Knee model: Comparison between heuristic and rigorous solutions for the Schumann resonance problem

• Schumann resonances and ELF waves in the Earth-ionosphere cavity.
• Knee profiles of the ionosphere and ELF propagation constant.
• A comparison between heuristic and rigorous solutions for the Schumann resonance.

Rapid development of computers allows for application of the direct numerical solution of the global electromagnetic resonance problem in the Earth-ionosphere cavity. Direct numerical solutions exploit the cavity models with the given conductivity profile of atmosphere such as exponential or the knee profiles. These profiles are usually derived from the knee model by Mushtak and Williams (2002) developed for obtaining the realistic ELF propagation constant. It is usually forgotten that profiles of the knee model are only a convenient approximate interpretation for the heuristic relations used in computations. We demonstrate that the rigorous full wave solution of the electromagnetic problem for such profiles deviates from that obtained in the knee model. Therefore the direct numerical solutions must also depart from the heuristic one. We evaluate deviations of the heuristic knee model data from those pertinent to equivalent profile of atmospheric conductivity.