From the analysis undertaken in this study, no minimum threshold in HE tonnage is resolved. In order to investigate this, data for smaller raids need to be included. In addition to the major raids considered here, there are many more smaller-scale raids involving fewer or smaller aircraft. For example, Mosquito aircraft were used in many hundreds of bombing raids throughout this period (Middlebrook and Everitt, 1985). Given the fact that the current list of major bombing raids used in this study is by no means comprehensive, it is likely that information about many hundreds of smaller raids would need to be included in order to tease out the signal of such raids from the background ionospheric variability in which further large raids were occurring. As such we consider this beyond the scope of the current study.

For the ionosphere at the altitude of the F2 region (∼200–300 km) above the UK to respond to bombing raids conducted at distances up to 1000 km away, the bombing must have generated pressure waves that were capable of propagating to ionospheric altitudes. A sound wave travelling this distance in the lower atmosphere would arrive within an hour. The speed of sound is temperature-dependent and the temperature decreases with altitude in the troposphere and mesosphere before increasing in the thermosphere. Since the thermosphere represents the most significant fraction of the vertical profile, it is likely that a sound wave propagating vertically as well as horizontally would arrive even sooner. One potential mechanism therefore is of a pressure wave propagating upwards in all directions. At higher altitudes its amplitude increases until it breaks in the upper atmosphere, depositing its energy as heat. A very rough estimate of the anticipated thermospheric temperature rise can be obtained by considering the specific heat capacity of the atmosphere which can be expressed as

(1) Q = C p n Δ T ,

where Q is the energy input in joules (4.184×1012 for 1000 metric tonnes of TNT), C p is the molar-specific heat capacity of N 2 (∼29.1 J mol−1 K−1), n is the number of moles of gas m−3 (at ionospheric altitudes, the number density of the atmosphere is ∼1016 m−3 or 1.66 × 10 - 8 moles m−3) and ΔT is the change in temperature (K). Assuming the energy is equally distributed throughout a cylinder of atmosphere 1000 km in radius and 300 km in height, this gives a temperature rise of ∼9 K.

The dominant ion species in the mid-latitude ionospheric F region is O+, whose loss rate is temperature-dependent (Rees, 1989). However, the dominant mechanism by which O+ ions are lost is through reaction with N 2 and O 2 molecules in the reactions

(R1) O + + N 2 → NO + + O , (R2) O + + O 2 → O 2 + + O .

The overall loss rate, β, for O+ ions can therefore be expressed as

(2) β = k 1 ⋅ N 2 + k 2 ⋅ [ O 2 ] ,

where [N 2 ] and [O 2 ] are the concentrations of N 2 and O 2 molecules respectively and k 1 and k 2 are the rate coefficients for the two reactions. These rate coefficients are also temperature-dependent (Rees, 1989). The combined loss rate for O+ ions is therefore dependent on both reaction rates and the concentration of thermospheric species. Müller-Wodarg et al. (1998) modelled the ionospheric and thermospheric response to localised thermospheric cooling (≤40 K) during a total solar eclipse. They predicted an 8 % increase in foF2 (∼0.2 MHz) due to the contraction of the atmosphere and an increase in the [O] ∕ [N 2 ] ratio caused, in part, by a reduction in the concentration of N 2 . It is reasonable to assume that the atmospheric expansion due to energy from localised bombing raids would have an analogous, if opposite, effect on the ionosphere and thermosphere. A rise in the background thermospheric temperature would result in an enhanced loss rate, with the equilibrium between production and loss being established at a lower peak electron concentration. Such equilibrium would be reached within minutes of perturbation, well within the resolution of the ionospheric data. Grandin et al. (2015) studied the impact on foF2 of high-speed streams on Earth. They found that a thermospheric temperature increase of 20–50 K may result in a decrease in foF2 by 0.5–1.0 MHz.

If the bombing resulted in the generation of shock waves or atmospheric gravity waves, their horizontal propagation speed would need to be of the order of 300 km h−1, while the vertical velocity component would need to be around 100 km h−1 in order to affect the atmosphere above Slough. There is evidence that turbulence generated in the lower thermosphere by space shuttle launches can propagate 1000 km horizontally within 8 h (Kelley et al., 2009). While this example was specific to the lower thermosphere at altitudes between 100 and 115 km, it nevertheless has a similar time constant to that observed for the ionospheric response to bombing in the current study. Such a mechanism may therefore contribute to the observed effect.

Infrasonic waves generated by explosions are launched preferentially in a vertical direction (e.g. Blanc, 1985). Any impact on the upper atmosphere overhead would then require horizontal transport to move that region over Slough. For the scale sizes involved this would require winds of the order of 300 km h−1 to blow consistently in a westward direction for the impact to be observed within 3 h, as suggested by the data. For this to happen continuously throughout the epoch being studied is unlikely. Whatever the cause of the ionospheric depletion, the impact appears to last less than 24 h, since only the subsequent noon value is affected.

One metric ton of TNT has an explosive energy of 4.184×109 J, which is of the same order of energy as a cloud to ground lightning stroke. While a ground-based explosion and a lightning stroke are somewhat different in location and duration, it is not unfeasible that wave energy generated by lightning could also influence the ionosphere in a similar way. Since the occurrence of lightning has distinctive diurnal and seasonal cycles, it is feasible that this mechanism could contribute to the observed seasonal anomaly in ionospheric F-region electron concentrations (Rishbeth and Müller-Wodarg, 2006).