1. Modelling electric fields above thunderstorms produced by tropospheric and high-altitude lightning discharges Anna Odzimek University of Leicester, UK Michael J. Rycroft, CAESAR Consultancy, Cambridge, UK, and University of Bath, UK Oscar van der Velde, Universitat Politecnica de Catalunya, Terrassa, Spain Session 1: „Thunderstorms and Lightning” – Workshop on Coupling of Thunderstorms and Lightning Discharges to Near-Earth Space Corte, Corsica, 23 - 27 June 2008

2. Modelling with PSpice TLE Workshop, Session 1: Thunderstorms and Lightning Corte, 23-27 June 2008 PSpice is a computer program dedicated to simulations of electrical and electronic circuits. It can solve equations, including differential and nonlinear. Uses built-in models of electric elements such as resistors, capacitors etc., or electric switches. It could be used to model various phenomena. Modelling thunderstorm phenomena with PSpice seemed appropriate. We currently use PSpice A/D from the software package OrCad Unison Suites version 10.3.

3. Positive CG discharges – PSpice simulation (1-D) Model thunderstorm and model circuit with switches for the simulation of cloud-to-ground (CG) lightning discharges TLE Workshop, Session 1: Thunderstorms and Lightning Corte, 23-27 June 2008 Rycroft et al. 2007

4. Mesospheric effects of +CGs Time after +CG and altitude where threshold fields E b, E n and E p are exceeded +30 kA TLE Workshop, Session 1: Thunderstorms and Lightning Corte, 23-27 June 2008 RS RS+CC +50 kA+110 kA ~+2 kA Note: the effect of electric field on conductivity (and subsequently current flow and electric fields) not taken into account

5. Two populations of sprites: Columns and Carrots Conclusions of e.g. Stanley et al., GRL, 1999; McHarg et al., GRL, 2007, EuroSprite Column sprites: Initiated at high altitudes (~75-80 km) Streamers propagate downwards Carrot sprites: Initiated at lower altitudes (~65-75 km) Streamers propagate both downwards and upwards More delayed (by up to tens of ms) EuroSprite observations confirm these conclusions; they also suggest that column sprites tend to be associated with stronger positive CG strokes, while carrot sprites follow weaker +CG strokes, and that continuing currents play a role Sprites on 17 August 2006 (EuroSprite images) TLE Workshop, Session 1: Thunderstorms and Lightning Corte, 23-27 June 2008

6. Two populations of +CGs – current characteristics +CG type A: 110 kA return stroke current (RS) no continuing current Transfers ~20 C to ground +CG type B: 30 kA return stroke current (RS) 90 ms, 2 kA continuing current (CC) Transfers ~70 C to ground TLE Workshop, Session 1: Thunderstorms and Lightning Corte, 23-27 June 2008

7. Two populations of +CGs - mesospheric effects Time after +CG and altitude where threshold fields E b, E n and E p are exceeded Sprite type A (column-like): initiated at ~80 km altitude ~1 ms after the onset of RS Sprite type B (carrot-like): initiated at ~65 km altitude ~10 ms after the onset of RS TLE Workshop, Session 1: Thunderstorms and Lightning Corte, 23-27 June 2008

8. SPRITE discharge – PSpice simulation 1-D model thunderstorm and sprite area - model circuit with +CG and similar sprite switches controlling the discharges TLE Workshop, Session 1: Thunderstorms and Lightning Corte, 23-27 June 2008

9. Two populations of +CG/SPRITES – electric field profiles +CG: 110 kA RS, followed by Sprite A (“Column”) from 80 km to 45 km +CG: 30 kA RS, 2 kA CC, followed by Sprite B (“Carrot”) initiated at 65 km and expanding downwards to 45 km and upwards to 80 km TLE Workshop, Session 1: Thunderstorms and Lightning Corte, 23-27 June 2008

10. Larger thunderstorm with a positive charge layer at ~5 km - mesospheric effects E - profile TLE Workshop, Session 1: Thunderstorms and Lightning Corte, 23-27 June 2008 V - profile E – profiles (log)E- thresholds 30 kA RS +2 kA CC 110 kA RS + 2 kA CC

11. JET following a -CG – lower atmosphere effects (attempt of reproduction the Krehbiel et al. example 1 - very recent simulation) Q - profile TLE Workshop, Session 1: Thunderstorms and Lightning Corte, 23-27 June 2008 V – profile E – profiles (1 ms, 1001 and 1040 ms after the -CG, here jet starts after 1s) Evolution after –CG (~30 kA RS) and a small jet 10-14 km, r JET ~1 km  V ion = ~+1V Negative discharge Krehbiel et al., Nature, 2008 E – profile

12. Conclusions The presented model of a thunderstorm has its advantages (using electric elements and solving a circuit made by the programme, thunderstorm connected to the rest of global circuit) and disadvantages (not self-consistent, discharges forced, maybe too small resolution, too low dimension). Simulation imply qualitatively that very strong +CG stroke produce enhanced field at the bottom of the ionosphere from ~0.1 to 1 ms after CG initiation. This can lead to a column sprite discharge initiated at ~80 km altitude ~1 ms after the discharge onset. A moderate +CG followed by a 2 kA (strong) continuing current lasting for several tens of ms produces significant enhancements after ~10 ms. Perhaps this can lead to a carrot sprite initiated at ~65 km expanding both downwards and upwards. A small upward jet following a –CGs discharge as observed by Krehbiel et al. is a negative type of discharge which can increase the ionospheric potential by ~1 V. Questions: how the model should be developed and what should be improved in the first place? Can discharges be simulated by electric switches at all? Or have the changes of the electric potentials and fields to be calculated self-consistently, using electric-field dependent variations, and is it enough for this purpose? TLE Workshop, Session 1: Thunderstorms and Lightning Corte, 23-27 June 2008 Anna Odzimek acknowledges funding from the EC WP7 programme „People” through the Marie Curie European Reintegration Grant No. PERG-GA-2007-203298