The electric field in the model provides the excitation leading to the
green ghost 557.7 nm emissions. The time constant indicates how fast the
field, and therefore the added excitation, decays. At any given time the
excitation will add to the atomic oxygen state leading to the green
emission. Therefore the observed decay time constant should be expected
to be larger than the ‘no added excitation’ time constant calculated
based on the equations and rate constant given by Vallance Jones (1974).
This ‘no added excitation’ time constant is listed in the line
Calculated t0, and it is indeed less than the observed
time constant on the line above. For the 25 May 2020 event the observed
decay rate is a constant 0.40 s for all boxes. The altitude is
decreasing from 93.5 km (box 3) to 85.9 km (box 8) and with the denser
atmosphere at lower altitudes the effect of quenching will increase
which will lower the ‘no added excitation’ time constant as seen in the
line “Calculated t0”. The model E-field must then make
up the difference and we see this in the increase of the E-field decay
time constant between box 3 and 8.
There is uncertainty on the parameters involved in the analysis. We have
assumed that the sprites are above the location of the lightning strike,
but sprites may be several 10s of km from the strike (a review of this
is given in Stenbaek-Nielsen et al. (2020)). A reasonable uncertainty on
the altitude would be 5 km. A change in altitude will seriously affect
the quenching and therefore the expected decay time constant. Another
set of uncertainties is associated with the rate constants used when
calculating the decay time constant, especially the atomic oxygen
quenching rate constant. This rate constant may be significantly larger
than given by Vallance Jones (1974). The uncertainties will affect the
model fit, however, the uncertainties do not appear to affect the
overall qualitative results of the analysis presented here.