1. Radar Detection of Lightning
Williams et al. (1989, J. Atmos. Sci.)
Observations of lightning by radar has a history as long as radar itself.
Generally accepted that radar echoes from lightning are reflections from thin highly ionized channels created by the intense heating of air due to a lightning discharge. The temperature of the plasma determines the electron density of the plasma which then dictates the EM backscattering characteristics.
A key feature here is
how the plasma
frequency compares
to the frequency of
the incident radar
wave
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 C)
m is the mass of an electron (9 x kg)
ε0 is the permittivity of free space (8.85 pF m-1)
N on order of 1019 – 1020
m-3

2. Williams et al. (1989), J. Atmos. Sci.
The figure at left shows the plasma
frequency as a function of temperature. Also
illustrated are frequencies of various
radar bands. For two background pressures.
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 by 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 the natural
oscillation frequency of the plasma. A plasma
at frequency f can readily “respond” to any
EM wave at a frequency < f.

3. Radar detection of lightning has a long historyλ

4. 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
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.

5. 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.

6. 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
For an underdense plasma, the plasma has only a sluggish response to the impinging
EM wave and the backscatter is far less compared to the case of a overdense plasma.

7. Ligda, 1956.
radarmet.atmos.colostate.edu/AT741/papers/Ligda_Film/

8. 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).

9. Lightning channels “emerge”
from the Rayleigh backscatter
at long
wavelengths.
Illustrates masking effects of precipitation.

10. Ray plots during flash
High Ldr as well
ZDR mostly negative
Vertical channels

11. 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,
ηlight ~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).