Following some lightning flashes from energetic thunderclouds, blue jets and red sprites are observed in the atmosphere above the cloud and into the ionosphere. In order to understand the physical processes leading to these and associated phenomena, both the temporal and spatial evolution of the electric (and magnetic) fields due to the thundercloud and the lightning discharge are modelled. These numerical simulations are carried out either using a quasi-electrostatic code or an electromagnetic code, with appropriate boundary conditions and grids. The redistribution of electric charge and the electromagnetic pulse due to the lightning, can accelerate electrons, which collide with neutrals and ions, heating them, and also ionising the atmosphere. Runaway electrons and/or electrical breakdown of the atmosphere can also occur. The first and second positive bands of molecular nitrogen are excited appreciably if sufficient energy is produced. The situation is strongly nonlinear. The results (see also Cho and Rycroft, this issue) show the temporal and spatial development of (a) the electric field divided by the neutral gas density, and (b) the energy density of optical emissions (up to 10~(13) photons m~(-3) s~(-1)). They show that energy propagates up to the ionosphere in 0.3 ms, at the speed of light. A ring of optical emissions is created, the outer rim of which propagates horizontally in the ionosphere at an altitude ～ 90 km, reading a radial distance of 280 km in a further 0.7 ms. At the same time, the intense electric field at > 07 km altitude above the thundercloud creates a much enhanced (～ 10~3 *) electron density (with a radius up to 25 km) which lasts for several ms. This heated region modifies the amplitude and phase characteristics of VLF radio waves propagating in the Earth-ionosphere waveguide.
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