A key feature here is
how the plasma
frequency compares
to the frequency of
the incident radar
wave
f p  1/ 2 (ne2 / 0m)1/2
N on order of 1019 – 1020
m-3
n is the electron density (in this case produced by
intense heating in the lightning channel)
e is the charge of an electron (-1.6 x 10-19 C)
m is the mass of an electron (9 x 10-31 kg)
ε0 is the permittivity of free space (8.85 pF m-1)
Williams et al. (1989), J. Atmos. Sci.
Plasma frequency as a function of
temperature. Also illustrated are
frequencies of various radar bands.
The key physical process here is the
relationship between the plasma
frequency and the frequency of the
incident (radar) radiation impinging on
it.
The plasma frequency is basically
determined how hot the plasma is,
ie, its temperature. The temperature
of the plasma determines the level of
ionization, which is given by the
concentration of electrons (or ionized
species). For T > 5000K, plasma
frequency is larger than the frequency
at the various radar wavelengths.
Plasma frequency refers to how rapidly the
electron density changes with time. Viscous
and EM forces are at work in the plasma.
Radar detection of lightning has a long history
λ
Overdense Plasma
For an overdense plasma, the characteristic frequency of the
plasma is greater than the frequency of the EM wave that impinges on it.
That is,
fP > fEM
The plasma can be considered to have a period of oscillation or natural
frequency. Recall that the period of an EM wave (or oscillation) is inversely
proportional to frequency.
So for an overdense plasma, Tp < TEM
That is, the oscillation period of the plasma is short compared to the EM wave period.
This means that the plasma can respond to the EM wave by having
electrons on its outer sheath oscillate at the frequency of the incident wave. So the
plasma acts as a conductor since the incident wave only interacts with the outer
portion of the sheath. Just like a metal conductor.
Underdense plasma
For an underdense plasma,
fP < fEM
or TP > TEM
The period of oscillation of the plasma is longer than that of the incident
EM wave so in this case the response of the plasma is “sluggish”. That is, it
behaves as a dielectric. In this case the incident wave penetrates into the
plasma and the backscatter of the incident EM is greatly reduced. Cold plasmas
are generally underdense.
As the lightning channel cools, the electron density will fall rapidly so the ability of the
channel to backscatter radar waves will diminish. Observations and theory show the
reflectivity falls at 0.2 db/ms (Holmes et al., 1980). So the observation of lightning
channels is a very transient thing!
Incident wave
Reflected wave
Overdense
Conductor
Underdense
Dielectric
Debye distance is short for overdense plasmas. Debye distance is related to ratio
of viscous forces to EM forces in the plasma. So for short Debye distance, EM
forces large compared to viscous forces and plasma can “respond” to impinging EM
wave.
Dielectric response regime
3500K
Overdense plasma regime
5000K
A-scope display of lightning “spikes”
Ligda, 1956
Ligda, 1956.
radarmet.atmos.colostate.edu/AT741/papers/Ligda_Film/
Reflectivities from lightning plasma.
Broad spectrum from
lightning—greater spatial
complexity of the target
compared to weather echo.
We expect λ-4 dependence
for Rayleigh targets
(r < 0.07λ).
h =p K l Z
5
2
-4
dBZ = 10 log10 Z
Lightning channels “emerge”
from the Rayleigh backscatter
at long
wavelengths.
Illustrates masking effects of precipitation.
http://www.met.rdg.ac.uk/radar/research/lightning/
Ray plots during flash
High Ldr as well
ZDR mostly negative
Vertical channels
Negative phi dp in anvil associated with strong vertical E fields
Courtesy Chilbolton radar facility, UK
Radar Detection of Lightning: Conclusions
1. Lightning plasma is generally overdense at all meteorological wavelengths.
Hence, lightning channel responds like a metallic conductor for times on the
order of hundreds of ms (when high T is maintained).
2. The lightning echo behaves as a volume target to radar. Attributed to a 3-D
dendritic structure composed of overdense channel segments, which are long
and thin compared to the radar wavelength.
3. Apparent radar wavelength dependence of lightning echoes is highly
variable and strongly influenced by precipitation masking - on average,
λlight ~1/λ2
4. Tendency of strongest lightning echoes to occur in regions of more intense
precipitation.
5. Infrequent detection of lightning at radar wavelengths attributed to
precipitation masking, especially at shorter wavelengths (S-band and below).