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.