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 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) N on order of 1019 – 1020 m-3

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.

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 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 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.

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).

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

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

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).