
• Lightning discharges
radiate a broad
spectrum of
electromagnetic (EM)
waves, including waves
in the ELF and VLF
frequency bands (i.e.
300 Hz to 30 kHz)
 These waves propagate in the earth-ionosphere waveguide
 A fraction of the wave energy couples into the
magnetosphere and propagates as a whistler mode wave
5
LEP Characteristics & Dependencies
Key: • Narrowband measurable
• Dependence
• Geomagnetic conditions
• tr: Recovery time
• Energy of precip. electrons
• ∆t/td: Onset delay/duration
• Source lightning
• Location (l,j)
• Spectrum
• Duration
• DA/Df: Amplitude/Phase change
• Deposition profile
• Mode pattern present
6
LEP Characteristics & Dependencies
Key: Broadband data
Other Data
Modeling/Unknown
• Geomagnetic conditions
• tr: Recovery time
• Energy of precip. electrons
• ∆t/td: Onset delay/duration
• Source lightning
• Location (l,j)
• Spectrum
• Duration
• DA/Df: Amplitude/Phase change
• Deposition profile
• Mode pattern present
7
LEP Characteristics & Dependencies
• Geomagnetic conditions
• tr: Recovery time
• Energy of precip. electrons
• ∆t/td: Onset delay/duration
• Source lightning
• Location (l,j)
• Spectrum
• Duration
• DA/Df: Amplitude/Phase change
• Deposition profile
• Mode pattern present
8
Geomagnetic Conditions: Kp/Dst
Whistlers are launched
by nearly every lightning
stroke
Only when there are
sufficient electrons
present will we observe
LEP events
Source: [Peter, 2007]
9
LEP Characteristics & Dependencies
• Geomagnetic conditions
• tr: Recovery time
• Energy of precip. electrons
• ∆t/td: Onset delay/duration
• Source lightning
• Location (l,j)
• Spectrum
• Duration
• DA/Df: Amplitude/Phase change
• Deposition profile
• Mode pattern present
10
Lightning (whistler) induced electron
precipitation
• Wave-Particle Interaction
•
•
•
•
•
Whistler Wave propagates with
Right Hand Circular Polarization
(RHCP)
Counter-streaming electrons gyrate
in same direction
In the equatorial region Dopplershifted wave frequency equals the
electron gyrofrequency
Electron experiences a constant
electric field
Electrons gain or lose energy 
change electron pitch angle
11
Resonant Energy
•
Neq influences refractive index n
•
Lightning Geomagnetic Latitude
•
l-Geomagetic longitude (l=0 peak resonance)
•
Lightning Source Characteristics
•
Broadband VLF Data
12
Monte Carlo Energy Deposition and
Secondary Ionization
Source: [Peter, 2007]
13
Recovery Time vs. Altitude
14
LEP Characteristics & Dependencies
• Geomagnetic conditions
• tr: Recovery time
• Energy of precip. electrons
• ∆t/td: Onset delay/duration
• Source lightning
• Location (l,j)
• Spectrum
• Duration
• DA/Df: Amplitude/Phase change
• Deposition profile
• Mode pattern present
15
Calculate at HAIL and East Coast
How does geomagnetic
longitude affect the
LEP signature or
occurrence rate?
Calculate expected
LEP Characteristics
For:
HAIL (255)
East Coast (300)
USA
225-300 E
16
16
16
Evolution of Precipitating Electrons
Initial
Distribution:
(E=300
keV,a200=77o)
j=200oE
17
Comparison of j=255oE and j=300oE
j=255oE
j=300oE
180
Backscattered
Precipitating
Northern-hemisphere
Southern-hemisphere
0
180
Backscattered
Precipitating
More backscatter at
0
j=300oE than at j=255oE
18
Average LEP Characteristics
19
Modeling/Data Opportunities
• Lightning occurrence &
disturbed conditions
• Δt/td Correction due to
Atmospheric Backscatter
• Predictions for characteristics
around the globe need
verification/checking
– Longitudinal dependence of Δt/td
– Latitudinal dependence on tR.
• DA/ Df – discuss later
20
Subionospheric VLF Perturbations
∆t – EMP/whistler & precipitating
electron propagation time
td – Precipitation/secondary
ionization
tr – recovery; return to chemical
equilibrium
DA/Df – Change in amplitude and
phase
LEP Dependencies
∆t - Location (l,j), Kp
td - Location (l,j) , Kp
tr – Energy of electrons
Early VLF Dependencies
DA/Df – many factors
∆t < 20 ms (Early) - Direct Effect
td
<20 ms (Fast) - Impulsive
>20 ms (Slow) – Extended
}
Physical Mechanism
Under Debate
tr – Altitude profile of disturbance
DA/Df – many factors
21
On the VLF Reflection Height
from J.A. Ratcliffe [1948, pp.110]
• X=p2/2 ; Z=/
• For Z=0, reflection
occurs at X=1 ( =0)
• With collisions,  is
never zero, and full
wave treatment is
needed
• For VLF, Z is too large
at X=1 for  to fall to a
small value
• Reflection occurs when
X=Z, assuming the
gradients are steep
enough
22
22
Modal Structure
23
Attenuation Rate of Different Modes
24
Importance of Modal Profile
and Electron Density Profile
?
25
Scattering Problems
Source: [Poulsen, 1991]
26
Example Fields
Source: [Marshall, 2009]
27
Ambient Conditions
28
Modal Interference Pattern
Source: [Marshall, 2009] 29
Event Modeling: LEP
Source: [Peter, 2007]
30
Model/Data Comparison
Source: [Peter, 2007]
31
31
31
Event Modeling: Early VLF
Source: [Marshall, 2009] 32
Event Modeling: Early VLF
Source: [Marshall, 2009] 33
Disturbance Location vs.
Perturbation Magnitude: Early VLF
Source: [Marshall, 2009] 34
Problems (and Solutions) in Modeling
Subionospheric VLF Propagation
Problems/Unknowns
Measurables/Models
1. Ambient Electron Density Profile
–
–
http://ccmc.gsfc.nasa.gov/modelweb/
Broadband Lightning, e.g. Cummer, Said …
2. Location of Disturbance
–
Multiple Paths to “triangulate” or use lightning
3. Ambient VLF Modal Structure
–
LWPC/FWM/FDTD
4. Disturbance Ionization Profile
1. LEP: WIPP, Monte Carlo
2. Early VLF: Sprites/Halos/EMP/ Elves/Heating
3. MORE DATA & MODELING FROM MORE LOCATIONS!
35
Problems (and Solutions) in Modeling
Subionospheric VLF Propagation
1. LEP Events: GLOBAL ELECTRON LOSS RATE
a)
b)
c)
d)
Kp/Dst
Location Location LOCATION
Source Lightning Characteristics
Solar cycle dependence?
2. Early VLF Events CAUSATIVE MECHANISM
a) Altitude Profile
b) Classify Early VLF Events by other metrics
a)
b)
c)
d)
e)
Early/Fast vs. Early/Slow
Sprite-related Events
Other TLE-related Events?
Classify by type of causative lightning?
Location?
36