Joule heating in the Lower Thermosphere-Ionosphere (LTI) arises as magnetospheric currents flow through the ionosphere, due to the resulting collisions between ions and neutral particles of the thermosphere. Ohmic heating and Frictional heating are essentially the same geophysical quantity, approached through three different measurement methodologies. An analogy of Joule heating from electrical systems is the DC power consumption, given by Q = V*I, where V is the voltage and I the current. Using Ohm’s law: I = V/R, where R is the resistance, the power consumption can also be written as Q = V2/R. Finally, expressed in terms of the resistance and current, heating can also be written as Q = R*I2. This means that if you measure both voltage and the current, then this gives not only the power consumption, but also the resistance, R=V/I.
Similarly, in the LTI there are the three methods to derive the heat production, which are as follows, with the electrical analogy in the last column:
| Term | Derivation | Electrical systems equivalent |
|---|---|---|
| Joule heating | qj = j·E | V*I |
| Ohmic heating | qΩ = σP E2 | V2/R |
| Frictional heating | qf = jP2/σP | R*I2 |
The need for obtaining all three estimations arises from the difficulties in accurately measuring all involved parameters across the transition region in the LTI, and in particular in the 100 to 200 km altitude range.