The "knee" model of ionospheric conductivity

The "knee" model (Mushtak & Williams) refines the description of the ionospheric conductivity profile by approximating it with two exponentials joined at a "knee" at a height of approximately 50-60 km. Below the knee and above the knee the conductivity has a different characteristic scale, so the model captures the actual shape of the profile better than a single exponential (see #20).

The advantage of the model is that it reproduces well the phase velocity and attenuation of ELF waves over a broad range of frequencies in the Schumann resonance band. Thanks to this, the properties of the cavity can be estimated backward from the measured parameters (position and width of the lines), and vice versa — from a model of the cavity one can predict the position of the resonances.

The "knee" model is thus a practical bridge between the microphysics of the ionosphere (conductivity vs. height) and the macroscopically observed quantities (frequency, Q-factor, phase velocity). The term "knee" refers precisely to the point where the two exponentials in the profile bend.