Evolution of the modeled ⟨E⟩ as a function of the CR. The cyan and magenta confidence bands represent the uncertainty on the inverted mean energy, taking the CH₄ variability in the auroral regions into account, for the kappa and monoenergetic distribution cases, respectively. In this example, we illustrate the evolution of the uncertainty in the inverted mean energy as a function of the CR for an emission angle θ = 0°. For higher emission angles, the uncertainty follows a similar pattern.